Study the influence of config on plant

active_damping/matlab/act_damp_variability_plant.m

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+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+open('active_damping/matlab/sim_nass_active_damping.slx')
+load('mat/conf_simscape.mat');
+
+% Initialize the Simulation
+% We initialize all the stages with the default parameters.
+
+initializeGround();
+initializeGranite();
+initializeTy();
+initializeRy();
+initializeRz();
+initializeMicroHexapod();
+initializeAxisc();
+initializeMirror();
+
+
+
+% No disturbances.
+
+initializeDisturbances('enable', false);
+
+
+
+% The nano-hexapod is a piezoelectric hexapod.
+
+initializeNanoHexapod('actuator', 'piezo');
+
+
+
+% We set the references to zero.
+
+initializeReferences();
+
+
+
+% And all the controllers are set to 0.
+
+K = tf(zeros(6));
+save('./mat/controllers.mat', 'K', '-append');
+K_ine = tf(zeros(6));
+save('./mat/controllers.mat', 'K_ine', '-append');
+K_iff = tf(zeros(6));
+save('./mat/controllers.mat', 'K_iff', '-append');
+K_dvf = tf(zeros(6));
+save('./mat/controllers.mat', 'K_dvf', '-append');
+
+% Identification
+% First, we identify the dynamics of the system using the =linearize= function.
+
+%% Options for Linearized
+options = linearizeOptions;
+options.SampleTime = 0;
+
+%% Name of the Simulink File
+mdl = 'sim_nass_active_damping';
+
+%% Input/Output definition
+clear io; io_i = 1;
+io(io_i) = linio([mdl, '/Fnl'],           1, 'openinput');              io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vlm');  io_i = io_i + 1;
+
+masses = [1, 10, 50];
+
+Gm     = {zeros(length(masses))};
+Gm_iff = {zeros(length(masses))};
+Gm_dvf = {zeros(length(masses))};
+Gm_ine = {zeros(length(masses))};
+
+for i = 1:length(masses)
+  initializeSample('mass', masses(i));
+
+  %% Run the linearization
+  G = linearize(mdl, io, 0.1, options);
+  G.InputName  = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
+  G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
+                  'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
+                  'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'};
+  Gm(i) = {G};
+  Gm_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
+  Gm_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
+  Gm_ine(i) = {minreal(G({'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
+end
+
+save('./active_damping/mat/plants_variable.mat', 'Gm_iff', 'Gm_dvf', 'Gm_ine', '-append');
+
+% Plots
+
+load('./active_damping/mat/plants_variable.mat', 'Gm_iff', 'Gm_dvf', 'Gm_ine');
+
+freqs = logspace(0, 3, 1000);
+
+figure;
+
+ax1 = subplot(2, 1, 1);
+hold on;
+for i = 1:length(Gm)
+  set(gca,'ColorOrderIndex',i);
+  plot(freqs, abs(squeeze(freqresp(Gm_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))));
+  for j = 2:6
+    set(gca,'ColorOrderIndex',i);
+    plot(freqs, abs(squeeze(freqresp(Gm_iff{i}(['Fnlm', num2str(i)], ['Fnl', num2str(i)]), freqs, 'Hz'))));
+  end
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
+
+ax2 = subplot(2, 1, 2);
+hold on;
+for i = 1:length(Gm)
+  set(gca,'ColorOrderIndex',i);
+  plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$M = %.0f$ [kg]', masses(i)));
+  for j = 2:6
+    set(gca,'ColorOrderIndex',i);
+    plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_iff{i}(['Fnlm', num2str(i)], ['Fnl', num2str(i)]), freqs, 'Hz'))), 'HandleVisibility', 'off');
+  end
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+legend('location', 'southwest');
