All analysis is performed
- Matlab models are working - Figures are computed
This commit is contained in:
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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addpath('APA300ML/');
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open('APA300ML.slx');
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% Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates
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% We first extract the stiffness and mass matrices.
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K = readmatrix('APA300ML_mat_K.CSV');
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M = readmatrix('APA300ML_mat_M.CSV');
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% #+caption: First 10x10 elements of the Mass matrix
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% #+RESULTS:
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% | 0.01 | -2e-06 | 1e-06 | 6e-09 | 5e-05 | -5e-09 | -0.0005 | -7e-07 | 6e-07 | -3e-09 |
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% | -2e-06 | 0.01 | 8e-07 | -2e-05 | -8e-09 | 2e-09 | -9e-07 | -0.0002 | 1e-08 | -9e-07 |
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% | 1e-06 | 8e-07 | 0.009 | 5e-10 | 1e-09 | -1e-09 | -5e-07 | 3e-08 | 6e-05 | 1e-10 |
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% | 6e-09 | -2e-05 | 5e-10 | 3e-07 | 2e-11 | -3e-12 | 3e-09 | 9e-07 | -4e-10 | 3e-09 |
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% | 5e-05 | -8e-09 | 1e-09 | 2e-11 | 6e-07 | -4e-11 | -1e-06 | -2e-09 | 1e-09 | -8e-12 |
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% | -5e-09 | 2e-09 | -1e-09 | -3e-12 | -4e-11 | 1e-07 | -2e-09 | -1e-09 | -4e-10 | -5e-12 |
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% | -0.0005 | -9e-07 | -5e-07 | 3e-09 | -1e-06 | -2e-09 | 0.01 | 1e-07 | -3e-07 | -2e-08 |
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% | -7e-07 | -0.0002 | 3e-08 | 9e-07 | -2e-09 | -1e-09 | 1e-07 | 0.01 | -4e-07 | 2e-05 |
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% | 6e-07 | 1e-08 | 6e-05 | -4e-10 | 1e-09 | -4e-10 | -3e-07 | -4e-07 | 0.009 | -2e-10 |
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% | -3e-09 | -9e-07 | 1e-10 | 3e-09 | -8e-12 | -5e-12 | -2e-08 | 2e-05 | -2e-10 | 3e-07 |
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% Then, we extract the coordinates of the interface nodes.
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[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('APA300ML_out_nodes_3D.txt');
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% Piezoelectric parameters
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% In order to make the conversion from applied voltage to generated force or from the strain to the generated voltage, we need to defined some parameters corresponding to the piezoelectric material:
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d33 = 300e-12; % Strain constant [m/V]
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n = 80; % Number of layers per stack
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eT = 1.6e-8; % Permittivity under constant stress [F/m]
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sD = 1e-11; % Compliance under constant electric displacement [m2/N]
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ka = 235e6; % Stack stiffness [N/m]
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C = 5e-6; % Stack capactiance [F]
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% The ratio of the developed force to applied voltage is:
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% #+name: eq:piezo_voltage_to_force
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% \begin{equation}
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% F_a = g_a V_a, \quad g_a = d_{33} n k_a
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% \end{equation}
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% where:
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% - $F_a$: developed force in [N]
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% - $n$: number of layers of the actuator stack
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% - $d_{33}$: strain constant in [m/V]
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% - $k_a$: actuator stack stiffness in [N/m]
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% - $V_a$: applied voltage in [V]
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% If we take the numerical values, we obtain:
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d33*n*ka % [N/V]
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% #+RESULTS:
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% : 5.64
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% From cite:fleming14_desig_model_contr_nanop_system (page 123), the relation between relative displacement of the sensor stack and generated voltage is:
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% #+name: eq:piezo_strain_to_voltage
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% \begin{equation}
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% V_s = \frac{d_{33}}{\epsilon^T s^D n} \Delta h
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% \end{equation}
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% where:
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% - $V_s$: measured voltage in [V]
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% - $d_{33}$: strain constant in [m/V]
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% - $\epsilon^T$: permittivity under constant stress in [F/m]
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% - $s^D$: elastic compliance under constant electric displacement in [m^2/N]
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% - $n$: number of layers of the sensor stack
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% - $\Delta h$: relative displacement in [m]
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% If we take the numerical values, we obtain:
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1e-6*d33/(eT*sD*n) % [V/um]
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% Stiffness
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m = 0.001;
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% The transfer function from vertical external force to the relative vertical displacement is identified.
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%% Name of the Simulink File
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mdl = 'APA300ML';
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%% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/Fd'], 1, 'openinput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
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G = linearize(mdl, io);
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% The inverse of its DC gain is the axial stiffness of the APA:
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1e-6/dcgain(G) % [N/um]
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% Resonance Frequency
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% The resonance frequency is specified to be between 650Hz and 840Hz.
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% This is also the case for the FEM model (Figure [[fig:apa300ml_resonance]]).
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freqs = logspace(2, 4, 5000);
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G, freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude');
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hold off;
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% Amplification factor
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% The amplification factor is the ratio of the vertical displacement to the stack displacement.
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%% Name of the Simulink File
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mdl = 'APA300ML';
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%% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/d'], 1, 'openoutput'); io_i = io_i + 1;
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G = linearize(mdl, io);
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% The ratio of the two displacement is computed from the FEM model.
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abs(dcgain(G(1,1))./dcgain(G(2,1)))
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% #+RESULTS:
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% : 5.0749
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% This is actually correct and approximately corresponds to the ratio of the piezo height and length:
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75/15
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% Stroke
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% Estimation of the actuator stroke:
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% \[ \Delta H = A n \Delta L \]
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% with:
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% - $\Delta H$ Axial Stroke of the APA
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% - $A$ Amplification factor (5 for the APA300ML)
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% - $n$ Number of stack used
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% - $\Delta L$ Stroke of the stack (0.1% of its length)
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1e6 * 5 * 3 * 20e-3 * 0.1e-2
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% Identification of the Dynamics from actuator to replace displacement
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% We first set the mass to be approximately zero.
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m = 0.01;
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% The dynamics is identified from the applied force to the measured relative displacement.
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%% Name of the Simulink File
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mdl = 'APA300ML';
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%% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
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Gh = -linearize(mdl, io);
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% The same dynamics is identified for a payload mass of 10Kg.
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m = 10;
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%% Name of the Simulink File
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mdl = 'APA300ML';
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%% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
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Ghm = -linearize(mdl, io);
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freqs = logspace(0, 4, 5000);
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
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ax1 = nexttile([2,1]);
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hold on;
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plot(freqs, abs(squeeze(freqresp(Gh, freqs, 'Hz'))), '-');
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plot(freqs, abs(squeeze(freqresp(Ghm, freqs, 'Hz'))), '-');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude'); set(gca, 'XTickLabel',[]);
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hold off;
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ax2 = nexttile;
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hold on;
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gh, freqs, 'Hz')))), '-', ...
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'DisplayName', '$m = 0kg$');
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Ghm, freqs, 'Hz')))), '-', ...
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'DisplayName', '$m = 10kg$');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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yticks(-360:90:360);
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ylim([-360 0]);
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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hold off;
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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legend('location', 'southwest');
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% #+name: fig:apa300ml_plant_dynamics
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% #+caption: Transfer function from forces applied by the stack to the axial displacement of the APA
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% #+RESULTS:
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% [[file:figs/apa300ml_plant_dynamics.png]]
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% The root locus corresponding to Direct Velocity Feedback with a mass of 10kg is shown in Figure [[fig:apa300ml_dvf_root_locus]].
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figure;
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gains = logspace(0, 5, 500);
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hold on;
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plot(real(pole(Ghm)), imag(pole(G)), 'kx');
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plot(real(tzero(Ghm)), imag(tzero(G)), 'ko');
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for k = 1:length(gains)
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cl_poles = pole(feedback(Ghm, gains(k)*s));
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plot(real(cl_poles), imag(cl_poles), 'k.');
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end
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hold off;
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axis square;
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xlim([-500, 10]); ylim([0, 510]);
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xlabel('Real Part'); ylabel('Imaginary Part');
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% Identification of the Dynamics from actuator to force sensor
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% Let's use 2 stacks as a force sensor and 1 stack as force actuator.
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% The transfer function from actuator voltage to sensor voltage is identified and shown in Figure [[fig:apa300ml_iff_plant]].
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m = 10;
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%% Name of the Simulink File
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mdl = 'APA300ML';
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%% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/Va'], 1, 'openinput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1;
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Giff = -linearize(mdl, io);
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freqs = logspace(0, 4, 5000);
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
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ax1 = nexttile([2,1]);
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hold on;
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plot(freqs, abs(squeeze(freqresp(Giff, freqs, 'Hz'))), '-');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude'); set(gca, 'XTickLabel',[]);
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hold off;
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ax2 = nexttile;
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hold on;
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Giff, freqs, 'Hz')))), '-');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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yticks(-360:90:360);
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ylim([-180 180]);
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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hold off;
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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% #+name: fig:apa300ml_iff_plant
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% #+caption: Transfer function from actuator to force sensor
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% #+RESULTS:
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% [[file:figs/apa300ml_iff_plant.png]]
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% For root locus corresponding to IFF is shown in Figure [[fig:apa300ml_iff_root_locus]].
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figure;
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gains = logspace(0, 5, 500);
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hold on;
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plot(real(pole(Giff)), imag(pole(Giff)), 'kx');
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plot(real(tzero(Giff)), imag(tzero(Giff)), 'ko');
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for k = 1:length(gains)
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cl_poles = pole(feedback(Giff, gains(k)/s));
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plot(real(cl_poles), imag(cl_poles), 'k.');
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end
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hold off;
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axis square;
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xlim([-500, 10]); ylim([0, 510]);
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xlabel('Real Part'); ylabel('Imaginary Part');
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% Identification for a simpler model
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% The goal in this section is to identify the parameters of a simple APA model from the FEM.
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% This can be useful is a lower order model is to be used for simulations.
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% The presented model is based on cite:souleille18_concep_activ_mount_space_applic.
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% The model represents the Amplified Piezo Actuator (APA) from Cedrat-Technologies (Figure [[fig:souleille18_model_piezo]]).
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% The parameters are shown in the table below.
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% #+name: fig:souleille18_model_piezo
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% #+caption: Picture of an APA100M from Cedrat Technologies. Simplified model of a one DoF payload mounted on such isolator
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% [[file:./figs/souleille18_model_piezo.png]]
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% #+caption:Parameters used for the model of the APA 100M
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% | | Meaning |
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% |-------+----------------------------------------------------------------|
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% | $k_e$ | Stiffness used to adjust the pole of the isolator |
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% | $k_1$ | Stiffness of the metallic suspension when the stack is removed |
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% | $k_a$ | Stiffness of the actuator |
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% | $c_1$ | Added viscous damping |
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% The goal is to determine $k_e$, $k_a$ and $k_1$ so that the simplified model fits the FEM model.
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% \[ \alpha = \frac{x_1}{f}(\omega=0) = \frac{\frac{k_e}{k_e + k_a}}{k_1 + \frac{k_e k_a}{k_e + k_a}} \]
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% \[ \beta = \frac{x_1}{F}(\omega=0) = \frac{1}{k_1 + \frac{k_e k_a}{k_e + k_a}} \]
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% If we can fix $k_a$, we can determine $k_e$ and $k_1$ with:
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% \[ k_e = \frac{k_a}{\frac{\beta}{\alpha} - 1} \]
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% \[ k_1 = \frac{1}{\beta} - \frac{k_e k_a}{k_e + k_a} \]
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m = 10;
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%% Name of the Simulink File
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mdl = 'APA300ML';
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%% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/Fd'], 1, 'openinput'); io_i = io_i + 1; % External Vertical Force [N]
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io(io_i) = linio([mdl, '/w'], 1, 'openinput'); io_i = io_i + 1; % Base Motion [m]
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io(io_i) = linio([mdl, '/Fa'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force [N]
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io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1; % Vertical Displacement [m]
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io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensor [V]
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io(io_i) = linio([mdl, '/d'], 1, 'openoutput'); io_i = io_i + 1; % Stack Displacement [m]
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G = linearize(mdl, io);
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G.InputName = {'Fd', 'w', 'Fa'};
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G.OutputName = {'y', 'Fs', 'd'};
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% From the identified dynamics, compute $\alpha$ and $\beta$
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alpha = abs(dcgain(G('y', 'Fa')));
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beta = abs(dcgain(G('y', 'Fd')));
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% $k_a$ is estimated using the following formula:
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ka = 0.8/abs(dcgain(G('y', 'Fa')));
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% The factor can be adjusted to better match the curves.
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% Then $k_e$ and $k_1$ are computed.
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ke = ka/(beta/alpha - 1);
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k1 = 1/beta - ke*ka/(ke + ka);
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% #+RESULTS:
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% | | Value [N/um] |
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% |----+--------------|
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% | ka | 40.5 |
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% | ke | 1.5 |
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% | k1 | 0.4 |
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% The damping in the system is adjusted to match the FEM model if necessary.
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c1 = 1e2;
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% The analytical model of the simpler system is defined below:
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Ga = 1/(m*s^2 + k1 + c1*s + ke*ka/(ke + ka)) * ...
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[ 1 , k1 + c1*s + ke*ka/(ke + ka) , ke/(ke + ka) ;
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-ke*ka/(ke + ka), ke*ka/(ke + ka)*m*s^2 , -ke/(ke + ka)*(m*s^2 + c1*s + k1)];
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Ga.InputName = {'Fd', 'w', 'Fa'};
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Ga.OutputName = {'y', 'Fs'};
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% And the DC gain is adjusted for the force sensor:
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F_gain = dcgain(G('Fs', 'Fd'))/dcgain(Ga('Fs', 'Fd'));
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|
||||
% The dynamics of the FEM model and the simpler model are compared in Figure [[fig:apa300ml_comp_simpler_model]].
|
||||
|
||||
|
||||
freqs = logspace(0, 5, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(2, 3, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G( 'y', 'w'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(Ga('y', 'w'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
set(gca, 'XTickLabel',[]);
|
||||
ylabel('$x_1/w$ [m/m]');
|
||||
ylim([1e-6, 1e2]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G( 'y', 'Fa'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(Ga('y', 'Fa'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
set(gca, 'XTickLabel',[]);
|
||||
ylabel('$x_1/f$ [m/N]');
|
||||
ylim([1e-14, 1e-6]);
|
||||
|
||||
ax3 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G( 'y', 'Fd'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(Ga('y', 'Fd'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
set(gca, 'XTickLabel',[]);
|
||||
ylabel('$x_1/F$ [m/N]');
|
||||
ylim([1e-14, 1e-4]);
|
||||
|
||||
ax4 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G( 'Fs', 'w'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(F_gain*Ga('Fs', 'w'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]');
|
||||
ylabel('$F_s/w$ [m/m]');
|
||||
ylim([1e2, 1e8]);
|
||||
|
||||
ax5 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G( 'Fs', 'Fa'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(F_gain*Ga('Fs', 'Fa'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]');
|
||||
ylabel('$F_s/f$ [m/N]');
|
||||
ylim([1e-4, 1e1]);
|
||||
|
||||
ax6 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G( 'Fs', 'Fd'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(F_gain*Ga('Fs', 'Fd'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]');
|
||||
ylabel('$F_s/F$ [m/N]');
|
||||
ylim([1e-7, 1e2]);
|
||||
|
||||
linkaxes([ax1,ax2,ax3,ax4,ax5,ax6],'x');
|
||||
|
||||
|
||||
|
||||
% #+name: fig:apa300ml_comp_simpler_model
|
||||
% #+caption: Comparison of the Dynamics between the FEM model and the simplified one
|
||||
% #+RESULTS:
|
||||
% [[file:figs/apa300ml_comp_simpler_model.png]]
|
||||
|
||||
% The simplified model has also been implemented in Simscape.
|
||||
|
||||
% The dynamics of the Simscape simplified model is identified and compared with the FEM one in Figure [[fig:apa300ml_comp_simpler_simscape]].
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'APA300ML_simplified';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Fd'], 1, 'openinput'); io_i = io_i + 1; % External Vertical Force [N]
|
||||
io(io_i) = linio([mdl, '/w'], 1, 'openinput'); io_i = io_i + 1; % Base Motion [m]
|
||||
io(io_i) = linio([mdl, '/Fa'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force [N]
|
||||
io(io_i) = linio([mdl, '/y'], 1, 'openoutput'); io_i = io_i + 1; % Vertical Displacement [m]
|
||||
io(io_i) = linio([mdl, '/Fs'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensor [V]
|
||||
|
||||
Gs = linearize(mdl, io);
|
||||
|
||||
Gs.InputName = {'Fd', 'w', 'Fa'};
|
||||
Gs.OutputName = {'y', 'Fs'};
|
||||
|
||||
freqs = logspace(0, 5, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(2, 3, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G( 'y', 'w'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(Gs('y', 'w'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
set(gca, 'XTickLabel',[]);
|
||||
ylabel('$x_1/w$ [m/m]');
|
||||
ylim([1e-6, 1e2]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G( 'y', 'Fa'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(Gs('y', 'Fa'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
set(gca, 'XTickLabel',[]);
|
||||
ylabel('$x_1/f$ [m/N]');
|
||||
ylim([1e-14, 1e-6]);
|
||||
|
||||
ax3 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G( 'y', 'Fd'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(Gs('y', 'Fd'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
set(gca, 'XTickLabel',[]);
|
||||
ylabel('$x_1/F$ [m/N]');
|
||||
ylim([1e-14, 1e-4]);
|
||||
|
||||
ax4 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G( 'Fs', 'w'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(F_gain*Gs('Fs', 'w'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]');
|
||||
ylabel('$F_s/w$ [m/m]');
|
||||
ylim([1e2, 1e8]);
|
||||
|
||||
ax5 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G( 'Fs', 'Fa'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(F_gain*Gs('Fs', 'Fa'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]');
|
||||
ylabel('$F_s/f$ [m/N]');
|
||||
ylim([1e-4, 1e1]);
|
||||
|
||||
ax6 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G( 'Fs', 'Fd'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(F_gain*Gs('Fs', 'Fd'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]');
|
||||
ylabel('$F_s/F$ [m/N]');
|
||||
ylim([1e-7, 1e2]);
|
||||
|
||||
linkaxes([ax1,ax2,ax3,ax4,ax5,ax6],'x');
|
||||
|
||||
% Integral Force Feedback
|
||||
% In this section, Integral Force Feedback control architecture is applied on the APA300ML.
|
||||
|
||||
% First, the plant (dynamics from voltage actuator to voltage sensor is identified).
|
||||
|
||||
Kiff = tf(0);
|
||||
|
||||
|
||||
|
||||
% The payload mass is set to 10kg.
|
||||
|
||||
m = 10;
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'APA300ML_IFF';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/w'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Fd'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/APA300ML'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
G_ol = linearize(mdl, io);
|
||||
G_ol.InputName = {'w', 'f', 'F'};
|
||||
G_ol.OutputName = {'x1', 'Fs'};
|
||||
|
||||
G = G_ol({'Fs'}, {'f'});
|
||||
|
||||
|
||||
|
||||
% The obtained dynamics is shown in Figure [[fig:piezo_amplified_iff_plant]].
|
||||
|
||||
|
||||
freqs = logspace(1, 5, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G, freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G, freqs, 'Hz')))));
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
yticks(-360:90:360);
|
||||
ylim([-390 30]);
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
|
||||
|
||||
|
||||
% #+name: fig:piezo_amplified_iff_plant
|
||||
% #+caption: IFF Plant
|
||||
% #+RESULTS:
|
||||
% [[file:figs/piezo_amplified_iff_plant.png]]
|
||||
|
||||
% The controller is defined below and the loop gain is shown in Figure [[fig:piezo_amplified_iff_loop_gain]].
|
||||
|
||||
Kiff = -1e3/s;
|
||||
|
||||
freqs = logspace(1, 5, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G*Kiff, freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G*Kiff, freqs, 'Hz')))));
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
yticks(-360:90:360);
|
||||
ylim([-180 180]);
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
|
||||
|
||||
|
||||
% #+name: fig:piezo_amplified_iff_loop_gain
|
||||
% #+caption: IFF Loop Gain
|
||||
% #+RESULTS:
|
||||
% [[file:figs/piezo_amplified_iff_loop_gain.png]]
|
||||
|
||||
% Now the closed-loop system is identified again and compare with the open loop system in Figure [[fig:piezo_amplified_iff_comp]].
|
||||
|
||||
% It is the expected behavior as shown in the Figure [[fig:souleille18_results]] (from cite:souleille18_concep_activ_mount_space_applic).
|
||||
|
||||
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/w'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Fd'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/APA300ML'], 1, 'output'); io_i = io_i + 1;
|
||||
|
||||
Giff = linearize(mdl, io);
|
||||
Giff.InputName = {'w', 'f', 'F'};
|
||||
Giff.OutputName = {'x1', 'Fs'};
|
||||
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(2, 3, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_ol('x1', 'w'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(Giff('x1', 'w'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
set(gca, 'XTickLabel',[]); ylabel('$x_1/w$ [m/m]')
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_ol('x1', 'f'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(Giff('x1', 'f'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
set(gca, 'XTickLabel',[]); ylabel('$x_1/f$ [m/N]');
|
||||
|
||||
ax3 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_ol('x1', 'F'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(Giff('x1', 'F'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
set(gca, 'XTickLabel',[]); ylabel('$x_1/F$ [m/N]');
|
||||
|
||||
ax4 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_ol('Fs', 'w'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(Giff('Fs', 'w'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('$F_s/w$ [N/m]');
|
||||
|
||||
ax5 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_ol('Fs', 'f'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(Giff('Fs', 'f'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('$F_s/f$ [N/N]');
|
||||
|
||||
ax6 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_ol('Fs', 'F'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(Giff('Fs', 'F'), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('$F_s/F$ [N/N]');
|
||||
|
||||
linkaxes([ax1,ax2,ax3,ax4,ax5,ax6],'x');
|
||||
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matlab/STEPS/APA300ML.STEP
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matlab/STEPS/APA300ML.STEP
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matlab/STEPS/Spindle_Stator.STEP
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matlab/STEPS/Tilt_Guide.STEP
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matlab/STEPS/Tilt_Motor_Axis.STEP
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matlab/STEPS/Ty_Guide.STEP
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matlab/STEPS/Ty_Guide_11.STEP
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matlab/STEPS/Ty_Guide_11.STEP
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matlab/STEPS/Ty_Guide_12.STEP
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matlab/STEPS/Ty_Guide_21.STEP
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matlab/STEPS/Ty_Guide_21.STEP
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matlab/STEPS/Ty_Guide_22.STEP
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matlab/STEPS/Ty_Motor_Rotor.STEP
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matlab/STEPS/Ty_Motor_Rotor.STEP
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matlab/STEPS/Ty_Motor_Stator.STEP
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matlab/STEPS/Ty_Motor_Stator.STEP
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matlab/STEPS/Ty_Stage.STEP
Normal file
77974
matlab/STEPS/Ty_Stage.STEP
Normal file
File diff suppressed because it is too large
Load Diff
23602
matlab/STEPS/granite.STEP
Normal file
23602
matlab/STEPS/granite.STEP
Normal file
File diff suppressed because it is too large
Load Diff
BIN
matlab/detail_fem_APA300ML.slx
Normal file
BIN
matlab/detail_fem_APA300ML.slx
Normal file
Binary file not shown.
BIN
matlab/detail_fem_APA300ML_2dof.slx
Normal file
BIN
matlab/detail_fem_APA300ML_2dof.slx
Normal file
Binary file not shown.
BIN
matlab/detail_fem_joint.slx
Normal file
BIN
matlab/detail_fem_joint.slx
Normal file
Binary file not shown.
BIN
matlab/detail_fem_nass.slx
Normal file
BIN
matlab/detail_fem_nass.slx
Normal file
Binary file not shown.
BIN
matlab/detail_fem_super_element.slx
Normal file
BIN
matlab/detail_fem_super_element.slx
Normal file
Binary file not shown.
@@ -1,140 +0,0 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
addpath('flexor_025/');
|
||||
|
||||
open('flexor_025.slx');
|
||||
|
||||
% Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates
|
||||
% We first extract the stiffness and mass matrices.
|
||||
|
||||
K = readmatrix('flex025_mat_K.CSV');
|
||||
M = readmatrix('flex025_mat_M.CSV');
|
||||
|
||||
|
||||
|
||||
% #+caption: First 10x10 elements of the Mass matrix
|
||||
% #+RESULTS:
|
||||
% | 0.006 | 8e-09 | -2e-08 | -1e-10 | 3e-05 | 3e-08 | 0.003 | -3e-09 | 9e-09 | 2e-12 |
|
||||
% | 8e-09 | 0.02 | 1e-07 | -3e-05 | 1e-11 | 6e-10 | 1e-08 | 0.003 | -5e-08 | 3e-09 |
|
||||
% | -2e-08 | 1e-07 | 0.01 | -6e-08 | -6e-11 | -8e-12 | -1e-07 | 1e-08 | 0.003 | -1e-08 |
|
||||
% | -1e-10 | -3e-05 | -6e-08 | 1e-06 | 7e-14 | 6e-13 | 1e-10 | 1e-06 | -1e-08 | 3e-10 |
|
||||
% | 3e-05 | 1e-11 | -6e-11 | 7e-14 | 2e-07 | 1e-10 | 3e-08 | -7e-12 | 6e-11 | -6e-16 |
|
||||
% | 3e-08 | 6e-10 | -8e-12 | 6e-13 | 1e-10 | 5e-07 | 1e-08 | -5e-10 | -1e-11 | 1e-13 |
|
||||
% | 0.003 | 1e-08 | -1e-07 | 1e-10 | 3e-08 | 1e-08 | 0.02 | -2e-08 | 1e-07 | -4e-12 |
|
||||
% | -3e-09 | 0.003 | 1e-08 | 1e-06 | -7e-12 | -5e-10 | -2e-08 | 0.006 | -8e-08 | 3e-05 |
|
||||
% | 9e-09 | -5e-08 | 0.003 | -1e-08 | 6e-11 | -1e-11 | 1e-07 | -8e-08 | 0.01 | -6e-08 |
|
||||
% | 2e-12 | 3e-09 | -1e-08 | 3e-10 | -6e-16 | 1e-13 | -4e-12 | 3e-05 | -6e-08 | 2e-07 |
|
||||
|
||||
|
||||
% Then, we extract the coordinates of the interface nodes.
|
||||
|
||||
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('flex025_out_nodes_3D.txt');
|
||||
|
||||
% Identification of the parameters using Simscape
|
||||
% The flexor is now imported into Simscape and its parameters are estimated using an identification.
|
||||
|
||||
|
||||
m = 1;
|
||||
|
||||
|
||||
|
||||
% The dynamics is identified from the applied force/torque to the measured displacement/rotation of the flexor.
