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Use new argument function validation technique

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Thomas Dehaeze 2020-01-13 11:42:31 +01:00
parent 994fe2ccc7
commit a2917a50e9
20 changed files with 770 additions and 660 deletions
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active_damping/index.org
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@ -97,7 +97,7 @@ The performance of this undamped system will be compared with the damped system
#+end_src
#+begin_src matlab
open('active_damping/matlab/sim_nano_station_id.slx')
open('active_damping/matlab/sim_nass_active_damping.slx')
#+end_src
** Init
@ -114,8 +114,8 @@ The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 1);
#+end_src
All the controllers are set to 0.
@ -124,16 +124,321 @@ All the controllers are set to 0.
save('./mat/controllers.mat', 'K', '-append');
K_iff = tf(zeros(6));
save('./mat/controllers.mat', 'K_iff', '-append');
K_rmc = tf(zeros(6));
save('./mat/controllers.mat', 'K_rmc', '-append');
K_dvf = tf(zeros(6));
save('./mat/controllers.mat', 'K_dvf', '-append');
#+end_src
** Identification
We identify the various transfer functions of the system
** Identification of the transfer function from disturbance to position error
#+begin_src matlab
G = identifyPlant();
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'sim_nass_active_damping';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Dwx'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Dwy'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Dwz'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/Compute Error in NASS base'], 2, 'openoutput'); io_i = io_i + 1;
%% Run the linearization
G = linearize(mdl, io, options);
G.InputName = {'Dwx', 'Dwy', 'Dwz'};
G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
#+end_src
#+begin_src matlab :exports none
freqs = logspace(0, 3, 1000);
figure;
hold on;
plot(freqs, abs(squeeze(freqresp(G('Edx', 'Dwx'), freqs, 'Hz'))), 'DisplayName', 'x');
plot(freqs, abs(squeeze(freqresp(G('Edy', 'Dwz'), freqs, 'Hz'))), 'DisplayName', 'y');
plot(freqs, abs(squeeze(freqresp(G('Edz', 'Dwz'), freqs, 'Hz'))), 'DisplayName', 'z');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
legend('location', 'southeast')
#+end_src
** Identification of the plant
#+begin_src matlab
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'sim_nass_active_damping';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Fnl'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/Compute Error in NASS base'], 2, 'openoutput'); io_i = io_i + 1;
%% Run the linearization
G = linearize(mdl, io, options);
G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
#+end_src
#+begin_src matlab
load('mat/stages.mat', 'nano_hexapod');
G_cart = G*inv(nano_hexapod.J');
G_cart.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'};
#+end_src
#+begin_src matlab :exports none
freqs = logspace(0, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(freqs, abs(squeeze(freqresp(G_cart('Edx', 'Fnx'), freqs, 'Hz'))), 'DisplayName', '$T_{x}$');
plot(freqs, abs(squeeze(freqresp(G_cart('Edy', 'Fny'), freqs, 'Hz'))), 'DisplayName', '$T_{y}$');
plot(freqs, abs(squeeze(freqresp(G_cart('Edz', 'Fnz'), freqs, 'Hz'))), 'DisplayName', '$T_{z}$');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
legend('location', 'southwest')
ax2 = subplot(2, 1, 2);
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart('Edx', 'Fnx'), freqs, 'Hz'))));
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart('Edy', 'Fny'), freqs, 'Hz'))));
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart('Edz', 'Fnz'), freqs, 'Hz'))));
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');
#+end_src
#+begin_src matlab :exports none
freqs = logspace(0, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(freqs, abs(squeeze(freqresp(G_cart('Erx', 'Mnx'), freqs, 'Hz'))), 'DisplayName', '$R_{x}$');
plot(freqs, abs(squeeze(freqresp(G_cart('Ery', 'Mny'), freqs, 'Hz'))), 'DisplayName', '$R_{y}$');
