Add css and js. Add lots of org mode files.

old/active_damping/act_damp_iff_generate.m

@@ -0,0 +1,36 @@
+%%
+clear; close all; clc;
+
+%% Load the transfer functions
+load('./mat/G.mat', 'G_light_vc', 'G_light_pz', 'G_heavy_vc', 'G_heavy_pz');
+
+%% Load Configuration file
+load('./mat/config.mat', 'save_fig', 'freqs');
+
+%%
+s = tf('s');
+
+%% Light Voice Coil
+%sisotool(-G_light_vc.G_iff('Fm1', 'F1')/s);
+
+K_iff_light_vc = 105/s*tf(eye(6));
+
+%% Light Piezo
+%sisotool(-G_light_pz.G_iff('Fm1', 'F1')/s);
+
+K_iff_light_pz = 3300/s*tf(eye(6));
+
+%% Heavy Voice Coil
+%sisotool(-G_heavy_vc.G_iff('Fm1', 'F1')/s);
+
+K_iff_heavy_vc = 22.7/s*tf(eye(6));
+
+%% Heavy Piezo
+%sisotool(-G_heavy_pz.G_iff('Fm1', 'F1')/s);
+
+K_iff_heavy_pz = 720/s*tf(eye(6));
+
+%% Save Controllers
+save('./mat/K_iff_sisotool.mat', ...
+    'K_iff_light_vc', 'K_iff_light_pz', ...
+    'K_iff_heavy_vc', 'K_iff_heavy_pz');

old/active_damping/act_damp_iff_id.m

@@ -0,0 +1,45 @@
+%%
+clear; close all; clc;
+
+%% Load Configuration file
+load('./mat/config.mat', 'save_fig', 'freqs');
+
+%% Load controllers
+load('./mat/K_iff_sisotool.mat', ...
+    'K_iff_light_vc', 'K_iff_light_pz', ...
+    'K_iff_heavy_vc', 'K_iff_heavy_pz');
+
+%%
+initializeSample(struct('mass', 1));
+
+initializeHexapod(struct('actuator', 'lorentz'));
+K_iff = K_iff_light_vc; %#ok
+save('./mat/controllers.mat', 'K_iff', '-append');
+
+G_light_vc_iff = identifyPlant();
+
+initializeHexapod(struct('actuator', 'piezo'));
+K_iff = K_iff_light_pz; %#ok
+save('./mat/controllers.mat', 'K_iff', '-append');
+
+G_light_pz_iff = identifyPlant();
+
+%%
+initializeSample(struct('mass', 50));
+
+initializeHexapod(struct('actuator', 'lorentz'));
+K_iff = K_iff_heavy_vc; %#ok
+save('./mat/controllers.mat', 'K_iff', '-append');
+
+G_heavy_vc_iff = identifyPlant();
+
+initializeHexapod(struct('actuator', 'piezo'));
+K_iff = K_iff_heavy_pz;
+save('./mat/controllers.mat', 'K_iff', '-append');
+
+G_heavy_pz_iff = identifyPlant();
+
+%% Save the obtained transfer functions
+save('./mat/G_iff.mat', ...
+    'G_light_vc_iff', 'G_light_pz_iff', ...
+    'G_heavy_vc_iff', 'G_heavy_pz_iff');

