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tdehaeze committed 2025-02-25 19:05:33 +01:00
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matlab/APA300ML.m
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%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
addpath('APA300ML/');
open('APA300ML.slx');
% Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates
% We first extract the stiffness and mass matrices.
K = readmatrix('APA300ML_mat_K.CSV');
M = readmatrix('APA300ML_mat_M.CSV');
% #+caption: First 10x10 elements of the Mass matrix
% #+RESULTS:
% | 0.01 | -2e-06 | 1e-06 | 6e-09 | 5e-05 | -5e-09 | -0.0005 | -7e-07 | 6e-07 | -3e-09 |
% | -2e-06 | 0.01 | 8e-07 | -2e-05 | -8e-09 | 2e-09 | -9e-07 | -0.0002 | 1e-08 | -9e-07 |
% | 1e-06 | 8e-07 | 0.009 | 5e-10 | 1e-09 | -1e-09 | -5e-07 | 3e-08 | 6e-05 | 1e-10 |
% | 6e-09 | -2e-05 | 5e-10 | 3e-07 | 2e-11 | -3e-12 | 3e-09 | 9e-07 | -4e-10 | 3e-09 |
% | 5e-05 | -8e-09 | 1e-09 | 2e-11 | 6e-07 | -4e-11 | -1e-06 | -2e-09 | 1e-09 | -8e-12 |
% | -5e-09 | 2e-09 | -1e-09 | -3e-12 | -4e-11 | 1e-07 | -2e-09 | -1e-09 | -4e-10 | -5e-12 |
% | -0.0005 | -9e-07 | -5e-07 | 3e-09 | -1e-06 | -2e-09 | 0.01 | 1e-07 | -3e-07 | -2e-08 |
% | -7e-07 | -0.0002 | 3e-08 | 9e-07 | -2e-09 | -1e-09 | 1e-07 | 0.01 | -4e-07 | 2e-05 |
% | 6e-07 | 1e-08 | 6e-05 | -4e-10 | 1e-09 | -4e-10 | -3e-07 | -4e-07 | 0.009 | -2e-10 |
% | -3e-09 | -9e-07 | 1e-10 | 3e-09 | -8e-12 | -5e-12 | -2e-08 | 2e-05 | -2e-10 | 3e-07 |
% Then, we extract the coordinates of the interface nodes.
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('APA300ML_out_nodes_3D.txt');
% Piezoelectric parameters
% 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:
d33 = 300e-12; % Strain constant [m/V]
n = 80; % Number of layers per stack
eT = 1.6e-8; % Permittivity under constant stress [F/m]
sD = 1e-11; % Compliance under constant electric displacement [m2/N]
ka = 235e6; % Stack stiffness [N/m]
C = 5e-6; % Stack capactiance [F]
% The ratio of the developed force to applied voltage is:
% #+name: eq:piezo_voltage_to_force
% \begin{equation}
% F_a = g_a V_a, \quad g_a = d_{33} n k_a
% \end{equation}
% where:
% - $F_a$: developed force in [N]
% - $n$: number of layers of the actuator stack
% - $d_{33}$: strain constant in [m/V]
% - $k_a$: actuator stack stiffness in [N/m]
% - $V_a$: applied voltage in [V]
% If we take the numerical values, we obtain:
d33*n*ka % [N/V]
% #+RESULTS:
% : 5.64
% From cite:fleming14_desig_model_contr_nanop_system (page 123), the relation between relative displacement of the sensor stack and generated voltage is:
% #+name: eq:piezo_strain_to_voltage
% \begin{equation}
% V_s = \frac{d_{33}}{\epsilon^T s^D n} \Delta h
% \end{equation}
% where:
% - $V_s$: measured voltage in [V]
% - $d_{33}$: strain constant in [m/V]
% - $\epsilon^T$: permittivity under constant stress in [F/m]
% - $s^D$: elastic compliance under constant electric displacement in [m^2/N]
% - $n$: number of layers of the sensor stack
% - $\Delta h$: relative displacement in [m]
% If we take the numerical values, we obtain:
1e-6*d33/(eT*sD*n) % [V/um]
% Stiffness
m = 0.001;
% The transfer function from vertical external force to the relative vertical displacement is identified.
%% 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;
io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
G = linearize(mdl, io);
% The inverse of its DC gain is the axial stiffness of the APA:
1e-6/dcgain(G) % [N/um]
% Resonance Frequency
% The resonance frequency is specified to be between 650Hz and 840Hz.
% This is also the case for the FEM model (Figure [[fig:apa300ml_resonance]]).
freqs = logspace(2, 4, 5000);
figure;
hold on;
plot(freqs, abs(squeeze(freqresp(G, freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude');
hold off;
% Amplification factor
% The amplification factor is the ratio of the vertical displacement to the stack displacement.