+
+linkaxes([ax1,ax2],'x');
+
+
+
+% #+NAME: fig:act_damp_variability_iff_sample_mass
+% #+CAPTION: Variability of the IFF plant with the Spindle Angle ([[./figs/act_damp_variability_iff_sample_mass.png][png]], [[./figs/act_damp_variability_iff_sample_mass.pdf][pdf]])
+% [[file:figs/act_damp_variability_iff_sample_mass.png]]
+
+
+freqs = logspace(0, 3, 1000);
+
+figure;
+
+ax1 = subplot(2, 1, 1);
+hold on;
+
+for i = 1:length(Gm)
+  set(gca,'ColorOrderIndex',i);
+  plot(freqs, abs(squeeze(freqresp(Gm_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))));
+  for j = 2:6
+    set(gca,'ColorOrderIndex',i);
+    plot(freqs, abs(squeeze(freqresp(Gm_dvf{i}(['Dnlm', num2str(i)], ['Fnl', num2str(i)]), freqs, 'Hz'))));
+  end
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
+
+ax2 = subplot(2, 1, 2);
+hold on;
+for i = 1:length(Gm)
+  set(gca,'ColorOrderIndex',i);
+  plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$M = %.0f$ [kg]', masses(i)));
+  for j = 2:6
+    set(gca,'ColorOrderIndex',i);
+    plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_dvf{i}(['Dnlm', num2str(i)], ['Fnl', num2str(i)]), freqs, 'Hz'))), 'HandleVisibility', 'off');
+  end
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+legend('location', 'southwest');
+
+linkaxes([ax1,ax2],'x');
+
+
+
+% #+NAME: fig:act_damp_variability_dvf_sample_mass
+% #+CAPTION: Variability of the DVF plant with the Spindle Angle ([[./figs/act_damp_variability_dvf_sample_mass.png][png]], [[./figs/act_damp_variability_dvf_sample_mass.pdf][pdf]])
+% [[file:figs/act_damp_variability_dvf_sample_mass.png]]
+
+
+freqs = logspace(0, 3, 1000);
+
+figure;
+
+ax1 = subplot(2, 1, 1);
+hold on;
+for i = 1:length(Gm)
+  set(gca,'ColorOrderIndex',i);
+  plot(freqs, abs(squeeze(freqresp(Gm_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))));
+  for j = 2:6
+    set(gca,'ColorOrderIndex',i);
+    plot(freqs, abs(squeeze(freqresp(Gm_ine{i}(['Vnlm', num2str(i)], ['Fnl', num2str(i)]), freqs, 'Hz'))));
+  end
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]);
+
+ax2 = subplot(2, 1, 2);
+hold on;
+for i = 1:length(Gm)
+  set(gca,'ColorOrderIndex',i);
+  plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$M = %.0f$ [kg]', masses(i)));
+  for j = 2:6
+    set(gca,'ColorOrderIndex',i);
+    plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_ine{i}(['Vnlm', num2str(i)], ['Fnl', num2str(i)]), freqs, 'Hz'))), 'HandleVisibility', 'off');
+  end
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+legend('location', 'southwest');
+
+linkaxes([ax1,ax2],'x');
+
+% Initialize the Simulation
+% We initialize all the stages with the default parameters.
+
+initializeGround();
+initializeGranite();
+initializeTy();
+initializeRy();
+initializeRz();
+initializeMicroHexapod();
+initializeAxisc();
+initializeMirror();
+
+
+
+% No disturbances.
+
+initializeDisturbances('enable', false);
+
+
+
+% The nano-hexapod is a piezoelectric hexapod.
+
+initializeNanoHexapod('actuator', 'piezo');
+initializeSample('mass', 50);
+
+
+
+% And all the controllers are set to 0.
+
+K = tf(zeros(6));
+save('./mat/controllers.mat', 'K', '-append');
+K_ine = tf(zeros(6));
+save('./mat/controllers.mat', 'K_ine', '-append');
+K_iff = tf(zeros(6));
+save('./mat/controllers.mat', 'K_iff', '-append');
+K_dvf = tf(zeros(6));
+save('./mat/controllers.mat', 'K_dvf', '-append');
+
+% Identification
+% First, we identify the dynamics of the system using the =linearize= function.