old/active_damping/act_damp_iff_plots.m

@@ -0,0 +1,133 @@
+%%
+clear; close all; clc;
+
+%% Load Configuration file
+load('./mat/config.mat', 'save_fig', 'freqs');
+
+%% Load
+load('./mat/G_iff.mat', 'G_light_vc_iff', 'G_light_pz_iff', 'G_heavy_vc_iff', 'G_heavy_pz_iff');
+load('./mat/G.mat', 'G_light_vc', 'G_light_pz', 'G_heavy_vc', 'G_heavy_pz');
+
+%% New Damped Plant - Horizontal Direction
+figure;
+% Amplitude
+ax1 = subaxis(2,1,1);
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_cart('Dx', 'Fx'), freqs, 'Hz'))));
+plot(freqs, abs(squeeze(freqresp(G_light_pz.G_cart('Dx', 'Fx'), freqs, 'Hz'))));
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(G_light_vc_iff.G_cart('Dx', 'Fx'), freqs, 'Hz'))), '--');
+plot(freqs, abs(squeeze(freqresp(G_light_pz_iff.G_cart('Dx', 'Fx'), freqs, 'Hz'))), '--');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+set(gca, 'XTickLabel',[]);
+ylabel('Amplitude [m/N]');
+hold off;
+
+% Phase
+ax2 = subaxis(2,1,2);
+hold on;
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_vc.G_cart('Dx', 'Fx'), freqs, 'Hz'))), 'DisplayName', 'VC - Light');
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_pz.G_cart('Dx', 'Fx'), freqs, 'Hz'))), 'DisplayName', 'PZ - Light');
+set(gca,'ColorOrderIndex',1)
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_vc_iff.G_cart('Dx', 'Fx'), freqs, 'Hz'))), '--', 'DisplayName', 'VC - Heavy');
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_pz_iff.G_cart('Dx', 'Fx'), freqs, 'Hz'))), '--', 'DisplayName', 'PZ - Heavy');
+set(gca,'xscale','log');
+yticks(-180:90:180);
+ylim([-180 180]);
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+legend('Location', 'southwest');
+hold off;
+
+linkaxes([ax1,ax2],'x');
+
+if save_fig; exportFig('G_hori_iff', 'normal-normal', struct('path', 'active_damping')); end
+
+%% New Damped Plant - Vertical Direction
+figure;
+% Amplitude
+ax1 = subaxis(2,1,1);
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_cart('Dz', 'Fz'), freqs, 'Hz'))));
+plot(freqs, abs(squeeze(freqresp(G_light_pz.G_cart('Dz', 'Fz'), freqs, 'Hz'))));
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(G_light_vc_iff.G_cart('Dz', 'Fz'), freqs, 'Hz'))), '--');
+plot(freqs, abs(squeeze(freqresp(G_light_pz_iff.G_cart('Dz', 'Fz'), freqs, 'Hz'))), '--');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+set(gca, 'XTickLabel',[]);
+ylabel('Amplitude [m/N]');
+hold off;
+
+% Phase
+ax2 = subaxis(2,1,2);
+hold on;
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_vc.G_cart('Dz', 'Fz'), freqs, 'Hz'))), 'DisplayName', 'VC - Light');
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_pz.G_cart('Dz', 'Fz'), freqs, 'Hz'))), 'DisplayName', 'PZ - Light');
+set(gca,'ColorOrderIndex',1)
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_vc_iff.G_cart('Dz', 'Fz'), freqs, 'Hz'))), '--', 'DisplayName', 'VC - Heavy');
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_pz_iff.G_cart('Dz', 'Fz'), freqs, 'Hz'))), '--', 'DisplayName', 'PZ - Heavy');
+set(gca,'xscale','log');
+yticks(-180:90:180);
+ylim([-180 180]);
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+legend('Location', 'southwest');
+hold off;
+
+linkaxes([ax1,ax2],'x');
+
+if save_fig; exportFig('G_vert_iff', 'normal-normal', struct('path', 'active_damping')); end
+
+%% Ground motion Transmissibility - Horizontal Direction
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_db('Dx', 'Dbx'), freqs, 'Hz'))));
+plot(freqs, abs(squeeze(freqresp(G_light_pz.G_db('Dx', 'Dbx'), freqs, 'Hz'))));
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(G_light_vc_iff.G_db('Dx', 'Dbx'), freqs, 'Hz'))), '--');
+plot(freqs, abs(squeeze(freqresp(G_light_pz_iff.G_db('Dx', 'Dbx'), freqs, 'Hz'))), '--');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
+hold off;
+
+if save_fig; exportFig('G_db_hori_iff', 'normal-normal', struct('path', 'active_damping')); end
+
+%% Ground motion Transmissibility - Vertical Direction
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_db('Dz', 'Dbz'), freqs, 'Hz'))));
+plot(freqs, abs(squeeze(freqresp(G_light_pz.G_db('Dz', 'Dbz'), freqs, 'Hz'))));
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(G_light_vc_iff.G_db('Dz', 'Dbz'), freqs, 'Hz'))), '--');
+plot(freqs, abs(squeeze(freqresp(G_light_pz_iff.G_db('Dz', 'Dbz'), freqs, 'Hz'))), '--');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
+hold off;
+
+if save_fig; exportFig('G_db_vert_iff', 'normal-normal', struct('path', 'active_damping')); end
+
+%% Direct Forces Compliance - Horizontal Direction
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_fi('Dx', 'Fix'), freqs, 'Hz'))));
+plot(freqs, abs(squeeze(freqresp(G_light_pz.G_fi('Dx', 'Fix'), freqs, 'Hz'))));
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(G_light_vc_iff.G_fi('Dx', 'Fix'), freqs, 'Hz'))), '--');
+plot(freqs, abs(squeeze(freqresp(G_light_pz_iff.G_fi('Dx', 'Fix'), freqs, 'Hz'))), '--');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
+hold off;
+
+if save_fig; exportFig('G_fi_hori_iff', 'normal-normal', struct('path', 'active_damping')); end
+
+%% Direct Forces Compliance - Vertical Direction
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_fi('Dz', 'Fiz'), freqs, 'Hz'))));
+plot(freqs, abs(squeeze(freqresp(G_light_pz.G_fi('Dz', 'Fiz'), freqs, 'Hz'))));
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(G_light_vc_iff.G_fi('Dz', 'Fiz'), freqs, 'Hz'))), '--');
+plot(freqs, abs(squeeze(freqresp(G_light_pz_iff.G_fi('Dz', 'Fiz'), freqs, 'Hz'))), '--');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
+hold off;
+
+if save_fig; exportFig('G_fi_vert_iff', 'normal-normal', struct('path', 'active_damping')); end