plot(freqs, abs(squeeze(freqresp(G_cart('Erz', 'Mnz'), freqs, 'Hz'))), 'DisplayName', '$R_{z}$');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
legend('location', 'southwest')
ax2 = subplot(2, 1, 2);
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart('Erx', 'Mnx'), freqs, 'Hz'))));
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart('Ery', 'Mny'), freqs, 'Hz'))));
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart('Erz', 'Mnz'), freqs, 'Hz'))));
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');
#+end_src
** test
#+begin_src matlab
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'sim_nass_active_damping';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Micro-Station/Dy'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/Compute Error in NASS base'], 2, 'openoutput'); io_i = io_i + 1;
%% Run the linearization
G = linearize(mdl, io, options);
G.InputName = {'Dy'};
G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
#+end_src
#+begin_src matlab :exports none
freqs = logspace(0, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(freqs, abs(squeeze(freqresp(G('Edy', 'Dy(1)'), freqs, 'Hz'))), 'DisplayName', '$T_{x}$');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
legend('location', 'southwest')
ax2 = subplot(2, 1, 2);
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(G('Edy', 'Dy(1)'), freqs, 'Hz'))));
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');
#+end_src
#+begin_src matlab :exports none
freqs = logspace(0, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(freqs, abs(squeeze(freqresp(G_cart('Erx', 'Mnx'), freqs, 'Hz'))), 'DisplayName', '$R_{x}$');
plot(freqs, abs(squeeze(freqresp(G_cart('Ery', 'Mny'), freqs, 'Hz'))), 'DisplayName', '$R_{y}$');
plot(freqs, abs(squeeze(freqresp(G_cart('Erz', 'Mnz'), freqs, 'Hz'))), 'DisplayName', '$R_{z}$');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
legend('location', 'southwest')
ax2 = subplot(2, 1, 2);
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart('Erx', 'Mnx'), freqs, 'Hz'))));
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart('Ery', 'Mny'), freqs, 'Hz'))));
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart('Erz', 'Mnz'), freqs, 'Hz'))));
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');
#+end_src
** test on hexapod
#+begin_src matlab
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'test_nano_hexapod';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Fnl'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/x'], 1, 'openoutput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/y'], 1, 'openoutput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
%% Run the linearization
G = linearize(mdl, io, options);
G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
G.OutputName = {'x', 'y', 'z'};
#+end_src
#+begin_src matlab
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'test_nano_hexapod';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Fx'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/x'], 1, 'openoutput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/y'], 1, 'openoutput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
%% Run the linearization
G = linearize(mdl, io, options);
G.InputName = {'Fx'};
G.OutputName = {'x', 'y', 'z'};
#+end_src
#+begin_src matlab :exports none
freqs = logspace(0, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(freqs, abs(squeeze(freqresp(G('Edy', 'Dy(1)'), freqs, 'Hz'))), 'DisplayName', '$T_{x}$');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
legend('location', 'southwest')
ax2 = subplot(2, 1, 2);
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(G('Edy', 'Dy(1)'), freqs, 'Hz'))));
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');
#+end_src
#+begin_src matlab :exports none
freqs = logspace(0, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(freqs, abs(squeeze(freqresp(G_cart('Erx', 'Mnx'), freqs, 'Hz'))), 'DisplayName', '$R_{x}$');