+
+%% Options for Linearized
+options = linearizeOptions;
+options.SampleTime = 0;
+
+%% Name of the Simulink File
+mdl = 'sim_nass_active_damping';
+
+%% Input/Output definition
+clear io; io_i = 1;
+io(io_i) = linio([mdl, '/Fnl'],           1, 'openinput');              io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vlm');  io_i = io_i + 1;
+
+Rz_amplitudes = [0, pi/4, pi/2, pi]; % [rad]
+
+Ga     = {zeros(length(Rz_amplitudes))};
+Ga_iff = {zeros(length(Rz_amplitudes))};
+Ga_dvf = {zeros(length(Rz_amplitudes))};
+Ga_ine = {zeros(length(Rz_amplitudes))};
+
+for i = 1:length(Rz_amplitudes)
+initializeReferences('Rz_type', 'constant', 'Rz_amplitude', Rz_amplitudes(i))
+
+  %% Run the linearization
+  G = linearize(mdl, io, 0.1, options);
+  G.InputName  = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
+  G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
+                  'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
+                  'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'};
+  Ga(i) = {G};
+  Ga_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
+  Ga_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
+  Ga_ine(i) = {minreal(G({'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
+end
+
+save('./active_damping/mat/plants_variable.mat', 'Ga_iff', 'Ga_dvf', 'Ga_ine', '-append');
+
+% Plots
+
+load('./active_damping/mat/plants_variable.mat', 'Ga_iff', 'Ga_dvf', 'Ga_ine');
+
+freqs = logspace(0, 3, 1000);
+
+figure;
+
+ax1 = subplot(2, 1, 1);
+hold on;
+for i = 1:length(Ga)
+  plot(freqs, abs(squeeze(freqresp(Ga_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
+
+ax2 = subplot(2, 1, 2);
+hold on;
+for i = 1:length(Ga)
+  plot(freqs, 180/pi*angle(squeeze(freqresp(Ga_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [deg]', Rz_amplitudes(i)*180/pi));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+legend('location', 'southwest');
+
+linkaxes([ax1,ax2],'x');
+
+
+
+% #+NAME: fig:act_damp_variability_iff_spindle_angle
+% #+CAPTION: Variability of the IFF plant with the Spindle Angle ([[./figs/act_damp_variability_iff_spindle_angle.png][png]], [[./figs/act_damp_variability_iff_spindle_angle.pdf][pdf]])
+% [[file:figs/act_damp_variability_iff_spindle_angle.png]]
+
+
+freqs = logspace(0, 3, 1000);
+
+figure;
+
+ax1 = subplot(2, 1, 1);
+hold on;
+
+for i = 1:length(Ga)
+  plot(freqs, abs(squeeze(freqresp(Ga_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
+
+ax2 = subplot(2, 1, 2);
+hold on;
+for i = 1:length(Ga)
+  plot(freqs, 180/pi*angle(squeeze(freqresp(Ga_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [deg]', Rz_amplitudes(i)*180/pi));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+legend('location', 'southwest');
+
+linkaxes([ax1,ax2],'x');
+
+
+
+% #+NAME: fig:act_damp_variability_dvf_spindle_angle
+% #+CAPTION: Variability of the DVF plant with the Spindle Angle ([[./figs/act_damp_variability_dvf_spindle_angle.png][png]], [[./figs/act_damp_variability_dvf_spindle_angle.pdf][pdf]])
+% [[file:figs/act_damp_variability_dvf_spindle_angle.png]]
+
+
+freqs = logspace(0, 3, 1000);
+
+figure;
+
+ax1 = subplot(2, 1, 1);
+hold on;
+for i = 1:length(Ga)
+  plot(freqs, abs(squeeze(freqresp(Ga_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]);
+
+ax2 = subplot(2, 1, 2);
+hold on;
+for i = 1:length(Ga)
+  plot(freqs, 180/pi*angle(squeeze(freqresp(Ga_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [deg]', Rz_amplitudes(i)*180/pi));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+legend('location', 'southwest');
+
+linkaxes([ax1,ax2],'x');
+
+% Initialize the Simulation
+% We initialize all the stages with the default parameters.
+
+initializeGround();
+initializeGranite();
+initializeTy();
+initializeRy();
+initializeRz();
+initializeMicroHexapod();
+initializeAxisc();
+initializeMirror();
+
+
+
+% No disturbances.
+
+initializeDisturbances('enable', false);
+
+
+
+% The nano-hexapod is a piezoelectric hexapod.
+
+initializeNanoHexapod('actuator', 'piezo');
+initializeSample('mass', 50);
+
+
+
+% And all the controllers are set to 0.
+
+K = tf(zeros(6));
+save('./mat/controllers.mat', 'K', '-append');
+K_ine = tf(zeros(6));
+save('./mat/controllers.mat', 'K_ine', '-append');
+K_iff = tf(zeros(6));
+save('./mat/controllers.mat', 'K_iff', '-append');
+K_dvf = tf(zeros(6));
+save('./mat/controllers.mat', 'K_dvf', '-append');
+
+% Identification
+% First, we identify the dynamics of the system using the =linearize= function.