old/active_damping/act_damp_main.m

@@ -0,0 +1,8 @@
+% Generate the IFF controls
+run act_damp_iff_generate.m
+
+% Identification of the damped plant
+run act_damp_iff_id.m
+
+% Plot new transfer functions
+run act_damp_iff_plots.m

old/analysis/analysis_stiffness.m

@@ -0,0 +1,14 @@
+%%
+clear; close all; clc;
+
+%%
+sys_0   = initializeHexapod(struct('actuator', 'piezo', 'jacobian', 0));
+sys_100 = initializeHexapod(struct('actuator', 'piezo', 'jacobian', 100));
+sys_200 = initializeHexapod(struct('actuator', 'piezo', 'jacobian', 1000000));
+
+%%
+K_0   = getStiffnessMatrix(sys_0.Leg.k.ax,   sys_0.J  );
+K_100 = getStiffnessMatrix(sys_100.Leg.k.ax, sys_100.J);
+K_200 = getStiffnessMatrix(sys_200.Leg.k.ax, sys_200.J);
+
+%%

old/analyze_jacobian.m

@@ -0,0 +1,49 @@
+%% Script Description
+%
+
+%%
+figure;
+plot(d_meas.Time, d.Data-d_meas.Data)
+
+%%
+figure;
+plot(error.Time, error.Data)
+legend({'x', 'y', 'z', 'theta_x', 'theta_y', 'theta_z'})
+
+%%
+J = jacobian.Data(:, :, 1);
+
+% Norm of the jacobian with time
+J_change = (jacobian.Data - J)./J;
+
+figure;
+hold on;
+plot(jacobian.Time, squeeze(J_change(1, 1, :)));
+plot(jacobian.Time, squeeze(J_change(2, 2, :)));
+plot(jacobian.Time, squeeze(J_change(3, 3, :)));
+plot(jacobian.Time, squeeze(J_change(4, 4, :)));
+plot(jacobian.Time, squeeze(J_change(5, 5, :)));
+plot(jacobian.Time, squeeze(J_change(6, 6, :)));
+legend({'Jxx', 'Jyy', 'Jzz', 'Jmx', 'Jmy', 'Jmz'})
+hold off;
+
+%% K change
+K_init = J'*J;
+K = zeros(size(jacobian.Data));
+
+for i=1:length(jacobian.Time)
+    K(:, :, i) = jacobian.Data(:, :, i)'*jacobian.Data(:, :, i);
+end
+
+K_change = (permute(K, [2, 1, 3]) - K_init)./K_init;
+
+figure;
+hold on;
+plot(jacobian.Time, squeeze(K_change(1, 1, :)));
+plot(jacobian.Time, squeeze(K_change(2, 2, :)));
+plot(jacobian.Time, squeeze(K_change(3, 3, :)));
+plot(jacobian.Time, squeeze(K_change(4, 4, :)));
+plot(jacobian.Time, squeeze(K_change(5, 5, :)));
+plot(jacobian.Time, squeeze(K_change(6, 6, :)));
+legend({'Kxx', 'Kyy', 'Kzz', 'Kmx', 'Kmy', 'Kmz'})
+hold off;

old/config.m

@@ -0,0 +1,12 @@
+%%
+addpath('active_damping');
+addpath('analysis');
+addpath('identification');
+addpath('library');
+addpath('studies');
+addpath('src');
+
+%%
+freqs = logspace(-1, 3, 1000);
+save_fig = false;
+save('./mat/config.mat', 'freqs', 'save_fig');

old/identification/id_G.m

@@ -0,0 +1,20 @@
+%% Script Description
+% Script used to identify various transfer functions
+% of the Stewart platform
+
+%%
+clear; close all; clc;
+
+%%
+K_iff = tf(zeros(6));
+save('./mat/controllers.mat', 'K_iff', '-append');
+
+%% Initialize System
+initializeSample(struct('mass', 50));
+initializeHexapod(struct('actuator', 'piezo'));
+
+%% Identification
+G = identifyPlant();
+
+%% Save
+save('./mat/G.mat', 'G');