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'flexor_025';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/T'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
G = linearize(mdl, io);
|
||||
|
||||
% Simpler Model
|
||||
% Let's now model the flexible joint with a "perfect" Bushing joint as shown in Figure [[fig:flexible_joint_simscape]].
|
||||
|
||||
% #+name: fig:flexible_joint_simscape
|
||||
% #+caption: Bushing Joint used to model the flexible joint
|
||||
% [[file:figs/flexible_joint_simscape.png]]
|
||||
|
||||
% The parameters of the Bushing joint (stiffnesses) are estimated from the Stiffness matrix that was computed from the FEM.
|
||||
|
||||
Kx = K(1,1); % [N/m]
|
||||
Ky = K(2,2); % [N/m]
|
||||
Kz = K(3,3); % [N/m]
|
||||
Krx = K(4,4); % [Nm/rad]
|
||||
Kry = K(5,5); % [Nm/rad]
|
||||
Krz = K(6,6); % [Nm/rad]
|
||||
|
||||
|
||||
|
||||
% The dynamics from the applied force/torque to the measured displacement/rotation of the flexor is identified again for this simpler model.
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'flexor_025_simplified';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/T'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
Gs = linearize(mdl, io);
|
||||
|
||||
|
||||
|
||||
% The two obtained dynamics are compared in Figure
|
||||
|
||||
|
||||
freqs = logspace(0, 5, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(G(1,1), freqs, 'Hz'))), '-', 'DisplayName', '$D_x/F_x$');
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(1,1), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(G(2,2), freqs, 'Hz'))), '-', 'DisplayName', '$D_y/F_y$');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(2,2), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(G(3,3), freqs, 'Hz'))), '-', 'DisplayName', '$D_z/F_z$');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(3,3), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(G(4,4), freqs, 'Hz'))), '-', 'DisplayName', '$R_x/M_x$');
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(4,4), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(G(5,5), freqs, 'Hz'))), '-', 'DisplayName', '$R_y/M_y$');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(5,5), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(G(6,6), freqs, 'Hz'))), '-', 'DisplayName', '$R_z/M_z$');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(6,6), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [rad/Nm]');
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
% Comparison with a stiffer Flexible Joint
|
||||
% The stiffness matrix with the flexible joint with a "hinge" size of 0.50mm is loaded.
|
||||
|
||||
K_050 = readmatrix('flex050_mat_K.CSV');
|
||||
Binary file not shown.
@@ -1,18 +0,0 @@
|
||||
2.5754630031250000e+07,-4.2712304687500000e+02,9.8287363937095506e+02,-1.7335510253906250e-01,-4.4769378662109375e+02,1.3719102478027344e+02,-2.5754630231555372e+07,4.2802952639819705e+02,-9.8287489818129689e+02,1.7549634272245385e-01,4.4764333847140233e+02,-1.3719858364899471e+02,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
-4.2712304687500000e+02,2.5755431550781250e+07,9.2766113281250000e+00,-7.0793685913085938e+02,4.8019409179687500e-02,-3.7032165527343750e+00,4.2713989735614450e+02,-2.5755431479663994e+07,-9.4205187247134745e+00,7.0798853475961914e+02,-4.8307011624274310e-02,3.7038846055879588e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
9.8287363937095506e+02,9.2766113281250000e+00,1.2465681387304688e+08,-6.2329087066650391e+02,-2.9795289039611816e-02,-2.0934855937957764e+00,-9.8287517688667867e+02,-9.7232561896089464e+00,-1.2465681387478238e+08,6.2327723664234827e+02,2.9786983064695960e-02,2.1346355473849030e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
-1.7335510253906250e-01,-7.0793685913085938e+02,-6.2329087066650391e+02,2.5996113300323486e+01,-3.5762786865234375e-07,-1.7011165618896484e-03,1.7350277768809974e-01,7.0793702391491649e+02,6.2329084741144834e+02,-2.5996114268074809e+01,-1.8741666600874396e-06,1.7019125586293926e-03,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
-4.4769378662109375e+02,4.8019409179687500e-02,-2.9795289039611816e-02,-3.5762786865234375e-07,2.5982229232788086e+01,-6.3159465789794922e-03,4.4769484901414762e+02,-4.7471478482042251e-02,2.9788838680602225e-02,-1.2213699259072154e-06,-2.5982218562570559e+01,6.3092922445503637e-03,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
1.3719102478027344e+02,-3.7032165527343750e+00,-2.0934855937957764e+00,-1.7011165618896484e-03,-6.3159465789794922e-03,5.3803079116344452e+02,-1.3719066901348401e+02,3.7048334432208634e+00,2.0934831215067788e+00,1.7111118565274128e-03,6.3100069062436148e-03,-5.3803081028251358e+02,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
-2.5754630231555372e+07,4.2713989735614450e+02,-9.8287517688667867e+02,1.7350277768809974e-01,4.4769484901414762e+02,-1.3719066901348401e+02,2.5754630263671875e+07,-4.2803005981445313e+02,9.8287525177001953e+02,-1.7550706863403320e-01,-4.4764308929443359e+02,1.3719856643676758e+02,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
4.2802952639819705e+02,-2.5755431479663994e+07,-9.7232561896089464e+00,7.0793702391491649e+02,-4.7471478482042251e-02,3.7048334432208634e+00,-4.2803005981445313e+02,2.5755431467773438e+07,9.8679199218750000e+00,-7.0798818969726563e+02,4.8238277435302734e-02,-3.7051738500595093e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
-9.8287489818129689e+02,-9.4205187247134745e+00,-1.2465681387478238e+08,6.2329084741144834e+02,2.9788838680602225e-02,2.0934831215067788e+00,9.8287525177001953e+02,9.8679199218750000e+00,1.2465681385253906e+08,-6.2327721166610718e+02,-2.9794454574584961e-02,-2.1346325874328613e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
1.7549634272245385e-01,7.0798853475961914e+02,6.2327723664234827e+02,-2.5996114268074809e+01,-1.2213699259072154e-06,1.7111118565274128e-03,-1.7550706863403320e-01,-7.0798818969726563e+02,-6.2327721166610718e+02,2.5996115207672119e+01,1.3196840882301331e-06,-1.7108507454395294e-03,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
4.4764333847140233e+02,-4.8307011624274310e-02,2.9786983064695960e-02,-1.8741666600874396e-06,-2.5982218562570559e+01,6.3100069062436148e-03,-4.4764308929443359e+02,4.8238277435302734e-02,-2.9794454574584961e-02,1.3196840882301331e-06,2.5982219338417053e+01,-6.3097774982452393e-03,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
-1.3719858364899471e+02,3.7038846055879588e+00,2.1346355473849030e+00,1.7019125586293926e-03,6.3092922445503637e-03,-5.3803081028251358e+02,1.3719856643676758e+02,-3.7051738500595093e+00,-2.1346325874328613e+00,-1.7108507454395294e-03,-6.3097774982452393e-03,5.3803082811832428e+02,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,2.0324356517907178e+09,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,6.5028284807042255e+09,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,6.5030840409031916e+09,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,1.1688606513278921e+10,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,1.5408447495394880e+10,0.0000000000000000e+00
|
||||
0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,1.7288981152109577e+10
|
||||
|
@@ -1,18 +0,0 @@
|
||||
6.9924933059303945e-03,-9.8764622522007350e-09,-4.2706346702493098e-08,-7.7566032310777584e-10,2.7008426141513918e-05,4.1471606524281276e-08,3.8473380874905439e-03,-3.1297790035129685e-08,3.6056126777783606e-08,-2.6657135026145262e-11,1.9141276820691673e-06,2.4309324061848354e-08,9.8156688445413667e-06,1.9913655606096422e-02,3.4067815405184936e-02,8.3297811316313415e-08,6.6564552724555761e-07,2.5562611584369105e-03
|
||||
-9.8764622522007350e-09,1.4555815631436229e-02,5.1699328773481652e-08,-2.8944646371945645e-05,8.7483744776401320e-11,2.4365811430949926e-09,1.0102997079063458e-07,3.8474657983129617e-03,-8.2921352366596745e-09,-1.5818009723742116e-08,2.7532795999526204e-10,1.1620315036577555e-09,4.9949873204491496e-06,8.3037561249954900e-02,-4.8537308743124931e-02,-1.3257998049398440e-06,-6.5930474324472712e-07,-1.3155411350887885e-02
|
||||
-4.2706346702493098e-08,5.1699328773481652e-08,1.2710535988233717e-02,-6.3938130589595463e-08,-5.4778776094730231e-11,-1.5022612245078194e-09,-1.6619687066756622e-07,-5.7008517478105126e-08,1.9109286635876400e-03,-9.6965193790782562e-09,-1.1503404782207693e-09,-9.5232525232897943e-10,-1.7844177003900562e-06,-2.1041705175076758e-06,-1.8021252748223115e-06,3.1038399657355057e-02,5.5086486995811708e-02,-8.9068668636294463e-06
|
||||
-7.7566032310777584e-10,-2.8944646371945645e-05,-6.3938130589595463e-08,1.0686195002613165e-06,-2.4277507265876614e-13,-1.1734315496481052e-12,8.5336797985625878e-10,1.8760067804115542e-06,-9.2585532262035468e-09,1.3659642338387410e-09,1.4381880983104784e-13,2.7096461913305968e-12,9.5595218157779795e-09,1.1170994843808959e-04,-6.5297500456989389e-05,-1.5868506919015904e-07,-1.1921663596014279e-07,6.6298991959861384e-04
|
||||
2.7008426141513918e-05,8.7483744776401320e-11,-5.4778776094730231e-11,-2.4277507265876614e-13,1.7618322179119962e-07,1.3301909131908001e-10,2.3105626858177232e-08,-3.7349994450460863e-11,5.2847010299670575e-11,-8.5714983688142616e-15,1.3850051324263041e-09,-1.9891208194933100e-12,-3.9787248948855476e-09,2.8238190623315227e-07,4.8528212139365325e-07,-5.7410163207087771e-11,5.6804229234630236e-10,-9.3246499046465763e-07
|
||||
4.1471606524281276e-08,2.4365811430949926e-09,-1.5022612245078194e-09,-1.1734315496481052e-12,1.3301909131908001e-10,4.7022010972884661e-07,1.5476917845357745e-08,-1.6319634548610560e-09,1.3434326257156190e-09,-8.2458859043553941e-13,1.5127724879914289e-11,2.8291633354898898e-07,5.3282016561555776e-04,1.1550317399575746e-07,2.0353608848066868e-07,4.2470146141165478e-10,9.4677838931774368e-10,1.4435307808829224e-08
|
||||
3.8473380874905439e-03,1.0102997079063458e-07,-1.6619687066756622e-07,8.5336797985625878e-10,2.3105626858177232e-08,1.5476917845357745e-08,1.4556232882728433e-02,-6.0061547290019869e-08,1.7284710960045399e-07,-5.4269250510237085e-11,-2.8799499943817674e-05,6.5060187776725949e-08,-1.3925520896127101e-05,4.8539719333802564e-02,8.3038632892332584e-02,1.4977932351330600e-06,2.7653863861400322e-07,1.0496187329528837e-02
|
||||
-3.1297790035129685e-08,3.8474657983129617e-03,-5.7008517478105126e-08,1.8760067804115542e-06,-3.7349994450460863e-11,-1.6319634548610560e-09,-6.0061547290019869e-08,6.9926551355764532e-03,1.3746858959193568e-08,2.6938313220175835e-05,-3.2839674748191459e-10,-1.9697435811367894e-09,-2.8881686825106493e-06,3.4069308650194828e-02,-1.9915466209036958e-02,-7.0063407116543913e-07,-7.7859602111904658e-07,-3.2046022066166214e-03
|
||||
3.6056126777783606e-08,-8.2921352366596745e-09,1.9109286635876400e-03,-9.2585532262035468e-09,5.2847010299670575e-11,1.3434326257156190e-09,1.7284710960045399e-07,1.3746858959193568e-08,1.2711009048340483e-02,-6.3420783115290293e-08,1.1538116246481933e-09,1.1063192142160378e-09,2.1953383979722170e-06,1.9123582408630362e-06,7.5995753019334908e-08,3.1062144974170900e-02,-5.5072495312596545e-02,8.3323932311411790e-06
|
||||
-2.6657135026145262e-11,-1.5818009723742116e-08,-9.6965193790782562e-09,1.3659642338387410e-09,-8.5714983688142616e-15,-8.2458859043553941e-13,-5.4269250510237085e-11,2.6938313220175835e-05,-6.3420783115290293e-08,1.7564434494297000e-07,4.3176551084531376e-14,-7.7698758353546320e-13,-1.5353796159173823e-09,1.3969612065443123e-07,-8.2501662426896980e-08,-1.5610236862568981e-07,2.7672926606997853e-07,1.1973039641814081e-06
|
||||
1.9141276820691673e-06,2.7532795999526204e-10,-1.1503404782207693e-09,1.4381880983104784e-13,1.3850051324263041e-09,1.5127724879914289e-11,-2.8799499943817674e-05,-3.2839674748191459e-10,1.1538116246481933e-09,4.3176551084531376e-14,1.0680417363676656e-06,-1.4542342019428284e-10,7.3084373663706831e-09,6.5770814046545479e-05,1.1254384204610682e-04,-3.4352495892409903e-08,-2.1834465215620278e-08,-5.2885254658484066e-04
|
||||
2.4309324061848354e-08,1.1620315036577555e-09,-9.5232525232897943e-10,2.7096461913305968e-12,-1.9891208194933100e-12,2.8291633354898898e-07,6.5060187776725949e-08,-1.9697435811367894e-09,1.1063192142160378e-09,-7.7698758353546320e-13,-1.4542342019428284e-10,4.7018662565161254e-07,5.3278790026013180e-04,2.2809599232664796e-07,4.2097933737588112e-07,-2.0526562010327096e-09,-6.8090109773123356e-10,5.5702807830388697e-08
|
||||
9.8156688445413667e-06,4.9949873204491496e-06,-1.7844177003900562e-06,9.5595218157779795e-09,-3.9787248948855476e-09,5.3282016561555776e-04,-1.3925520896127101e-05,-2.8881686825106493e-06,2.1953383979722170e-06,-1.5353796159173823e-09,7.3084373663706831e-09,5.3278790026013180e-04,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
1.9913655606096422e-02,8.3037561249954900e-02,-2.1041705175076758e-06,1.1170994843808959e-04,2.8238190623315227e-07,1.1550317399575746e-07,4.8539719333802564e-02,3.4069308650194828e-02,1.9123582408630362e-06,1.3969612065443123e-07,6.5770814046545479e-05,2.2809599232664796e-07,0.0000000000000000e+00,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
3.4067815405184936e-02,-4.8537308743124931e-02,-1.8021252748223115e-06,-6.5297500456989389e-05,4.8528212139365325e-07,2.0353608848066868e-07,8.3038632892332584e-02,-1.9915466209036958e-02,7.5995753019334908e-08,-8.2501662426896980e-08,1.1254384204610682e-04,4.2097933737588112e-07,0.0000000000000000e+00,0.0000000000000000e+00,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
8.3297811316313415e-08,-1.3257998049398440e-06,3.1038399657355057e-02,-1.5868506919015904e-07,-5.7410163207087771e-11,4.2470146141165478e-10,1.4977932351330600e-06,-7.0063407116543913e-07,3.1062144974170900e-02,-1.5610236862568981e-07,-3.4352495892409903e-08,-2.0526562010327096e-09,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
6.6564552724555761e-07,-6.5930474324472712e-07,5.5086486995811708e-02,-1.1921663596014279e-07,5.6804229234630236e-10,9.4677838931774368e-10,2.7653863861400322e-07,-7.7859602111904658e-07,-5.5072495312596545e-02,2.7672926606997853e-07,-2.1834465215620278e-08,-6.8090109773123356e-10,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,1.0000000000000000e+00,0.0000000000000000e+00
|
||||
2.5562611584369105e-03,-1.3155411350887885e-02,-8.9068668636294463e-06,6.6298991959861384e-04,-9.3246499046465763e-07,1.4435307808829224e-08,1.0496187329528837e-02,-3.2046022066166214e-03,8.3323932311411790e-06,1.1973039641814081e-06,-5.2885254658484066e-04,5.5702807830388697e-08,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,1.0000000000000000e+00
|
||||
|
@@ -1,40 +0,0 @@
|
||||
|
||||
LIST ALL SELECTED NODES. DSYS= 0
|
||||
|
||||
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
|
||||
DISTRIBUTED ANSYS Academic Research
|
||||
|
||||
00208316 VERSION=WINDOWS x64 10:53:12 AUG 28, 2020 CP= 4.531
|
||||
|
||||
Flex-DC-reduction--Modal (B5)
|
||||
|
||||
|
||||
|
||||
NODE X Y Z THXY THYZ THZX
|
||||
528875 0.0000 0.0000 0.10000E-008 0.00 0.00 0.00
|
||||
528876 0.0000 0.0000 -0.10000E-008 0.00 0.00 0.00
|
||||
|
||||
LIST MASTERS ON ALL SELECTED NODES.
|
||||
CURRENT DOF SET= UX UY UZ ROTX ROTY ROTZ
|
||||
|
||||
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
|
||||
DISTRIBUTED ANSYS Academic Research
|
||||
|
||||
00208316 VERSION=WINDOWS x64 10:53:12 AUG 28, 2020 CP= 4.781
|
||||
|
||||
Flex-DC-reduction--Modal (B5)
|
||||
|
||||
|
||||
NODE LABEL SUPPORT
|
||||
528875 UX
|
||||
528875 UY
|
||||
528875 UZ
|
||||
528875 ROTX
|
||||
528875 ROTY
|
||||
528875 ROTZ
|
||||
528876 UX
|
||||
528876 UY
|
||||
528876 UZ
|
||||
528876 ROTX
|
||||
528876 ROTY
|
||||
528876 ROTZ
|
||||
File diff suppressed because it is too large
Load Diff
Binary file not shown.
@@ -1,134 +0,0 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
addpath('flexor_ID16/');
|
||||
|
||||
open('flexor_ID16.slx');
|
||||
|
||||
% Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates
|
||||
% We first extract the stiffness and mass matrices.
|
||||
|
||||
K = extractMatrix('mat_K_6modes_2MDoF.matrix');
|
||||
M = extractMatrix('mat_M_6modes_2MDoF.matrix');
|
||||
|
||||
|
||||
|
||||
% #+caption: First 10x10 elements of the Mass matrix
|
||||
% #+RESULTS:
|
||||
% | 0.02 | 1e-09 | -4e-08 | -1e-10 | 0.0002 | -3e-11 | 0.004 | 5e-08 | 7e-08 | 1e-10 |
|
||||
% | 1e-09 | 0.02 | -3e-07 | -0.0002 | -1e-10 | -2e-09 | 2e-08 | 0.004 | 3e-07 | 1e-05 |
|
||||
% | -4e-08 | -3e-07 | 0.02 | 7e-10 | -2e-09 | 1e-09 | 3e-07 | 7e-08 | 0.003 | 1e-09 |
|
||||
% | -1e-10 | -0.0002 | 7e-10 | 4e-06 | -1e-12 | -6e-13 | 2e-10 | -7e-06 | -8e-10 | -1e-09 |
|
||||
% | 0.0002 | -1e-10 | -2e-09 | -1e-12 | 3e-06 | 2e-13 | 9e-06 | 4e-11 | 2e-09 | -3e-13 |
|
||||
% | -3e-11 | -2e-09 | 1e-09 | -6e-13 | 2e-13 | 4e-07 | 8e-11 | 9e-10 | -1e-09 | 2e-12 |
|
||||
% | 0.004 | 2e-08 | 3e-07 | 2e-10 | 9e-06 | 8e-11 | 0.02 | -7e-08 | -3e-07 | -2e-10 |
|
||||
% | 5e-08 | 0.004 | 7e-08 | -7e-06 | 4e-11 | 9e-10 | -7e-08 | 0.01 | -4e-08 | 0.0002 |
|
||||
% | 7e-08 | 3e-07 | 0.003 | -8e-10 | 2e-09 | -1e-09 | -3e-07 | -4e-08 | 0.02 | -1e-09 |
|
||||
% | 1e-10 | 1e-05 | 1e-09 | -1e-09 | -3e-13 | 2e-12 | -2e-10 | 0.0002 | -1e-09 | 2e-06 |
|
||||
|
||||
% Then, we extract the coordinates of the interface nodes.
|
||||
|
||||
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('out_nodes_3D.txt');
|
||||
|
||||
% Identification of the parameters using Simscape and looking at the Stiffness Matrix
|
||||
% The flexor is now imported into Simscape and its parameters are estimated using an identification.
|
||||
|
||||
|
||||
m = 1;
|
||||
|
||||
|
||||
|
||||
% The dynamics is identified from the applied force/torque to the measured displacement/rotation of the flexor.
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'flexor_ID16';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/T'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
G = linearize(mdl, io);
|
||||
|
||||
% Simpler Model
|
||||
% Let's now model the flexible joint with a "perfect" Bushing joint as shown in Figure [[fig:flexible_joint_simscape]].
|
||||
|
||||
% #+name: fig:flexible_joint_simscape
|
||||
% #+caption: Bushing Joint used to model the flexible joint
|
||||
% [[file:figs/flexible_joint_simscape.png]]
|
||||
|
||||
% The parameters of the Bushing joint (stiffnesses) are estimated from the Stiffness matrix that was computed from the FEM.
|
||||
|
||||
Kx = K(1,1); % [N/m]
|
||||
Ky = K(2,2); % [N/m]
|
||||
Kz = K(3,3); % [N/m]
|
||||
Krx = K(4,4); % [Nm/rad]
|
||||
Kry = K(5,5); % [Nm/rad]
|
||||
Krz = K(6,6); % [Nm/rad]
|
||||
|
||||
|
||||
|
||||
% The dynamics from the applied force/torque to the measured displacement/rotation of the flexor is identified again for this simpler model.
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'flexor_ID16_simplified';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/T'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
Gs = linearize(mdl, io);
|
||||
|
||||
|
||||
|
||||
% The two obtained dynamics are compared in Figure
|
||||
|
||||
|
||||
freqs = logspace(0, 5, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(G(1,1), freqs, 'Hz'))), '-', 'DisplayName', '$D_x/F_x$');
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(1,1), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(G(2,2), freqs, 'Hz'))), '-', 'DisplayName', '$D_y/F_y$');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(2,2), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(G(3,3), freqs, 'Hz'))), '-', 'DisplayName', '$D_z/F_z$');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(3,3), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(G(4,4), freqs, 'Hz'))), '-', 'DisplayName', '$R_x/M_x$');
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(4,4), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(G(5,5), freqs, 'Hz'))), '-', 'DisplayName', '$R_y/M_y$');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(5,5), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(G(6,6), freqs, 'Hz'))), '-', 'DisplayName', '$R_z/M_z$');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(6,6), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [rad/Nm]');
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
Binary file not shown.
Binary file not shown.