plot(freqs, abs(squeeze(freqresp(G_cart('Ery', 'Mny'), freqs, 'Hz'))), 'DisplayName', '$R_{y}$');
plot(freqs, abs(squeeze(freqresp(G_cart('Erz', 'Mnz'), freqs, 'Hz'))), 'DisplayName', '$R_{z}$');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
legend('location', 'southwest')
ax2 = subplot(2, 1, 2);
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart('Erx', 'Mnx'), freqs, 'Hz'))));
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart('Ery', 'Mny'), freqs, 'Hz'))));
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart('Erz', 'Mnz'), freqs, 'Hz'))));
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');
#+end_src
** Identification of the dynamics for Active Damping
#+begin_src matlab
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'sim_nass_active_damping';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Fnl'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1;
%% Run the linearization
G = linearize(mdl, io, options);
G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'};
#+end_src
And we save it for further analysis.
@ -141,6 +446,63 @@ And we save it for further analysis.
save('./active_damping/mat/plants.mat', 'G', '-append');
#+end_src
** Plant for Active Damping
#+begin_src matlab :exports none
freqs = logspace(0, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:6
plot(freqs, abs(squeeze(freqresp(G(['Fnlm', num2str(i)], ['Fnl', num2str(i)]), 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 = 1:6
plot(freqs, 180/pi*angle(squeeze(freqresp(G(['Fnlm', num2str(i)], ['Fnl', num2str(i)]), 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');
#+end_src
#+begin_src matlab :exports none
freqs = logspace(0, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:6
plot(freqs, abs(squeeze(freqresp(G(['Dnlm', num2str(i)], ['Fnl', num2str(i)]), 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 = 1:6
plot(freqs, 180/pi*angle(squeeze(freqresp(G(['Dnlm', num2str(i)], ['Fnl', num2str(i)]), 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');
#+end_src
** Sensitivity to disturbances
The sensitivity to disturbances are shown on figure [[fig:sensitivity_dist_undamped]].
@ -242,6 +604,7 @@ The "plant" (transfer function from forces applied by the nano-hexapod to the me
#+CAPTION: Transfer Function from cartesian forces to displacement for the undamped plant ([[./figs/plant_undamped.png][png]], [[./figs/plant_undamped.pdf][pdf]])
[[file:figs/plant_undamped.png]]
** Tomography Experiment
* Integral Force Feedback
:PROPERTIES:
:header-args:matlab+: :tangle matlab/iff.m
@ -269,185 +632,6 @@ Integral Force Feedback is applied.
In section [[sec:iff_1dof]], IFF is applied on a uni-axial system to understand its behavior.
Then, it is applied on the simscape model.
** One degree-of-freedom example
:PROPERTIES:
:header-args:matlab+: :tangle no
:END:
<<sec:iff_1dof>>
*** Equations
#+begin_src latex :file iff_1dof.pdf :post pdf2svg(file=*this*, ext="png") :exports results
\begin{tikzpicture}
% Ground
\draw (-1, 0) -- (1, 0);
% Ground Displacement
\draw[dashed] (-1, 0) -- ++(-0.5, 0) coordinate(w);
\draw[->] (w) -- ++(0, 0.5) node[left]{$w$};
% Mass
\draw[fill=white] (-1, 1.4) rectangle ++(2, 0.8) node[pos=0.5]{$m$};
\node[forcesensor={0.4}{0.4}] (fsensn) at (0, 1){};
\draw[] (-0.8, 1) -- (0.8, 1);
\node[left] at (fsensn.west) {$F_m$};
% Displacement of the mass
\draw[dashed] (-1, 2.2) -- ++(-0.5, 0) coordinate(x);
\draw[->] (x) -- ++(0, 0.5) node[left]{$x$};
% Spring, Damper, and Actuator
\draw[spring] (-0.8, 0) -- (-0.8, 1) node[midway, left=0.1]{$k$};
\draw[damper] (0, 0) -- (0, 1) node[midway, left=0.2]{$c$};
\draw[actuator={0.4}{0.2}] (0.8, 0) -- (0.8, 1) coordinate[midway, right=0.1](F);
% Displacements
\node[block={0.8cm}{0.6cm}, right=0.6 of F] (Kiff) {$K$};
\draw[->] (Kiff.west) -- (F) node[above right]{$F$};
\draw[<-] (Kiff.east) -- ++(0.5, 0) |- (fsensn.east);
\end{tikzpicture}
#+end_src
#+name: fig:iff_1dof
#+caption: Integral Force Feedback applied to a 1dof system
#+RESULTS:
[[file:figs/iff_1dof.png]]
The dynamic of the system is described by the following equation:
\begin{equation}
ms^2x = F_d - kx - csx + kw + csw + F
\end{equation}
The measured force $F_m$ is:
\begin{align}
F_m &= F - kx - csx + kw + csw \\
&= ms^2 x - F_d
\end{align}
The Integral Force Feedback controller is $K = -\frac{g}{s}$, and thus the applied force by this controller is:
\begin{equation}
F_{\text{IFF}} = -\frac{g}{s} F_m = -\frac{g}{s} (ms^2 x - F_d)
\end{equation}
Once the IFF is applied, the new dynamics of the system is:
\begin{equation}
ms^2x = F_d + F - kx - csx + kw + csw - \frac{g}{s} (ms^2x - F_d)
\end{equation}
And finally:
\begin{equation}
x = F_d \frac{1 + \frac{g}{s}}{ms^2 + (mg + c)s + k} + F \frac{1}{ms^2 + (mg + c)s + k} + w \frac{k + cs}{ms^2 + (mg + c)s + k}
\end{equation}
We can see that this:
- adds damping to the system by a value $mg$
- lower the compliance as low frequency by a factor: $1 + g/s$
If we want critical damping:
\begin{equation}
\xi = \frac{1}{2} \frac{c + gm}{\sqrt{km}} = \frac{1}{2}
\end{equation}
This is attainable if we have:
\begin{equation}
g = \frac{\sqrt{km} - c}{m}
\end{equation}
*** 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>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
*** Matlab Example
Let define the system parameters.
#+begin_src matlab
m = 50; % [kg]
k = 1e6; % [N/m]
c = 1e3; % [N/(m/s)]
#+end_src
The state space model of the system is defined below.
#+begin_src matlab
A = [-c/m -k/m;
1 0];
B = [1/m 1/m -1;
0 0 0];
C = [ 0 1;
-c -k];
D = [0 0 0;
1 0 0];
sys = ss(A, B, C, D);
sys.InputName = {'F', 'Fd', 'wddot'};
sys.OutputName = {'d', 'Fm'};
sys.StateName = {'ddot', 'd'};
#+end_src
The controller $K_\text{IFF}$ is:
#+begin_src matlab
Kiff = -((sqrt(k*m)-c)/m)/s;
Kiff.InputName = {'Fm'};
Kiff.OutputName = {'F'};
#+end_src
And the closed loop system is computed below.
#+begin_src matlab
sys_iff = feedback(sys, Kiff, 'name', +1);
#+end_src
#+begin_src matlab :exports none
freqs = logspace(0, 3, 1000);
figure;
subplot(2, 2, 1);
title('Fd to d')
hold on;
plot(freqs, abs(squeeze(freqresp(sys('d', 'Fd'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(sys_iff('d', 'Fd'), freqs, 'Hz'))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
xlim([freqs(1), freqs(end)]);
subplot(2, 2, 3);
title('Fd to x')
hold on;
plot(freqs, abs(squeeze(freqresp(sys('d', 'Fd'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(sys_iff('d', 'Fd'), freqs, 'Hz'))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
xlim([freqs(1), freqs(end)]);
subplot(2, 2, 2);
title('w to d')
hold on;
plot(freqs, abs(squeeze(freqresp(sys('d', 'wddot')*s^2, freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(sys_iff('d', 'wddot')*s^2, freqs, 'Hz'))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
xlim([freqs(1), freqs(end)]);
subplot(2, 2, 4);
title('w to x')
hold on;
plot(freqs, abs(squeeze(freqresp(1+sys('d', 'wddot')*s^2, freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(1+sys_iff('d', 'wddot')*s^2, freqs, 'Hz'))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
xlim([freqs(1), freqs(end)]);
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/iff_1dof_sensitivitiy.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:iff_1dof_sensitivitiy
#+CAPTION: Sensitivity to disturbance when IFF is applied on the 1dof system ([[./figs/iff_1dof_sensitivitiy.png][png]], [[./figs/iff_1dof_sensitivitiy.pdf][pdf]])
[[file:figs/iff_1dof_sensitivitiy.png]]
** 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>>
@ -566,8 +750,8 @@ Let's initialize the system prior to identification.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
All the controllers are set to 0.
@ -1106,8 +1290,8 @@ Let's initialize the system prior to identification.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
And initialize the controllers.
@ -1617,8 +1801,8 @@ Let's initialize the system prior to identification.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
And initialize the controllers.

