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nass-simscape/matlab/optimal_stiffness.m

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Continue analysis of optimal_stiffness
2020-04-02 21:38:31 +02:00
%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
load('mat/conf_simulink.mat');
open('nass_model.slx')
% Initialization
% We initialize all the stages with the default parameters.
initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
% The worst case scenario is a rotation speed of 60rpm with a payload mass of 10Kg.
initializeSample('mass', 10);
% We don't include gravity nor disturbances in this model as it adds complexity to the simulations and does not alter the obtained dynamics.
initializeSimscapeConfiguration('gravity', true);
initializeDisturbances('enable', false);
initializeLoggingConfiguration('log', 'none');
%% Name of the Simulink File
mdl = 'nass_model';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'], 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, '/Tracking Error'], 1, 'openoutput', [], 'En'); io_i = io_i + 1;
% Identification when not rotating
% We set the range of stiffness that we want to use.
Ks = logspace(3,9,7); % [N/m]
% We don't move any stage and no controller is used.
initializeReferences();
initializeController();
Gk_iff = {zeros(length(Ks))};
Gk_dvf = {zeros(length(Ks))};
Gk_err = {zeros(length(Ks))};
for i = 1:length(Ks)
initializeNanoHexapod('k', Ks(i));
%% Run the linearization
G = linearize(mdl, io);
G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
Gk_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
Gk_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
Jinvt = tf(inv(nano_hexapod.J)');
Jinvt.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
Jinvt.OutputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
Gk_err(i) = {-minreal(G({'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))*Jinvt};
end
% Identification when rotating at maximum speed
% We now set the reference path such that the Spindle is rotating at 60rpm and such that it is at the zero position at the time of the identification.
Rz_rpm = 60;
initializeReferences('Rz_type', 'rotating', ...
'Rz_period', 60/Rz_rpm, ... % Rotation period [s]
'Rz_amplitude', -0.2*(2*pi*Rz_rpm/60)); % Angle offset [rad]
load('mat/nass_references.mat', 'Rz'); % We load the reference for the Spindle
[~, i_end] = min(abs(Rz.signals.values)); % Obtain the indice where the spindle angle is zero
t_sim = Rz.time(i_end); % Simulation time before identification [s]
% We here use a decentralized controller that is used to stabilize the nano-hexapod until the identification is made.
% This controller virtually adds stiffness in each of the nano-hexapod leg.
k_sta = -1e8;
initializeController('type', 'stabilizing');
Gk_wz_iff = {zeros(length(Ks))};
Gk_wz_dvf = {zeros(length(Ks))};
Gk_wz_err = {zeros(length(Ks))};
for i = 1:length(Ks)
initializeNanoHexapod('k', Ks(i));
%% Run the linearization
G = linearize(mdl, io, t_sim);
G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
Gk_wz_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
Gk_wz_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
Jinvt = tf(inv(nano_hexapod.J)');
Jinvt.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
Jinvt.OutputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
Gk_wz_err(i) = {-minreal(G({'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))*Jinvt};
end
save('mat/optimal_stiffness_Gk_wz.mat', 'Ks', ...
'Gk_iff', 'Gk_dvf', 'Gk_err', ...
'Gk_wz_iff', 'Gk_wz_dvf', 'Gk_wz_err');
% Change of dynamics
load('mat/optimal_stiffness_Gk_wz.mat');
% Change of dynamics for decentralized IFF control.
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:length(Gk_iff)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gk_iff{i}( 'Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-');
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gk_wz_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '--');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
title('Soft Nano-Hexapod');
ax2 = subplot(2, 1, 2);
hold on;
for i = 1:length(Gk_iff)
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gk_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gk_wz_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '--', ...
'HandleVisibility', 'off');
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', 'northeast');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% Change of dynamics from $F_x$ to $D_x$.
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:length(Gk_err)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gk_err{i}( 'Ex', 'Fx'), freqs, 'Hz'))), '-');
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gk_wz_err{i}('Ex', 'Fx'), 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(Gk_err)
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gk_err{i}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gk_wz_err{i}('Ex', 'Fx'), freqs, 'Hz'))), '--', ...