File diff suppressed because it is too large
Load Diff
@@ -1,20 +0,0 @@
|
||||
|
||||
MAT_K:
|
||||
[ 1, 1]: 1.122e+07 [ 1, 2]: 1.950e+02 [ 1, 3]: 2.215e+03 [ 1, 4]:-7.188e-01 [ 1, 5]:-2.652e+02 [ 1, 6]: 1.594e+00 [ 1, 7]:-1.122e+07 [ 1, 8]:-2.132e+02 [ 1, 9]:-2.217e+03 [ 1,10]: 1.471e-01 [ 1,11]: 2.656e+02 [ 1,12]:-1.333e+00 [ 1,13]: 0.000e+00 [ 1,14]: 0.000e+00 [ 1,15]: 0.000e+00 [ 1,16]: 0.000e+00 [ 1,17]: 0.000e+00 [ 1,18]: 0.000e+00
|
||||
[ 2, 1]: 1.950e+02 [ 2, 2]: 1.143e+07 [ 2, 3]: 1.286e+03 [ 2, 4]:-1.484e+02 [ 2, 5]:-1.875e-01 [ 2, 6]: 2.414e+00 [ 2, 7]:-2.122e+02 [ 2, 8]:-1.143e+07 [ 2, 9]:-1.286e+03 [ 2,10]: 1.484e+02 [ 2,11]: 1.357e-01 [ 2,12]:-2.542e+00 [ 2,13]: 0.000e+00 [ 2,14]: 0.000e+00 [ 2,15]: 0.000e+00 [ 2,16]: 0.000e+00 [ 2,17]: 0.000e+00 [ 2,18]: 0.000e+00
|
||||
[ 3, 1]: 2.215e+03 [ 3, 2]: 1.286e+03 [ 3, 3]: 1.194e+08 [ 3, 4]: 1.309e+00 [ 3, 5]: 1.488e+00 [ 3, 6]: 1.789e+00 [ 3, 7]:-2.221e+03 [ 3, 8]:-1.286e+03 [ 3, 9]:-1.194e+08 [ 3,10]:-1.310e+00 [ 3,11]:-1.329e+00 [ 3,12]:-1.784e+00 [ 3,13]: 0.000e+00 [ 3,14]: 0.000e+00 [ 3,15]: 0.000e+00 [ 3,16]: 0.000e+00 [ 3,17]: 0.000e+00 [ 3,18]: 0.000e+00
|
||||
[ 4, 1]:-7.188e-01 [ 4, 2]:-1.484e+02 [ 4, 3]: 1.309e+00 [ 4, 4]: 3.296e+01 [ 4, 5]: 4.883e-04 [ 4, 6]:-9.766e-04 [ 4, 7]: 1.410e-01 [ 4, 8]: 1.483e+02 [ 4, 9]:-1.309e+00 [ 4,10]:-3.297e+01 [ 4,11]: 2.641e-04 [ 4,12]: 3.780e-04 [ 4,13]: 0.000e+00 [ 4,14]: 0.000e+00 [ 4,15]: 0.000e+00 [ 4,16]: 0.000e+00 [ 4,17]: 0.000e+00 [ 4,18]: 0.000e+00
|
||||
[ 5, 1]:-2.652e+02 [ 5, 2]:-1.875e-01 [ 5, 3]: 1.488e+00 [ 5, 4]: 4.883e-04 [ 5, 5]: 3.298e+01 [ 5, 6]: 2.930e-03 [ 5, 7]: 2.658e+02 [ 5, 8]: 1.537e-01 [ 5, 9]:-1.488e+00 [ 5,10]: 2.599e-04 [ 5,11]:-3.294e+01 [ 5,12]:-2.446e-03 [ 5,13]: 0.000e+00 [ 5,14]: 0.000e+00 [ 5,15]: 0.000e+00 [ 5,16]: 0.000e+00 [ 5,17]: 0.000e+00 [ 5,18]: 0.000e+00
|
||||
[ 6, 1]: 1.594e+00 [ 6, 2]: 2.414e+00 [ 6, 3]: 1.789e+00 [ 6, 4]:-9.766e-04 [ 6, 5]: 2.930e-03 [ 6, 6]: 2.358e+02 [ 6, 7]:-1.323e+00 [ 6, 8]:-2.547e+00 [ 6, 9]:-1.792e+00 [ 6,10]: 3.789e-04 [ 6,11]:-2.516e-03 [ 6,12]:-2.358e+02 [ 6,13]: 0.000e+00 [ 6,14]: 0.000e+00 [ 6,15]: 0.000e+00 [ 6,16]: 0.000e+00 [ 6,17]: 0.000e+00 [ 6,18]: 0.000e+00
|
||||
[ 7, 1]:-1.122e+07 [ 7, 2]:-2.122e+02 [ 7, 3]:-2.221e+03 [ 7, 4]: 1.410e-01 [ 7, 5]: 2.658e+02 [ 7, 6]:-1.323e+00 [ 7, 7]: 1.145e+07 [ 7, 8]: 2.458e+04 [ 7, 9]: 1.637e+03 [ 7,10]: 1.200e+02 [ 7,11]:-4.800e+03 [ 7,12]:-4.800e+01 [ 7,13]: 0.000e+00 [ 7,14]: 0.000e+00 [ 7,15]: 0.000e+00 [ 7,16]: 0.000e+00 [ 7,17]: 0.000e+00 [ 7,18]: 0.000e+00
|
||||
[ 8, 1]:-2.132e+02 [ 8, 2]:-1.143e+07 [ 8, 3]:-1.286e+03 [ 8, 4]: 1.483e+02 [ 8, 5]: 1.537e-01 [ 8, 6]:-2.547e+00 [ 8, 7]: 2.458e+04 [ 8, 8]: 1.143e+07 [ 8, 9]: 1.287e+03 [ 8,10]:-7.200e+01 [ 8,11]:-6.400e+01 [ 8,12]:-8.000e+00 [ 8,13]: 0.000e+00 [ 8,14]: 0.000e+00 [ 8,15]: 0.000e+00 [ 8,16]: 0.000e+00 [ 8,17]: 0.000e+00 [ 8,18]: 0.000e+00
|
||||
[ 9, 1]:-2.217e+03 [ 9, 2]:-1.286e+03 [ 9, 3]:-1.194e+08 [ 9, 4]:-1.309e+00 [ 9, 5]:-1.488e+00 [ 9, 6]:-1.792e+00 [ 9, 7]: 1.637e+03 [ 9, 8]: 1.287e+03 [ 9, 9]: 1.194e+08 [ 9,10]: 1.320e+00 [ 9,11]: 1.188e+01 [ 9,12]: 2.216e+00 [ 9,13]: 0.000e+00 [ 9,14]: 0.000e+00 [ 9,15]: 0.000e+00 [ 9,16]: 0.000e+00 [ 9,17]: 0.000e+00 [ 9,18]: 0.000e+00
|
||||
[10, 1]: 1.471e-01 [10, 2]: 1.484e+02 [10, 3]:-1.310e+00 [10, 4]:-3.297e+01 [10, 5]: 2.599e-04 [10, 6]: 3.789e-04 [10, 7]: 1.200e+02 [10, 8]:-7.200e+01 [10, 9]: 1.320e+00 [10,10]: 3.469e+01 [10,11]:-7.750e+00 [10,12]:-5.000e-01 [10,13]: 0.000e+00 [10,14]: 0.000e+00 [10,15]: 0.000e+00 [10,16]: 0.000e+00 [10,17]: 0.000e+00 [10,18]: 0.000e+00
|
||||
[11, 1]: 2.656e+02 [11, 2]: 1.357e-01 [11, 3]:-1.329e+00 [11, 4]: 2.641e-04 [11, 5]:-3.294e+01 [11, 6]:-2.516e-03 [11, 7]:-4.800e+03 [11, 8]:-6.400e+01 [11, 9]: 1.188e+01 [11,10]:-7.750e+00 [11,11]: 1.300e+02 [11,12]:-5.000e-01 [11,13]: 0.000e+00 [11,14]: 0.000e+00 [11,15]: 0.000e+00 [11,16]: 0.000e+00 [11,17]: 0.000e+00 [11,18]: 0.000e+00
|
||||
[12, 1]:-1.333e+00 [12, 2]:-2.542e+00 [12, 3]:-1.784e+00 [12, 4]: 3.780e-04 [12, 5]:-2.446e-03 [12, 6]:-2.358e+02 [12, 7]:-4.800e+01 [12, 8]:-8.000e+00 [12, 9]: 2.216e+00 [12,10]:-5.000e-01 [12,11]:-5.000e-01 [12,12]: 2.385e+02 [12,13]: 0.000e+00 [12,14]: 0.000e+00 [12,15]: 0.000e+00 [12,16]: 0.000e+00 [12,17]: 0.000e+00 [12,18]: 0.000e+00
|
||||
[13, 1]: 0.000e+00 [13, 2]: 0.000e+00 [13, 3]: 0.000e+00 [13, 4]: 0.000e+00 [13, 5]: 0.000e+00 [13, 6]: 0.000e+00 [13, 7]: 0.000e+00 [13, 8]: 0.000e+00 [13, 9]: 0.000e+00 [13,10]: 0.000e+00 [13,11]: 0.000e+00 [13,12]: 0.000e+00 [13,13]: 4.356e+09 [13,14]: 0.000e+00 [13,15]: 0.000e+00 [13,16]: 0.000e+00 [13,17]: 0.000e+00 [13,18]: 0.000e+00
|
||||
[14, 1]: 0.000e+00 [14, 2]: 0.000e+00 [14, 3]: 0.000e+00 [14, 4]: 0.000e+00 [14, 5]: 0.000e+00 [14, 6]: 0.000e+00 [14, 7]: 0.000e+00 [14, 8]: 0.000e+00 [14, 9]: 0.000e+00 [14,10]: 0.000e+00 [14,11]: 0.000e+00 [14,12]: 0.000e+00 [14,13]: 0.000e+00 [14,14]: 4.593e+09 [14,15]: 0.000e+00 [14,16]: 0.000e+00 [14,17]: 0.000e+00 [14,18]: 0.000e+00
|
||||
[15, 1]: 0.000e+00 [15, 2]: 0.000e+00 [15, 3]: 0.000e+00 [15, 4]: 0.000e+00 [15, 5]: 0.000e+00 [15, 6]: 0.000e+00 [15, 7]: 0.000e+00 [15, 8]: 0.000e+00 [15, 9]: 0.000e+00 [15,10]: 0.000e+00 [15,11]: 0.000e+00 [15,12]: 0.000e+00 [15,13]: 0.000e+00 [15,14]: 0.000e+00 [15,15]: 4.948e+09 [15,16]: 0.000e+00 [15,17]: 0.000e+00 [15,18]: 0.000e+00
|
||||
[16, 1]: 0.000e+00 [16, 2]: 0.000e+00 [16, 3]: 0.000e+00 [16, 4]: 0.000e+00 [16, 5]: 0.000e+00 [16, 6]: 0.000e+00 [16, 7]: 0.000e+00 [16, 8]: 0.000e+00 [16, 9]: 0.000e+00 [16,10]: 0.000e+00 [16,11]: 0.000e+00 [16,12]: 0.000e+00 [16,13]: 0.000e+00 [16,14]: 0.000e+00 [16,15]: 0.000e+00 [16,16]: 1.919e+10 [16,17]: 0.000e+00 [16,18]: 0.000e+00
|
||||
[17, 1]: 0.000e+00 [17, 2]: 0.000e+00 [17, 3]: 0.000e+00 [17, 4]: 0.000e+00 [17, 5]: 0.000e+00 [17, 6]: 0.000e+00 [17, 7]: 0.000e+00 [17, 8]: 0.000e+00 [17, 9]: 0.000e+00 [17,10]: 0.000e+00 [17,11]: 0.000e+00 [17,12]: 0.000e+00 [17,13]: 0.000e+00 [17,14]: 0.000e+00 [17,15]: 0.000e+00 [17,16]: 0.000e+00 [17,17]: 2.147e+10 [17,18]: 0.000e+00
|
||||
[18, 1]: 0.000e+00 [18, 2]: 0.000e+00 [18, 3]: 0.000e+00 [18, 4]: 0.000e+00 [18, 5]: 0.000e+00 [18, 6]: 0.000e+00 [18, 7]: 0.000e+00 [18, 8]: 0.000e+00 [18, 9]: 0.000e+00 [18,10]: 0.000e+00 [18,11]: 0.000e+00 [18,12]: 0.000e+00 [18,13]: 0.000e+00 [18,14]: 0.000e+00 [18,15]: 0.000e+00 [18,16]: 0.000e+00 [18,17]: 0.000e+00 [18,18]: 3.336e+10
|
||||
@@ -1,20 +0,0 @@
|
||||
|
||||
MAT_M:
|
||||
[ 1, 1]: 1.624e-02 [ 1, 2]: 9.999e-10 [ 1, 3]:-3.692e-08 [ 1, 4]:-1.155e-10 [ 1, 5]: 2.049e-04 [ 1, 6]:-2.881e-11 [ 1, 7]: 4.064e-03 [ 1, 8]: 4.955e-08 [ 1, 9]: 7.368e-08 [ 1,10]: 1.379e-10 [ 1,11]:-7.160e-06 [ 1,12]: 6.897e-11 [ 1,13]:-2.028e-05 [ 1,14]: 5.554e-02 [ 1,15]: 3.599e-06 [ 1,16]: 2.900e-06 [ 1,17]: 8.272e-02 [ 1,18]:-2.468e-06
|
||||
[ 2, 1]: 9.999e-10 [ 2, 2]: 1.848e-02 [ 2, 3]:-3.219e-07 [ 2, 4]:-2.074e-04 [ 2, 5]:-1.119e-10 [ 2, 6]:-2.255e-09 [ 2, 7]: 2.195e-08 [ 2, 8]: 4.013e-03 [ 2, 9]: 2.886e-07 [ 2,10]: 9.997e-06 [ 2,11]:-3.644e-10 [ 2,12]:-3.744e-12 [ 2,13]:-1.437e-05 [ 2,14]:-5.095e-06 [ 2,15]: 8.806e-02 [ 2,16]:-1.237e-02 [ 2,17]: 1.500e-07 [ 2,18]: 3.313e-02
|
||||
[ 3, 1]:-3.692e-08 [ 3, 2]:-3.219e-07 [ 3, 3]: 1.804e-02 [ 3, 4]: 7.130e-10 [ 3, 5]:-1.637e-09 [ 3, 6]: 1.340e-09 [ 3, 7]: 3.136e-07 [ 3, 8]: 7.272e-08 [ 3, 9]: 2.993e-03 [ 3,10]: 1.259e-09 [ 3,11]:-5.922e-10 [ 3,12]: 1.317e-09 [ 3,13]: 5.819e-06 [ 3,14]: 3.227e-06 [ 3,15]:-3.103e-06 [ 3,16]: 4.241e-06 [ 3,17]:-9.604e-07 [ 3,18]:-2.639e-06
|
||||
[ 4, 1]:-1.155e-10 [ 4, 2]:-2.074e-04 [ 4, 3]: 7.130e-10 [ 4, 4]: 3.510e-06 [ 4, 5]:-1.359e-12 [ 4, 6]:-5.567e-13 [ 4, 7]: 1.778e-10 [ 4, 8]:-6.847e-06 [ 4, 9]:-7.847e-10 [ 4,10]:-1.254e-09 [ 4,11]: 9.463e-13 [ 4,12]: 1.958e-12 [ 4,13]: 4.641e-08 [ 4,14]: 1.613e-08 [ 4,15]:-2.170e-04 [ 4,16]: 6.874e-05 [ 4,17]:-1.637e-08 [ 4,18]:-5.990e-04
|
||||
[ 5, 1]: 2.049e-04 [ 5, 2]:-1.119e-10 [ 5, 3]:-1.637e-09 [ 5, 4]:-1.359e-12 [ 5, 5]: 3.311e-06 [ 5, 6]: 1.683e-13 [ 5, 7]: 9.441e-06 [ 5, 8]: 3.860e-11 [ 5, 9]: 1.766e-09 [ 5,10]:-2.762e-13 [ 5,11]:-1.297e-09 [ 5,12]: 1.810e-12 [ 5,13]:-6.036e-08 [ 5,14]: 1.813e-04 [ 5,15]: 9.642e-09 [ 5,16]: 2.704e-08 [ 5,17]: 8.113e-04 [ 5,18]:-2.302e-08
|
||||
[ 6, 1]:-2.881e-11 [ 6, 2]:-2.255e-09 [ 6, 3]: 1.340e-09 [ 6, 4]:-5.567e-13 [ 6, 5]: 1.683e-13 [ 6, 6]: 3.708e-07 [ 6, 7]: 8.410e-11 [ 6, 8]: 9.292e-10 [ 6, 9]:-1.086e-09 [ 6,10]: 2.396e-12 [ 6,11]:-5.002e-13 [ 6,12]: 6.502e-08 [ 6,13]: 2.552e-04 [ 6,14]: 9.650e-08 [ 6,15]: 6.459e-09 [ 6,16]:-9.240e-10 [ 6,17]:-5.548e-09 [ 6,18]: 3.141e-08
|
||||
[ 7, 1]: 4.064e-03 [ 7, 2]: 2.195e-08 [ 7, 3]: 3.136e-07 [ 7, 4]: 1.778e-10 [ 7, 5]: 9.441e-06 [ 7, 6]: 8.410e-11 [ 7, 7]: 1.674e-02 [ 7, 8]:-7.211e-08 [ 7, 9]:-3.482e-07 [ 7,10]:-2.155e-10 [ 7,11]:-1.699e-04 [ 7,12]:-6.684e-11 [ 7,13]:-3.188e-05 [ 7,14]: 8.552e-02 [ 7,15]: 4.929e-06 [ 7,16]:-4.308e-06 [ 7,17]:-9.224e-03 [ 7,18]: 1.941e-06
|
||||
[ 8, 1]: 4.955e-08 [ 8, 2]: 4.013e-03 [ 8, 3]: 7.272e-08 [ 8, 4]:-6.847e-06 [ 8, 5]: 3.860e-11 [ 8, 6]: 9.292e-10 [ 8, 7]:-7.211e-08 [ 8, 8]: 1.459e-02 [ 8, 9]:-3.946e-08 [ 8,10]: 1.670e-04 [ 8,11]: 4.772e-10 [ 8,12]: 1.298e-09 [ 8,13]: 2.789e-06 [ 8,14]:-2.877e-06 [ 8,15]: 5.546e-02 [ 8,16]: 7.601e-02 [ 8,17]:-2.596e-06 [ 8,18]:-6.673e-03
|
||||
[ 9, 1]: 7.368e-08 [ 9, 2]: 2.886e-07 [ 9, 3]: 2.993e-03 [ 9, 4]:-7.847e-10 [ 9, 5]: 1.766e-09 [ 9, 6]:-1.086e-09 [ 9, 7]:-3.482e-07 [ 9, 8]:-3.946e-08 [ 9, 9]: 1.708e-02 [ 9,10]:-1.230e-09 [ 9,11]: 4.937e-10 [ 9,12]:-1.568e-09 [ 9,13]:-5.366e-06 [ 9,14]:-4.779e-06 [ 9,15]: 2.951e-06 [ 9,16]:-1.252e-06 [ 9,17]: 5.979e-06 [ 9,18]:-2.257e-06
|
||||
[10, 1]: 1.379e-10 [10, 2]: 9.997e-06 [10, 3]: 1.259e-09 [10, 4]:-1.254e-09 [10, 5]:-2.762e-13 [10, 6]: 2.396e-12 [10, 7]:-2.155e-10 [10, 8]: 1.670e-04 [10, 9]:-1.230e-09 [10,10]: 2.413e-06 [10,11]:-1.085e-13 [10,12]:-1.860e-12 [10,13]: 9.566e-09 [10,14]:-1.039e-08 [10,15]: 1.953e-04 [10,16]: 6.785e-04 [10,17]:-2.458e-08 [10,18]:-7.855e-05
|
||||
[11, 1]:-7.160e-06 [11, 2]:-3.644e-10 [11, 3]:-5.922e-10 [11, 4]: 9.463e-13 [11, 5]:-1.297e-09 [11, 6]:-5.002e-13 [11, 7]:-1.699e-04 [11, 8]: 4.772e-10 [11, 9]: 4.937e-10 [11,10]:-1.085e-13 [11,11]: 2.569e-06 [11,12]:-1.144e-12 [11,13]: 7.355e-08 [11,14]:-2.049e-04 [11,15]:-1.424e-08 [11,16]: 5.036e-08 [11,17]: 4.737e-05 [11,18]:-1.820e-08
|
||||
[12, 1]: 6.897e-11 [12, 2]:-3.744e-12 [12, 3]: 1.317e-09 [12, 4]: 1.958e-12 [12, 5]: 1.810e-12 [12, 6]: 6.502e-08 [12, 7]:-6.684e-11 [12, 8]: 1.298e-09 [12, 9]:-1.568e-09 [12,10]:-1.860e-12 [12,11]:-1.144e-12 [12,12]: 4.129e-07 [12,13]: 2.609e-04 [12,14]: 9.485e-08 [12,15]: 4.034e-08 [12,16]:-2.487e-08 [12,17]: 4.305e-09 [12,18]: 7.568e-09
|
||||
[13, 1]:-2.028e-05 [13, 2]:-1.437e-05 [13, 3]: 5.819e-06 [13, 4]: 4.641e-08 [13, 5]:-6.036e-08 [13, 6]: 2.552e-04 [13, 7]:-3.188e-05 [13, 8]: 2.789e-06 [13, 9]:-5.366e-06 [13,10]: 9.566e-09 [13,11]: 7.355e-08 [13,12]: 2.609e-04 [13,13]: 1.000e+00 [13,14]: 0.000e+00 [13,15]: 0.000e+00 [13,16]: 0.000e+00 [13,17]: 0.000e+00 [13,18]: 0.000e+00
|
||||
[14, 1]: 5.554e-02 [14, 2]:-5.095e-06 [14, 3]: 3.227e-06 [14, 4]: 1.613e-08 [14, 5]: 1.813e-04 [14, 6]: 9.650e-08 [14, 7]: 8.552e-02 [14, 8]:-2.877e-06 [14, 9]:-4.779e-06 [14,10]:-1.039e-08 [14,11]:-2.049e-04 [14,12]: 9.485e-08 [14,13]: 0.000e+00 [14,14]: 1.000e+00 [14,15]: 0.000e+00 [14,16]: 0.000e+00 [14,17]: 0.000e+00 [14,18]: 0.000e+00
|
||||
[15, 1]: 3.599e-06 [15, 2]: 8.806e-02 [15, 3]:-3.103e-06 [15, 4]:-2.170e-04 [15, 5]: 9.642e-09 [15, 6]: 6.459e-09 [15, 7]: 4.929e-06 [15, 8]: 5.546e-02 [15, 9]: 2.951e-06 [15,10]: 1.953e-04 [15,11]:-1.424e-08 [15,12]: 4.034e-08 [15,13]: 0.000e+00 [15,14]: 0.000e+00 [15,15]: 1.000e+00 [15,16]: 0.000e+00 [15,17]: 0.000e+00 [15,18]: 0.000e+00
|
||||
[16, 1]: 2.900e-06 [16, 2]:-1.237e-02 [16, 3]: 4.241e-06 [16, 4]: 6.874e-05 [16, 5]: 2.704e-08 [16, 6]:-9.240e-10 [16, 7]:-4.308e-06 [16, 8]: 7.601e-02 [16, 9]:-1.252e-06 [16,10]: 6.785e-04 [16,11]: 5.036e-08 [16,12]:-2.487e-08 [16,13]: 0.000e+00 [16,14]: 0.000e+00 [16,15]: 0.000e+00 [16,16]: 1.000e+00 [16,17]: 0.000e+00 [16,18]: 0.000e+00
|
||||
[17, 1]: 8.272e-02 [17, 2]: 1.500e-07 [17, 3]:-9.604e-07 [17, 4]:-1.637e-08 [17, 5]: 8.113e-04 [17, 6]:-5.548e-09 [17, 7]:-9.224e-03 [17, 8]:-2.596e-06 [17, 9]: 5.979e-06 [17,10]:-2.458e-08 [17,11]: 4.737e-05 [17,12]: 4.305e-09 [17,13]: 0.000e+00 [17,14]: 0.000e+00 [17,15]: 0.000e+00 [17,16]: 0.000e+00 [17,17]: 1.000e+00 [17,18]: 0.000e+00
|
||||
[18, 1]:-2.468e-06 [18, 2]: 3.313e-02 [18, 3]:-2.639e-06 [18, 4]:-5.990e-04 [18, 5]:-2.302e-08 [18, 6]: 3.141e-08 [18, 7]: 1.941e-06 [18, 8]:-6.673e-03 [18, 9]:-2.257e-06 [18,10]:-7.855e-05 [18,11]:-1.820e-08 [18,12]: 7.568e-09 [18,13]: 0.000e+00 [18,14]: 0.000e+00 [18,15]: 0.000e+00 [18,16]: 0.000e+00 [18,17]: 0.000e+00 [18,18]: 1.000e+00
|
||||
@@ -1,40 +0,0 @@
|
||||
|
||||
LIST ALL SELECTED NODES. DSYS= 0
|
||||
|
||||
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
|
||||
DISTRIBUTED ANSYS Academic Research
|
||||
|
||||
00208316 VERSION=WINDOWS x64 16:37:53 JUL 30, 2020 CP= 3.062
|
||||
|
||||
Flex-FV--Modal (B5)
|
||||
|
||||
|
||||
|
||||
NODE X Y Z THXY THYZ THZX
|
||||
181278 0.0000 0.0000 0.10000E-008 0.00 0.00 0.00
|
||||
181279 0.0000 0.0000 -0.10000E-008 0.00 0.00 0.00
|
||||
|
||||
LIST MASTERS ON ALL SELECTED NODES.
|
||||
CURRENT DOF SET= UX UY UZ ROTX ROTY ROTZ
|
||||
|
||||
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
|
||||
DISTRIBUTED ANSYS Academic Research
|
||||
|
||||
00208316 VERSION=WINDOWS x64 16:37:53 JUL 30, 2020 CP= 3.062
|
||||
|
||||
Flex-FV--Modal (B5)
|
||||
|
||||
|
||||
NODE LABEL SUPPORT
|
||||
181278 UX
|
||||
181278 UY
|
||||
181278 UZ
|
||||
181278 ROTX
|
||||
181278 ROTY
|
||||
181278 ROTZ
|
||||
181279 UX
|
||||
181279 UY
|
||||
181279 UZ
|
||||
181279 ROTX
|
||||
181279 ROTY
|
||||
181279 ROTZ
|
||||
Binary file not shown.
36
matlab/mat/APA300ML_flex_mat_K.CSV
Normal file
36
matlab/mat/APA300ML_flex_mat_K.CSV
Normal file
@@ -0,0 +1,36 @@
|
||||
1.7025906652166748e+08,-5.0847898776903749e+03,-1.7824821763551235e+05,-1.3466069715889171e+02,-2.5055546540293694e+06,-3.4394740807618946e+03,1.6611123384494107e+07,-2.0265744364734564e+03,2.3453712127264356e+04,4.2503680078144953e+01,2.4562537687728583e+05,-2.6047031936489020e+01,-9.3271694320415661e+07,-4.8050791696289554e+04,-1.4158079942445016e+07,3.2969659612063697e+02,-5.9350973070021451e+05,1.1040980022378790e+02,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,-9.3598495585884690e+07,5.5162155885093205e+04,1.4312874447986556e+07,-3.2316960961190051e+02,-5.9457478563968907e+05,2.5872288588175991e+02,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
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36
matlab/mat/APA300ML_flex_mat_M.CSV
Normal file
36
matlab/mat/APA300ML_flex_mat_M.CSV
Normal file
@@ -0,0 +1,36 @@
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|
||||
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||||
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||||
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||||
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|
||||
|
61
matlab/mat/APA300ML_flex_out_nodes_3D.txt
Normal file
61
matlab/mat/APA300ML_flex_out_nodes_3D.txt
Normal file
@@ -0,0 +1,61 @@
|
||||
|
||||
LIST ALL SELECTED NODES. DSYS= 0
|
||||
|
||||
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
|
||||
DISTRIBUTED ANSYS Mechanical Enterprise
|
||||
|
||||
00208316 VERSION=WINDOWS x64 10:10:05 MAR 26, 2021 CP= 2.188
|
||||
|
||||
Unknown
|
||||
|
||||
|
||||
|
||||
NODE X Y Z THXY THYZ THZX
|
||||
1 0.0000 0.0000 0.28000E-001 0.00 0.00 0.00
|
||||
1228810 0.0000 0.0000 -0.28000E-001 0.00 0.00 0.00
|
||||
1228811 -0.30000E-001 0.0000 0.0000 0.00 0.00 0.00
|
||||
1228812 0.10000E-001 0.0000 0.0000 0.00 0.00 0.00
|
||||
1228813 0.30000E-001 0.0000 0.0000 0.00 0.00 0.00
|
||||
|
||||
LIST MASTERS ON ALL SELECTED NODES.
|
||||
CURRENT DOF SET= UX UY UZ ROTX ROTY ROTZ
|
||||
|
||||
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
|
||||
DISTRIBUTED ANSYS Mechanical Enterprise
|
||||
|
||||
00208316 VERSION=WINDOWS x64 10:10:05 MAR 26, 2021 CP= 2.188
|
||||
|
||||
Unknown
|
||||
|
||||
|
||||
NODE LABEL SUPPORT
|
||||
1 UX
|
||||
1 UY
|
||||
1 UZ
|
||||
1 ROTX
|
||||
1 ROTY
|
||||
1 ROTZ
|
||||
1228810 UX
|
||||
1228810 UY
|
||||
1228810 UZ
|
||||
1228810 ROTX
|
||||
1228810 ROTY
|
||||
1228810 ROTZ
|
||||
1228811 UX
|
||||
1228811 UY
|
||||
1228811 UZ
|
||||
1228811 ROTX
|
||||
1228811 ROTY
|
||||
1228811 ROTZ
|
||||
1228812 UX
|
||||
1228812 UY
|
||||
1228812 UZ
|
||||
1228812 ROTX
|
||||
1228812 ROTY
|
||||
1228812 ROTZ
|
||||
1228813 UX
|
||||
1228813 UY
|
||||
1228813 UZ
|
||||
1228813 ROTX
|
||||
1228813 ROTY
|
||||
1228813 ROTZ
|
||||
|
Can't render this file because it is too large.
|
|
Can't render this file because it is too large.