42
active_damping_uniaxial/index.org
View File

@ -1,4 +1,4 @@
#+TITLE: Active Damping
#+TITLE: Active Damping with an uni-axial model
:DRAWER:
#+STARTUP: overview
@ -97,7 +97,7 @@ The performance of this undamped system will be compared with the damped system
#+end_src
#+begin_src matlab
open('active_damping/matlab/sim_nano_station_id.slx')
open('active_damping_uniaxial/matlab/sim_nano_station_id.slx')
#+end_src
** Init
@ -114,8 +114,8 @@ The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
All the controllers are set to 0.
@ -138,7 +138,7 @@ We identify the various transfer functions of the system
And we save it for further analysis.
#+begin_src matlab
save('./active_damping/mat/plants.mat', 'G', '-append');
save('./active_damping_uniaxial/mat/plants.mat', 'G', '-append');
#+end_src
** Sensitivity to disturbances
@ -462,13 +462,13 @@ And the closed loop system is computed below.
#+end_src
#+begin_src matlab
open('active_damping/matlab/sim_nano_station_id.slx')
open('active_damping_uniaxial/matlab/sim_nano_station_id.slx')
#+end_src
** Control Design
Let's load the undamped plant:
#+begin_src matlab
load('./active_damping/mat/plants.mat', 'G');
load('./active_damping_uniaxial/mat/plants.mat', 'G');
#+end_src
Let's look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor (figure [[fig:iff_plant]]).
@ -566,8 +566,8 @@ Let's initialize the system prior to identification.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
All the controllers are set to 0.
@ -589,7 +589,7 @@ We identify the system dynamics now that the IFF controller is ON.
And we save the damped plant for further analysis
#+begin_src matlab
save('./active_damping/mat/plants.mat', 'G_iff', '-append');
save('./active_damping_uniaxial/mat/plants.mat', 'G_iff', '-append');
#+end_src
** Sensitivity to disturbances
@ -1001,13 +1001,13 @@ And the closed loop system is computed below.
#+end_src
#+begin_src matlab
open('active_damping/matlab/sim_nano_station_id.slx')
open('active_damping_uniaxial/matlab/sim_nano_station_id.slx')
#+end_src
** Control Design
Let's load the undamped plant:
#+begin_src matlab
load('./active_damping/mat/plants.mat', 'G');
load('./active_damping_uniaxial/mat/plants.mat', 'G');
#+end_src
Let's look at the transfer function from actuator forces in the nano-hexapod to the measured displacement of the actuator for all 6 pairs of actuator/sensor (figure [[fig:rmc_plant]]).
@ -1106,8 +1106,8 @@ Let's initialize the system prior to identification.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
And initialize the controllers.
@ -1129,7 +1129,7 @@ We identify the system dynamics now that the RMC controller is ON.
And we save the damped plant for further analysis.
#+begin_src matlab
save('./active_damping/mat/plants.mat', 'G_rmc', '-append');
save('./active_damping_uniaxial/mat/plants.mat', 'G_rmc', '-append');
#+end_src
** Sensitivity to disturbances
@ -1514,13 +1514,13 @@ The obtained sensitivity to disturbances is shown in figure [[fig:dvf_1dof_sensi
#+end_src
#+begin_src matlab
open('active_damping/matlab/sim_nano_station_id.slx')
open('active_damping_uniaxial/matlab/sim_nano_station_id.slx')
#+end_src
** Control Design
Let's load the undamped plant:
#+begin_src matlab
load('./active_damping/mat/plants.mat', 'G');
load('./active_damping_uniaxial/mat/plants.mat', 'G');
#+end_src
Let's look at the transfer function from actuator forces in the nano-hexapod to the measured velocity of the nano-hexapod platform in the direction of the corresponding actuator for all 6 pairs of actuator/sensor (figure [[fig:dvf_plant]]).
@ -1617,8 +1617,8 @@ Let's initialize the system prior to identification.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
And initialize the controllers.
@ -1640,7 +1640,7 @@ We identify the system dynamics now that the RMC controller is ON.
And we save the damped plant for further analysis.
#+begin_src matlab
save('./active_damping/mat/plants.mat', 'G_dvf', '-append');
save('./active_damping_uniaxial/mat/plants.mat', 'G_dvf', '-append');
#+end_src
** Sensitivity to disturbances
@ -1812,7 +1812,7 @@ Direct Velocity Feedback:
** Load the plants
#+begin_src matlab
load('./active_damping/mat/plants.mat', 'G', 'G_iff', 'G_rmc', 'G_dvf');
load('./active_damping_uniaxial/mat/plants.mat', 'G', 'G_iff', 'G_rmc', 'G_dvf');
#+end_src
** Sensitivity to Disturbance