'HandleVisibility', 'off');
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', 'northeast');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% Change of dynamics from $F_z$ to $D_z$.
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:length(Gk_err)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gk_err{i}( 'Ez', 'Fz'), freqs, 'Hz'))), '-');
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gk_wz_err{i}('Ez', 'Fz'), freqs, 'Hz'))), '--');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
title('Soft Nano-Hexapod');
ax2 = subplot(2, 1, 2);
hold on;
for i = 1:length(Gk_err)
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gk_err{i}('Ez', 'Fz'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gk_wz_err{i}('Ez', 'Fz'), freqs, 'Hz'))), '--', ...
'HandleVisibility', 'off');
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', 'northeast');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% Change of coupling
load('mat/optimal_stiffness_Gk_wz.mat');
% Change of coupling from $F_x$ to $D_y$ when not rotating and when rotating at 60rpm.
freqs = logspace(-1, 3, 1000);
figure;
hold on;
for i = 1:length(Gk_err)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gk_err{i}( 'Ey', 'Fx'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gk_wz_err{i}('Ey', 'Fx'), freqs, 'Hz'))), '--', ...
'HandleVisibility', 'off');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
xlim([freqs(1), freqs(end)]);
legend('location', 'northeast');
% Comparison of the coupling from $F_x$ to $D_y$ when rotating at 60rpm to the direct term $F_x$ to $D_x$.
freqs = logspace(-1, 3, 1000);
figure;
hold on;
for i = 1:length(Gk_err)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gk_wz_err{i}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gk_wz_err{i}('Ey', 'Fx'), freqs, 'Hz'))), '--', ...
'HandleVisibility', 'off');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
xlim([freqs(1), freqs(end)]);
legend('location', 'northeast');
%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
load('mat/conf_simulink.mat');
open('nass_model.slx')
% Identification of the micro-station compliance
% We initialize all the stages with the default parameters.
initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod('type', 'compliance');
% We put nothing on top of the micro-hexapod.
initializeAxisc('type', 'none');
initializeMirror('type', 'none');
initializeNanoHexapod('type', 'none');
initializeSample('type', 'none');
initializeReferences();
initializeDisturbances();
initializeController();
initializeSimscapeConfiguration();
initializeLoggingConfiguration();
% And we identify the dynamics from forces/torques applied on the micro-hexapod top platform to the motion of the micro-hexapod top platform at the same point.
%% Name of the Simulink File
mdl = 'nass_model';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Micro-Station/Micro Hexapod/Compliance/Fm'], 1, 'openinput'); io_i = io_i + 1; % Direct Forces/Torques applied on the micro-hexapod top platform
io(io_i) = linio([mdl, '/Micro-Station/Micro Hexapod/Compliance/Dm'], 1, 'output'); io_i = io_i + 1; % Absolute displacement of the top platform
%% Run the linearization
Gm = linearize(mdl, io, 0);
Gm.InputName = {'Fmx', 'Fmy', 'Fmz', 'Mmx', 'Mmy', 'Mmz'};
Gm.OutputName = {'Dx', 'Dy', 'Dz', 'Drx', 'Dry', 'Drz'};
labels = {'$D_x/F_{x}$', '$D_y/F_{y}$', '$D_z/F_{z}$', '$R_{x}/M_{x}$', '$R_{y}/M_{y}$', '$R_{R}/M_{z}$'};
freqs = logspace(1, 3, 1000);
figure;
hold on;
plot(freqs, abs(squeeze(freqresp(Gm(1, 1), freqs, 'Hz'))), 'k-', 'DisplayName', labels{1});
for i = 2:6
plot(freqs, abs(squeeze(freqresp(Gm(1, i), freqs, 'Hz'))), 'DisplayName', labels{i});
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]');
ylabel('Compliance');
legend('location', 'northwest');
% Initialization
initializeReferences();
initializeDisturbances();
initializeController();
initializeSimscapeConfiguration();
initializeLoggingConfiguration();
initializeSimscapeConfiguration('gravity', false);
%% Name of the Simulink File
mdl = 'nass_model';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'], 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, '/Tracking Error'], 1, 'openoutput', [], 'En'); io_i = io_i + 1;
Ks = logspace(3,9,7); % [N/m]
initializeSample('type', 'rigid', 'mass', 20);
% Rigid micro-station
initializeGround('type', 'rigid');
initializeGranite('type', 'rigid');
initializeTy('type', 'rigid');
initializeRy('type', 'rigid');
initializeRz('type', 'rigid');
initializeMicroHexapod('type', 'rigid');
initializeAxisc('type', 'rigid');
initializeMirror('type', 'rigid');