|
48
matlab/mat/APA95ML_K.CSV
Normal file
48
matlab/mat/APA95ML_K.CSV
Normal file
@@ -0,0 +1,48 @@
|
||||
2.8006425939072037e+08,-1.1121063492149115e+03,-2.7040964416936040e+04,-3.5940302362199873e+01,6.7202605779747944e+04,2.6563254029862583e+02,2.1550991792595461e+07,-2.7820061825215816e+01,-4.8864206375679933e+03,5.3746878486444984e+00,6.4147340757886577e+03,-6.9103225309070694e+01,-1.4902141053418255e+08,3.1993703876761720e+02,-8.4307353501717746e+07,-2.9571954231443669e+01,-9.7299097071200621e+05,-1.3674596425725031e+02,-1.8070558000868903e+06,-1.0795929480872983e+03,5.1952510213221348e+05,-4.5224368059107145e-01,2.6079383186555438e+03,5.4511244925179270e+00,4.8873270218593927e+04,9.4489019778934278e+00,-5.8397983819284718e+03,-3.2531085247855203e-02,-6.2918471367302182e+01,-1.2496202936659717e-01,-1.7731842407893836e+06,8.1375478259346767e+02,-5.1123347039108997e+05,1.2194408523968672e+01,2.5877380652997472e+03,-2.1293177717594958e+00,-1.4906247387838435e+08,1.0763786171675904e+03,8.4336829053448841e+07,1.5902058186794040e+01,-9.7339666199497378e+05,-1.1780862216647753e+02,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
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|
48
matlab/mat/APA95ML_M.CSV
Normal file
48
matlab/mat/APA95ML_M.CSV
Normal file
@@ -0,0 +1,48 @@
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|
||||
1.3106492228986189e-05,-3.5723349268193733e-03,1.6572383417626479e-05,-2.4524528394658456e-04,-1.2883784457938332e-07,1.3929093978201961e-06,-2.0053507774652502e-06,3.5728283551551688e-03,1.1824141280798525e-05,-2.4569778440730589e-04,8.1551244794981474e-08,-1.3764616335374010e-06,-1.5481986761443345e-05,-1.9044813141402933e-06,7.4544369185691846e-06,-4.4752055263868424e-04,-1.8068106002131866e-07,2.4370502902649210e-08,2.5687112618053921e-06,4.1655314389244600e-08,3.4122220147010140e-07,6.2083014580506038e-07,3.3940992746034015e-09,3.0044442082434653e-10,-7.1708411131971589e-08,-5.1027076387319601e-09,-6.2175221737627398e-09,-9.7248995910835063e-09,-4.6159749121076536e-11,-3.9694148835885484e-11,2.6170179656636316e-06,1.1901652322187288e-06,4.4732338266589198e-07,6.1967397606540059e-07,-1.7074057077706677e-09,4.5938289091603020e-09,8.6144457711177801e-06,1.7922379514314945e-05,1.6394035147424517e-05,-4.5310817532855151e-04,1.0946019552401556e-07,-1.6079171905942081e-07,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,1.0000000000000000e+00
|
||||
|
75
matlab/mat/APA95ML_out_nodes_3D.txt
Normal file
75
matlab/mat/APA95ML_out_nodes_3D.txt
Normal file
@@ -0,0 +1,75 @@
|
||||
|
||||
LIST ALL SELECTED NODES. DSYS= 0
|
||||
|
||||
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
|
||||
DISTRIBUTED ANSYS Academic Research
|
||||
|
||||
00208316 VERSION=WINDOWS x64 15:24:46 NOV 18, 2020 CP= 2.031
|
||||
|
||||
Piezo-APA95ML-3DElm--Modal (A5)
|
||||
|
||||
|
||||
|
||||
NODE X Y Z THXY THYZ THZX
|
||||
40467 0.0000 0.0000 0.29997E-001 0.00 0.00 0.00
|
||||
40469 0.0000 0.0000 -0.29997E-001 0.00 0.00 0.00
|
||||
40470 -0.35000E-001 0.0000 0.0000 0.00 0.00 0.00
|
||||
40475 -0.15000E-001 0.0000 0.0000 0.00 0.00 0.00
|
||||
40476 -0.50000E-002 0.0000 0.0000 0.00 0.00 0.00
|
||||
40477 0.15000E-001 0.0000 0.0000 0.00 0.00 0.00
|
||||
40478 0.35000E-001 0.0000 0.0000 0.00 0.00 0.00
|
||||
|
||||
LIST MASTERS ON ALL SELECTED NODES.
|
||||
CURRENT DOF SET= UX UY UZ ROTX ROTY ROTZ
|
||||
|
||||
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
|
||||
DISTRIBUTED ANSYS Academic Research
|
||||
|
||||
00208316 VERSION=WINDOWS x64 15:24:46 NOV 18, 2020 CP= 2.156
|
||||
|
||||
Piezo-APA95ML-3DElm--Modal (A5)
|
||||
|
||||
|
||||
NODE LABEL SUPPORT
|
||||
40467 UX
|
||||
40467 UY
|
||||
40467 UZ
|
||||
40467 ROTX
|
||||
40467 ROTY
|
||||
40467 ROTZ
|
||||
40469 UX
|
||||
40469 UY
|
||||
40469 UZ
|
||||
40469 ROTX
|
||||
40469 ROTY
|
||||
40469 ROTZ
|
||||
40470 UX
|
||||
40470 UY
|
||||
40470 UZ
|
||||
40470 ROTX
|
||||
40470 ROTY
|
||||
40470 ROTZ
|
||||
40475 UX
|
||||
40475 UY
|
||||
40475 UZ
|
||||
40475 ROTX
|
||||
40475 ROTY
|
||||
40475 ROTZ
|
||||
40476 UX
|
||||
40476 UY
|
||||
40476 UZ
|
||||
40476 ROTX
|
||||
40476 ROTY
|
||||
40476 ROTZ
|
||||
40477 UX
|
||||
40477 UY
|
||||
40477 UZ
|
||||
40477 ROTX
|
||||
40477 ROTY
|
||||
40477 ROTZ
|
||||
40478 UX
|
||||
40478 UY
|
||||
40478 UZ
|
||||
40478 ROTX
|
||||
40478 ROTY
|
||||
40478 ROTZ
|
||||
BIN
matlab/mat/apa95ml_5kg_2a_1s.mat
Normal file
BIN
matlab/mat/apa95ml_5kg_2a_1s.mat
Normal file
Binary file not shown.
BIN
matlab/mat/apa95ml_iff_test.mat
Normal file
BIN
matlab/mat/apa95ml_iff_test.mat
Normal file
Binary file not shown.
BIN
matlab/mat/nass_model_conf_log.mat
Normal file
BIN
matlab/mat/nass_model_conf_log.mat
Normal file
Binary file not shown.
BIN
matlab/mat/nass_model_conf_simscape.mat
Normal file
BIN
matlab/mat/nass_model_conf_simscape.mat
Normal file
Binary file not shown.
BIN
matlab/mat/nass_model_controller.mat
Normal file
BIN
matlab/mat/nass_model_controller.mat
Normal file
Binary file not shown.
BIN
matlab/mat/nass_model_disturbances.mat
Normal file
BIN
matlab/mat/nass_model_disturbances.mat
Normal file
Binary file not shown.
BIN
matlab/mat/nass_model_references.mat
Normal file
BIN
matlab/mat/nass_model_references.mat
Normal file
Binary file not shown.
BIN
matlab/mat/nass_model_stages.mat
Normal file
BIN
matlab/mat/nass_model_stages.mat
Normal file
Binary file not shown.
37
matlab/src/computeJacobian.m
Normal file
37
matlab/src/computeJacobian.m
Normal file
@@ -0,0 +1,37 @@
|
||||
function [stewart] = computeJacobian(stewart)
|
||||
% computeJacobian -
|
||||
%
|
||||
% Syntax: [stewart] = computeJacobian(stewart)
|
||||
%
|
||||
% Inputs:
|
||||
% - stewart - With at least the following fields:
|
||||
% - geometry.As [3x6] - The 6 unit vectors for each strut expressed in {A}
|
||||
% - geometry.Ab [3x6] - The 6 position of the joints bi expressed in {A}
|
||||
% - actuators.K [6x1] - Total stiffness of the actuators
|
||||
%
|
||||
% Outputs:
|
||||
% - stewart - With the 3 added field:
|
||||
% - geometry.J [6x6] - The Jacobian Matrix
|
||||
% - geometry.K [6x6] - The Stiffness Matrix
|
||||
% - geometry.C [6x6] - The Compliance Matrix
|
||||
|
||||
assert(isfield(stewart.geometry, 'As'), 'stewart.geometry should have attribute As')
|
||||
As = stewart.geometry.As;
|
||||
|
||||
assert(isfield(stewart.geometry, 'Ab'), 'stewart.geometry should have attribute Ab')
|
||||
Ab = stewart.geometry.Ab;
|
||||
|
||||
assert(isfield(stewart.actuators, 'k'), 'stewart.actuators should have attribute k')
|
||||
Ki = stewart.actuators.k;
|
||||
|
||||
J = [As' , cross(Ab, As)'];
|
||||
|
||||
K = J'*diag(Ki)*J;
|
||||
|
||||
C = inv(K);
|
||||
|
||||
stewart.geometry.J = J;
|
||||
stewart.geometry.K = K;
|
||||
stewart.geometry.C = C;
|
||||
|
||||
end
|
||||
80
matlab/src/computeJointsPose.m
Normal file
80
matlab/src/computeJointsPose.m
Normal file
@@ -0,0 +1,80 @@
|
||||
function [stewart] = computeJointsPose(stewart)
|
||||
% computeJointsPose -
|
||||
%
|
||||
% Syntax: [stewart] = computeJointsPose(stewart)
|
||||
%
|
||||
% Inputs:
|
||||
% - stewart - A structure with the following fields
|
||||
% - platform_F.Fa [3x6] - Its i'th column is the position vector of joint ai with respect to {F}
|
||||
% - platform_M.Mb [3x6] - Its i'th column is the position vector of joint bi with respect to {M}
|
||||
% - platform_F.FO_A [3x1] - Position of {A} with respect to {F}
|
||||
% - platform_M.MO_B [3x1] - Position of {B} with respect to {M}
|
||||
% - geometry.FO_M [3x1] - Position of {M} with respect to {F}
|
||||
%
|
||||
% Outputs:
|
||||
% - stewart - A structure with the following added fields
|
||||
% - geometry.Aa [3x6] - The i'th column is the position of ai with respect to {A}
|
||||
% - geometry.Ab [3x6] - The i'th column is the position of bi with respect to {A}
|
||||
% - geometry.Ba [3x6] - The i'th column is the position of ai with respect to {B}
|
||||
% - geometry.Bb [3x6] - The i'th column is the position of bi with respect to {B}
|
||||
% - geometry.l [6x1] - The i'th element is the initial length of strut i
|
||||
% - geometry.As [3x6] - The i'th column is the unit vector of strut i expressed in {A}
|
||||
% - geometry.Bs [3x6] - The i'th column is the unit vector of strut i expressed in {B}
|
||||
% - struts_F.l [6x1] - Length of the Fixed part of the i'th strut
|
||||
% - struts_M.l [6x1] - Length of the Mobile part of the i'th strut
|
||||
% - platform_F.FRa [3x3x6] - The i'th 3x3 array is the rotation matrix to orientate the bottom of the i'th strut from {F}
|
||||
% - platform_M.MRb [3x3x6] - The i'th 3x3 array is the rotation matrix to orientate the top of the i'th strut from {M}
|
||||
|
||||
assert(isfield(stewart.platform_F, 'Fa'), 'stewart.platform_F should have attribute Fa')
|
||||
Fa = stewart.platform_F.Fa;
|
||||
|
||||
assert(isfield(stewart.platform_M, 'Mb'), 'stewart.platform_M should have attribute Mb')
|
||||
Mb = stewart.platform_M.Mb;
|
||||
|
||||
assert(isfield(stewart.platform_F, 'FO_A'), 'stewart.platform_F should have attribute FO_A')
|
||||
FO_A = stewart.platform_F.FO_A;
|
||||
|
||||
assert(isfield(stewart.platform_M, 'MO_B'), 'stewart.platform_M should have attribute MO_B')
|
||||
MO_B = stewart.platform_M.MO_B;
|
||||
|
||||
assert(isfield(stewart.geometry, 'FO_M'), 'stewart.geometry should have attribute FO_M')
|
||||
FO_M = stewart.geometry.FO_M;
|
||||
|
||||
Aa = Fa - repmat(FO_A, [1, 6]);
|
||||
Bb = Mb - repmat(MO_B, [1, 6]);
|
||||
|
||||
Ab = Bb - repmat(-MO_B-FO_M+FO_A, [1, 6]);
|
||||
Ba = Aa - repmat( MO_B+FO_M-FO_A, [1, 6]);
|
||||
|
||||
As = (Ab - Aa)./vecnorm(Ab - Aa); % As_i is the i'th vector of As
|
||||
|
||||
l = vecnorm(Ab - Aa)';
|
||||
|
||||
Bs = (Bb - Ba)./vecnorm(Bb - Ba);
|
||||
|
||||
FRa = zeros(3,3,6);
|
||||
MRb = zeros(3,3,6);
|
||||
|
||||
for i = 1:6
|
||||
FRa(:,:,i) = [cross([0;1;0], As(:,i)) , cross(As(:,i), cross([0;1;0], As(:,i))) , As(:,i)];
|
||||
FRa(:,:,i) = FRa(:,:,i)./vecnorm(FRa(:,:,i));
|
||||
|
||||
MRb(:,:,i) = [cross([0;1;0], Bs(:,i)) , cross(Bs(:,i), cross([0;1;0], Bs(:,i))) , Bs(:,i)];
|
||||
MRb(:,:,i) = MRb(:,:,i)./vecnorm(MRb(:,:,i));
|
||||
end
|
||||
|
||||
stewart.geometry.Aa = Aa;
|
||||
stewart.geometry.Ab = Ab;
|
||||
stewart.geometry.Ba = Ba;
|
||||
stewart.geometry.Bb = Bb;
|
||||
stewart.geometry.As = As;
|
||||
stewart.geometry.Bs = Bs;
|
||||
stewart.geometry.l = l;
|
||||
|
||||
stewart.struts_F.l = l/2;
|
||||
stewart.struts_M.l = l/2;
|
||||
|
||||
stewart.platform_F.FRa = FRa;
|
||||
stewart.platform_M.MRb = MRb;
|
||||
|
||||
end
|
||||
77
matlab/src/computeReferencePose.m
Normal file
77
matlab/src/computeReferencePose.m
Normal file
@@ -0,0 +1,77 @@
|
||||
function [WTr] = computeReferencePose(Dy, Ry, Rz, Dh, Dn)
|
||||
% computeReferencePose - Compute the homogeneous transformation matrix corresponding to the wanted pose of the sample
|
||||
%
|
||||
% Syntax: [WTr] = computeReferencePose(Dy, Ry, Rz, Dh, Dn)
|
||||
%
|
||||
% Inputs:
|
||||
% - Dy - Reference of the Translation Stage [m]
|
||||
% - Ry - Reference of the Tilt Stage [rad]
|
||||
% - Rz - Reference of the Spindle [rad]
|
||||
% - Dh - Reference of the Micro Hexapod (Pitch, Roll, Yaw angles) [m, m, m, rad, rad, rad]
|
||||
% - Dn - Reference of the Nano Hexapod [m, m, m, rad, rad, rad]
|
||||
%
|
||||
% Outputs:
|
||||
% - WTr -
|
||||
|
||||
%% Translation Stage
|
||||
Rty = [1 0 0 0;
|
||||
0 1 0 Dy;
|
||||
0 0 1 0;
|
||||
0 0 0 1];
|
||||
|
||||
%% Tilt Stage - Pure rotating aligned with Ob
|
||||
Rry = [ cos(Ry) 0 sin(Ry) 0;
|
||||
0 1 0 0;
|
||||
-sin(Ry) 0 cos(Ry) 0;
|
||||
0 0 0 1];
|
||||
|
||||
%% Spindle - Rotation along the Z axis
|
||||
Rrz = [cos(Rz) -sin(Rz) 0 0 ;
|
||||
sin(Rz) cos(Rz) 0 0 ;
|
||||
0 0 1 0 ;
|
||||
0 0 0 1 ];
|
||||
|
||||
|
||||
%% Micro-Hexapod
|
||||
Rhx = [1 0 0;
|
||||
0 cos(Dh(4)) -sin(Dh(4));
|
||||
0 sin(Dh(4)) cos(Dh(4))];
|
||||
|
||||
Rhy = [ cos(Dh(5)) 0 sin(Dh(5));
|
||||
0 1 0;
|
||||
-sin(Dh(5)) 0 cos(Dh(5))];
|
||||
|
||||
Rhz = [cos(Dh(6)) -sin(Dh(6)) 0;
|
||||
sin(Dh(6)) cos(Dh(6)) 0;
|
||||
0 0 1];
|
||||
|
||||
Rh = [1 0 0 Dh(1) ;
|
||||
0 1 0 Dh(2) ;
|
||||
0 0 1 Dh(3) ;
|
||||
0 0 0 1 ];
|
||||
|
||||
Rh(1:3, 1:3) = Rhz*Rhy*Rhx;
|
||||
|
||||
%% Nano-Hexapod
|
||||
Rnx = [1 0 0;
|
||||
0 cos(Dn(4)) -sin(Dn(4));
|
||||
0 sin(Dn(4)) cos(Dn(4))];
|
||||
|
||||
Rny = [ cos(Dn(5)) 0 sin(Dn(5));
|
||||
0 1 0;
|
||||
-sin(Dn(5)) 0 cos(Dn(5))];
|
||||
|
||||
Rnz = [cos(Dn(6)) -sin(Dn(6)) 0;
|
||||
sin(Dn(6)) cos(Dn(6)) 0;
|
||||
0 0 1];
|
||||
|
||||
Rn = [1 0 0 Dn(1) ;
|
||||
0 1 0 Dn(2) ;
|
||||
0 0 1 Dn(3) ;
|
||||
0 0 0 1 ];
|
||||
|
||||
Rn(1:3, 1:3) = Rnz*Rny*Rnx;
|
||||
|
||||
%% Total Homogeneous transformation
|
||||
WTr = Rty*Rry*Rrz*Rh*Rn;
|
||||
end
|
||||
141
matlab/src/describeMicroStationSetup.m
Normal file
141
matlab/src/describeMicroStationSetup.m
Normal file
@@ -0,0 +1,141 @@
|
||||
function [] = describeMicroStationSetup()
|
||||
% describeMicroStationSetup -
|
||||
%
|
||||
% Syntax: [] = describeMicroStationSetup()
|
||||
%
|
||||
% Inputs:
|
||||
% - -
|
||||
%
|
||||
% Outputs:
|
||||
% - -
|
||||
|
||||
load('./mat/nass_model_conf_simscape.mat', 'conf_simscape');
|
||||
|
||||
fprintf('Simscape Configuration:\n');
|
||||
|
||||
if conf_simscape.type == 1
|
||||
fprintf('- Gravity is included\n');
|
||||
else
|
||||
fprintf('- Gravity is not included\n');
|
||||
end
|
||||
|
||||
fprintf('\n');
|
||||
|
||||
load('./mat/nass_model_disturbances.mat', 'args');
|
||||
|
||||
fprintf('Disturbances:\n');
|
||||
if ~args.enable
|
||||
fprintf('- No disturbance is included\n');
|
||||
else
|
||||
if args.Dwx && args.Dwy && args.Dwz
|
||||
fprintf('- Ground motion\n');
|
||||
end
|
||||
if args.Fdy_x && args.Fdy_z
|
||||
fprintf('- Vibrations of the Translation Stage\n');
|
||||
end
|
||||
if args.Frz_z
|
||||
fprintf('- Vibrations of the Spindle\n');
|
||||
end
|
||||
end
|
||||
fprintf('\n');
|
||||
|
||||
load('./mat/nass_model_references.mat', 'args');
|
||||
|
||||
fprintf('Reference Tracking:\n');
|
||||
fprintf('- Translation Stage:\n');
|
||||
switch args.Dy_type
|
||||
case 'constant'
|
||||
fprintf(' - Constant Position\n');
|
||||
fprintf(' - Dy = %.0f [mm]\n', args.Dy_amplitude*1e3);
|
||||
case 'triangular'
|
||||
fprintf(' - Triangular Path\n');
|
||||
fprintf(' - Amplitude = %.0f [mm]\n', args.Dy_amplitude*1e3);
|
||||
fprintf(' - Period = %.0f [s]\n', args.Dy_period);
|
||||
case 'sinusoidal'
|
||||
fprintf(' - Sinusoidal Path\n');
|
||||
fprintf(' - Amplitude = %.0f [mm]\n', args.Dy_amplitude*1e3);
|
||||
fprintf(' - Period = %.0f [s]\n', args.Dy_period);
|
||||
end
|
||||
|
||||
fprintf('- Tilt Stage:\n');
|
||||
switch args.Ry_type
|
||||
case 'constant'
|
||||
fprintf(' - Constant Position\n');
|
||||
fprintf(' - Ry = %.0f [mm]\n', args.Ry_amplitude*1e3);
|
||||
case 'triangular'
|
||||
fprintf(' - Triangular Path\n');
|
||||
fprintf(' - Amplitude = %.0f [mm]\n', args.Ry_amplitude*1e3);
|
||||
fprintf(' - Period = %.0f [s]\n', args.Ry_period);
|
||||
case 'sinusoidal'
|
||||
fprintf(' - Sinusoidal Path\n');
|
||||
fprintf(' - Amplitude = %.0f [mm]\n', args.Ry_amplitude*1e3);
|
||||
fprintf(' - Period = %.0f [s]\n', args.Ry_period);
|
||||
end
|
||||
|
||||
fprintf('- Spindle:\n');
|
||||
switch args.Rz_type
|
||||
case 'constant'
|
||||
fprintf(' - Constant Position\n');
|
||||
fprintf(' - Rz = %.0f [deg]\n', 180/pi*args.Rz_amplitude);
|
||||
case { 'rotating', 'rotating-not-filtered' }
|
||||
fprintf(' - Rotating\n');
|
||||
fprintf(' - Speed = %.0f [rpm]\n', 60/args.Rz_period);
|
||||
end
|
||||
|
||||
|
||||
fprintf('- Micro Hexapod:\n');
|
||||
switch args.Dh_type
|
||||
case 'constant'
|
||||
fprintf(' - Constant Position\n');
|
||||
fprintf(' - Dh = %.0f, %.0f, %.0f [mm]\n', args.Dh_pos(1), args.Dh_pos(2), args.Dh_pos(3));
|
||||
fprintf(' - Rh = %.0f, %.0f, %.0f [deg]\n', args.Dh_pos(4), args.Dh_pos(5), args.Dh_pos(6));
|
||||
end
|
||||
|
||||
fprintf('\n');
|
||||
|
||||
load('./mat/nass_model_stages.mat', 'ground', 'granite', 'ty', 'ry', 'rz', 'micro_hexapod', 'axisc');
|
||||
|
||||
fprintf('Micro Station:\n');
|
||||
|
||||
if granite.type == 1 && ...
|
||||
ty.type == 1 && ...
|
||||
ry.type == 1 && ...
|
||||
rz.type == 1 && ...
|
||||
micro_hexapod.type == 1;
|
||||
fprintf('- All stages are rigid\n');
|
||||
elseif granite.type == 2 && ...
|
||||
ty.type == 2 && ...
|
||||
ry.type == 2 && ...
|
||||
rz.type == 2 && ...