4
disturbances/index.org
View File

@ -217,8 +217,8 @@ We initialize all the stages.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
* Identification

28
experiment_tomography/index.org
View File

@ -93,14 +93,14 @@ We first initialize all the stages.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 1));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 1);
#+end_src
We initialize the reference path for all the stages.
All stage is set to its zero position except the Spindle which is rotating at 60rpm.
#+begin_src matlab
initializeReferences(struct('Rz_type', 'rotating', 'Rz_period', 1));
initializeReferences('Rz_type', 'rotating', 'Rz_period', 1);
#+end_src
* Tomography Experiment with no disturbances
@ -110,7 +110,7 @@ All stage is set to its zero position except the Spindle which is rotating at 60
** Simulation Setup
And we initialize the disturbances to be equal to zero.
#+begin_src matlab
opts = struct(...
initDisturbances(...
'Dwx', false, ... % Ground Motion - X direction
'Dwy', false, ... % Ground Motion - Y direction
'Dwz', false, ... % Ground Motion - Z direction
@ -118,7 +118,6 @@ And we initialize the disturbances to be equal to zero.
'Fty_z', false, ... % Translation Stage - Z direction
'Frz_z', false ... % Spindle - Z direction
);
initDisturbances(opts);
#+end_src
We simulate the model.
@ -221,7 +220,7 @@ And we save the obtained data.
** Simulation Setup
We now activate the disturbances.
#+begin_src matlab
opts = struct(...
initDisturbances(...
'Dwx', true, ... % Ground Motion - X direction
'Dwy', true, ... % Ground Motion - Y direction
'Dwz', true, ... % Ground Motion - Z direction
@ -229,7 +228,6 @@ We now activate the disturbances.
'Fty_z', true, ... % Translation Stage - Z direction
'Frz_z', true ... % Spindle - Z direction
);
initDisturbances(opts);
#+end_src
We simulate the model.
@ -336,17 +334,17 @@ We first set the wanted translation of the Micro Hexapod.
We initialize the reference path.
#+begin_src matlab
initializeReferences(struct('Dh_pos', [P_micro_hexapod; 0; 0; 0], 'Rz_type', 'rotating', 'Rz_period', 1));
initializeReferences('Dh_pos', [P_micro_hexapod; 0; 0; 0], 'Rz_type', 'rotating', 'Rz_period', 1);
#+end_src
We initialize the stages.
#+begin_src matlab
initializeMicroHexapod(struct('AP', P_micro_hexapod));
initializeMicroHexapod('AP', P_micro_hexapod);
#+end_src
And we initialize the disturbances to zero.
#+begin_src matlab
opts = struct(...
initDisturbances(...
'Dwx', false, ... % Ground Motion - X direction
'Dwy', false, ... % Ground Motion - Y direction
'Dwz', false, ... % Ground Motion - Z direction
@ -354,7 +352,6 @@ And we initialize the disturbances to zero.
'Fty_z', false, ... % Translation Stage - Z direction
'Frz_z', false ... % Spindle - Z direction
);
initDisturbances(opts);
#+end_src
We simulate the model.
@ -456,7 +453,7 @@ And we save the obtained data.
** Simulation Setup
We set the reference path.
#+begin_src matlab
initializeReferences(struct('Dy_type', 'triangular', 'Dy_amplitude', 10e-3, 'Dy_period', 1));
initializeReferences('Dy_type', 'triangular', 'Dy_amplitude', 10e-3, 'Dy_period', 1);
#+end_src
We initialize the stages.
@ -469,13 +466,13 @@ We initialize the stages.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 1));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 1);
#+end_src
And we initialize the disturbances to zero.
#+begin_src matlab
opts = struct(...
initDisturbances(...
'Dwx', false, ... % Ground Motion - X direction
'Dwy', false, ... % Ground Motion - Y direction
'Dwz', false, ... % Ground Motion - Z direction
@ -483,7 +480,6 @@ And we initialize the disturbances to zero.
'Fty_z', false, ... % Translation Stage - Z direction
'Frz_z', false ... % Spindle - Z direction
);
initDisturbances(opts);
#+end_src
We simulate the model.