Gmr_iff = {zeros(length(Ks))};
Gmr_dvf = {zeros(length(Ks))};
Gmr_err = {zeros(length(Ks))};
for i = 1:length(Ks)
initializeNanoHexapod('k', Ks(i));
G = linearize(mdl, io);
G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
Gmr_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
Gmr_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
Jinvt = tf(inv(nano_hexapod.J)');
Jinvt.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
Jinvt.OutputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
Gmr_err(i) = {-minreal(G({'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))*Jinvt};
end
% Flexible micro-station
initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
Gmf_iff = {zeros(length(Ks))};
Gmf_dvf = {zeros(length(Ks))};
Gmf_err = {zeros(length(Ks))};
for i = 1:length(Ks)
initializeNanoHexapod('k', Ks(i));
G = linearize(mdl, io);
G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
Gmf_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
Gmf_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
Jinvt = tf(inv(nano_hexapod.J)');
Jinvt.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
Jinvt.OutputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
Gmf_err(i) = {-minreal(G({'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))*Jinvt};
end
save('mat/optimal_stiffness_micro_station_compliance.mat', 'Ks', ...
'Gmr_iff', 'Gmr_dvf', 'Gmr_err', ...
'Gmf_iff', 'Gmf_dvf', 'Gmf_err');
% Obtained Dynamics
load('mat/optimal_stiffness_micro_station_compliance.mat');
% IFF plant
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:length(Ks)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gmr_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-');
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gmf_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(Ks)
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gmr_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-');
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gmf_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '--');
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]);
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% DVF plant
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:length(Ks)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gmr_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), '-');
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gmf_dvf{i}('Dnlm1', '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(Ks)
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gmr_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), '-');
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gmf_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), '--');
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]);
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% X direction
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:length(Ks)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gmr_err{i}('Ex', 'Fx'), freqs, 'Hz'))), '-');
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gmf_err{i}('Ex', 'Fx'), 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(Ks)
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gmr_err{i}('Ex', 'Fx'), freqs, 'Hz'))), '-');
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gmf_err{i}('Ex', 'Fx'), freqs, 'Hz'))), '--');
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]);
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% Z direction
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:length(Ks)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gmr_err{i}('Ez', 'Fz'), freqs, 'Hz'))), '-');
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gmf_err{i}('Ez', 'Fz'), 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(Ks)
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gmr_err{i}('Ez', 'Fz'), freqs, 'Hz'))), '-');
set(gca,'ColorOrderIndex',i);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gmf_err{i}('Ez', 'Fz'), freqs, 'Hz'))), '--');
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]);
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
load('mat/conf_simulink.mat');
open('nass_model.slx')
% Initialization
% We initialize all the stages with the default parameters.
initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
% We don't include disturbances in this model as it adds complexity to the simulations and does not alter the obtained dynamics.
initializeSimscapeConfiguration('gravity', true);
initializeDisturbances('enable', false);
% We set the controller type to Open-Loop, and we do not need to log any signal.