|
||||
micro_hexapod.type == 2;
|
||||
fprintf('- All stages are flexible\n');
|
||||
else
|
||||
if granite.type == 1 || granite.type == 4
|
||||
fprintf('- Granite is rigid\n');
|
||||
else
|
||||
fprintf('- Granite is flexible\n');
|
||||
end
|
||||
if ty.type == 1 || ty.type == 4
|
||||
fprintf('- Translation Stage is rigid\n');
|
||||
else
|
||||
fprintf('- Translation Stage is flexible\n');
|
||||
end
|
||||
if ry.type == 1 || ry.type == 4
|
||||
fprintf('- Tilt Stage is rigid\n');
|
||||
else
|
||||
fprintf('- Tilt Stage is flexible\n');
|
||||
end
|
||||
if rz.type == 1 || rz.type == 4
|
||||
fprintf('- Spindle is rigid\n');
|
||||
else
|
||||
fprintf('- Spindle is flexible\n');
|
||||
end
|
||||
if micro_hexapod.type == 1 || micro_hexapod.type == 4
|
||||
fprintf('- Micro Hexapod is rigid\n');
|
||||
else
|
||||
fprintf('- Micro Hexapod is flexible\n');
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
fprintf('\n');
|
||||
80
matlab/src/describeStewartPlatform.m
Normal file
80
matlab/src/describeStewartPlatform.m
Normal file
@@ -0,0 +1,80 @@
|
||||
function [] = describeStewartPlatform(stewart)
|
||||
% describeStewartPlatform - Display some text describing the current defined Stewart Platform
|
||||
%
|
||||
% Syntax: [] = describeStewartPlatform(args)
|
||||
%
|
||||
% Inputs:
|
||||
% - stewart
|
||||
%
|
||||
% Outputs:
|
||||
|
||||
arguments
|
||||
stewart
|
||||
end
|
||||
|
||||
fprintf('GEOMETRY:\n')
|
||||
fprintf('- The height between the fixed based and the top platform is %.3g [mm].\n', 1e3*stewart.geometry.H)
|
||||
|
||||
if stewart.platform_M.MO_B(3) > 0
|
||||
fprintf('- Frame {A} is located %.3g [mm] above the top platform.\n', 1e3*stewart.platform_M.MO_B(3))
|
||||
else
|
||||
fprintf('- Frame {A} is located %.3g [mm] below the top platform.\n', - 1e3*stewart.platform_M.MO_B(3))
|
||||
end
|
||||
|
||||
fprintf('- The initial length of the struts are:\n')
|
||||
fprintf('\t %.3g, %.3g, %.3g, %.3g, %.3g, %.3g [mm]\n', 1e3*stewart.geometry.l)
|
||||
fprintf('\n')
|
||||
|
||||
fprintf('ACTUATORS:\n')
|
||||
if stewart.actuators.type == 1
|
||||
fprintf('- The actuators are modelled as 1DoF.\n')
|
||||
fprintf('- The Stiffness and Damping of each actuators is:\n')
|
||||
fprintf('\t k = %.0e [N/m] \t c = %.0e [N/(m/s)]\n', stewart.actuators.k(1), stewart.actuators.c(1))
|
||||
if stewart.actuators.kp > 0
|
||||
fprintf('\t Added parallel stiffness: kp = %.0e [N/m] \t c = %.0e [N/(m/s)]\n', stewart.actuators.kp(1))
|
||||
end
|
||||
elseif stewart.actuators.type == 2
|
||||
fprintf('- The actuators are modelled as 2DoF (APA).\n')
|
||||
fprintf('- The vertical stiffness and damping contribution of the piezoelectric stack is:\n')
|
||||
fprintf('\t ka = %.0e [N/m] \t ca = %.0e [N/(m/s)]\n', stewart.actuators.ka(1), stewart.actuators.ca(1))
|
||||
fprintf('- Vertical stiffness when the piezoelectric stack is removed is:\n')
|
||||
fprintf('\t kr = %.0e [N/m] \t cr = %.0e [N/(m/s)]\n', stewart.actuators.kr(1), stewart.actuators.cr(1))
|
||||
elseif stewart.actuators.type == 3
|
||||
fprintf('- The actuators are modelled with a flexible element (FEM).\n')
|
||||
end
|
||||
fprintf('\n')
|
||||
|
||||
fprintf('JOINTS:\n')
|
||||
|
||||
switch stewart.joints_F.type
|
||||
case 1
|
||||
fprintf('- The joints on the fixed based are universal joints (2DoF)\n')
|
||||
case 2
|
||||
fprintf('- The joints on the fixed based are spherical joints (3DoF)\n')
|
||||
end
|
||||
|
||||
switch stewart.joints_M.type
|
||||
case 1
|
||||
fprintf('- The joints on the mobile based are universal joints (2DoF)\n')
|
||||
case 2
|
||||
fprintf('- The joints on the mobile based are spherical joints (3DoF)\n')
|
||||
end
|
||||
|
||||
fprintf('- The position of the joints on the fixed based with respect to {F} are (in [mm]):\n')
|
||||
fprintf('\t % .3g \t % .3g \t % .3g\n', 1e3*stewart.platform_F.Fa)
|
||||
|
||||
fprintf('- The position of the joints on the mobile based with respect to {M} are (in [mm]):\n')
|
||||
fprintf('\t % .3g \t % .3g \t % .3g\n', 1e3*stewart.platform_M.Mb)
|
||||
fprintf('\n')
|
||||
|
||||
fprintf('KINEMATICS:\n')
|
||||
|
||||
if isfield(stewart.kinematics, 'K')
|
||||
fprintf('- The Stiffness matrix K is (in [N/m]):\n')
|
||||
fprintf('\t % .0e \t % .0e \t % .0e \t % .0e \t % .0e \t % .0e\n', stewart.kinematics.K)
|
||||
end
|
||||
|
||||
if isfield(stewart.kinematics, 'C')
|
||||
fprintf('- The Damping matrix C is (in [m/N]):\n')
|
||||
fprintf('\t % .0e \t % .0e \t % .0e \t % .0e \t % .0e \t % .0e\n', stewart.kinematics.C)
|
||||
end
|
||||
240
matlab/src/displayArchitecture.m
Normal file
240
matlab/src/displayArchitecture.m
Normal file
@@ -0,0 +1,240 @@
|
||||
function [] = displayArchitecture(stewart, args)
|
||||
% displayArchitecture - 3D plot of the Stewart platform architecture
|
||||
%
|
||||
% Syntax: [] = displayArchitecture(args)
|
||||
%
|
||||
% Inputs:
|
||||
% - stewart
|
||||
% - args - Structure with the following fields:
|
||||
% - AP [3x1] - The wanted position of {B} with respect to {A}
|
||||
% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
|
||||
% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
|
||||
% - F_color [color] - Color used for the Fixed elements
|
||||
% - M_color [color] - Color used for the Mobile elements
|
||||
% - L_color [color] - Color used for the Legs elements
|
||||
% - frames [true/false] - Display the Frames
|
||||
% - legs [true/false] - Display the Legs
|
||||
% - joints [true/false] - Display the Joints
|
||||
% - labels [true/false] - Display the Labels
|
||||
% - platforms [true/false] - Display the Platforms
|
||||
% - views ['all', 'xy', 'yz', 'xz', 'default'] -
|
||||
%
|
||||
% Outputs:
|
||||
|
||||
arguments
|
||||
stewart
|
||||
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
||||
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
||||
args.F_color = [0 0.4470 0.7410]
|
||||
args.M_color = [0.8500 0.3250 0.0980]
|
||||
args.L_color = [0 0 0]
|
||||
args.frames logical {mustBeNumericOrLogical} = true
|
||||
args.legs logical {mustBeNumericOrLogical} = true
|
||||
args.joints logical {mustBeNumericOrLogical} = true
|
||||
args.labels logical {mustBeNumericOrLogical} = true
|
||||
args.platforms logical {mustBeNumericOrLogical} = true
|
||||
args.views char {mustBeMember(args.views,{'all', 'xy', 'xz', 'yz', 'default'})} = 'default'
|
||||
end
|
||||
|
||||
assert(isfield(stewart.platform_F, 'FO_A'), 'stewart.platform_F should have attribute FO_A')
|
||||
FO_A = stewart.platform_F.FO_A;
|
||||
|
||||
assert(isfield(stewart.platform_M, 'MO_B'), 'stewart.platform_M should have attribute MO_B')
|
||||
MO_B = stewart.platform_M.MO_B;
|
||||
|
||||
assert(isfield(stewart.geometry, 'H'), 'stewart.geometry should have attribute H')
|
||||
H = stewart.geometry.H;
|
||||
|
||||
assert(isfield(stewart.platform_F, 'Fa'), 'stewart.platform_F should have attribute Fa')
|
||||
Fa = stewart.platform_F.Fa;
|
||||
|
||||
assert(isfield(stewart.platform_M, 'Mb'), 'stewart.platform_M should have attribute Mb')
|
||||
Mb = stewart.platform_M.Mb;
|
||||
|
||||
if ~strcmp(args.views, 'all')
|
||||
figure;
|
||||
else
|
||||
f = figure('visible', 'off');
|
||||
end
|
||||
|
||||
hold on;
|
||||
|
||||
FTa = [eye(3), FO_A; ...
|
||||
zeros(1,3), 1];
|
||||
ATb = [args.ARB, args.AP; ...
|
||||
zeros(1,3), 1];
|
||||
BTm = [eye(3), -MO_B; ...
|
||||
zeros(1,3), 1];
|
||||
|
||||
FTm = FTa*ATb*BTm;
|
||||
|
||||
d_unit_vector = H/4;
|
||||
|
||||
d_label = H/20;
|
||||
|
||||
Ff = [0, 0, 0];
|
||||
if args.frames
|
||||
quiver3(Ff(1)*ones(1,3), Ff(2)*ones(1,3), Ff(3)*ones(1,3), ...
|
||||
[d_unit_vector 0 0], [0 d_unit_vector 0], [0 0 d_unit_vector], '-', 'Color', args.F_color)
|
||||
|
||||
if args.labels
|
||||
text(Ff(1) + d_label, ...
|
||||
Ff(2) + d_label, ...
|
||||
Ff(3) + d_label, '$\{F\}$', 'Color', args.F_color);
|
||||
end
|
||||
end
|
||||
|
||||
if args.frames
|
||||
quiver3(FO_A(1)*ones(1,3), FO_A(2)*ones(1,3), FO_A(3)*ones(1,3), ...
|
||||
[d_unit_vector 0 0], [0 d_unit_vector 0], [0 0 d_unit_vector], '-', 'Color', args.F_color)
|
||||
|
||||
if args.labels
|
||||
text(FO_A(1) + d_label, ...
|
||||
FO_A(2) + d_label, ...
|
||||
FO_A(3) + d_label, '$\{A\}$', 'Color', args.F_color);
|
||||
end
|
||||
end
|
||||
|
||||
if args.platforms && stewart.platform_F.type == 1
|
||||
theta = [0:0.01:2*pi+0.01]; % Angles [rad]
|
||||
v = null([0; 0; 1]'); % Two vectors that are perpendicular to the circle normal
|
||||
center = [0; 0; 0]; % Center of the circle
|
||||
radius = stewart.platform_F.R; % Radius of the circle [m]
|
||||
|
||||
points = center*ones(1, length(theta)) + radius*(v(:,1)*cos(theta) + v(:,2)*sin(theta));
|
||||
|
||||
plot3(points(1,:), ...
|
||||
points(2,:), ...
|
||||
points(3,:), '-', 'Color', args.F_color);
|
||||
end
|
||||
|
||||
if args.joints
|
||||
scatter3(Fa(1,:), ...
|
||||
Fa(2,:), ...
|
||||
Fa(3,:), 'MarkerEdgeColor', args.F_color);
|
||||
if args.labels
|
||||
for i = 1:size(Fa,2)
|
||||
text(Fa(1,i) + d_label, ...
|
||||
Fa(2,i), ...
|
||||
Fa(3,i), sprintf('$a_{%i}$', i), 'Color', args.F_color);
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
Fm = FTm*[0; 0; 0; 1]; % Get the position of frame {M} w.r.t. {F}
|
||||
|
||||
if args.frames
|
||||
FM_uv = FTm*[d_unit_vector*eye(3); zeros(1,3)]; % Rotated Unit vectors
|
||||
quiver3(Fm(1)*ones(1,3), Fm(2)*ones(1,3), Fm(3)*ones(1,3), ...
|
||||
FM_uv(1,1:3), FM_uv(2,1:3), FM_uv(3,1:3), '-', 'Color', args.M_color)
|
||||
|
||||
if args.labels
|
||||
text(Fm(1) + d_label, ...
|
||||
Fm(2) + d_label, ...
|
||||
Fm(3) + d_label, '$\{M\}$', 'Color', args.M_color);
|
||||
end
|
||||
end
|
||||
|
||||
FB = FO_A + args.AP;
|
||||
|
||||
if args.frames
|
||||
FB_uv = FTm*[d_unit_vector*eye(3); zeros(1,3)]; % Rotated Unit vectors
|
||||
quiver3(FB(1)*ones(1,3), FB(2)*ones(1,3), FB(3)*ones(1,3), ...
|
||||
FB_uv(1,1:3), FB_uv(2,1:3), FB_uv(3,1:3), '-', 'Color', args.M_color)
|
||||
|
||||
if args.labels
|
||||
text(FB(1) - d_label, ...
|
||||
FB(2) + d_label, ...
|
||||
FB(3) + d_label, '$\{B\}$', 'Color', args.M_color);
|
||||
end
|
||||
end
|
||||
|
||||
if args.platforms && stewart.platform_M.type == 1
|
||||
theta = [0:0.01:2*pi+0.01]; % Angles [rad]
|
||||
v = null((FTm(1:3,1:3)*[0;0;1])'); % Two vectors that are perpendicular to the circle normal
|
||||
center = Fm(1:3); % Center of the circle
|
||||
radius = stewart.platform_M.R; % Radius of the circle [m]
|
||||
|
||||
points = center*ones(1, length(theta)) + radius*(v(:,1)*cos(theta) + v(:,2)*sin(theta));
|
||||
|
||||
plot3(points(1,:), ...
|
||||
points(2,:), ...
|
||||
points(3,:), '-', 'Color', args.M_color);
|
||||
end
|
||||
|
||||
if args.joints
|
||||
Fb = FTm*[Mb;ones(1,6)];
|
||||
|
||||
scatter3(Fb(1,:), ...
|
||||
Fb(2,:), ...
|
||||
Fb(3,:), 'MarkerEdgeColor', args.M_color);
|
||||
|
||||
if args.labels
|
||||
for i = 1:size(Fb,2)
|
||||
text(Fb(1,i) + d_label, ...
|
||||
Fb(2,i), ...
|
||||
Fb(3,i), sprintf('$b_{%i}$', i), 'Color', args.M_color);
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
if args.legs
|
||||
for i = 1:6
|
||||
plot3([Fa(1,i), Fb(1,i)], ...
|
||||
[Fa(2,i), Fb(2,i)], ...
|
||||
[Fa(3,i), Fb(3,i)], '-', 'Color', args.L_color);
|
||||
|
||||
if args.labels
|
||||
text((Fa(1,i)+Fb(1,i))/2 + d_label, ...
|
||||
(Fa(2,i)+Fb(2,i))/2, ...
|
||||
(Fa(3,i)+Fb(3,i))/2, sprintf('$%i$', i), 'Color', args.L_color);
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
switch args.views
|
||||
case 'default'
|
||||
view([1 -0.6 0.4]);
|
||||
case 'xy'
|
||||
view([0 0 1]);
|
||||
case 'xz'
|
||||
view([0 -1 0]);
|
||||
case 'yz'
|
||||
view([1 0 0]);
|
||||
end
|
||||
axis equal;
|
||||
axis off;
|
||||
|
||||
if strcmp(args.views, 'all')
|
||||
hAx = findobj('type', 'axes');
|
||||
|
||||
figure;
|
||||
s1 = subplot(2,2,1);
|
||||
copyobj(get(hAx(1), 'Children'), s1);
|
||||
view([0 0 1]);
|
||||
axis equal;
|
||||
axis off;
|
||||
title('Top')
|
||||
|
||||
s2 = subplot(2,2,2);
|
||||
copyobj(get(hAx(1), 'Children'), s2);
|
||||
view([1 -0.6 0.4]);
|
||||
axis equal;
|
||||
axis off;
|
||||
|
||||
s3 = subplot(2,2,3);
|
||||
copyobj(get(hAx(1), 'Children'), s3);
|
||||
view([1 0 0]);
|
||||
axis equal;
|
||||
axis off;
|
||||
title('Front')
|
||||
|
||||
s4 = subplot(2,2,4);
|
||||
copyobj(get(hAx(1), 'Children'), s4);
|
||||
view([0 -1 0]);
|
||||
axis equal;
|
||||
axis off;
|
||||
title('Side')
|
||||
|
||||
close(f);
|
||||
end
|
||||
41
matlab/src/generateGeneralConfiguration.m
Normal file
41
matlab/src/generateGeneralConfiguration.m
Normal file
@@ -0,0 +1,41 @@
|
||||
function [stewart] = generateGeneralConfiguration(stewart, args)
|
||||
% generateGeneralConfiguration - Generate a Very General Configuration
|
||||
%
|
||||
% Syntax: [stewart] = generateGeneralConfiguration(stewart, args)
|
||||
%
|
||||
% Inputs:
|
||||
% - args - Can have the following fields:
|
||||
% - FH [1x1] - Height of the position of the fixed joints with respect to the frame {F} [m]
|
||||
% - FR [1x1] - Radius of the position of the fixed joints in the X-Y [m]
|
||||
% - FTh [6x1] - Angles of the fixed joints in the X-Y plane with respect to the X axis [rad]
|
||||
% - MH [1x1] - Height of the position of the mobile joints with respect to the frame {M} [m]
|
||||
% - FR [1x1] - Radius of the position of the mobile joints in the X-Y [m]
|
||||
% - MTh [6x1] - Angles of the mobile joints in the X-Y plane with respect to the X axis [rad]
|
||||
%
|
||||
% Outputs:
|
||||
% - stewart - updated Stewart structure with the added fields:
|
||||
% - platform_F.Fa [3x6] - Its i'th column is the position vector of joint ai with respect to {F}
|
||||
% - platform_M.Mb [3x6] - Its i'th column is the position vector of joint bi with respect to {M}
|
||||
|
||||
arguments
|
||||
stewart
|
||||
args.FH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
|
||||
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 115e-3;
|
||||
args.FTh (6,1) double {mustBeNumeric} = [-10, 10, 120-10, 120+10, 240-10, 240+10]*(pi/180);
|
||||
args.MH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
|
||||
args.MR (1,1) double {mustBeNumeric, mustBePositive} = 90e-3;
|
||||
args.MTh (6,1) double {mustBeNumeric} = [-60+10, 60-10, 60+10, 180-10, 180+10, -60-10]*(pi/180);
|
||||
end
|
||||
|
||||
Fa = zeros(3,6);
|
||||
Mb = zeros(3,6);
|
||||
|
||||
for i = 1:6
|
||||
Fa(:,i) = [args.FR*cos(args.FTh(i)); args.FR*sin(args.FTh(i)); args.FH];
|
||||
Mb(:,i) = [args.MR*cos(args.MTh(i)); args.MR*sin(args.MTh(i)); -args.MH];
|
||||
end
|
||||
|
||||
stewart.platform_F.Fa = Fa;
|
||||
stewart.platform_M.Mb = Mb;
|
||||
|
||||
end
|
||||
45
matlab/src/initializeController.m
Normal file
45
matlab/src/initializeController.m
Normal file
@@ -0,0 +1,45 @@
|
||||
function [] = initializeController(args)
|
||||
|
||||
arguments
|
||||
args.type char {mustBeMember(args.type,{'open-loop', 'iff', 'dvf', 'hac-dvf', 'ref-track-L', 'ref-track-iff-L', 'cascade-hac-lac', 'hac-iff', 'stabilizing'})} = 'open-loop'
|
||||
end
|
||||
|
||||
controller = struct();
|
||||
|
||||
switch args.type
|
||||
case 'open-loop'
|
||||
controller.type = 1;
|
||||
controller.name = 'Open-Loop';
|
||||
case 'dvf'
|
||||
controller.type = 2;
|
||||
controller.name = 'Decentralized Direct Velocity Feedback';
|
||||
case 'iff'
|
||||
controller.type = 3;
|
||||
controller.name = 'Decentralized Integral Force Feedback';
|
||||
case 'hac-dvf'
|
||||
controller.type = 4;
|
||||
controller.name = 'HAC-DVF';
|
||||
case 'ref-track-L'
|
||||
controller.type = 5;
|
||||
controller.name = 'Reference Tracking in the frame of the legs';
|
||||
case 'ref-track-iff-L'
|
||||
controller.type = 6;
|
||||
controller.name = 'Reference Tracking in the frame of the legs + IFF';
|
||||
case 'cascade-hac-lac'
|
||||
controller.type = 7;
|
||||
controller.name = 'Cascade Control + HAC-LAC';
|
||||
case 'hac-iff'
|
||||
controller.type = 8;
|
||||
controller.name = 'HAC-IFF';
|
||||
case 'stabilizing'
|
||||
controller.type = 9;
|
||||
controller.name = 'Stabilizing Controller';
|
||||
end
|
||||
|
||||
if exist('./mat', 'dir')
|
||||
save('mat/nass_model_controller.mat', 'controller');
|
||||
elseif exist('./matlab', 'dir')
|
||||
save('matlab/mat/nass_model_controller.mat', 'controller');
|
||||
end
|
||||
|
||||
end
|
||||
61
matlab/src/initializeCylindricalPlatforms.m
Normal file
61
matlab/src/initializeCylindricalPlatforms.m
Normal file
@@ -0,0 +1,61 @@
|
||||
function [stewart] = initializeCylindricalPlatforms(stewart, args)
|
||||
% initializeCylindricalPlatforms - Initialize the geometry of the Fixed and Mobile Platforms
|
||||
%
|
||||
% Syntax: [stewart] = initializeCylindricalPlatforms(args)
|
||||
%
|
||||
% Inputs:
|
||||
% - args - Structure with the following fields:
|
||||
% - Fpm [1x1] - Fixed Platform Mass [kg]
|
||||
% - Fph [1x1] - Fixed Platform Height [m]
|
||||
% - Fpr [1x1] - Fixed Platform Radius [m]
|
||||
% - Mpm [1x1] - Mobile Platform Mass [kg]
|
||||
% - Mph [1x1] - Mobile Platform Height [m]
|
||||
% - Mpr [1x1] - Mobile Platform Radius [m]
|
||||
%
|
||||
% Outputs:
|
||||
% - stewart - updated Stewart structure with the added fields:
|
||||
% - platform_F [struct] - structure with the following fields:
|
||||
% - type = 1
|
||||
% - M [1x1] - Fixed Platform Mass [kg]
|
||||
% - I [3x3] - Fixed Platform Inertia matrix [kg*m^2]
|
||||
% - H [1x1] - Fixed Platform Height [m]
|
||||
% - R [1x1] - Fixed Platform Radius [m]
|
||||
% - platform_M [struct] - structure with the following fields:
|
||||
% - M [1x1] - Mobile Platform Mass [kg]
|
||||
% - I [3x3] - Mobile Platform Inertia matrix [kg*m^2]
|
||||
% - H [1x1] - Mobile Platform Height [m]
|
||||
% - R [1x1] - Mobile Platform Radius [m]
|
||||
|
||||
arguments
|
||||
stewart
|
||||
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
||||
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
|
||||
args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 125e-3
|
||||
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
||||
args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
|
||||
args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
|
||||
end
|
||||
|
||||
I_F = diag([1/12*args.Fpm * (3*args.Fpr^2 + args.Fph^2), ...
|
||||
1/12*args.Fpm * (3*args.Fpr^2 + args.Fph^2), ...
|
||||
1/2 *args.Fpm * args.Fpr^2]);
|
||||
|
||||
I_M = diag([1/12*args.Mpm * (3*args.Mpr^2 + args.Mph^2), ...
|
||||
1/12*args.Mpm * (3*args.Mpr^2 + args.Mph^2), ...
|
||||
1/2 *args.Mpm * args.Mpr^2]);
|
||||
|
||||
stewart.platform_F.type = 1;
|
||||
|
||||
stewart.platform_F.I = I_F;
|
||||
stewart.platform_F.M = args.Fpm;
|
||||
stewart.platform_F.R = args.Fpr;
|
||||
stewart.platform_F.H = args.Fph;
|
||||
|
||||
stewart.platform_M.type = 1;
|
||||
|
||||
stewart.platform_M.I = I_M;
|
||||
stewart.platform_M.M = args.Mpm;
|
||||
stewart.platform_M.R = args.Mpr;
|
||||
stewart.platform_M.H = args.Mph;
|
||||
|
||||
end
|
||||
69
matlab/src/initializeCylindricalStruts.m
Normal file
69
matlab/src/initializeCylindricalStruts.m
Normal file
@@ -0,0 +1,69 @@
|
||||
function [stewart] = initializeCylindricalStruts(stewart, args)
|
||||
% initializeCylindricalStruts - Define the mass and moment of inertia of cylindrical struts
|
||||
%
|
||||
% Syntax: [stewart] = initializeCylindricalStruts(args)
|
||||
%
|
||||
% Inputs:
|
||||
% - args - Structure with the following fields:
|
||||
% - Fsm [1x1] - Mass of the Fixed part of the struts [kg]
|
||||
% - Fsh [1x1] - Height of cylinder for the Fixed part of the struts [m]
|
||||
% - Fsr [1x1] - Radius of cylinder for the Fixed part of the struts [m]
|
||||
% - Msm [1x1] - Mass of the Mobile part of the struts [kg]
|
||||
% - Msh [1x1] - Height of cylinder for the Mobile part of the struts [m]
|
||||
% - Msr [1x1] - Radius of cylinder for the Mobile part of the struts [m]
|
||||
%
|
||||
% Outputs:
|
||||
% - stewart - updated Stewart structure with the added fields:
|
||||
% - struts_F [struct] - structure with the following fields:
|
||||
% - M [6x1] - Mass of the Fixed part of the struts [kg]
|
||||
% - I [3x3x6] - Moment of Inertia for the Fixed part of the struts [kg*m^2]
|
||||
% - H [6x1] - Height of cylinder for the Fixed part of the struts [m]
|
||||
% - R [6x1] - Radius of cylinder for the Fixed part of the struts [m]
|
||||
% - struts_M [struct] - structure with the following fields:
|
||||
% - M [6x1] - Mass of the Mobile part of the struts [kg]
|
||||
% - I [3x3x6] - Moment of Inertia for the Mobile part of the struts [kg*m^2]
|
||||
% - H [6x1] - Height of cylinder for the Mobile part of the struts [m]
|
||||
% - R [6x1] - Radius of cylinder for the Mobile part of the struts [m]
|
||||
|
||||
arguments
|
||||
stewart
|
||||
args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
|
||||
args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
|
||||
args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
|
||||
args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
|
||||
args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
|
||||
args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
|
||||
end
|
||||
|
||||
stewart.struts_M.type = 1;
|
||||
|
||||
%% Compute the properties of the cylindrical struts
|
||||
Fsm = args.Fsm;
|
||||
Fsh = args.Fsh;
|
||||
Fsr = args.Fsr;
|
||||
|
||||
Msm = args.Msm;
|
||||
Msh = args.Msh;
|
||||
Msr = args.Msr;
|
||||
|
||||
I_F = [1/12 * Fsm * (3*Fsr^2 + Fsh^2), ...
|
||||
1/12 * Fsm * (3*Fsr^2 + Fsh^2), ...
|
||||
1/2 * Fsm * Fsr^2];
|
||||
|
||||
I_M = [1/12 * Msm * (3*Msr^2 + Msh^2), ...
|
||||
1/12 * Msm * (3*Msr^2 + Msh^2), ...