+
+%% Options for Linearized
+options = linearizeOptions;
+options.SampleTime = 0;
+
+%% Name of the Simulink File
+mdl = 'sim_nass_active_damping';
+
+%% Input/Output definition
+clear io; io_i = 1;
+io(io_i) = linio([mdl, '/Fnl'],           1, 'openinput');              io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vlm');  io_i = io_i + 1;
+
+Rz_periods = [60, 10, 1]; % [s]
+
+Gw     = {zeros(length(Rz_periods))};
+Gw_iff = {zeros(length(Rz_periods))};
+Gw_dvf = {zeros(length(Rz_periods))};
+Gw_ine = {zeros(length(Rz_periods))};
+
+for i = 1:length(Rz_periods)
+  initializeReferences('Rz_type', 'rotating', 'Rz_period', Rz_periods(i));
+
+  %% Run the linearization
+  G = linearize(mdl, io, 0.5, options);
+  G.InputName  = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
+  G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
+                  'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
+                  'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'};
+  Gw(i) = {G};
+  Gw_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
+  Gw_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
+  Gw_ine(i) = {minreal(G({'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
+end
+
+save('./active_damping/mat/plants_variable.mat', 'Gw_iff', 'Gw_dvf', 'Gw_ine', '-append');
+
+% Plots
+
+load('./active_damping/mat/plants_variable.mat', 'Gw_iff', 'Gw_dvf', 'Gw_ine');
+
+freqs = logspace(0, 3, 1000);
+
+figure;
+
+ax1 = subplot(2, 1, 1);
+hold on;
+for i = 1:length(Gw)
+  plot(freqs, abs(squeeze(freqresp(Gw_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
+
+ax2 = subplot(2, 1, 2);
+hold on;
+for i = 1:length(Gw)
+  plot(freqs, 180/pi*angle(squeeze(freqresp(Gw_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [rpm]', 60/Rz_periods(i)));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+legend('location', 'southwest');
+
+linkaxes([ax1,ax2],'x');
+
+
+
+% #+NAME: fig:act_damp_variability_iff_spindle_speed
+% #+CAPTION: Variability of the IFF plant with the Spindle Angle ([[./figs/act_damp_variability_iff_spindle_speed.png][png]], [[./figs/act_damp_variability_iff_spindle_speed.pdf][pdf]])
+% [[file:figs/act_damp_variability_iff_spindle_speed.png]]
+
+
+freqs = logspace(0, 3, 1000);
+
+figure;
+
+ax1 = subplot(2, 1, 1);
+hold on;
+
+for i = 1:length(Gw)
+  plot(freqs, abs(squeeze(freqresp(Gw_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
+
+ax2 = subplot(2, 1, 2);
+hold on;
+for i = 1:length(Gw)
+  plot(freqs, 180/pi*angle(squeeze(freqresp(Gw_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [rpm]', 60/Rz_periods(i)));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+legend('location', 'southwest');
+
+linkaxes([ax1,ax2],'x');
+
+
+
+% #+NAME: fig:act_damp_variability_dvf_spindle_speed
+% #+CAPTION: Variability of the DVF plant with the Spindle Angle ([[./figs/act_damp_variability_dvf_spindle_speed.png][png]], [[./figs/act_damp_variability_dvf_spindle_speed.pdf][pdf]])
+% [[file:figs/act_damp_variability_dvf_spindle_speed.png]]
+
+
+freqs = logspace(0, 2, 5000);
+
+figure;
+
+ax1 = subplot(2, 1, 1);
+hold on;
+for i = 1:length(Gw)
+  plot(freqs, abs(squeeze(freqresp(Gw_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]);
+
+ax2 = subplot(2, 1, 2);
+hold on;
+for i = 1:length(Gw)
+  plot(freqs, 180/pi*angle(squeeze(freqresp(Gw_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [rpm]', 60/Rz_periods(i)));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+legend('location', 'southwest');
+
+linkaxes([ax1,ax2],'x');
+
+% Initialize the Simulation
+% We initialize all the stages with the default parameters.
+
+initializeGround();
+initializeGranite();
+initializeTy();
+initializeRy();
+initializeRz();
+initializeMicroHexapod();
+initializeAxisc();
+initializeMirror();
+
+
+
+% No disturbances.
+
+initializeDisturbances('enable', false);
+
+
+
+% The nano-hexapod is a piezoelectric hexapod.
+
+initializeNanoHexapod('actuator', 'piezo');
+initializeSample('mass', 50);
+
+
+
+% And all the controllers are set to 0.