old/identification/id_jacobian.m

@@ -0,0 +1,38 @@
+%% Script Description
+%%
+clear; close all; clc;
+
+%%
+K_iff = tf(zeros(6));
+save('./mat/controllers.mat', 'K_iff', '-append');
+
+%% System - perfectly aligned
+initializeHexapod(struct('actuator', 'piezo', 'jacobian', 1, 'density', 0.1));
+initializeSample(struct('mass', 50, 'height', 1, 'measheight', 1, 'offset', [0, 0, -25.5]));
+
+% Identification
+G_center = identifyPlant();
+
+%% System - Jacobian is too high
+initializeHexapod(struct('actuator', 'piezo', 'jacobian', 160));
+initializeSample(struct('mass', 50, 'height', 300, 'measheight', 150));
+
+% Identification
+G_Jac_offset = identifyPlant();
+
+%% System - CoM is too low
+initializeHexapod(struct('actuator', 'piezo', 'jacobian', 150));
+initializeSample(struct('mass', 50, 'height', 280, 'measheight', 150));
+
+% Identification
+G_CoM_offset = identifyPlant();
+
+%% System - Meas point is too high
+initializeHexapod(struct('actuator', 'piezo', 'jacobian', 150));
+initializeSample(struct('mass', 50, 'height', 300, 'measheight', 160));
+
+% Identification
+G_Meas_offset = identifyPlant();
+
+%% Save
+save('./mat/G_jacobian.mat', 'G_center', 'G_Jac_offset', 'G_CoM_offset', 'G_Meas_offset');

old/identification/id_jacobian_plots.m

@@ -0,0 +1,43 @@
+%% Script Description
+% 
+%%
+clear; close all; clc;
+
+%%
+load('./mat/G_jacobian.mat');
+
+%%
+freqs = logspace(0, 3, 2000);
+
+%%
+bode_opts = bodeoptions;
+bode_opts.FreqUnits = 'Hz';
+bode_opts.MagUnits = 'abs';
+bode_opts.MagScale = 'log';
+bode_opts.PhaseVisible = 'off';
+
+%% Compare when the Jac is above Meas. point and CoM
+% => 
+figure;
+bode(G_center.G_cart, G_Jac_offset.G_cart, 2*pi*freqs, bode_opts);
+
+%% Compare when the CoM is bellow the Meas. point and Jac
+% => This make the tilt resonance frequency a little bit higher.
+figure;
+bode(G_center.G_cart, G_CoM_offset.G_cart, 2*pi*freqs, bode_opts);
+
+%% Compare when the measurement point is higher than CoM and Jac
+% => 
+figure;
+bode(G_center.G_cart, G_Meas_offset.G_cart, 2*pi*freqs, bode_opts);
+
+%% Compare direct forces and forces applied by actuators on the same point
+% => This should be the same is the support is rigid.
+% => Looks like it's close but not equal
+figure;
+bode(G_center.G_cart, G_center.G_comp, 2*pi*freqs, bode_opts);
+
+%% Compare relative sensor and absolute sensor
+% => This should be the same as the support is rigid
+figure;
+bode(G_center.G_iner, G_center.G_comp, 2*pi*freqs, bode_opts);

old/identification/id_main.m

@@ -0,0 +1,14 @@
+%%
+clear; close all; clc;
+
+%% Jacobian Study
+
+
+%% Identification of the system
+run id_G.m
+
+%% Plots of the identifications
+run id_plot_cart.m
+run id_plot_legs.m
+run id_plot_iff.m
+run id_plot_db.m