|
||||
1/2 * Msm * Msr^2];
|
||||
stewart.struts_M.I = I_M;
|
||||
stewart.struts_F.I = I_F;
|
||||
|
||||
stewart.struts_M.M = args.Msm;
|
||||
stewart.struts_M.R = args.Msr;
|
||||
stewart.struts_M.H = args.Msh;
|
||||
|
||||
stewart.struts_F.type = 1;
|
||||
|
||||
stewart.struts_F.M = args.Fsm;
|
||||
stewart.struts_F.R = args.Fsr;
|
||||
stewart.struts_F.H = args.Fsh;
|
||||
|
||||
end
|
||||
211
matlab/src/initializeDisturbances.m
Normal file
211
matlab/src/initializeDisturbances.m
Normal file
@@ -0,0 +1,211 @@
|
||||
function [] = initializeDisturbances(args)
|
||||
% initializeDisturbances - Initialize the disturbances
|
||||
%
|
||||
% Syntax: [] = initializeDisturbances(args)
|
||||
%
|
||||
% Inputs:
|
||||
% - args -
|
||||
|
||||
arguments
|
||||
% Global parameter to enable or disable the disturbances
|
||||
args.enable logical {mustBeNumericOrLogical} = true
|
||||
% Ground Motion - X direction
|
||||
args.Dw_x logical {mustBeNumericOrLogical} = true
|
||||
% Ground Motion - Y direction
|
||||
args.Dw_y logical {mustBeNumericOrLogical} = true
|
||||
% Ground Motion - Z direction
|
||||
args.Dw_z logical {mustBeNumericOrLogical} = true
|
||||
% Translation Stage - X direction
|
||||
args.Fdy_x logical {mustBeNumericOrLogical} = true
|
||||
% Translation Stage - Z direction
|
||||
args.Fdy_z logical {mustBeNumericOrLogical} = true
|
||||
% Spindle - X direction
|
||||
args.Frz_x logical {mustBeNumericOrLogical} = true
|
||||
% Spindle - Y direction
|
||||
args.Frz_y logical {mustBeNumericOrLogical} = true
|
||||
% Spindle - Z direction
|
||||
args.Frz_z logical {mustBeNumericOrLogical} = true
|
||||
end
|
||||
|
||||
% Initialization of random numbers
|
||||
rng("shuffle");
|
||||
|
||||
%% Ground Motion
|
||||
if args.enable
|
||||
% Load the PSD of disturbance
|
||||
load('ustation_disturbance_psd.mat', 'gm_dist')
|
||||
|
||||
% Frequency Data
|
||||
Dw.f = gm_dist.f;
|
||||
Dw.psd_x = gm_dist.pxx_x;
|
||||
Dw.psd_y = gm_dist.pxx_y;
|
||||
Dw.psd_z = gm_dist.pxx_z;
|
||||
|
||||
% Time data
|
||||
Fs = 2*Dw.f(end); % Sampling Frequency of data is twice the maximum frequency of the PSD vector [Hz]
|
||||
N = 2*length(Dw.f); % Number of Samples match the one of the wanted PSD
|
||||
T0 = N/Fs; % Signal Duration [s]
|
||||
Dw.t = linspace(0, T0, N+1)'; % Time Vector [s]
|
||||
|
||||
% ASD representation of the ground motion
|
||||
C = zeros(N/2,1);
|
||||
for i = 1:N/2
|
||||
C(i) = sqrt(Dw.psd_x(i)/T0);
|
||||
end
|
||||
|
||||
if args.Dw_x
|
||||
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
||||
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
||||
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
||||
Dw.x = N/sqrt(2)*ifft(Cx); % Ground Motion - x direction [m]
|
||||
else
|
||||
Dw.x = zeros(length(Dw.t), 1);
|
||||
end
|
||||
|
||||
if args.Dw_y
|
||||
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
||||
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
||||
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
||||
Dw.y = N/sqrt(2)*ifft(Cx); % Ground Motion - y direction [m]
|
||||
else
|
||||
Dw.y = zeros(length(Dw.t), 1);
|
||||
end
|
||||
|
||||
if args.Dw_y
|
||||
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
||||
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
||||
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
||||
Dw.z = N/sqrt(2)*ifft(Cx); % Ground Motion - z direction [m]
|
||||
else
|
||||
Dw.z = zeros(length(Dw.t), 1);
|
||||
end
|
||||
|
||||
else
|
||||
Dw.t = [0,1]; % Time Vector [s]
|
||||
Dw.x = [0,0]; % Ground Motion - X [m]
|
||||
Dw.y = [0,0]; % Ground Motion - Y [m]
|
||||
Dw.z = [0,0]; % Ground Motion - Z [m]
|
||||
end
|
||||
|
||||
%% Translation stage
|
||||
if args.enable
|
||||
% Load the PSD of disturbance
|
||||
load('ustation_disturbance_psd.mat', 'dy_dist')
|
||||
|
||||
% Frequency Data
|
||||
Dy.f = dy_dist.f;
|
||||
Dy.psd_x = dy_dist.pxx_fx;
|
||||
Dy.psd_z = dy_dist.pxx_fz;
|
||||
|
||||
% Time data
|
||||
Fs = 2*Dy.f(end); % Sampling Frequency of data is twice the maximum frequency of the PSD vector [Hz]
|
||||
N = 2*length(Dy.f); % Number of Samples match the one of the wanted PSD
|
||||
T0 = N/Fs; % Signal Duration [s]
|
||||
Dy.t = linspace(0, T0, N+1)'; % Time Vector [s]
|
||||
|
||||
% ASD representation of the disturbance voice
|
||||
C = zeros(N/2,1);
|
||||
for i = 1:N/2
|
||||
C(i) = sqrt(Dy.psd_x(i)/T0);
|
||||
end
|
||||
|
||||
if args.Fdy_x
|
||||
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
||||
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
||||
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
||||
Dy.x = N/sqrt(2)*ifft(Cx); % Translation stage disturbances - X direction [N]
|
||||
else
|
||||
Dy.x = zeros(length(Dy.t), 1);
|
||||
end
|
||||
|
||||
if args.Fdy_z
|
||||
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
||||
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
||||
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
||||
Dy.z = N/sqrt(2)*ifft(Cx); % Translation stage disturbances - Z direction [N]
|
||||
else
|
||||
Dy.z = zeros(length(Dy.t), 1);
|
||||
end
|
||||
|
||||
else
|
||||
Dy.t = [0,1]; % Time Vector [s]
|
||||
Dy.x = [0,0]; % Translation Stage disturbances - X [N]
|
||||
Dy.z = [0,0]; % Translation Stage disturbances - Z [N]
|
||||
end
|
||||
|
||||
%% Spindle
|
||||
if args.enable
|
||||
% Load the PSD of disturbance
|
||||
load('ustation_disturbance_psd.mat', 'rz_dist')
|
||||
|
||||
% Frequency Data
|
||||
Rz.f = rz_dist.f;
|
||||
Rz.psd_x = rz_dist.pxx_fx;
|
||||
Rz.psd_y = rz_dist.pxx_fy;
|
||||
Rz.psd_z = rz_dist.pxx_fz;
|
||||
|
||||
% Time data
|
||||
Fs = 2*Rz.f(end); % Sampling Frequency of data is twice the maximum frequency of the PSD vector [Hz]
|
||||
N = 2*length(Rz.f); % Number of Samples match the one of the wanted PSD
|
||||
T0 = N/Fs; % Signal Duration [s]
|
||||
Rz.t = linspace(0, T0, N+1)'; % Time Vector [s]
|
||||
|
||||
% ASD representation of the disturbance voice
|
||||
C = zeros(N/2,1);
|
||||
for i = 1:N/2
|
||||
C(i) = sqrt(Rz.psd_x(i)/T0);
|
||||
end
|
||||
|
||||
if args.Frz_x
|
||||
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
||||
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
||||
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
||||
Rz.x = N/sqrt(2)*ifft(Cx); % spindle disturbances - X direction [N]
|
||||
else
|
||||
Rz.x = zeros(length(Rz.t), 1);
|
||||
end
|
||||
|
||||
if args.Frz_y
|
||||
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
||||
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
||||
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
||||
Rz.y = N/sqrt(2)*ifft(Cx); % spindle disturbances - Y direction [N]
|
||||
else
|
||||
Rz.y = zeros(length(Rz.t), 1);
|
||||
end
|
||||
|
||||
if args.Frz_z
|
||||
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
||||
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
||||
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
||||
Rz.z = N/sqrt(2)*ifft(Cx); % spindle disturbances - Z direction [N]
|
||||
else
|
||||
Rz.z = zeros(length(Rz.t), 1);
|
||||
end
|
||||
|
||||
else
|
||||
Rz.t = [0,1]; % Time Vector [s]
|
||||
Rz.x = [0,0]; % Spindle disturbances - X [N]
|
||||
Rz.y = [0,0]; % Spindle disturbances - X [N]
|
||||
Rz.z = [0,0]; % Spindle disturbances - Z [N]
|
||||
end
|
||||
|
||||
u = zeros(100, 6);
|
||||
Fd = u;
|
||||
|
||||
Dw.x = Dw.x - Dw.x(1);
|
||||
Dw.y = Dw.y - Dw.y(1);
|
||||
Dw.z = Dw.z - Dw.z(1);
|
||||
|
||||
Dy.x = Dy.x - Dy.x(1);
|
||||
Dy.z = Dy.z - Dy.z(1);
|
||||
|
||||
Rz.x = Rz.x - Rz.x(1);
|
||||
Rz.y = Rz.y - Rz.y(1);
|
||||
Rz.z = Rz.z - Rz.z(1);
|
||||
|
||||
if exist('./mat', 'dir')
|
||||
save('mat/nass_model_disturbances.mat', 'Dw', 'Dy', 'Rz', 'Fd', 'args');
|
||||
elseif exist('./matlab', 'dir')
|
||||
save('matlab/mat/nass_model_disturbances.mat', 'Dw', 'Dy', 'Rz', 'Fd', 'args');
|
||||
end
|
||||
37
matlab/src/initializeFramesPositions.m
Normal file
37
matlab/src/initializeFramesPositions.m
Normal file
@@ -0,0 +1,37 @@
|
||||
function [stewart] = initializeFramesPositions(stewart, args)
|
||||
% initializeFramesPositions - Initialize the positions of frames {A}, {B}, {F} and {M}
|
||||
%
|
||||
% Syntax: [stewart] = initializeFramesPositions(stewart, args)
|
||||
%
|
||||
% Inputs:
|
||||
% - args - Can have the following fields:
|
||||
% - H [1x1] - Total Height of the Stewart Platform (height from {F} to {M}) [m]
|
||||
% - MO_B [1x1] - Height of the frame {B} with respect to {M} [m]
|
||||
%
|
||||
% Outputs:
|
||||
% - stewart - A structure with the following fields:
|
||||
% - geometry.H [1x1] - Total Height of the Stewart Platform [m]
|
||||
% - geometry.FO_M [3x1] - Position of {M} with respect to {F} [m]
|
||||
% - platform_M.MO_B [3x1] - Position of {B} with respect to {M} [m]
|
||||
% - platform_F.FO_A [3x1] - Position of {A} with respect to {F} [m]
|
||||
|
||||
arguments
|
||||
stewart
|
||||
args.H (1,1) double {mustBeNumeric, mustBePositive} = 90e-3
|
||||
args.MO_B (1,1) double {mustBeNumeric} = 50e-3
|
||||
end
|
||||
|
||||
H = args.H; % Total Height of the Stewart Platform [m]
|
||||
|
||||
FO_M = [0; 0; H]; % Position of {M} with respect to {F} [m]
|
||||
|
||||
MO_B = [0; 0; args.MO_B]; % Position of {B} with respect to {M} [m]
|
||||
|
||||
FO_A = MO_B + FO_M; % Position of {A} with respect to {F} [m]
|
||||
|
||||
stewart.geometry.H = H;
|
||||
stewart.geometry.FO_M = FO_M;
|
||||
stewart.platform_M.MO_B = MO_B;
|
||||
stewart.platform_F.FO_A = FO_A;
|
||||
|
||||
end
|
||||
48
matlab/src/initializeGranite.m
Normal file
48
matlab/src/initializeGranite.m
Normal file
@@ -0,0 +1,48 @@
|
||||
function [granite] = initializeGranite(args)
|
||||
|
||||
arguments
|
||||
args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none'})} = 'flexible'
|
||||
args.density (1,1) double {mustBeNumeric, mustBeNonnegative} = 2800 % Density [kg/m3]
|
||||
args.K (6,1) double {mustBeNumeric, mustBeNonnegative} = [5e9; 5e9; 5e9; 2.5e7; 2.5e7; 1e7] % [N/m]
|
||||
args.C (6,1) double {mustBeNumeric, mustBeNonnegative} = [4.0e5; 1.1e5; 9.0e5; 2e4; 2e4; 1e4] % [N/(m/s)]
|
||||
args.x0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the X direction [m]
|
||||
args.y0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the Y direction [m]
|
||||
args.z0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the Z direction [m]
|
||||
args.sample_pos (1,1) double {mustBeNumeric} = 0.775 % Height of the measurment point [m]
|
||||
end
|
||||
|
||||
granite = struct();
|
||||
|
||||
switch args.type
|
||||
case 'none'
|
||||
granite.type = 0;
|
||||
case 'rigid'
|
||||
granite.type = 1;
|
||||
case 'flexible'
|
||||
granite.type = 2;
|
||||
end
|
||||
|
||||
granite.density = args.density; % [kg/m3]
|
||||
granite.STEP = 'granite.STEP';
|
||||
|
||||
% Z-offset for the initial position of the sample with respect to the granite top surface.
|
||||
granite.sample_pos = args.sample_pos; % [m]
|
||||
|
||||
granite.K = args.K; % [N/m]
|
||||
granite.C = args.C; % [N/(m/s)]
|
||||
|
||||
if exist('./mat', 'dir')
|
||||
if exist('./mat/nass_model_stages.mat', 'file')
|
||||
save('mat/nass_model_stages.mat', 'granite', '-append');
|
||||
else
|
||||
save('mat/nass_model_stages.mat', 'granite');
|
||||
end
|
||||
elseif exist('./matlab', 'dir')
|
||||
if exist('./matlab/mat/nass_model_stages.mat', 'file')
|
||||
save('matlab/mat/nass_model_stages.mat', 'granite', '-append');
|
||||
else
|
||||
save('matlab/mat/nass_model_stages.mat', 'granite');
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
35
matlab/src/initializeGround.m
Normal file
35
matlab/src/initializeGround.m
Normal file
@@ -0,0 +1,35 @@
|
||||
function [ground] = initializeGround(args)
|
||||
|
||||
arguments
|
||||
args.type char {mustBeMember(args.type,{'none', 'rigid'})} = 'rigid'
|
||||
args.rot_point (3,1) double {mustBeNumeric} = zeros(3,1) % Rotation point for the ground motion [m]
|
||||
end
|
||||
|
||||
ground = struct();
|
||||
|
||||
switch args.type
|
||||
case 'none'
|
||||
ground.type = 0;
|
||||
case 'rigid'
|
||||
ground.type = 1;
|
||||
end
|
||||
|
||||
ground.shape = [2, 2, 0.5]; % [m]
|
||||
ground.density = 2800; % [kg/m3]
|
||||
|
||||
ground.rot_point = args.rot_point;
|
||||
|
||||
if exist('./mat', 'dir')
|
||||
if exist('./mat/nass_model_stages.mat', 'file')
|
||||
save('mat/nass_model_stages.mat', 'ground', '-append');
|
||||
else
|
||||
save('mat/nass_model_stages.mat', 'ground');
|
||||
end
|
||||
elseif exist('./matlab', 'dir')
|
||||
if exist('./matlab/mat/nass_model_stages.mat', 'file')
|
||||
save('matlab/mat/nass_model_stages.mat', 'ground', '-append');
|
||||
else
|
||||
save('matlab/mat/nass_model_stages.mat', 'ground');
|
||||
end
|
||||
end
|
||||
end
|
||||
48
matlab/src/initializeInertialSensor.m
Normal file
48
matlab/src/initializeInertialSensor.m
Normal file
@@ -0,0 +1,48 @@
|
||||
function [stewart] = initializeInertialSensor(stewart, args)
|
||||
% initializeInertialSensor - Initialize the inertial sensor in each strut
|
||||
%
|
||||
% Syntax: [stewart] = initializeInertialSensor(args)
|
||||
%
|
||||
% Inputs:
|
||||
% - args - Structure with the following fields:
|
||||
% - type - 'geophone', 'accelerometer', 'none'
|
||||
% - mass [1x1] - Weight of the inertial mass [kg]
|
||||
% - freq [1x1] - Cutoff frequency [Hz]
|
||||
%
|
||||
% Outputs:
|
||||
% - stewart - updated Stewart structure with the added fields:
|
||||
% - stewart.sensors.inertial
|
||||
% - type - 1 (geophone), 2 (accelerometer), 3 (none)
|
||||
% - K [1x1] - Stiffness [N/m]
|
||||
% - C [1x1] - Damping [N/(m/s)]
|
||||
% - M [1x1] - Inertial Mass [kg]
|
||||
% - G [1x1] - Gain
|
||||
|
||||
arguments
|
||||
stewart
|
||||
args.type char {mustBeMember(args.type,{'geophone', 'accelerometer', 'none'})} = 'none'
|
||||
args.mass (1,1) double {mustBeNumeric, mustBeNonnegative} = 1e-2
|
||||
args.freq (1,1) double {mustBeNumeric, mustBeNonnegative} = 1e3
|
||||
end
|
||||
|
||||
sensor = struct();
|
||||
|
||||
switch args.type
|
||||
case 'geophone'
|
||||
sensor.type = 1;
|
||||
|
||||
sensor.M = args.mass;
|
||||
sensor.K = sensor.M * (2*pi*args.freq)^2;
|
||||
sensor.C = 2*sqrt(sensor.M * sensor.K);
|
||||
case 'accelerometer'
|
||||
sensor.type = 2;
|
||||
|
||||
sensor.M = args.mass;
|
||||
sensor.K = sensor.M * (2*pi*args.freq)^2;
|
||||
sensor.C = 2*sqrt(sensor.M * sensor.K);
|
||||
sensor.G = -sensor.K/sensor.M;
|
||||
case 'none'
|
||||
sensor.type = 3;
|
||||
end
|
||||
|
||||
stewart.sensors.inertial = sensor;
|
||||
136
matlab/src/initializeJointDynamics.m
Normal file
136
matlab/src/initializeJointDynamics.m
Normal file
@@ -0,0 +1,136 @@
|
||||
function [stewart] = initializeJointDynamics(stewart, args)
|
||||
% initializeJointDynamics - Add Stiffness and Damping properties for the spherical joints
|
||||
%
|
||||
% Syntax: [stewart] = initializeJointDynamics(args)
|
||||
%
|
||||
% Inputs:
|
||||
% - args - Structure with the following fields:
|
||||
% - type_F - 'universal', 'spherical', 'universal_p', 'spherical_p'
|
||||
% - type_M - 'universal', 'spherical', 'universal_p', 'spherical_p'
|
||||
% - Kf_M [6x1] - Bending (Rx, Ry) Stiffness for each top joints [(N.m)/rad]
|
||||
% - Kt_M [6x1] - Torsion (Rz) Stiffness for each top joints [(N.m)/rad]
|
||||
% - Cf_M [6x1] - Bending (Rx, Ry) Damping of each top joint [(N.m)/(rad/s)]
|
||||
% - Ct_M [6x1] - Torsion (Rz) Damping of each top joint [(N.m)/(rad/s)]
|
||||
% - Kf_F [6x1] - Bending (Rx, Ry) Stiffness for each bottom joints [(N.m)/rad]
|
||||
% - Kt_F [6x1] - Torsion (Rz) Stiffness for each bottom joints [(N.m)/rad]
|
||||
% - Cf_F [6x1] - Bending (Rx, Ry) Damping of each bottom joint [(N.m)/(rad/s)]
|
||||
% - Cf_F [6x1] - Torsion (Rz) Damping of each bottom joint [(N.m)/(rad/s)]
|
||||
%
|
||||
% Outputs:
|
||||
% - stewart - updated Stewart structure with the added fields:
|
||||
% - stewart.joints_F and stewart.joints_M:
|
||||
% - type - 1 (universal), 2 (spherical), 3 (universal perfect), 4 (spherical perfect)
|
||||
% - Kx, Ky, Kz [6x1] - Translation (Tx, Ty, Tz) Stiffness [N/m]
|
||||
% - Kf [6x1] - Flexion (Rx, Ry) Stiffness [(N.m)/rad]
|
||||
% - Kt [6x1] - Torsion (Rz) Stiffness [(N.m)/rad]
|
||||
% - Cx, Cy, Cz [6x1] - Translation (Rx, Ry) Damping [N/(m/s)]
|
||||
% - Cf [6x1] - Flexion (Rx, Ry) Damping [(N.m)/(rad/s)]
|
||||
% - Cb [6x1] - Torsion (Rz) Damping [(N.m)/(rad/s)]
|
||||
|
||||
arguments
|
||||
stewart
|
||||
args.type_F char {mustBeMember(args.type_F,{'2dof', '3dof', '4dof', '2dof_axial', 'flexible'})} = '2dof'
|
||||
args.type_M char {mustBeMember(args.type_M,{'2dof', '3dof', '4dof', '2dof_axial', 'flexible'})} = '3dof'
|
||||
args.Kf_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Cf_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Kt_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Ct_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Kf_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Cf_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Kt_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Ct_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Ka_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Ca_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Kr_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Cr_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Ka_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Ca_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Kr_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Cr_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.K_M double {mustBeNumeric} = zeros(6,6)
|
||||
args.M_M double {mustBeNumeric} = zeros(6,6)
|
||||
args.n_xyz_M double {mustBeNumeric} = zeros(2,3)
|
||||
args.xi_M double {mustBeNumeric} = 0.1
|
||||
args.step_file_M char {} = 'flexor_025.STEP'
|
||||
args.K_F double {mustBeNumeric} = zeros(6,6)
|
||||
args.M_F double {mustBeNumeric} = zeros(6,6)
|
||||
args.n_xyz_F double {mustBeNumeric} = zeros(2,3)
|
||||
args.xi_F double {mustBeNumeric} = 0.1
|
||||
args.step_file_F char {} = 'flexor_025.STEP'
|
||||
end
|
||||
|
||||
switch args.type_F
|
||||
case '2dof'
|
||||
stewart.joints_F.type = 1;
|
||||
case '3dof'
|
||||
stewart.joints_F.type = 2;
|
||||
case '4dof'
|
||||
stewart.joints_F.type = 3;
|
||||
case '2dof_axial'
|
||||
stewart.joints_F.type = 4;
|
||||
case 'flexible'
|
||||
stewart.joints_F.type = 5;
|
||||
|
||||
K = readmatrix('flex025_mat_K.CSV');
|
||||
M = readmatrix('flex025_mat_M.CSV');
|
||||
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('flex025_out_nodes_3D.txt');
|
||||
|
||||
stewart.joints_F.M = M;
|
||||
stewart.joints_F.K = K;
|
||||
stewart.joints_F.n_xyz = int_xyz;
|
||||
stewart.joints_F.xi = 0.05;
|
||||
stewart.joints_F.step_file = args.step_file_F;
|
||||
otherwise
|
||||
error("joints_F are not correctly defined")
|
||||
end
|
||||
|
||||
switch args.type_M
|
||||
case '2dof'
|
||||
stewart.joints_M.type = 1;
|
||||
case '3dof'
|
||||
stewart.joints_M.type = 2;
|
||||
case '4dof'
|
||||
stewart.joints_M.type = 3;
|
||||
case '2dof_axial'
|
||||
stewart.joints_M.type = 4;
|
||||
case 'flexible'
|
||||
stewart.joints_M.type = 5;
|
||||
|
||||
K = readmatrix('flex025_mat_K.CSV');
|
||||
M = readmatrix('flex025_mat_M.CSV');
|
||||
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('flex025_out_nodes_3D.txt');
|
||||
|
||||
|
||||
stewart.joints_M.M = M;
|
||||
stewart.joints_M.K = K;
|
||||
stewart.joints_M.n_xyz = int_xyz;
|
||||
stewart.joints_M.xi = 0.05;
|
||||
stewart.joints_M.step_file = args.step_file_M;
|
||||
otherwise
|
||||
error("joints_M are not correctly defined")
|
||||
end
|
||||
|
||||
stewart.joints_M.Ka = args.Ka_M;
|
||||
stewart.joints_M.Kr = args.Kr_M;
|
||||
|
||||
stewart.joints_F.Ka = args.Ka_F;
|
||||
stewart.joints_F.Kr = args.Kr_F;
|
||||
|
||||
stewart.joints_M.Ca = args.Ca_M;
|
||||
stewart.joints_M.Cr = args.Cr_M;
|
||||
|
||||
stewart.joints_F.Ca = args.Ca_F;
|
||||
stewart.joints_F.Cr = args.Cr_F;
|
||||
|
||||
stewart.joints_M.Kf = args.Kf_M;
|
||||
stewart.joints_M.Kt = args.Kt_M;
|
||||
|
||||
stewart.joints_F.Kf = args.Kf_F;
|
||||
stewart.joints_F.Kt = args.Kt_F;
|
||||
|
||||
stewart.joints_M.Cf = args.Cf_M;
|
||||
stewart.joints_M.Ct = args.Ct_M;
|
||||
|
||||
stewart.joints_F.Cf = args.Cf_F;
|
||||
stewart.joints_F.Ct = args.Ct_F;
|
||||
end
|
||||
33
matlab/src/initializeLoggingConfiguration.m
Normal file
33
matlab/src/initializeLoggingConfiguration.m
Normal file
@@ -0,0 +1,33 @@
|
||||
function [] = initializeLoggingConfiguration(args)
|
||||
|
||||
arguments
|
||||
args.log char {mustBeMember(args.log,{'none', 'all', 'forces'})} = 'none'
|
||||
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3
|
||||
end
|
||||
|
||||
conf_log = struct();
|
||||
|
||||
switch args.log
|
||||
case 'none'
|
||||
conf_log.type = 0;
|
||||
case 'all'
|
||||
conf_log.type = 1;
|
||||
case 'forces'
|
||||
conf_log.type = 2;
|
||||
end
|
||||
|
||||
conf_log.Ts = args.Ts;
|
||||
|
||||
if exist('./mat', 'dir')
|
||||
if exist('./mat/nass_model_conf_log.mat', 'file')
|
||||
save('mat/nass_model_conf_log.mat', 'conf_log', '-append');
|
||||
else
|
||||
save('mat/nass_model_conf_log.mat', 'conf_log');
|
||||
end
|
||||
elseif exist('./matlab', 'dir')
|
||||
if exist('./matlab/mat/nass_model_conf_log.mat', 'file')
|
||||
save('matlab/mat/nass_model_conf_log.mat', 'conf_log', '-append');
|
||||
else
|
||||
save('matlab/mat/nass_model_conf_log.mat', 'conf_log');
|
||||
end
|
||||
end
|
||||
108
matlab/src/initializeMicroHexapod.m
Normal file
108
matlab/src/initializeMicroHexapod.m
Normal file
@@ -0,0 +1,108 @@
|
||||
function [micro_hexapod] = initializeMicroHexapod(args)
|
||||
|
||||
arguments
|
||||
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'flexible'
|
||||
% initializeFramesPositions
|
||||
args.H (1,1) double {mustBeNumeric, mustBePositive} = 350e-3
|
||||
args.MO_B (1,1) double {mustBeNumeric} = 270e-3
|
||||
% generateGeneralConfiguration
|
||||
args.FH (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
|
||||
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 175.5e-3
|
||||
args.FTh (6,1) double {mustBeNumeric} = [-10, 10, 120-10, 120+10, 240-10, 240+10]*(pi/180)
|
||||
args.MH (1,1) double {mustBeNumeric, mustBePositive} = 45e-3
|
||||
args.MR (1,1) double {mustBeNumeric, mustBePositive} = 118e-3
|
||||
args.MTh (6,1) double {mustBeNumeric} = [-60+10, 60-10, 60+10, 180-10, 180+10, -60-10]*(pi/180)
|
||||
% initializeStrutDynamics
|
||||
args.Ki (1,1) double {mustBeNumeric, mustBeNonnegative} = 2e7
|
||||
args.Ci (1,1) double {mustBeNumeric, mustBeNonnegative} = 1.4e3
|
||||
% initializeCylindricalPlatforms
|
||||
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 10
|
||||
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 26e-3
|
||||
args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 207.5e-3
|
||||
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 10
|
||||
args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 26e-3
|
||||
args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 150e-3
|
||||
% initializeCylindricalStruts
|
||||
args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
||||
args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
|
||||
args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 25e-3
|
||||
args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
||||
args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
|
||||
args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 25e-3
|
||||
% inverseKinematics
|
||||
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
||||
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
||||
end
|
||||
|
||||
stewart = initializeStewartPlatform();
|
||||
|
||||
stewart = initializeFramesPositions(stewart, ...
|
||||
'H', args.H, ...
|
||||
'MO_B', args.MO_B);
|
||||
|
||||
stewart = generateGeneralConfiguration(stewart, ...