%% Name of the Simulink File
mdl = 'APA300ML';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/F'], 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, '/d'], 1, 'openoutput'); io_i = io_i + 1;
G = linearize(mdl, io);
% The ratio of the two displacement is computed from the FEM model.
abs(dcgain(G(1,1))./dcgain(G(2,1)))
% #+RESULTS:
% : 5.0749
% This is actually correct and approximately corresponds to the ratio of the piezo height and length:
75/15
% Stroke
% Estimation of the actuator stroke:
% \[ \Delta H = A n \Delta L \]
% with:
% - $\Delta H$ Axial Stroke of the APA
% - $A$ Amplification factor (5 for the APA300ML)
% - $n$ Number of stack used
% - $\Delta L$ Stroke of the stack (0.1% of its length)
1e6 * 5 * 3 * 20e-3 * 0.1e-2
% Identification of the Dynamics from actuator to replace displacement
% We first set the mass to be approximately zero.
m = 0.01;
% The dynamics is identified from the applied force to the measured relative displacement.
%% Name of the Simulink File
mdl = 'APA300ML';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
Gh = -linearize(mdl, io);
% The same dynamics is identified for a payload mass of 10Kg.
m = 10;
%% Name of the Simulink File
mdl = 'APA300ML';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
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',[]);
hold off;
ax2 = nexttile;
hold on;
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gh, freqs, 'Hz')))), '-', ...
'DisplayName', '$m = 0kg$');
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Ghm, freqs, 'Hz')))), '-', ...
'DisplayName', '$m = 10kg$');
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
yticks(-360:90:360);
ylim([-360 0]);
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
legend('location', 'southwest');
% #+name: fig:apa300ml_plant_dynamics
% #+caption: Transfer function from forces applied by the stack to the axial displacement of the APA
% #+RESULTS:
% [[file:figs/apa300ml_plant_dynamics.png]]
% The root locus corresponding to Direct Velocity Feedback with a mass of 10kg is shown in Figure [[fig:apa300ml_dvf_root_locus]].
figure;
gains = logspace(0, 5, 500);
hold on;
plot(real(pole(Ghm)), imag(pole(G)), 'kx');
plot(real(tzero(Ghm)), imag(tzero(G)), 'ko');
for k = 1:length(gains)
cl_poles = pole(feedback(Ghm, gains(k)*s));
plot(real(cl_poles), imag(cl_poles), 'k.');
end
hold off;
axis square;
xlim([-500, 10]); ylim([0, 510]);
xlabel('Real Part'); ylabel('Imaginary Part');
% Identification of the Dynamics from actuator to force sensor
% Let's use 2 stacks as a force sensor and 1 stack as force actuator.
% The transfer function from actuator voltage to sensor voltage is identified and shown in Figure [[fig:apa300ml_iff_plant]].
m = 10;
%% Name of the Simulink File
mdl = 'APA300ML';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Va'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1;
Giff = -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(Giff, 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(Giff, 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:apa300ml_iff_plant
% #+caption: Transfer function from actuator to force sensor
% #+RESULTS:
% [[file:figs/apa300ml_iff_plant.png]]
% For root locus corresponding to IFF is shown in Figure [[fig:apa300ml_iff_root_locus]].
figure;
gains = logspace(0, 5, 500);
hold on;
plot(real(pole(Giff)), imag(pole(Giff)), 'kx');
plot(real(tzero(Giff)), imag(tzero(Giff)), 'ko');
for k = 1:length(gains)
cl_poles = pole(feedback(Giff, gains(k)/s));
plot(real(cl_poles), imag(cl_poles), 'k.');
end
hold off;
axis square;
xlim([-500, 10]); ylim([0, 510]);
xlabel('Real Part'); ylabel('Imaginary Part');
% Identification for a simpler model
% The goal in this section is to identify the parameters of a simple APA model from the FEM.
% This can be useful is a lower order model is to be used for simulations.
% The presented model is based on cite:souleille18_concep_activ_mount_space_applic.
% The model represents the Amplified Piezo Actuator (APA) from Cedrat-Technologies (Figure [[fig:souleille18_model_piezo]]).
% The parameters are shown in the table below.
% #+name: fig:souleille18_model_piezo
% #+caption: Picture of an APA100M from Cedrat Technologies. Simplified model of a one DoF payload mounted on such isolator
% [[file:./figs/souleille18_model_piezo.png]]
% #+caption:Parameters used for the model of the APA 100M
% | | Meaning |
% |-------+----------------------------------------------------------------|
% | $k_e$ | Stiffness used to adjust the pole of the isolator |
% | $k_1$ | 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');
% 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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%% 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');
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6 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
7 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
8 -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
9 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
10 -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
11 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
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matlab/flexor_025/flex050_out_nodes_3D.txt
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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
matlab/flexor_025/flexor_050.STEP
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matlab/flexor_025_simplified.slx
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matlab/flexor_ID16.m
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%% 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');
matlab/flexor_ID16.slx
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matlab/flexor_ID16/flexor_ID16.STEP
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matlab/flexor_ID16/mat_K_6modes_2MDoF.matrix
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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
matlab/flexor_ID16/mat_M_6modes_2MDoF.matrix
-20
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@@ -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
matlab/flexor_ID16/out_nodes_3D.txt
-40
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@@ -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
matlab/flexor_ID16_simplified.slx
BIN
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matlab/mat/APA300ML_flex_mat_K.CSV
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matlab/mat/APA300ML_flex_out_nodes_3D.txt
+61
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@@ -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
matlab/APA300ML/APA300ML_mat_K.CSV → matlab/mat/APA300ML_mat_K.CSV
View File
File renamed without changes.
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