+
+K = tf(zeros(6));
+save('./mat/controllers.mat', 'K', '-append');
+K_ine = tf(zeros(6));
+save('./mat/controllers.mat', 'K_ine', '-append');
+K_iff = tf(zeros(6));
+save('./mat/controllers.mat', 'K_iff', '-append');
+K_dvf = tf(zeros(6));
+save('./mat/controllers.mat', 'K_dvf', '-append');
+
+% Identification
+% First, we identify the dynamics of the system using the =linearize= function.
+
+%% Options for Linearized
+options = linearizeOptions;
+options.SampleTime = 0;
+
+%% Name of the Simulink File
+mdl = 'sim_nass_active_damping';
+
+%% Input/Output definition
+clear io; io_i = 1;
+io(io_i) = linio([mdl, '/Fnl'],           1, 'openinput');              io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vlm');  io_i = io_i + 1;
+
+Ry_amplitudes = [0, 3*pi/180]; % [rad]
+
+Gy     = {zeros(length(Ry_amplitudes))};
+Gy_iff = {zeros(length(Ry_amplitudes))};
+Gy_dvf = {zeros(length(Ry_amplitudes))};
+Gy_ine = {zeros(length(Ry_amplitudes))};
+
+for i = 1:length(Ry_amplitudes)
+  initializeReferences('Ry_type', 'constant', 'Ry_amplitude', Ry_amplitudes(i))
+
+  %% Run the linearization
+  G = linearize(mdl, io, 0.1, options);
+  G.InputName  = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
+  G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
+                  'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
+                  'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'};
+  Gy(i) = {G};
+  Gy_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
+  Gy_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
+  Gy_ine(i) = {minreal(G({'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
+end
+
+save('./active_damping/mat/plants_variable.mat', 'Gy_iff', 'Gy_dvf', 'Gy_ine', '-append');
+
+% Plots
+
+load('./active_damping/mat/plants_variable.mat', 'Gy_iff', 'Gy_dvf', 'Gy_ine');
+
+freqs = logspace(0, 3, 1000);
+
+figure;
+
+ax1 = subplot(2, 1, 1);
+hold on;
+for i = 1:length(Gy)
+  plot(freqs, abs(squeeze(freqresp(Gy_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
+
+ax2 = subplot(2, 1, 2);
+hold on;
+for i = 1:length(Gy)
+  plot(freqs, 180/pi*angle(squeeze(freqresp(Gy_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Ry = %.0f$ [deg]', Ry_amplitudes(i)*180/pi));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+legend('location', 'southwest');
+
+linkaxes([ax1,ax2],'x');
+
+
+
+% #+NAME: fig:act_damp_variability_iff_tilt_angle
+% #+CAPTION: Variability of the IFF plant with the Spindle Angle ([[./figs/act_damp_variability_iff_tilt_angle.png][png]], [[./figs/act_damp_variability_iff_tilt_angle.pdf][pdf]])
+% [[file:figs/act_damp_variability_iff_tilt_angle.png]]
+
+
+freqs = logspace(0, 3, 1000);
+
+figure;
+
+ax1 = subplot(2, 1, 1);
+hold on;
+
+for i = 1:length(Gy)
+  plot(freqs, abs(squeeze(freqresp(Gy_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
+
+ax2 = subplot(2, 1, 2);
+hold on;
+for i = 1:length(Gy)
+  plot(freqs, 180/pi*angle(squeeze(freqresp(Gy_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Ry = %.0f$ [deg]', Ry_amplitudes(i)*180/pi));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+legend('location', 'southwest');
+
+linkaxes([ax1,ax2],'x');
+
+
+
+% #+NAME: fig:act_damp_variability_dvf_tilt_angle
+% #+CAPTION: Variability of the DVF plant with the Spindle Angle ([[./figs/act_damp_variability_dvf_tilt_angle.png][png]], [[./figs/act_damp_variability_dvf_tilt_angle.pdf][pdf]])
+% [[file:figs/act_damp_variability_dvf_tilt_angle.png]]
+
+
+freqs = logspace(0, 3, 1000);
+
+figure;
+
+ax1 = subplot(2, 1, 1);
+hold on;
+for i = 1:length(Gy)
+  plot(freqs, abs(squeeze(freqresp(Gy_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]);
+
+ax2 = subplot(2, 1, 2);
+hold on;
+for i = 1:length(Gy)
+  plot(freqs, 180/pi*angle(squeeze(freqresp(Gy_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Ry = %.0f$ [deg]', Ry_amplitudes(i)*180/pi));
+end
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
+ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+legend('location', 'southwest');
+
+linkaxes([ax1,ax2],'x');