|
||||
'FH', args.FH, ...
|
||||
'FR', args.FR, ...
|
||||
'FTh', args.FTh, ...
|
||||
'MH', args.MH, ...
|
||||
'MR', args.MR, ...
|
||||
'MTh', args.MTh);
|
||||
|
||||
stewart = computeJointsPose(stewart);
|
||||
|
||||
stewart = initializeStrutDynamics(stewart, ...
|
||||
'k', args.Ki, ...
|
||||
'c', args.Ci);
|
||||
|
||||
stewart = initializeJointDynamics(stewart, ...
|
||||
'type_F', '2dof', ...
|
||||
'type_M', '3dof');
|
||||
|
||||
stewart = initializeCylindricalPlatforms(stewart, ...
|
||||
'Fpm', args.Fpm, ...
|
||||
'Fph', args.Fph, ...
|
||||
'Fpr', args.Fpr, ...
|
||||
'Mpm', args.Mpm, ...
|
||||
'Mph', args.Mph, ...
|
||||
'Mpr', args.Mpr);
|
||||
|
||||
stewart = initializeCylindricalStruts(stewart, ...
|
||||
'Fsm', args.Fsm, ...
|
||||
'Fsh', args.Fsh, ...
|
||||
'Fsr', args.Fsr, ...
|
||||
'Msm', args.Msm, ...
|
||||
'Msh', args.Msh, ...
|
||||
'Msr', args.Msr);
|
||||
|
||||
stewart = computeJacobian(stewart);
|
||||
|
||||
stewart = initializeStewartPose(stewart, ...
|
||||
'AP', args.AP, ...
|
||||
'ARB', args.ARB);
|
||||
|
||||
stewart = initializeInertialSensor(stewart, 'type', 'none');
|
||||
|
||||
switch args.type
|
||||
case 'none'
|
||||
stewart.type = 0;
|
||||
case 'rigid'
|
||||
stewart.type = 1;
|
||||
case 'flexible'
|
||||
stewart.type = 2;
|
||||
end
|
||||
|
||||
micro_hexapod = stewart;
|
||||
if exist('./mat', 'dir')
|
||||
if exist('./mat/nass_model_stages.mat', 'file')
|
||||
save('mat/nass_model_stages.mat', 'micro_hexapod', '-append');
|
||||
else
|
||||
save('mat/nass_model_stages.mat', 'micro_hexapod');
|
||||
end
|
||||
elseif exist('./matlab', 'dir')
|
||||
if exist('./matlab/mat/nass_model_stages.mat', 'file')
|
||||
save('matlab/mat/nass_model_stages.mat', 'micro_hexapod', '-append');
|
||||
else
|
||||
save('matlab/mat/nass_model_stages.mat', 'micro_hexapod');
|
||||
end
|
||||
end
|
||||
end
|
||||
199
matlab/src/initializeReferences.m
Normal file
199
matlab/src/initializeReferences.m
Normal file
@@ -0,0 +1,199 @@
|
||||
function [ref] = initializeReferences(args)
|
||||
|
||||
arguments
|
||||
% Sampling Frequency [s]
|
||||
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3
|
||||
% Maximum simulation time [s]
|
||||
args.Tmax (1,1) double {mustBeNumeric, mustBePositive} = 100
|
||||
% Either "constant" / "triangular" / "sinusoidal"
|
||||
args.Dy_type char {mustBeMember(args.Dy_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
|
||||
% Amplitude of the displacement [m]
|
||||
args.Dy_amplitude (1,1) double {mustBeNumeric} = 0
|
||||
% Period of the displacement [s]
|
||||
args.Dy_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
||||
% Either "constant" / "triangular" / "sinusoidal"
|
||||
args.Ry_type char {mustBeMember(args.Ry_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
|
||||
% Amplitude [rad]
|
||||
args.Ry_amplitude (1,1) double {mustBeNumeric} = 0
|
||||
% Period of the displacement [s]
|
||||
args.Ry_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
||||
% Either "constant" / "rotating"
|
||||
args.Rz_type char {mustBeMember(args.Rz_type,{'constant', 'rotating', 'rotating-not-filtered'})} = 'constant'
|
||||
% Initial angle [rad]
|
||||
args.Rz_amplitude (1,1) double {mustBeNumeric} = 0
|
||||
% Period of the rotating [s]
|
||||
args.Rz_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
||||
% For now, only constant is implemented
|
||||
args.Dh_type char {mustBeMember(args.Dh_type,{'constant'})} = 'constant'
|
||||
% Initial position [m,m,m,rad,rad,rad] of the top platform (Pitch-Roll-Yaw Euler angles)
|
||||
args.Dh_pos (6,1) double {mustBeNumeric} = zeros(6, 1), ...
|
||||
% For now, only constant is implemented
|
||||
args.Rm_type char {mustBeMember(args.Rm_type,{'constant'})} = 'constant'
|
||||
% Initial position of the two masses
|
||||
args.Rm_pos (2,1) double {mustBeNumeric} = [0; pi]
|
||||
% For now, only constant is implemented
|
||||
args.Dn_type char {mustBeMember(args.Dn_type,{'constant'})} = 'constant'
|
||||
% Initial position [m,m,m,rad,rad,rad] of the top platform
|
||||
args.Dn_pos (6,1) double {mustBeNumeric} = zeros(6,1)
|
||||
end
|
||||
|
||||
%% Set Sampling Time
|
||||
Ts = args.Ts;
|
||||
Tmax = args.Tmax;
|
||||
|
||||
%% Low Pass Filter to filter out the references
|
||||
s = zpk('s');
|
||||
w0 = 2*pi*10;
|
||||
xi = 1;
|
||||
H_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2);
|
||||
|
||||
%% Translation stage - Dy
|
||||
t = 0:Ts:Tmax; % Time Vector [s]
|
||||
Dy = zeros(length(t), 1);
|
||||
Dyd = zeros(length(t), 1);
|
||||
Dydd = zeros(length(t), 1);
|
||||
switch args.Dy_type
|
||||
case 'constant'
|
||||
Dy(:) = args.Dy_amplitude;
|
||||
Dyd(:) = 0;
|
||||
Dydd(:) = 0;
|
||||
case 'triangular'
|
||||
% This is done to unsure that we start with no displacement
|
||||
Dy_raw = args.Dy_amplitude*sawtooth(2*pi*t/args.Dy_period,1/2);
|
||||
i0 = find(t>=args.Dy_period/4,1);
|
||||
Dy(1:end-i0+1) = Dy_raw(i0:end);
|
||||
Dy(end-i0+2:end) = Dy_raw(end); % we fix the last value
|
||||
|
||||
% The signal is filtered out
|
||||
Dy = lsim(H_lpf, Dy, t);
|
||||
Dyd = lsim(H_lpf*s, Dy, t);
|
||||
Dydd = lsim(H_lpf*s^2, Dy, t);
|
||||
case 'sinusoidal'
|
||||
Dy(:) = args.Dy_amplitude*sin(2*pi/args.Dy_period*t);
|
||||
Dyd = args.Dy_amplitude*2*pi/args.Dy_period*cos(2*pi/args.Dy_period*t);
|
||||
Dydd = -args.Dy_amplitude*(2*pi/args.Dy_period)^2*sin(2*pi/args.Dy_period*t);
|
||||
otherwise
|
||||
warning('Dy_type is not set correctly');
|
||||
end
|
||||
|
||||
Dy = struct('time', t, 'signals', struct('values', Dy), 'deriv', Dyd, 'dderiv', Dydd);
|
||||
|
||||
%% Tilt Stage - Ry
|
||||
t = 0:Ts:Tmax; % Time Vector [s]
|
||||
Ry = zeros(length(t), 1);
|
||||
Ryd = zeros(length(t), 1);
|
||||
Rydd = zeros(length(t), 1);
|
||||
|
||||
switch args.Ry_type
|
||||
case 'constant'
|
||||
Ry(:) = args.Ry_amplitude;
|
||||
Ryd(:) = 0;
|
||||
Rydd(:) = 0;
|
||||
case 'triangular'
|
||||
Ry_raw = args.Ry_amplitude*sawtooth(2*pi*t/args.Ry_period,1/2);
|
||||
i0 = find(t>=args.Ry_period/4,1);
|
||||
Ry(1:end-i0+1) = Ry_raw(i0:end);
|
||||
Ry(end-i0+2:end) = Ry_raw(end); % we fix the last value
|
||||
|
||||
% The signal is filtered out
|
||||
Ry = lsim(H_lpf, Ry, t);
|
||||
Ryd = lsim(H_lpf*s, Ry, t);
|
||||
Rydd = lsim(H_lpf*s^2, Ry, t);
|
||||
case 'sinusoidal'
|
||||
Ry(:) = args.Ry_amplitude*sin(2*pi/args.Ry_period*t);
|
||||
|
||||
Ryd = args.Ry_amplitude*2*pi/args.Ry_period*cos(2*pi/args.Ry_period*t);
|
||||
Rydd = -args.Ry_amplitude*(2*pi/args.Ry_period)^2*sin(2*pi/args.Ry_period*t);
|
||||
otherwise
|
||||
warning('Ry_type is not set correctly');
|
||||
end
|
||||
|
||||
Ry = struct('time', t, 'signals', struct('values', Ry), 'deriv', Ryd, 'dderiv', Rydd);
|
||||
|
||||
%% Spindle - Rz
|
||||
t = 0:Ts:Tmax; % Time Vector [s]
|
||||
Rz = zeros(length(t), 1);
|
||||
Rzd = zeros(length(t), 1);
|
||||
Rzdd = zeros(length(t), 1);
|
||||
|
||||
switch args.Rz_type
|
||||
case 'constant'
|
||||
Rz(:) = args.Rz_amplitude;
|
||||
Rzd(:) = 0;
|
||||
Rzdd(:) = 0;
|
||||
case 'rotating-not-filtered'
|
||||
Rz(:) = 2*pi/args.Rz_period*t;
|
||||
|
||||
% The signal is filtered out
|
||||
Rz(:) = 2*pi/args.Rz_period*t;
|
||||
Rzd(:) = 2*pi/args.Rz_period;
|
||||
Rzdd(:) = 0;
|
||||
|
||||
% We add the angle offset
|
||||
Rz = Rz + args.Rz_amplitude;
|
||||
|
||||
case 'rotating'
|
||||
Rz(:) = 2*pi/args.Rz_period*t;
|
||||
|
||||
% The signal is filtered out
|
||||
Rz = lsim(H_lpf, Rz, t);
|
||||
Rzd = lsim(H_lpf*s, Rz, t);
|
||||
Rzdd = lsim(H_lpf*s^2, Rz, t);
|
||||
|
||||
% We add the angle offset
|
||||
Rz = Rz + args.Rz_amplitude;
|
||||
otherwise
|
||||
warning('Rz_type is not set correctly');
|
||||
end
|
||||
|
||||
Rz = struct('time', t, 'signals', struct('values', Rz), 'deriv', Rzd, 'dderiv', Rzdd);
|
||||
|
||||
%% Micro-Hexapod
|
||||
t = [0, Ts];
|
||||
Dh = zeros(length(t), 6);
|
||||
Dhl = zeros(length(t), 6);
|
||||
|
||||
switch args.Dh_type
|
||||
case 'constant'
|
||||
Dh = [args.Dh_pos, args.Dh_pos];
|
||||
|
||||
load('nass_model_stages.mat', 'micro_hexapod');
|
||||
|
||||
AP = [args.Dh_pos(1) ; args.Dh_pos(2) ; args.Dh_pos(3)];
|
||||
|
||||
tx = args.Dh_pos(4);
|
||||
ty = args.Dh_pos(5);
|
||||
tz = args.Dh_pos(6);
|
||||
|
||||
ARB = [cos(tz) -sin(tz) 0;
|
||||
sin(tz) cos(tz) 0;
|
||||
0 0 1]*...
|
||||
[ cos(ty) 0 sin(ty);
|
||||
0 1 0;
|
||||
-sin(ty) 0 cos(ty)]*...
|
||||
[1 0 0;
|
||||
0 cos(tx) -sin(tx);
|
||||
0 sin(tx) cos(tx)];
|
||||
|
||||
[~, Dhl] = inverseKinematics(micro_hexapod, 'AP', AP, 'ARB', ARB);
|
||||
Dhl = [Dhl, Dhl];
|
||||
otherwise
|
||||
warning('Dh_type is not set correctly');
|
||||
end
|
||||
|
||||
Dh = struct('time', t, 'signals', struct('values', Dh));
|
||||
Dhl = struct('time', t, 'signals', struct('values', Dhl));
|
||||
|
||||
if exist('./mat', 'dir')
|
||||
if exist('./mat/nass_model_references.mat', 'file')
|
||||
save('mat/nass_model_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'args', 'Ts', '-append');
|
||||
else
|
||||
save('mat/nass_model_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'args', 'Ts');
|
||||
end
|
||||
elseif exist('./matlab', 'dir')
|
||||
if exist('./matlab/mat/nass_model_references.mat', 'file')
|
||||
save('matlab/mat/nass_model_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'args', 'Ts', '-append');
|
||||
else
|
||||
save('matlab/mat/nass_model_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'args', 'Ts');
|
||||
end
|
||||
end
|
||||
57
matlab/src/initializeRy.m
Normal file
57
matlab/src/initializeRy.m
Normal file
@@ -0,0 +1,57 @@
|
||||
function [ry] = initializeRy(args)
|
||||
|
||||
arguments
|
||||
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'flexible'
|
||||
args.Ry_init (1,1) double {mustBeNumeric} = 0
|
||||
end
|
||||
|
||||
ry = struct();
|
||||
|
||||
switch args.type
|
||||
case 'none'
|
||||
ry.type = 0;
|
||||
case 'rigid'
|
||||
ry.type = 1;
|
||||
case 'flexible'
|
||||
ry.type = 2;
|
||||
end
|
||||
|
||||
% Ry - Guide for the tilt stage
|
||||
ry.guide.density = 7800; % [kg/m3]
|
||||
ry.guide.STEP = 'Tilt_Guide.STEP';
|
||||
|
||||
% Ry - Rotor of the motor
|
||||
ry.rotor.density = 2400; % [kg/m3]
|
||||
ry.rotor.STEP = 'Tilt_Motor_Axis.STEP';
|
||||
|
||||
% Ry - Motor
|
||||
ry.motor.density = 3200; % [kg/m3]
|
||||
ry.motor.STEP = 'Tilt_Motor.STEP';
|
||||
|
||||
% Ry - Plateau Tilt
|
||||
ry.stage.density = 7800; % [kg/m3]
|
||||
ry.stage.STEP = 'Tilt_Stage.STEP';
|
||||
|
||||
% Z-Offset so that the center of rotation matches the sample center;
|
||||
ry.z_offset = 0.58178; % [m]
|
||||
|
||||
ry.Ry_init = args.Ry_init; % [rad]
|
||||
|
||||
ry.K = [3.8e8; 4e8; 3.8e8; 1.2e8; 6e4; 1.2e8];
|
||||
ry.C = [1e5; 1e5; 1e5; 3e4; 1e3; 3e4];
|
||||
|
||||
if exist('./mat', 'dir')
|
||||
if exist('./mat/nass_model_stages.mat', 'file')
|
||||
save('mat/nass_model_stages.mat', 'ry', '-append');
|
||||
else
|
||||
save('mat/nass_model_stages.mat', 'ry');
|
||||
end
|
||||
elseif exist('./matlab', 'dir')
|
||||
if exist('./matlab/mat/nass_model_stages.mat', 'file')
|
||||
save('matlab/mat/nass_model_stages.mat', 'ry', '-append');
|
||||
else
|
||||
save('matlab/mat/nass_model_stages.mat', 'ry');
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
47
matlab/src/initializeRz.m
Normal file
47
matlab/src/initializeRz.m
Normal file
@@ -0,0 +1,47 @@
|
||||
function [rz] = initializeRz(args)
|
||||
|
||||
arguments
|
||||
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'flexible'
|
||||
end
|
||||
|
||||
rz = struct();
|
||||
|
||||
switch args.type
|
||||
case 'none'
|
||||
rz.type = 0;
|
||||
case 'rigid'
|
||||
rz.type = 1;
|
||||
case 'flexible'
|
||||
rz.type = 2;
|
||||
end
|
||||
|
||||
% Spindle - Slip Ring
|
||||
rz.slipring.density = 7800; % [kg/m3]
|
||||
rz.slipring.STEP = 'Spindle_Slip_Ring.STEP';
|
||||
|
||||
% Spindle - Rotor
|
||||
rz.rotor.density = 7800; % [kg/m3]
|
||||
rz.rotor.STEP = 'Spindle_Rotor.STEP';
|
||||
|
||||
% Spindle - Stator
|
||||
rz.stator.density = 7800; % [kg/m3]
|
||||
rz.stator.STEP = 'Spindle_Stator.STEP';
|
||||
|
||||
rz.K = [7e8; 7e8; 2e9; 1e7; 1e7; 1e7];
|
||||
rz.C = [4e4; 4e4; 7e4; 1e4; 1e4; 1e4];
|
||||
|
||||
if exist('./mat', 'dir')
|
||||
if exist('./mat/nass_model_stages.mat', 'file')
|
||||
save('mat/nass_model_stages.mat', 'rz', '-append');
|
||||
else
|
||||
save('mat/nass_model_stages.mat', 'rz');
|
||||
end
|
||||
elseif exist('./matlab', 'dir')
|
||||
if exist('./matlab/mat/nass_model_stages.mat', 'file')
|
||||
save('matlab/mat/nass_model_stages.mat', 'rz', '-append');
|
||||
else
|
||||
save('matlab/mat/nass_model_stages.mat', 'rz');
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
38
matlab/src/initializeSample.m
Normal file
38
matlab/src/initializeSample.m
Normal file
@@ -0,0 +1,38 @@
|
||||
function [sample] = initializeSample(args)
|
||||
|
||||
arguments
|
||||
args.type char {mustBeMember(args.type,{'none', 'cylindrical'})} = 'none'
|
||||
args.H (1,1) double {mustBeNumeric, mustBePositive} = 250e-3 % Height [m]
|
||||
args.R (1,1) double {mustBeNumeric, mustBePositive} = 110e-3 % Radius [m]
|
||||
args.m (1,1) double {mustBeNumeric, mustBePositive} = 1 % Mass [kg]
|
||||
end
|
||||
|
||||
sample = struct();
|
||||
|
||||
switch args.type
|
||||
case 'none'
|
||||
sample.type = 0;
|
||||
sample.m = 0;
|
||||
case 'cylindrical'
|
||||
sample.type = 1;
|
||||
|
||||
sample.H = args.H;
|
||||
sample.R = args.R;
|
||||
sample.m = args.m;
|
||||
end
|
||||
|
||||
if exist('./mat', 'dir')
|
||||
if exist('./mat/nass_model_stages.mat', 'file')
|
||||
save('mat/nass_model_stages.mat', 'sample', '-append');
|
||||
else
|
||||
save('mat/nass_model_stages.mat', 'sample');
|
||||
end
|
||||
elseif exist('./matlab', 'dir')
|
||||
if exist('./matlab/mat/nass_model_stages.mat', 'file')
|
||||
save('matlab/mat/nass_model_stages.mat', 'sample', '-append');
|
||||
else
|
||||
save('matlab/mat/nass_model_stages.mat', 'sample');
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
171
matlab/src/initializeSimplifiedNanoHexapod.m
Normal file
171
matlab/src/initializeSimplifiedNanoHexapod.m
Normal file
@@ -0,0 +1,171 @@
|
||||
function [nano_hexapod] = initializeSimplifiedNanoHexapod(args)
|
||||
|
||||
arguments
|
||||
args.type char {mustBeMember(args.type,{'none', 'stewart'})} = 'stewart'
|
||||
%% initializeFramesPositions
|
||||
args.H (1,1) double {mustBeNumeric, mustBePositive} = 95e-3 % Height of the nano-hexapod [m]
|
||||
args.MO_B (1,1) double {mustBeNumeric} = 150e-3 % Height of {B} w.r.t. {M} [m]
|
||||
%% generateGeneralConfiguration
|
||||
args.FH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3 % Height of fixed joints [m]
|
||||
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 120e-3 % Radius of fixed joints [m]
|
||||
args.FTh (6,1) double {mustBeNumeric} = [220, 320, 340, 80, 100, 200]*(pi/180) % Angles of fixed joints [rad]
|
||||
args.MH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3 % Height of mobile joints [m]
|
||||
args.MR (1,1) double {mustBeNumeric, mustBePositive} = 110e-3 % Radius of mobile joints [m]
|
||||
args.MTh (6,1) double {mustBeNumeric} = [255, 285, 15, 45, 135, 165]*(pi/180) % Angles of fixed joints [rad]
|
||||
%% Actuators
|
||||
args.actuator_type char {mustBeMember(args.actuator_type,{'1dof', '2dof', 'flexible', 'apa300ml'})} = '1dof'
|
||||
args.actuator_k (1,1) double {mustBeNumeric, mustBePositive} = 1e6
|
||||
args.actuator_kp (1,1) double {mustBeNumeric, mustBeNonnegative} = 5e4
|
||||
args.actuator_ke (1,1) double {mustBeNumeric, mustBePositive} = 4952605
|
||||
args.actuator_ka (1,1) double {mustBeNumeric, mustBePositive} = 2476302
|
||||
args.actuator_c (1,1) double {mustBeNumeric, mustBePositive} = 50
|
||||
args.actuator_cp (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.actuator_ce (1,1) double {mustBeNumeric, mustBePositive} = 100
|
||||
args.actuator_ca (1,1) double {mustBeNumeric, mustBePositive} = 50
|
||||
args.actuator_ga (1,1) double {mustBeNumeric} = 1
|
||||
args.actuator_gs (1,1) double {mustBeNumeric} = 5
|
||||
%% initializeCylindricalPlatforms
|
||||
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 5 % Mass of the fixed plate [kg]
|
||||
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3 % Thickness of the fixed plate [m]
|
||||
args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 150e-3 % Radius of the fixed plate [m]
|
||||
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 5 % Mass of the mobile plate [kg]
|
||||
args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3 % Thickness of the mobile plate [m]
|
||||
args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 150e-3 % Radius of the mobile plate [m]
|
||||
%% initializeCylindricalStruts
|
||||
args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % Mass of the fixed part of the strut [kg]
|
||||
args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 60e-3 % Length of the fixed part of the struts [m]
|
||||
args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3 % Radius of the fixed part of the struts [m]
|
||||
args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % Mass of the mobile part of the strut [kg]
|
||||
args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 60e-3 % Length of the mobile part of the struts [m]
|
||||
args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3 % Radius of the fixed part of the struts [m]
|
||||
%% Bottom and Top Flexible Joints
|
||||
args.flex_type_F char {mustBeMember(args.flex_type_F,{'2dof', '3dof', '4dof', '2dof_axial', 'flexible'})} = '2dof'
|
||||
args.flex_type_M char {mustBeMember(args.flex_type_M,{'2dof', '3dof', '4dof', '2dof_axial', 'flexible'})} = '3dof'
|
||||
args.Kf_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Cf_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Kt_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Ct_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Kf_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Cf_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Kt_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Ct_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Ka_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Ca_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Kr_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Cr_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Ka_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Ca_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Kr_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.Cr_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
%% inverseKinematics
|
||||
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
||||
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
||||
end
|
||||
|
||||
stewart = initializeStewartPlatform();
|
||||
|
||||
switch args.type
|
||||
case 'none'
|
||||
stewart.type = 0;
|
||||
case 'stewart'
|
||||
stewart.type = 1;
|
||||
end
|
||||
|
||||
stewart = initializeFramesPositions(stewart, ...
|
||||
'H', args.H, ...
|
||||
'MO_B', args.MO_B);
|
||||
|
||||
stewart = generateGeneralConfiguration(stewart, ...
|
||||
'FH', args.FH, ...
|
||||
'FR', args.FR, ...
|
||||
'FTh', args.FTh, ...
|
||||
'MH', args.MH, ...
|
||||
'MR', args.MR, ...
|
||||
'MTh', args.MTh);
|
||||
|
||||
stewart = computeJointsPose(stewart);
|
||||
|
||||
if strcmp(args.actuator_type, 'apa300ml')
|
||||
args.actuator_k = 0.3e6;
|
||||
args.actuator_ke = 4.3e6;
|
||||
args.actuator_ka = 2.15e6;
|
||||
args.actuator_c = 18;
|
||||
args.actuator_ce = 0.7;
|
||||
args.actuator_ca = 0.35;
|
||||
args.actuator_ga = -2.7;
|
||||
args.actuator_gs = 0.53e6;
|
||||
elseif strcmp(args.actuator_type, 'flexible')
|
||||
args.actuator_ga = 25.9;
|
||||
args.actuator_gs = -5.08e6;
|
||||
end
|
||||
|
||||
stewart = initializeStrutDynamics(stewart, ...
|
||||
'type', args.actuator_type, ...
|
||||
'k', args.actuator_k, ...
|
||||
'kp', args.actuator_kp, ...
|
||||
'ke', args.actuator_ke, ...
|
||||
'ka', args.actuator_ka, ...
|
||||
'c', args.actuator_c, ...
|
||||
'cp', args.actuator_cp, ...
|
||||
'ce', args.actuator_ce, ...
|
||||
'ca', args.actuator_ca, ...
|
||||
'ga', args.actuator_ga, ...
|
||||
'gs', args.actuator_gs);
|
||||
|
||||
stewart = initializeJointDynamics(stewart, ...
|
||||
'type_F', args.flex_type_F, ...
|
||||
'type_M', args.flex_type_M, ...
|
||||
'Kf_M', args.Kf_M, ...
|
||||
'Cf_M', args.Cf_M, ...
|
||||
'Kt_M', args.Kt_M, ...
|
||||
'Ct_M', args.Ct_M, ...
|
||||
'Kf_F', args.Kf_F, ...
|
||||
'Cf_F', args.Cf_F, ...
|
||||
'Kt_F', args.Kt_F, ...
|
||||
'Ct_F', args.Ct_F, ...
|
||||
'Ka_F', args.Ka_F, ...
|
||||
'Ca_F', args.Ca_F, ...
|
||||
'Kr_F', args.Kr_F, ...
|
||||
'Cr_F', args.Cr_F, ...
|
||||
'Ka_M', args.Ka_M, ...
|
||||
'Ca_M', args.Ca_M, ...
|
||||
'Kr_M', args.Kr_M, ...
|
||||
'Cr_M', args.Cr_M);
|
||||
|
||||
stewart = initializeCylindricalPlatforms(stewart, ...
|
||||
'Fpm', args.Fpm, ...
|
||||
'Fph', args.Fph, ...
|
||||
'Fpr', args.Fpr, ...
|
||||
'Mpm', args.Mpm, ...
|
||||
'Mph', args.Mph, ...