old/identification/id_plot_cart.m

@@ -0,0 +1,96 @@
+%%
+clear; close all; clc;
+
+%% Load the transfer functions
+load('./mat/G.mat', 'G_light_vc', 'G_light_pz', 'G_heavy_vc', 'G_heavy_pz');
+
+%% Load Configuration file
+load('./mat/config.mat', 'save_fig', 'freqs');
+
+%% Plant in the X direction
+figure;
+% Amplitude
+ax1 = subaxis(2,1,1);
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_cart('Dx', 'Fx'), freqs, 'Hz'))));
+plot(freqs, abs(squeeze(freqresp(G_light_pz.G_cart('Dx', 'Fx'), freqs, 'Hz'))));
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(G_heavy_vc.G_cart('Dx', 'Fx'), freqs, 'Hz'))), '--');
+plot(freqs, abs(squeeze(freqresp(G_heavy_pz.G_cart('Dx', 'Fx'), freqs, 'Hz'))), '--');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+set(gca, 'XTickLabel',[]);
+ylabel('Amplitude [m/N]');
+hold off;
+
+% Phase
+ax2 = subaxis(2,1,2);
+hold on;
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_vc.G_cart('Dx', 'Fx'), freqs, 'Hz'))), 'DisplayName', 'VC - Light');
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_pz.G_cart('Dx', 'Fx'), freqs, 'Hz'))), 'DisplayName', 'PZ - Light');
+set(gca,'ColorOrderIndex',1)
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_heavy_vc.G_cart('Dx', 'Fx'), freqs, 'Hz'))), '--', 'DisplayName', 'VC - Heavy');
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_heavy_pz.G_cart('Dx', 'Fx'), freqs, 'Hz'))), '--', 'DisplayName', 'PZ - Heavy');
+set(gca,'xscale','log');
+yticks(-180:90:180);
+ylim([-180 180]);
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+legend('Location', 'southwest');
+hold off;
+
+linkaxes([ax1,ax2],'x');
+
+if save_fig; exportFig('G_hori', 'normal-normal', struct('path', 'identification')); end
+
+%% Plant in the Z direction
+figure;
+% Amplitude
+ax1 = subaxis(2,1,1);
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_cart('Dz', 'Fz'), freqs, 'Hz'))));
+plot(freqs, abs(squeeze(freqresp(G_light_pz.G_cart('Dz', 'Fz'), freqs, 'Hz'))));
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(G_heavy_vc.G_cart('Dz', 'Fz'), freqs, 'Hz'))), '--');
+plot(freqs, abs(squeeze(freqresp(G_heavy_pz.G_cart('Dz', 'Fz'), freqs, 'Hz'))), '--');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+set(gca, 'XTickLabel',[]);
+ylabel('Amplitude [m/N]');
+hold off;
+
+% Phase
+ax2 = subaxis(2,1,2);
+hold on;
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_vc.G_cart('Dz', 'Fz'), freqs, 'Hz'))), 'DisplayName', 'VC - Light');
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_pz.G_cart('Dz', 'Fz'), freqs, 'Hz'))), 'DisplayName', 'PZ - Light');
+set(gca,'ColorOrderIndex',1)
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_heavy_vc.G_cart('Dz', 'Fz'), freqs, 'Hz'))), '--', 'DisplayName', 'VC - Heavy');
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_heavy_pz.G_cart('Dz', 'Fz'), freqs, 'Hz'))), '--', 'DisplayName', 'PZ - Heavy');
+set(gca,'xscale','log');
+yticks(-180:90:180);
+ylim([-180 180]);
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+legend('Location', 'southwest');
+hold off;
+
+linkaxes([ax1,ax2],'x');
+
+if save_fig; exportFig('G_vert', 'normal-normal', struct('path', 'identification')); end
+
+%% Coupling
+figure;
+
+for i_input = 1:3
+    for i_output = 1:3
+        subaxis(3,3,3*(i_input-1)+i_output);
+        hold on;
+        plot(freqs, abs(squeeze(freqresp(G_light_vc.G_cart(i_output, i_input), freqs, 'Hz'))));
+        plot(freqs, abs(squeeze(freqresp(G_light_pz.G_cart(i_output, i_input), freqs, 'Hz'))));
+        set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+        xlim([freqs(1) freqs(end)]); ylim([1e-22, 1e-2]);
+        yticks([1e-20, 1e-15, 1e-10, 1e-5]); xticks([0.1 1 10 100 1000]);
+        if i_output > 1; set(gca,'yticklabel',[]); end
+        if i_input < 3; set(gca,'xticklabel',[]); end
+        hold off;
+    end
+end
+
+if save_fig; exportFig('G_coupling', 'wide-tall', struct('path', 'identification')); end

