Analysis on dynamics variability to payload
This commit is contained in:
parent
295ba8bca1
commit
764b1292eb
Binary file not shown.
@ -51,11 +51,14 @@ We wish here to see if we can determine an optimal stiffness of the nano-hexapod
|
||||
- Section [[sec:micro_station_compliance]]: the support compliance dynamics is not much present in the nano-hexapod dynamics
|
||||
- Section [[sec:payload_impedance]]: the change of payload impedance has acceptable effect on the plant dynamics
|
||||
|
||||
The overall goal is to design a nano-hexapod that will allow the highest possible control bandwidth.
|
||||
|
||||
* Spindle Rotation Speed
|
||||
<<sec:spindle_rotation_speed>>
|
||||
|
||||
** Introduction :ignore:
|
||||
|
||||
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
<<matlab-dir>>
|
||||
@ -73,7 +76,318 @@ We wish here to see if we can determine an optimal stiffness of the nano-hexapod
|
||||
open('nass_model.slx')
|
||||
#+end_src
|
||||
|
||||
** Initialization
|
||||
We initialize all the stages with the default parameters.
|
||||
#+begin_src matlab
|
||||
initializeGround();
|
||||
initializeGranite();
|
||||
initializeTy();
|
||||
initializeRy();
|
||||
initializeRz();
|
||||
initializeMicroHexapod();
|
||||
initializeAxisc();
|
||||
initializeMirror();
|
||||
#+end_src
|
||||
|
||||
The worst case scenario is a rotation speed of 60rpm with a payload mass of 1Kg.
|
||||
#+begin_src matlab
|
||||
initializeSample('mass', 10);
|
||||
#+end_src
|
||||
|
||||
We don't include gravity nor disturbances in this model as it adds complexity to the simulations and does not alter the obtained dynamics.
|
||||
#+begin_src matlab
|
||||
initializeSimscapeConfiguration('gravity', false);
|
||||
initializeDisturbances('enable', false);
|
||||
#+end_src
|
||||
|
||||
We set the controller type to Open-Loop, and we do not need to log any signal.
|
||||
#+begin_src matlab
|
||||
initializeController('type', 'stabilizing');
|
||||
initializeLoggingConfiguration('log', 'none');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports 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;
|
||||
#+end_src
|
||||
|
||||
** Identification when not rotating
|
||||
We set the range of stiffness that we want to use.
|
||||
#+begin_src matlab
|
||||
Ks = logspace(3,9,7)
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
initializeReferences();
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Gk_iff = {zeros(length(Ks))};
|
||||
Gk_dvf = {zeros(length(Ks))};
|
||||
Gk_err = {zeros(length(Ks))};
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
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
|
||||
#+end_src
|
||||
|
||||
** Identification when rotating at maximum speed
|
||||
#+begin_src matlab
|
||||
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]
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
k_sta = -1e8;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Gk_wz_iff = {zeros(length(Ks))};
|
||||
Gk_wz_dvf = {zeros(length(Ks))};
|
||||
Gk_wz_err = {zeros(length(Ks))};
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
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
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
save('mat/optimal_stiffness_Gk_wz.mat', 'Ks', ...
|
||||
'Gk_iff', 'Gk_dvf', 'Gk_err', ...
|
||||
'Gk_wz_iff', 'Gk_wz_dvf', 'Gk_wz_err');
|
||||
#+end_src
|
||||
|
||||
** Change of dynamics
|
||||
#+begin_src matlab :exports none
|
||||
load('mat/optimal_stiffness_Gk_wz.mat');
|
||||
#+end_src
|
||||
|
||||
Change of dynamics for decentralized IFF control.
|
||||
#+begin_src matlab :exports none
|
||||
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)]);
|
||||
#+end_src
|
||||
|
||||
Change of dynamics from $F_x$ to $D_x$.
|
||||
#+begin_src matlab :exports none
|
||||
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)]);
|
||||
#+end_src
|
||||
|
||||
Change of dynamics from $F_z$ to $D_z$.
|
||||
#+begin_src matlab :exports none
|
||||
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)]);
|
||||
#+end_src
|
||||
|
||||
** Change of coupling
|
||||
#+begin_src matlab :exports none
|
||||
load('mat/optimal_stiffness_Gk_wz.mat');
|
||||
#+end_src
|
||||
|
||||
Change of coupling from $F_x$ to $D_y$ when not rotating and when rotating at 60rpm.
|
||||
#+begin_src matlab :exports none
|
||||
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');
|
||||
#+end_src
|
||||
|
||||
Comparison of the coupling from $F_x$ to $D_y$ when rotating at 60rpm to the direct term $F_x$ to $D_x$.
|
||||
#+begin_src matlab :exports none
|
||||
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');
|
||||
#+end_src
|
||||
|
||||
** Conclusion :ignore:
|
||||
#+begin_important
|
||||
The leg stiffness should be at higher than $k_i = 10^4\ [N/m]$ such that the main resonance frequency does not shift too much when rotating.
|
||||
For the coupling, it is more difficult to conclude about the minimum required leg stiffness.
|
||||
#+end_important
|
||||
|
||||
#+begin_notes
|
||||
Note that we can use very soft nano-hexapod if we limit the spindle rotating speed.
|
||||
#+end_notes
|
||||
|
||||
* Micro-Station Compliance Effect
|
||||
<<sec:micro_station_compliance>>
|
||||
|
||||
@ -121,5 +435,632 @@ We wish here to see if we can determine an optimal stiffness of the nano-hexapod
|
||||
open('nass_model.slx')
|
||||
#+end_src
|
||||
|
||||
** Initialization
|
||||
We initialize all the stages with the default parameters.