|
||||
'Mpr', args.Mpr);
|
||||
|
||||
stewart = initializeCylindricalStruts(stewart, ...
|
||||
'Fsm', args.Fsm, ...
|
||||
'Fsh', args.Fsh, ...
|
||||
'Fsr', args.Fsr, ...
|
||||
'Msm', args.Msm, ...
|
||||
'Msh', args.Msh, ...
|
||||
'Msr', args.Msr);
|
||||
|
||||
stewart = computeJacobian(stewart);
|
||||
|
||||
stewart = initializeStewartPose(stewart, ...
|
||||
'AP', args.AP, ...
|
||||
'ARB', args.ARB);
|
||||
|
||||
nano_hexapod = stewart;
|
||||
if exist('./mat', 'dir')
|
||||
if exist('./mat/nass_model_stages.mat', 'file')
|
||||
save('mat/nass_model_stages.mat', 'nano_hexapod', '-append');
|
||||
else
|
||||
save('mat/nass_model_stages.mat', 'nano_hexapod');
|
||||
end
|
||||
elseif exist('./matlab', 'dir')
|
||||
if exist('./matlab/mat/nass_model_stages.mat', 'file')
|
||||
save('matlab/mat/nass_model_stages.mat', 'nano_hexapod', '-append');
|
||||
else
|
||||
save('matlab/mat/nass_model_stages.mat', 'nano_hexapod');
|
||||
end
|
||||
end
|
||||
end
|
||||
27
matlab/src/initializeSimscapeConfiguration.m
Normal file
27
matlab/src/initializeSimscapeConfiguration.m
Normal file
@@ -0,0 +1,27 @@
|
||||
function [] = initializeSimscapeConfiguration(args)
|
||||
|
||||
arguments
|
||||
args.gravity logical {mustBeNumericOrLogical} = true
|
||||
end
|
||||
|
||||
conf_simscape = struct();
|
||||
|
||||
if args.gravity
|
||||
conf_simscape.type = 1;
|
||||
else
|
||||
conf_simscape.type = 2;
|
||||
end
|
||||
|
||||
if exist('./mat', 'dir')
|
||||
if exist('./mat/nass_model_conf_simscape.mat', 'file')
|
||||
save('mat/nass_model_conf_simscape.mat', 'conf_simscape', '-append');
|
||||
else
|
||||
save('mat/nass_model_conf_simscape.mat', 'conf_simscape');
|
||||
end
|
||||
elseif exist('./matlab', 'dir')
|
||||
if exist('./matlab/mat/nass_model_conf_simscape.mat', 'file')
|
||||
save('matlab/mat/nass_model_conf_simscape.mat', 'conf_simscape', '-append');
|
||||
else
|
||||
save('matlab/mat/nass_model_conf_simscape.mat', 'conf_simscape');
|
||||
end
|
||||
end
|
||||
33
matlab/src/initializeStewartPlatform.m
Normal file
33
matlab/src/initializeStewartPlatform.m
Normal file
@@ -0,0 +1,33 @@
|
||||
function [stewart] = initializeStewartPlatform()
|
||||
% initializeStewartPlatform - Initialize the stewart structure
|
||||
%
|
||||
% Syntax: [stewart] = initializeStewartPlatform(args)
|
||||
%
|
||||
% Outputs:
|
||||
% - stewart - A structure with the following sub-structures:
|
||||
% - platform_F -
|
||||
% - platform_M -
|
||||
% - joints_F -
|
||||
% - joints_M -
|
||||
% - struts_F -
|
||||
% - struts_M -
|
||||
% - actuators -
|
||||
% - geometry -
|
||||
% - properties -
|
||||
|
||||
stewart = struct();
|
||||
stewart.platform_F = struct();
|
||||
stewart.platform_M = struct();
|
||||
stewart.joints_F = struct();
|
||||
stewart.joints_M = struct();
|
||||
stewart.struts_F = struct();
|
||||
stewart.struts_M = struct();
|
||||
stewart.actuators = struct();
|
||||
stewart.sensors = struct();
|
||||
stewart.sensors.inertial = struct();
|
||||
stewart.sensors.force = struct();
|
||||
stewart.sensors.relative = struct();
|
||||
stewart.geometry = struct();
|
||||
stewart.kinematics = struct();
|
||||
|
||||
end
|
||||
29
matlab/src/initializeStewartPose.m
Normal file
29
matlab/src/initializeStewartPose.m
Normal file
@@ -0,0 +1,29 @@
|
||||
function [stewart] = initializeStewartPose(stewart, args)
|
||||
% initializeStewartPose - Determine the initial stroke in each leg to have the wanted pose
|
||||
% It uses the inverse kinematic
|
||||
%
|
||||
% Syntax: [stewart] = initializeStewartPose(stewart, args)
|
||||
%
|
||||
% Inputs:
|
||||
% - stewart - A structure with the following fields
|
||||
% - Aa [3x6] - The positions ai expressed in {A}
|
||||
% - Bb [3x6] - The positions bi expressed in {B}
|
||||
% - args - Can have the following fields:
|
||||
% - AP [3x1] - The wanted position of {B} with respect to {A}
|
||||
% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
|
||||
%
|
||||
% Outputs:
|
||||
% - stewart - updated Stewart structure with the added fields:
|
||||
% - actuators.Leq [6x1] - The 6 needed displacement of the struts from the initial position in [m] to have the wanted pose of {B} w.r.t. {A}
|
||||
|
||||
arguments
|
||||
stewart
|
||||
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
||||
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
||||
end
|
||||
|
||||
[Li, dLi] = inverseKinematics(stewart, 'AP', args.AP, 'ARB', args.ARB);
|
||||
|
||||
stewart.actuators.Leq = dLi;
|
||||
|
||||
end
|
||||
76
matlab/src/initializeStrutDynamics.m
Normal file
76
matlab/src/initializeStrutDynamics.m
Normal file
@@ -0,0 +1,76 @@
|
||||
function [stewart] = initializeStrutDynamics(stewart, args)
|
||||
% initializeStrutDynamics - Add Stiffness and Damping properties of each strut
|
||||
%
|
||||
% Syntax: [stewart] = initializeStrutDynamics(args)
|
||||
%
|
||||
% Inputs:
|
||||
% - args - Structure with the following fields:
|
||||
% - K [6x1] - Stiffness of each strut [N/m]
|
||||
% - C [6x1] - Damping of each strut [N/(m/s)]
|
||||
%
|
||||
% Outputs:
|
||||
% - stewart - updated Stewart structure with the added fields:
|
||||
% - actuators.type = 1
|
||||
% - actuators.K [6x1] - Stiffness of each strut [N/m]
|
||||
% - actuators.C [6x1] - Damping of each strut [N/(m/s)]
|
||||
|
||||
arguments
|
||||
stewart
|
||||
args.type char {mustBeMember(args.type,{'1dof', '2dof', 'flexible', 'apa300ml'})} = '1dof'
|
||||
args.k (1,1) double {mustBeNumeric, mustBeNonnegative} = 20e6
|
||||
args.kp (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.ke (1,1) double {mustBeNumeric, mustBeNonnegative} = 5e6
|
||||
args.ka (1,1) double {mustBeNumeric, mustBeNonnegative} = 60e6
|
||||
args.c (1,1) double {mustBeNumeric, mustBeNonnegative} = 2e1
|
||||
args.cp (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.ce (1,1) double {mustBeNumeric, mustBeNonnegative} = 1e6
|
||||
args.ca (1,1) double {mustBeNumeric, mustBeNonnegative} = 10
|
||||
args.ga (1,1) double {mustBeNumeric} = 1
|
||||
args.gs (1,1) double {mustBeNumeric} = 1
|
||||
|
||||
args.F_gain (1,1) double {mustBeNumeric} = 1
|
||||
args.me (1,1) double {mustBeNumeric} = 0.01
|
||||
args.ma (1,1) double {mustBeNumeric} = 0.01
|
||||
end
|
||||
|
||||
if strcmp(args.type, '1dof')
|
||||
stewart.actuators.type = 1;
|
||||
elseif strcmp(args.type, '2dof')
|
||||
stewart.actuators.type = 2;
|
||||
elseif strcmp(args.type, 'flexible')
|
||||
stewart.actuators.type = 3;
|
||||
|
||||
K = readmatrix('APA300ML_flex_mat_K.CSV');
|
||||
M = readmatrix('APA300ML_flex_mat_M.CSV');
|
||||
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('APA300ML_flex_out_nodes_3D.txt');
|
||||
|
||||
stewart.actuators.M = M;
|
||||
stewart.actuators.K = K;
|
||||
stewart.actuators.n_xyz = int_xyz;
|
||||
stewart.actuators.xi = 0.05;
|
||||
elseif strcmp(args.type, 'apa300ml')
|
||||
stewart.actuators.type = 4;
|
||||
end
|
||||
|
||||
stewart.actuators.k = args.k;
|
||||
stewart.actuators.c = args.c;
|
||||
|
||||
% Parallel stiffness
|
||||
stewart.actuators.kp = args.kp;
|
||||
stewart.actuators.cp = args.cp;
|
||||
|
||||
stewart.actuators.ka = args.ka;
|
||||
stewart.actuators.ca = args.ca;
|
||||
|
||||
stewart.actuators.ke = args.ke;
|
||||
stewart.actuators.ce = args.ce;
|
||||
|
||||
stewart.actuators.ga = args.ga;
|
||||
stewart.actuators.gs = args.gs;
|
||||
|
||||
stewart.actuators.F_gain = args.F_gain;
|
||||
|
||||
stewart.actuators.ma = args.ma;
|
||||
stewart.actuators.me = args.me;
|
||||
|
||||
end
|
||||
71
matlab/src/initializeTy.m
Normal file
71
matlab/src/initializeTy.m
Normal file
@@ -0,0 +1,71 @@
|
||||
function [ty] = initializeTy(args)
|
||||
|
||||
arguments
|
||||
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'flexible'
|
||||
end
|
||||
|
||||
ty = struct();
|
||||
|
||||
switch args.type
|
||||
case 'none'
|
||||
ty.type = 0;
|
||||
case 'rigid'
|
||||
ty.type = 1;
|
||||
case 'flexible'
|
||||
ty.type = 2;
|
||||
end
|
||||
|
||||
% Ty Granite frame
|
||||
ty.granite_frame.density = 7800; % [kg/m3] => 43kg
|
||||
ty.granite_frame.STEP = 'Ty_Granite_Frame.STEP';
|
||||
|
||||
% Guide Translation Ty
|
||||
ty.guide.density = 7800; % [kg/m3] => 76kg
|
||||
ty.guide.STEP = 'Ty_Guide.STEP';
|
||||
|
||||
% Ty - Guide_Translation12
|
||||
ty.guide12.density = 7800; % [kg/m3]
|
||||
ty.guide12.STEP = 'Ty_Guide_12.STEP';
|
||||
|
||||
% Ty - Guide_Translation11
|
||||
ty.guide11.density = 7800; % [kg/m3]
|
||||
ty.guide11.STEP = 'Ty_Guide_11.STEP';
|
||||
|
||||
% Ty - Guide_Translation22
|
||||
ty.guide22.density = 7800; % [kg/m3]
|
||||
ty.guide22.STEP = 'Ty_Guide_22.STEP';
|
||||
|
||||
% Ty - Guide_Translation21
|
||||
ty.guide21.density = 7800; % [kg/m3]
|
||||
ty.guide21.STEP = 'Ty_Guide_21.STEP';
|
||||
|
||||
% Ty - Plateau translation
|
||||
ty.frame.density = 7800; % [kg/m3]
|
||||
ty.frame.STEP = 'Ty_Stage.STEP';
|
||||
|
||||
% Ty Stator Part
|
||||
ty.stator.density = 5400; % [kg/m3]
|
||||
ty.stator.STEP = 'Ty_Motor_Stator.STEP';
|
||||
|
||||
% Ty Rotor Part
|
||||
ty.rotor.density = 5400; % [kg/m3]
|
||||
ty.rotor.STEP = 'Ty_Motor_Rotor.STEP';
|
||||
|
||||
ty.K = [2e8; 1e8; 2e8; 6e7; 9e7; 6e7]; % [N/m, N*m/rad]
|
||||
ty.C = [8e4; 5e4; 8e4; 2e4; 3e4; 1e4]; % [N/(m/s), N*m/(rad/s)]
|
||||
|
||||
if exist('./mat', 'dir')
|
||||
if exist('./mat/nass_model_stages.mat', 'file')
|
||||
save('mat/nass_model_stages.mat', 'ty', '-append');
|
||||
else
|
||||
save('mat/nass_model_stages.mat', 'ty');
|
||||
end
|
||||
elseif exist('./matlab', 'dir')
|
||||
if exist('./matlab/mat/nass_model_stages.mat', 'file')
|
||||
save('matlab/mat/nass_model_stages.mat', 'ty', '-append');
|
||||
else
|
||||
save('matlab/mat/nass_model_stages.mat', 'ty');
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
38
matlab/src/inverseKinematics.m
Normal file
38
matlab/src/inverseKinematics.m
Normal file
@@ -0,0 +1,38 @@
|
||||
function [Li, dLi] = inverseKinematics(stewart, args)
|
||||
% inverseKinematics - Compute the needed length of each strut to have the wanted position and orientation of {B} with respect to {A}
|
||||
%
|
||||
% Syntax: [stewart] = inverseKinematics(stewart)
|
||||
%
|
||||
% Inputs:
|
||||
% - stewart - A structure with the following fields
|
||||
% - geometry.Aa [3x6] - The positions ai expressed in {A}
|
||||
% - geometry.Bb [3x6] - The positions bi expressed in {B}
|
||||
% - geometry.l [6x1] - Length of each strut
|
||||
% - args - Can have the following fields:
|
||||
% - AP [3x1] - The wanted position of {B} with respect to {A}
|
||||
% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
|
||||
%
|
||||
% Outputs:
|
||||
% - Li [6x1] - The 6 needed length of the struts in [m] to have the wanted pose of {B} w.r.t. {A}
|
||||
% - dLi [6x1] - The 6 needed displacement of the struts from the initial position in [m] to have the wanted pose of {B} w.r.t. {A}
|
||||
|
||||
arguments
|
||||
stewart
|
||||
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
||||
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
||||
end
|
||||
|
||||
assert(isfield(stewart.geometry, 'Aa'), 'stewart.geometry should have attribute Aa')
|
||||
Aa = stewart.geometry.Aa;
|
||||
|
||||
assert(isfield(stewart.geometry, 'Bb'), 'stewart.geometry should have attribute Bb')
|
||||
Bb = stewart.geometry.Bb;
|
||||
|
||||
assert(isfield(stewart.geometry, 'l'), 'stewart.geometry should have attribute l')
|
||||
l = stewart.geometry.l;
|
||||
|
||||
Li = sqrt(args.AP'*args.AP + diag(Bb'*Bb) + diag(Aa'*Aa) - (2*args.AP'*Aa)' + (2*args.AP'*(args.ARB*Bb))' - diag(2*(args.ARB*Bb)'*Aa));
|
||||
|
||||
dLi = Li-l;
|
||||
|
||||
end
|
||||
@@ -1,103 +0,0 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
addpath('strut_encoder/');
|
||||
|
||||
open('strut_encoder.slx');
|
||||
|
||||
% Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates
|
||||
% We first extract the stiffness and mass matrices.
|
||||
|
||||
K = readmatrix('strut_encoder_mat_K.CSV');
|
||||
M = readmatrix('strut_encoder_mat_M.CSV');
|
||||
|
||||
|
||||
|
||||
% #+caption: First 10x10 elements of the Mass matrix
|
||||
% #+RESULTS:
|
||||
% | 0.04 | -0.005 | 0.007 | 2e-06 | 0.0001 | -5e-07 | -1e-05 | -9e-07 | 8e-05 | -5e-10 |
|
||||
% | -0.005 | 0.03 | 0.02 | -0.0001 | 1e-06 | -3e-07 | 3e-05 | -0.0001 | 8e-05 | -3e-08 |
|
||||
% | 0.007 | 0.02 | 0.08 | -6e-06 | -5e-06 | -7e-07 | 4e-05 | -0.0001 | 0.0005 | -3e-08 |
|
||||
% | 2e-06 | -0.0001 | -6e-06 | 2e-06 | -4e-10 | 2e-11 | -8e-09 | 3e-08 | -2e-08 | 6e-12 |
|
||||
% | 0.0001 | 1e-06 | -5e-06 | -4e-10 | 3e-06 | 2e-10 | -3e-09 | 3e-09 | -7e-09 | 6e-13 |
|
||||
% | -5e-07 | -3e-07 | -7e-07 | 2e-11 | 2e-10 | 5e-07 | -2e-08 | 5e-09 | -5e-09 | 1e-12 |
|
||||
% | -1e-05 | 3e-05 | 4e-05 | -8e-09 | -3e-09 | -2e-08 | 0.04 | 0.004 | 0.003 | 1e-06 |
|
||||
% | -9e-07 | -0.0001 | -0.0001 | 3e-08 | 3e-09 | 5e-09 | 0.004 | 0.02 | -0.02 | 0.0001 |
|
||||
% | 8e-05 | 8e-05 | 0.0005 | -2e-08 | -7e-09 | -5e-09 | 0.003 | -0.02 | 0.08 | -5e-06 |
|
||||
% | -5e-10 | -3e-08 | -3e-08 | 6e-12 | 6e-13 | 1e-12 | 1e-06 | 0.0001 | -5e-06 | 2e-06 |
|
||||
|
||||
|
||||
% Then, we extract the coordinates of the interface nodes.
|
||||
|
||||
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('strut_encoder_out_nodes_3D.txt');
|
||||
|
||||
% Piezoelectric parameters
|
||||
% Parameters for the APA300ML:
|
||||
|
||||
|
||||
d33 = 3e-10; % Strain constant [m/V]
|
||||
n = 80; % Number of layers per stack
|
||||
eT = 1.6e-8; % Permittivity under constant stress [F/m]
|
||||
sD = 2e-11; % Elastic compliance under constant electric displacement [m2/N]
|
||||
ka = 235e6; % Stack stiffness [N/m]
|
||||
C = 5e-6; % Stack capactiance [F]
|
||||
|
||||
na = 2; % Number of stacks used as actuator
|
||||
ns = 1; % Number of stacks used as force sensor
|
||||
|
||||
% Identification of the Dynamics
|
||||
|
||||
m = 0.01;
|
||||
|
||||
|
||||
|
||||
% The dynamics is identified from the applied force to the measured relative displacement.
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'strut_encoder';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Fa'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/L'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
Gh = -linearize(mdl, io);
|
||||
|
||||
|
||||
|
||||
% The same dynamics is identified for a payload mass of 10Kg.
|
||||
|
||||
m = 10;
|
||||
|
||||
Ghm = -linearize(mdl, io);
|
||||
|
||||
freqs = logspace(0, 4, 5000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(Gh, freqs, 'Hz'))), '-');
|
||||
plot(freqs, abs(squeeze(freqresp(Ghm, freqs, 'Hz'))), '-');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude'); set(gca, 'XTickLabel',[]);
|
||||
axis padded 'auto x'
|
||||
hold off;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gh, freqs, 'Hz'))), '-', ...
|
||||
'DisplayName', '$m = 0kg$');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Ghm, freqs, 'Hz'))), '-', ...
|
||||
'DisplayName', '$m = 10kg$');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
yticks(-360:90:360);
|
||||
ylim([-180 180]);
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
axis padded 'auto x'
|
||||
Binary file not shown.
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
@@ -1,54 +0,0 @@
|
||||
1.5008802597656250e+06,1.3591662994384766e+06,-3.1750683225097656e+06,-3.7048942279815674e+02,2.5182437133789063e+02,1.5497479248046875e+02,-2.9662726811534242e+01,1.5440372511383325e+03,-1.3760338424522370e+04,3.4293635583161308e-01,1.3523457419237422e-01,3.1652765382488317e+00,-1.8635612297072937e+06,-6.2838649894722819e+05,-5.1779640668775322e+05,3.9525300719654824e+03,-1.1390774989274973e+04,-3.8209937528507805e+02,-1.1766984607282331e+04,-6.3591396714007806e+02,4.2118967114711668e+03,-3.2507105351496275e+00,1.8150889910377142e+01,1.7263792747401254e+00,-9.3056291607956075e+02,-7.7328301889074524e+01,-7.8177333385786574e+02,-7.2152156506186213e-02,5.2377293799240325e+00,-1.0261649334284262e+00,-4.6016470341111871e+05,-1.7863435519943098e+05,2.6525774962708645e+05,1.1068341133415133e+03,-2.7855263640913299e+03,2.2625955971864482e+02,8.1969513429372362e+05,-5.7391367477588810e+05,3.4405467987211482e+06,1.1805079221981093e+03,-6.0817645957960140e+03,-9.3716096715659106e+01,1.5877673038756213e+04,2.0937443763514679e+04,-2.6096170282449702e+03,2.4042181940744388e+02,-1.8767187980458311e+02,-1.7371299088051327e+02,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
1.3591662994384766e+06,3.7461418359375000e+06,-7.7883536318359375e+06,-8.6688592529296875e+02,3.9393717384338379e+02,-4.7559764862060547e+01,-5.5200638646161615e+03,1.3062579332038909e+04,-1.7981921233264526e+04,2.9745497068479398e+00,1.6377601762753593e+00,8.9648259266088175e+00,-2.3456082426143256e+06,-1.0478667148958796e+06,-3.8664860149862641e+05,1.0387902979994975e+04,-1.5030220864556901e+04,-1.8948761908441920e+04,-1.5539561509697407e+04,-1.2373135240385966e+04,4.4273580994601925e+03,-6.1276301836818821e+00,2.0348002228565402e+01,6.2890807676440303e+01,4.8510688575932218e+03,-3.3767730543812613e+03,6.6057382885793413e+02,-3.2471290572423211e-01,-1.0882633713017938e+01,-4.6183891890765729e+01,1.3491967503407530e+06,-9.2539526215694612e+05,-2.5249733975292044e+05,9.7589810086692214e+03,7.5554778827675682e+03,1.8914101873729887e+04,-3.6400410516307759e+05,-1.9016455390199504e+06,8.4676754254961703e+06,1.1178923660731039e+04,-1.0277897695216607e+04,-1.0885939058168144e+03,1.7457825987438999e+04,1.3145294896004515e+05,-2.7281812183691804e+04,1.5037475168952622e+03,-4.6748597750179482e+02,-9.2266785392483928e+02,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
-3.1750683225097656e+06,-7.7883536318359375e+06,2.4755076406250000e+07,2.1226810131072998e+03,-9.2834524154663086e+02,1.6893780136108398e+02,-1.2256519307002767e+04,2.4945166046719798e+04,-2.5641657780582327e+05,7.2427117456017713e+00,3.6271170570266849e+00,-1.2943373573453133e+01,-1.2153439240326699e+07,2.3240857641591448e+06,-2.1858238444887502e+06,-1.4400239259905722e+04,-7.3154614154811425e+04,9.7336390539098193e+02,-8.0737387085159935e+04,2.0517774321875154e+03,2.1777968655293662e+04,1.1677669511033050e+01,1.0610513344925143e+02,-4.9923766166131411e+00,5.0238912165937669e+04,7.4456380585143609e+02,9.1766895798323621e+03,3.8804702972485918e+00,-1.1893551223341281e+02,8.0805604796612940e+00,1.4637790410370609e+07,2.1467072359661632e+06,-2.4810960152856139e+06,-1.3619688509529082e+04,9.1333997948493503e+04,-7.4982522164818056e+02,7.6697478410592966e+05,3.4081800090011139e+06,-1.9803480278672945e+07,-6.9599710354090221e+03,2.2963131934467754e+04,1.9457601868008112e+03,-3.3502555333087977e+04,-1.1836077075401953e+05,-5.9214463091327365e+04,-1.2281293468819740e+03,-2.1561028195646742e+02,8.7338653374216790e+02,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
-3.7048942279815674e+02,-8.6688592529296875e+02,2.1226810131072998e+03,5.0732622146606445e+00,-1.0740600340068340e-01,4.8024255782365799e-02,1.3287619787539005e+00,-3.1388299552074095e+00,5.5842411993704673e+00,-7.1999273911602210e-04,-3.9809124163149627e-04,-2.1437360980386374e-03,6.3866013908280036e+02,2.1648868858204838e+02,1.0538903938511393e+02,-2.2976252064642573e+00,4.0965254879297390e+00,4.6332604124864440e+00,4.2313002635025398e+00,3.0004241658895285e+00,-1.2066596045654492e+00,1.3002870865323395e-03,-5.5459675600723554e-03,-1.5346593517133918e-02,-1.3229514964057516e+00,8.1501630737501274e-01,-1.8032832350146830e-01,5.3321422446194332e-06,2.9691849665731316e-03,1.1186582548699271e-02,-3.6800001728231581e+02,1.8651863954951483e+02,6.8885518232604184e+01,-2.1412137401829918e+00,-2.0618327677367252e+00,-4.6290735489452528e+00,9.9889515909534765e+01,4.9358308125164712e+02,-2.3078328245448670e+03,-2.7268262896321147e+00,2.8130911033732198e+00,2.8228155538257960e-01,-4.2972974199464211e+00,-3.0380787052861571e+01,6.6799938420990497e+00,-3.4781373765205537e-01,1.1398718444813125e-01,2.1371173482076139e-01,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
|
||||
2.5182437133789063e+02,3.9393717384338379e+02,-9.2834524154663086e+02,-1.0740600340068340e-01,4.9079132080078125e+00,4.1145801544189453e-02,-1.1483555778907373e-01,5.3549435294154957e-01,-3.3448226192168264e+00,1.2307528029563728e-04,5.7496406393781921e-05,5.7091434769238861e-04,-4.3182337024612059e+02,-1.8382106159557352e+02,-1.2871670951755527e+02,1.1614786961276109e+00,-2.5547315657440128e+00,-1.1097879299356805e-01,-2.7099732871178603e+00,-1.8536456110912705e-01,9.8180338758826768e-01,-9.5586488969776799e-04,4.2640493168917774e-03,5.0215768937242930e-04,-8.0383819882549723e-02,-2.1694248538571805e-02,-1.5692524041174588e-01,-1.4210326305400371e-05,9.4252369707936365e-04,-2.9039346855092962e-04,-6.7879712367761044e+01,-5.0105452568542425e+01,6.3188500463258393e+01,3.0587621456367953e-01,-3.2650302494922540e-01,6.4909300564496827e-02,2.4728188957024975e+02,-1.6628029854571599e+02,9.9731486757794960e+02,3.3985536550681616e-01,-1.5392258639652168e+00,-1.1612379555951262e-02,3.5022331640023525e+00,5.9414676191208535e+00,-9.2144078104741423e-01,6.8627698277065191e-02,-4.5983652130640235e-02,-4.7403016648821655e-02,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
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Reference in New Issue
Block a user