593 lines
17 KiB
Mathematica
593 lines
17 KiB
Mathematica
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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('mat_K.CSV');
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M = readmatrix('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('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 |
|
||
|
|
% | $k_a$ | Stiffness of the actuator |
|
||
|
|
% | $c_1$ | Added viscous damping |
|
||
|
|
|
||
|
|
% The goal is to determine $k_e$, $k_a$ and $k_1$ so that the simplified model fits the FEM model.
|
||
|
|
|
||
|
|
% \[ \alpha = \frac{x_1}{f}(\omega=0) = \frac{\frac{k_e}{k_e + k_a}}{k_1 + \frac{k_e k_a}{k_e + k_a}} \]
|
||
|
|
% \[ \beta = \frac{x_1}{F}(\omega=0) = \frac{1}{k_1 + \frac{k_e k_a}{k_e + k_a}} \]
|
||
|
|
|
||
|
|
% If we can fix $k_a$, we can determine $k_e$ and $k_1$ with:
|
||
|
|
% \[ k_e = \frac{k_a}{\frac{\beta}{\alpha} - 1} \]
|
||
|
|
% \[ k_1 = \frac{1}{\beta} - \frac{k_e k_a}{k_e + k_a} \]
|
||
|
|
|
||
|
|
|
||
|
|
m = 10;
|
||
|
|
|
||
|
|
%% Name of the Simulink File
|
||
|
|
mdl = 'APA300ML';
|
||
|
|
|
||
|
|
%% 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, '/z'], 1, 'openoutput'); io_i = io_i + 1; % Vertical Displacement [m]
|
||
|
|
io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensor [V]
|
||
|
|
io(io_i) = linio([mdl, '/d'], 1, 'openoutput'); io_i = io_i + 1; % Stack Displacement [m]
|
||
|
|
|
||
|
|
G = linearize(mdl, io);
|
||
|
|
|
||
|
|
G.InputName = {'Fd', 'w', 'Fa'};
|
||
|
|
G.OutputName = {'y', 'Fs', 'd'};
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
% From the identified dynamics, compute $\alpha$ and $\beta$
|
||
|
|
|
||
|
|
alpha = abs(dcgain(G('y', 'Fa')));
|
||
|
|
beta = abs(dcgain(G('y', 'Fd')));
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
% $k_a$ is estimated using the following formula:
|
||
|
|
|
||
|
|
ka = 0.8/abs(dcgain(G('y', 'Fa')));
|
||
|
|
|
||
|
|
|
||
|
|
% The factor can be adjusted to better match the curves.
|
||
|
|
|
||
|
|
% Then $k_e$ and $k_1$ are computed.
|
||
|
|
|
||
|
|
ke = ka/(beta/alpha - 1);
|
||
|
|
k1 = 1/beta - ke*ka/(ke + ka);
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
% #+RESULTS:
|
||
|
|
% | | Value [N/um] |
|
||
|
|
% |----+--------------|
|
||
|
|
% | ka | 40.5 |
|
||
|
|
% | ke | 1.5 |
|
||
|
|
% | k1 | 0.4 |
|
||
|
|
|
||
|
|
% The damping in the system is adjusted to match the FEM model if necessary.
|
||
|
|
|
||
|
|
c1 = 1e2;
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
% The analytical model of the simpler system is defined below:
|
||
|
|
|
||
|
|
Ga = 1/(m*s^2 + k1 + c1*s + ke*ka/(ke + ka)) * ...
|
||
|
|
[ 1 , k1 + c1*s + ke*ka/(ke + ka) , ke/(ke + ka) ;
|
||
|
|
-ke*ka/(ke + ka), ke*ka/(ke + ka)*m*s^2 , -ke/(ke + ka)*(m*s^2 + c1*s + k1)];
|
||
|
|
|
||
|
|
Ga.InputName = {'Fd', 'w', 'Fa'};
|
||
|
|
Ga.OutputName = {'y', 'Fs'};
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
% And the DC gain is adjusted for the force sensor:
|
||
|
|
|
||
|
|
F_gain = dcgain(G('Fs', 'Fd'))/dcgain(Ga('Fs', 'Fd'));
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
% 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');
|