old/identification/id_plot_db.m

@@ -0,0 +1,40 @@
+%%
+clear; close all; clc;
+
+%% Load the transfer functions
+load('./mat/G.mat', 'G_light_vc', 'G_light_pz', 'G_heavy_vc', 'G_heavy_pz');
+
+%% Load Configuration file
+load('./mat/config.mat', 'save_fig', 'freqs');
+
+%%
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_db('Dx', 'Dbx'), freqs, 'Hz'))), 'DisplayName', 'VC - Light');
+plot(freqs, abs(squeeze(freqresp(G_light_pz.G_db('Dx', 'Dbx'), freqs, 'Hz'))), 'DisplayName', 'PZ - Light');
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(G_heavy_vc.G_db('Dx', 'Dbx'), freqs, 'Hz'))), '--', 'DisplayName', 'VC - Heavy');
+plot(freqs, abs(squeeze(freqresp(G_heavy_pz.G_db('Dx', 'Dbx'), freqs, 'Hz'))), '--', 'DisplayName', 'PZ - Heavy');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
+hold off;
+legend('Location', 'southeast');
+
+if save_fig; exportFig('G_db_hori', 'normal-normal', struct('path', 'identification')); end
+
+%%
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_db('Dz', 'Dbz'), freqs, 'Hz'))), 'DisplayName', 'VC - Light');
+plot(freqs, abs(squeeze(freqresp(G_light_pz.G_db('Dz', 'Dbz'), freqs, 'Hz'))), 'DisplayName', 'PZ - Light');
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(G_heavy_vc.G_db('Dz', 'Dbz'), freqs, 'Hz'))), '--', 'DisplayName', 'VC - Heavy');
+plot(freqs, abs(squeeze(freqresp(G_heavy_pz.G_db('Dz', 'Dbz'), freqs, 'Hz'))), '--', 'DisplayName', 'PZ - Heavy');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
+hold off;
+legend('Location', 'southeast');
+
+if save_fig; exportFig('G_db_vert', 'normal-normal', struct('path', 'identification')); end
+
+%%

old/identification/id_plot_iff.m

@@ -0,0 +1,57 @@
+%%
+clear; close all; clc;
+
+%% Load the transfer functions
+load('./mat/G.mat', 'G_light_vc', 'G_light_pz', 'G_heavy_vc', 'G_heavy_pz');
+
+%% Load Configuration file
+load('./mat/config.mat', 'save_fig', 'freqs');
+
+%%
+figure;
+% Amplitude
+ax1 = subaxis(2,1,1);
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_iff('Fm1', 'F1'), freqs, 'Hz'))));
+plot(freqs, abs(squeeze(freqresp(G_light_pz.G_iff('Fm1', 'F1'), freqs, 'Hz'))));
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(G_heavy_vc.G_iff('Fm1', 'F1'), freqs, 'Hz'))), '--');
+plot(freqs, abs(squeeze(freqresp(G_heavy_pz.G_iff('Fm1', 'F1'), freqs, 'Hz'))), '--');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+set(gca, 'XTickLabel',[]);
+ylabel('Amplitude [m/N]');
+hold off;
+
+% Phase
+ax2 = subaxis(2,1,2);
+hold on;
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_vc.G_iff('Fm1', 'F1'), freqs, 'Hz'))), 'DisplayName', 'VC - Light');
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_pz.G_iff('Fm1', 'F1'), freqs, 'Hz'))), 'DisplayName', 'PZ - Light');
+set(gca,'ColorOrderIndex',1)
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_heavy_vc.G_iff('Fm1', 'F1'), freqs, 'Hz'))), '--', 'DisplayName', 'VC - Heavy');
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_heavy_pz.G_iff('Fm1', 'F1'), freqs, 'Hz'))), '--', 'DisplayName', 'PZ - Heavy');
+set(gca,'xscale','log');
+yticks(-180:90:180);
+ylim([-180 180]);
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+legend('Location', 'southwest');
+hold off;
+
+linkaxes([ax1,ax2],'x');
+
+if save_fig; exportFig('G_iff', 'normal-normal', struct('path', 'identification')); end
+
+%% Coupling
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_iff('Fm1', 'F1'), freqs, 'Hz'))), 'k-');
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_iff('Fm2', 'F1'), freqs, 'Hz'))), 'k--');
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_iff('Fm3', 'F1'), freqs, 'Hz'))), 'k--');
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_iff('Fm4', 'F1'), freqs, 'Hz'))), 'k--');
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_iff('Fm5', 'F1'), freqs, 'Hz'))), 'k--');
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_iff('Fm6', 'F1'), freqs, 'Hz'))), 'k--');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
+hold off;
+
+if save_fig; exportFig('G_iff_coupling', 'normal-normal', struct('path', 'identification')); end