initializeController();
initializeLoggingConfiguration('log', 'none');
initializeReferences();
%% Name of the Simulink File
mdl = 'nass_model';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'], 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, '/Tracking Error'], 1, 'openoutput', [], 'En'); io_i = io_i + 1;
% Identification of the dynamics while change the payload dynamics
% - Change of mass: from 1kg to 50kg
% - Change of resonance frequency: from 50Hz to 500Hz
% - The damping ratio of the payload is fixed to $\xi = 0.2$
% We identify the dynamics for the following payload masses =Ms= and nano-hexapod leg's stiffnesses =Ks=:
Ms = [1, 20, 50]; % [Kg]
Ks = logspace(3,9,7); % [N/m]
Gm_iff = {zeros(length(Ks), length(Ms))};
Gm_dvf = {zeros(length(Ks), length(Ms))};
Gm_err = {zeros(length(Ks), length(Ms))};
for i = 1:length(Ks)
for j = 1:length(Ms)
initializeNanoHexapod('k', Ks(i));
initializeSample('mass', Ms(j), 'freq', 100*ones(6,1));
G = linearize(mdl, io);
G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
Gm_iff(i,j) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
Gm_dvf(i,j) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
Jinvt = tf(inv(nano_hexapod.J)');
Jinvt.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
Jinvt.OutputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
Gm_err(i,j) = {-minreal(G({'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))*Jinvt};
end
end
% We then identify the dynamics for the following payload resonance frequencies =Fs=:
Fs = [50, 200, 500]; % [Hz]
Gf_iff = {zeros(length(Ks), length(Fs))};
Gf_dvf = {zeros(length(Ks), length(Fs))};
Gf_err = {zeros(length(Ks), length(Fs))};
for i = 1:length(Ks)
for j = 1:length(Fs)
initializeNanoHexapod('k', Ks(i));
initializeSample('mass', 20, 'freq', Fs(j)*ones(6,1));
G = linearize(mdl, io);
G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
Gf_iff(i,j) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
Gf_dvf(i,j) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
Jinvt = tf(inv(nano_hexapod.J)');
Jinvt.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
Jinvt.OutputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
Gf_err(i,j) = {-minreal(G({'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))*Jinvt};
end
end
save('mat/optimal_stiffness_Gm_Gf.mat', 'Ks', 'Ms', 'Fs', ...
'Gm_iff', 'Gm_dvf', 'Gm_err', ...
'Gf_iff', 'Gf_dvf', 'Gf_err');
% Change of optimal gain for decentralized control
% For each payload, compute the optimal gain for the IFF control.
% The optimal value corresponds to critical damping to *all* the 6 modes of the nano-hexapod.
load('mat/optimal_stiffness_Gm_Gf.mat');
% Change of Mass
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:length(Ks)
for j = 1:length(Ms)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gm_iff{i,j}('Fnlm1', 'Fnl1'), 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(Ks)
for j = 1:length(Ms)
set(gca,'ColorOrderIndex',i);
if j == 1
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_iff{i,j}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$K = %.0e$ [N/m]', Ks(i)));
else
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_iff{i,j}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-', ...
'HandleVisibility', 'off');
end
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', 'northeast');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% Change of payload resonance frequency
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:length(Ks)
for j = 1:length(Fs)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gf_iff{i,j}('Fnlm1', 'Fnl1'), 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(Ks)
for j = 1:length(Fs)
set(gca,'ColorOrderIndex',i);
if j == 1
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_iff{i,j}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$K = %.0e$ [N/m]', Ks(i)));
else
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_iff{i,j}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-', ...
'HandleVisibility', 'off');
end
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', 'northeast');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% Change of dynamics for the primary controller
% For each stiffness, plot the total spread of dynamics.
load('mat/optimal_stiffness_Gm_Gf.mat');
% Frequency variation
% Same payload mass, but different stiffness resulting in different resonance frequency.