|
||||
#+begin_src matlab
|
||||
initializeGround();
|
||||
initializeGranite();
|
||||
initializeTy();
|
||||
initializeRy();
|
||||
initializeRz();
|
||||
initializeMicroHexapod();
|
||||
initializeAxisc();
|
||||
initializeMirror();
|
||||
#+end_src
|
||||
|
||||
We don't include gravity nor disturbances in this model as it adds complexity to the simulations and does not alter the obtained dynamics.
|
||||
#+begin_src matlab
|
||||
initializeSimscapeConfiguration('gravity', false);
|
||||
initializeDisturbances('enable', false);
|
||||
#+end_src
|
||||
|
||||
We set the controller type to Open-Loop, and we do not need to log any signal.
|
||||
#+begin_src matlab
|
||||
initializeController('type', 'stabilizing');
|
||||
initializeLoggingConfiguration('log', 'none');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports 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;
|
||||
#+end_src
|
||||
|
||||
** Change of 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 $\xi = 0.2$
|
||||
|
||||
#+begin_src matlab
|
||||
initializeReferences();
|
||||
Ks = logspace(3,9,7) % [N/m]
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Ms = [1, 20, 50]; % [Kg]
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Gm_iff = {zeros(length(Ks), length(Ms))};
|
||||
Gm_dvf = {zeros(length(Ks), length(Ms))};
|
||||
Gm_err = {zeros(length(Ks), length(Ms))};
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
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
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Fs = [50, 200, 500]; % [Hz]
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Gf_iff = {zeros(length(Ks), length(Fs))};
|
||||
Gf_dvf = {zeros(length(Ks), length(Fs))};
|
||||
Gf_err = {zeros(length(Ks), length(Fs))};
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
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
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
save('mat/optimal_stiffness_Gm_Gf.mat', 'Ks', 'Ms', 'Fs', ...
|
||||
'Gm_iff', 'Gm_dvf', 'Gm_err', ...
|
||||
'Gf_iff', 'Gf_dvf', 'Gf_err');
|
||||
#+end_src
|
||||
|
||||
** Plots
|
||||
** 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.
|
||||
|
||||
#+begin_src matlab
|
||||
load('mat/optimal_stiffness_Gm_Gf.mat');
|
||||
#+end_src
|
||||
|
||||
Change of Mass
|
||||
#+begin_src matlab :exports none
|
||||
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)]);
|
||||
#+end_src
|
||||
|
||||
Change of payload resonance frequency
|
||||
#+begin_src matlab :exports none
|
||||
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)]);
|
||||
#+end_src
|
||||
|
||||
** Change of dynamics for the primary controller
|
||||
For each stiffness, plot the total spread of dynamics.
|
||||
|
||||
#+begin_src matlab
|
||||
load('mat/optimal_stiffness_Gm_Gf.mat');
|
||||
#+end_src
|
||||
|
||||
*** Frequency variation
|
||||
Same payload mass, but different stiffness resulting in different resonance frequency.
|
||||
|
||||
All curves
|
||||
#+begin_src matlab :exports none
|
||||
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)]);
|
||||
#+end_src
|
||||
|
||||
X direction
|
||||
#+begin_src matlab :exports none
|
||||
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)]);
|
||||
#+end_src
|
||||
|
||||
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 $\frac{1}{m_n s^2}$
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
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)]);
|
||||
#+end_src
|
||||
|
||||
*** Mass variation
|
||||
All mixed, X direction
|
||||
#+begin_src matlab :exports none
|
||||
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)]);
|
||||
#+end_src
|
||||
|
||||
All mixed, Z direction
|
||||
#+begin_src matlab :exports none
|
||||
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)]);
|
||||
#+end_src
|
||||
|
||||
Z direction
|
||||
#+begin_src matlab :exports none
|
||||
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)]);
|
||||
#+end_src
|
||||
|
||||
*** 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
|
||||
#+begin_src matlab :exports none
|
||||
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)]);
|
||||
#+end_src
|
||||
|
||||
For a stiff nano-hexapod
|
||||
#+begin_src matlab :exports none
|
||||
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)]);
|
||||
#+end_src
|
||||
|
||||
|
||||
** Conclusion :ignore:
|
||||
|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
function [] = initializeController(args)
|
||||
|
||||
arguments
|
||||
args.type char {mustBeMember(args.type,{'open-loop', 'iff', 'dvf', 'hac-dvf', 'ref-track-L', 'ref-track-iff-L', 'cascade-hac-lac', 'hac-iff'})} = 'open-loop'
|
||||
args.type char {mustBeMember(args.type,{'open-loop', 'iff', 'dvf', 'hac-dvf', 'ref-track-L', 'ref-track-iff-L', 'cascade-hac-lac', 'hac-iff', 'stabilizing'})} = 'open-loop'
|
||||
end
|
||||
|
||||
controller = struct();
|
||||
@ -23,6 +23,8 @@ switch args.type
|
||||
controller.type = 7;
|
||||
case 'hac-iff'
|
||||
controller.type = 8;
|
||||
case 'stabilizing'
|
||||
controller.type = 9;
|
||||
end
|
||||
|
||||
save('./mat/controller.mat', 'controller');
|
||||
|
||||
Loading…
Reference in New Issue
Block a user