old/identification/id_plot_legs.m

@@ -0,0 +1,57 @@
+%%
+clear; close all; clc;
+
+%% Load the transfer functions
+load('./mat/G.mat', 'G_light_vc', 'G_light_pz', 'G_heavy_vc', 'G_heavy_pz');
+
+%% Load Configuration file
+load('./mat/config.mat', 'save_fig', 'freqs');
+
+%%
+figure;
+% Amplitude
+ax1 = subaxis(2,1,1);
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_legs('D1', 'F1'), freqs, 'Hz'))));
+plot(freqs, abs(squeeze(freqresp(G_light_pz.G_legs('D1', 'F1'), freqs, 'Hz'))));
+set(gca,'ColorOrderIndex',1);
+plot(freqs, abs(squeeze(freqresp(G_heavy_vc.G_legs('D1', 'F1'), freqs, 'Hz'))), '--');
+plot(freqs, abs(squeeze(freqresp(G_heavy_pz.G_legs('D1', 'F1'), freqs, 'Hz'))), '--');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+set(gca, 'XTickLabel',[]);
+ylabel('Amplitude [m/N]');
+hold off;
+
+% Phase
+ax2 = subaxis(2,1,2);
+hold on;
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_vc.G_legs('D1', 'F1'), freqs, 'Hz'))), 'DisplayName', 'VC - Light');
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_light_pz.G_legs('D1', 'F1'), freqs, 'Hz'))), 'DisplayName', 'PZ - Light');
+set(gca,'ColorOrderIndex',1)
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_heavy_vc.G_legs('D1', 'F1'), freqs, 'Hz'))), '--', 'DisplayName', 'VC - Heavy');
+plot(freqs, 180/pi*angle(squeeze(freqresp(G_heavy_pz.G_legs('D1', 'F1'), freqs, 'Hz'))), '--', 'DisplayName', 'PZ - Heavy');
+set(gca,'xscale','log');
+yticks(-180:90:180);
+ylim([-180 180]);
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+legend('Location', 'southwest');
+hold off;
+
+linkaxes([ax1,ax2],'x');
+
+if save_fig; exportFig('G_legs', 'normal-normal', struct('path', 'identification')); end
+
+%% Coupling
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_legs('D1', 'F1'), freqs, 'Hz'))), 'k-');
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_legs('D2', 'F1'), freqs, 'Hz'))), 'k--');
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_legs('D3', 'F1'), freqs, 'Hz'))), 'k--');
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_legs('D4', 'F1'), freqs, 'Hz'))), 'k--');
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_legs('D5', 'F1'), freqs, 'Hz'))), 'k--');
+plot(freqs, abs(squeeze(freqresp(G_light_vc.G_legs('D6', 'F1'), freqs, 'Hz'))), 'k--');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
+hold off;
+
+if save_fig; exportFig('G_legs_coupling', 'normal-normal', struct('path', 'identification')); end

old/main.m

@@ -0,0 +1,11 @@
+%%
+clear; close all; clc;
+
+%% Configuration File
+run config.m
+
+%% Identification
+open id_main.m
+
+%% Active Damping
+open act_damp_main.m

old/plot_max_positions.m

@@ -0,0 +1,19 @@
+%% Script Description
+% 
+
+%%
+clear; close all; clc;
+
+%%
+init_simulink;
+
+%%
+[X, Y, Z] = getMaxPositions(stewart);
+
+%%
+figure;
+hold on;
+mesh(X, Y, Z);
+grid on;
+colorbar;
+hold off;

old/studies/com.m

@@ -0,0 +1,44 @@
+clear; close all; clc;
+
+%% System - center of mass in the plane of joints
+initializeHexapod(struct('actuator', 'piezo', 'jacobian', 150, 'density', 0.1));
+initializeSample(struct('mass', 50, 'height', 300, 'measheight', 150));
+
+%% Identification
+G_aligned = identifyPlant();
+
+%%
+initializeHexapod(struct('actuator', 'piezo', 'jacobian', 160, 'density', 0.1));
+initializeSample(struct('mass', 50, 'height', 300, 'measheight', 160));
+
+%% Identification
+G_com = identifyPlant();
+
+%%
+freqs = logspace(0, 3, 2000);
+
+%%
+bode_opts = bodeoptions;
+bode_opts.FreqUnits = 'Hz';
+bode_opts.MagUnits = 'abs';
+bode_opts.MagScale = 'log';
+bode_opts.PhaseVisible = 'off';
+
+%%
+figure;
+bode(G_aligned.G_cart, G_com.G_cart, 2*pi*freqs, bode_opts);
+
+exportFig('G_com', 'wide-tall', struct('path', 'studies'));
+
+
+%%
+initializeHexapod(struct('actuator', 'piezo', 'jacobian', 150, 'density', 0.1));
+initializeSample(struct('mass', 1, 'height', 300, 'measheight', 150));
+
+%% Identification
+G_massless = identifyPlant();
+
+
+%%
+figure;
+bode(G_aligned.G_cart, G_massless.G_cart, 2*pi*freqs, bode_opts);

