1243 lines
36 KiB
Matlab
1243 lines
36 KiB
Matlab
%% 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)]);
|