% All curves
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:length(Ks)
for j = 1:length(Fs)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), 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(Ks)
for j = 1:length(Fs)
set(gca,'ColorOrderIndex',i);
if j == 1
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$K = %.0e$ [N/m]', Ks(i)));
else
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
'HandleVisibility', 'off');
end
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', 'northeast');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% X direction
i = 1;
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 2, 1);
hold on;
for j = 1:length(Fs)
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
title(sprintf('$k = %.0e$ [N/m]', Ks(i)))
ax2 = subplot(2, 2, 3);
hold on;
for j = 1:length(Fs)
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$\\omega_0 = %.0f$ [Hz]', Fs(j)));
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', 'northeast');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
i = 7;
ax1 = subplot(2, 2, 2);
hold on;
for j = 1:length(Fs)
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
title(sprintf('$k = %.0e$ [N/m]', Ks(i)))
ax2 = subplot(2, 2, 4);
hold on;
for j = 1:length(Fs)
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$\\omega_0 = %.0f$ [Hz]', Fs(j)));
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', 'northeast');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% Z direction:
% We can see two mass lines for the soft nano-hexapod:
% - The first mass line corresponds to $\frac{1}{(m_n + m_p)s^2}$ where $m_p = 20\ [kg]$ is the mass of the payload and $m_n = 15\ [Kg]$ is the mass of the nano-hexapod top platform and attached mirror
% - The second mass line corresponds to $\frac{1}{m_n s^2}$
i = 1;
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 2, 1);
hold on;
for j = 1:length(Fs)
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
title(sprintf('$k = %.0e$ [N/m]', Ks(i)))
ax2 = subplot(2, 2, 3);
hold on;
for j = 1:length(Fs)
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$\\omega_0 = %.0f$ [Hz]', Fs(j)));
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', 'northeast');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
i = 7;
ax1 = subplot(2, 2, 2);
hold on;
for j = 1:length(Fs)
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
title(sprintf('$k = %.0e$ [N/m]', Ks(i)))
ax2 = subplot(2, 2, 4);
hold on;
for j = 1:length(Fs)
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$\\omega_0 = %.0f$ [Hz]', Fs(j)));
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', 'northeast');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% Mass variation
% All mixed, X direction
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:length(Ks)
for j = 1:length(Ms)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), 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(Ks)
for j = 1:length(Ms)
set(gca,'ColorOrderIndex',i);
if j == 1
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$K = %.0e$ [N/m]', Ks(i)));
else
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
'HandleVisibility', 'off');
end
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', 'northeast');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% All mixed, Z direction
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:length(Ks)
for j = 1:length(Ms)
set(gca,'ColorOrderIndex',i);
plot(freqs, abs(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), 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(Ks)
for j = 1:length(Ms)
set(gca,'ColorOrderIndex',i);
if j == 1
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$K = %.0e$ [N/m]', Ks(i)));
else
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-', ...
'HandleVisibility', 'off');
end
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', 'northeast');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% Z direction
freqs = logspace(-1, 3, 1000);
figure;
i = 1;
ax1 = subplot(2, 2, 1);
hold on;
for j = 1:length(Ms)
plot(freqs, abs(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
title(sprintf('$k = %.0e$ [N/m]', Ks(i)))
ax2 = subplot(2, 2, 3);
hold on;
for j = 1:length(Ms)
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-');
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]);
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
i = 7;
ax1 = subplot(2, 2, 2);
hold on;
for j = 1:length(Ms)
plot(freqs, abs(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
title(sprintf('$k = %.0e$ [N/m]', Ks(i)))
ax2 = subplot(2, 2, 4);
hold on;
for j = 1:length(Ms)
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-', ...
'DisplayName', sprintf('$m_p = %.0f$ [kg]', Ms(j)));
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', 'northeast');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% Total variation
% Total change of dynamics due to change of the payload:
% - mass from 1kg to 50kg
% - main resonance from 50Hz to 500Hz
% For a soft nano-hexapod
i = 1;
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for j = 1:length(Fs)
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
end
for j = 1:length(Ms)
plot(freqs, abs(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
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 j = 1:length(Fs)
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
for j = 1:length(Ms)
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
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]);
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
% For a stiff nano-hexapod
i = 7;
freqs = logspace(-1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for j = 1:length(Fs)
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
end
for j = 1:length(Ms)
plot(freqs, abs(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
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 j = 1:length(Fs)
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
for j = 1:length(Ms)
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
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]);
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
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