old/studies/coupling.m

@@ -0,0 +1,41 @@
+clear; close all; clc;
+
+%% System - center of mass in the plane of joints
+initializeHexapod(struct('actuator', 'piezo', 'jacobian', -25, 'density', 0.1));
+initializeSample(struct('mass', 50, 'height', 1, 'measheight', -25, 'offset', [0, 0, -25.5]));
+
+%% Identification
+G_aligned = identifyPlant();
+
+%%
+freqs = logspace(0, 3, 2000);
+
+%%
+bode_opts = bodeoptions;
+bode_opts.FreqUnits = 'Hz';
+bode_opts.MagUnits = 'abs';
+bode_opts.MagScale = 'log';
+bode_opts.PhaseVisible = 'off';
+
+%%
+figure;
+bode(G_aligned.G_legs, 2*pi*freqs, bode_opts);
+
+
+%% Change height of stewart platform
+for height = [50, 70, 90, 110, 130]
+    initializeHexapod(struct('actuator', 'piezo', 'jacobian', -25, 'density', 0.1, 'height', height));
+    G.(['h_' num2str(height)]) = identifyPlant();
+end
+
+%%
+figure;
+bode( ...
+    G.h_50.G_legs, ...
+    G.h_70.G_legs, ...
+    G.h_90.G_legs, ...
+    G.h_110.G_legs, ...
+    G.h_130.G_legs, ...
+    2*pi*freqs, bode_opts);
+% legend({'60', '80', '100', '120', '140'})
+

old/studies/stiffness_matrix.m

@@ -0,0 +1,26 @@
+%%
+clear; close all; clc;
+
+%%
+K_iff = tf(zeros(6));
+save('./mat/controllers.mat', 'K_iff', '-append');
+
+%% Initialize System
+hexapod = initializeHexapod(struct('actuator', 'piezo', 'jacobian', 150));
+initializeSample(struct('mass', 50, 'height', 300, 'measheight', 150));
+
+%% Identify transfer functions
+G = identifyPlant();
+
+%% Run to obtain the computed Jacobian
+sim stewart_identification
+
+%% Compare the two Jacobian matrices
+J_rel = (J.data(:, :, 1)-hexapod.J)./hexapod.J;
+
+%% Compute the Stiffness Matrix
+K = hexapod.Leg.k.ax*hexapod.J'*hexapod.J;
+K_id = pinv(freqresp(G.G_cart, 0));
+
+K_rel = (K-K_id)./K;
+

old/study_architecture.m

@@ -0,0 +1,55 @@
+%%
+clear; close all; clc;
+
+%%
+run stewart_parameters.m
+
+%% Study the effect of the radius of the top platform position of the legs
+leg_radius = 50:1:120;
+max_disp   = zeros(length(leg_radius), 6);
+stiffness  = zeros(length(leg_radius), 6, 6);
+
+for i_leg = 1:length(leg_radius)
+    TP.leg.rad = leg_radius(i_leg);
+    run stewart_init.m;
+    max_disp(i_leg, :) = getMaxPureDisplacement(Leg, J)';
+    stiffness(i_leg, :, :) = getStiffnessMatrix(Leg, J);
+end
+
+%% Plot everything
+figure;
+hold on;
+plot(leg_radius, max_disp(:, 1))
+plot(leg_radius, max_disp(:, 2))
+plot(leg_radius, max_disp(:, 3))
+hold off;
+legend({'tx', 'ty', 'tz'})
+xlabel('Leg Radius at the platform'); ylabel('Maximum translation (m)');
+
+figure;
+hold on;
+plot(leg_radius, max_disp(:, 4))
+plot(leg_radius, max_disp(:, 5))
+plot(leg_radius, max_disp(:, 6))
+hold off;
+legend({'rx', 'ry', 'rz'})
+xlabel('Leg Radius at the platform'); ylabel('Maximum rotations (rad)');
+
+figure;
+hold on;
+plot(leg_radius, stiffness(:, 1, 1))
+plot(leg_radius, stiffness(:, 2, 2))
+plot(leg_radius, stiffness(:, 3, 3))
+hold off;
+legend({'kx', 'ky', 'kz'})
+xlabel('Leg Radius at the platform'); ylabel('Stiffness in translation (N/m)');
+
+figure;
+hold on;
+plot(leg_radius, stiffness(:, 4, 4))
+plot(leg_radius, stiffness(:, 5, 5))
+plot(leg_radius, stiffness(:, 6, 6))
+hold off;
+legend({'mx', 'my', 'mz'})
+xlabel('Leg Radius at the platform'); ylabel('Stiffness in rotations (N/(m/rad))');
+