12
identification/index.org
View File

@ -88,8 +88,8 @@ We initialize all the stages.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
** Compute the transfer functions
@ -173,8 +173,8 @@ We initialize all the stages.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
** Identification
@ -297,8 +297,8 @@ We initialize all the stages.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
** Estimate the position of the CoM of each solid and compare with the one took for the Measurement Analysis

3
kinematics/index.org
View File

@ -177,7 +177,7 @@ We define the wanted position/orientation of the Hexapod under study.
ARB = Rz*Ry*Rx;
AP = [0.01; 0.02; 0.03]; % [m]
hexapod = initializeMicroHexapod(struct('AP', AP, 'ARB', ARB));
hexapod = initializeMicroHexapod('AP', AP, 'ARB', ARB);
#+end_src
We run the simulation.
@ -203,6 +203,7 @@ And we verify that we indeed succeed to go to the wanted position.
| -1.2659e-10 | 6.5603e-11 | 6.2183e-10 |
| 1.0354e-10 | -5.2439e-11 | -5.2425e-10 |
| -5.9816e-10 | 5.532e-10 | -1.7737e-10 |
* TODO Tests on the transformation from reference to wanted position :noexport:
:PROPERTIES:
:header-args:matlab+: :eval no

34
positioning_error/index.org
View File

@ -102,13 +102,13 @@ We initialize all the stages.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
We setup the reference path to be constant.
#+begin_src matlab
opts = struct( ...
initializeReferences(...
'Ts', 1e-3, ... % Sampling Frequency [s]
'Dy_type', 'constant', ... % Either "constant" / "triangular" / "sinusoidal"
'Dy_amplitude', 5e-3, ... % Amplitude of the displacement [m]
@ -126,9 +126,6 @@ We setup the reference path to be constant.
'Dn_type', 'constant', ... % For now, only constant is implemented
'Dn_pos', [1e-3; 2e-3; 3e-3; 1*pi/180; 0; 1*pi/180] ... % Initial position [m,m,m,rad,rad,rad] of the top platform
);
initializeReferences(opts);
#+end_src
No position error for now (perfect positioning).
@ -253,13 +250,13 @@ We initialize all the stages.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
We setup the reference path to be constant.
#+begin_src matlab
opts = struct( ...
initializeReferences(...
'Ts', 1e-3, ... % Sampling Frequency [s]
'Dy_type', 'constant', ... % Either "constant" / "triangular" / "sinusoidal"
'Dy_amplitude', 0, ... % Amplitude of the displacement [m]
@ -274,8 +271,6 @@ We setup the reference path to be constant.
'Dn_type', 'constant', ... % For now, only constant is implemented
'Dn_pos', [0; 0; 0; 0; 0; 0] ... % Initial position [m,m,m,rad,rad,rad] of the top platform
);
initializeReferences(opts);
#+end_src
Now we introduce some positioning error.
@ -383,8 +378,21 @@ Verify that the pose error corresponds to the positioning error of the stages.
** Verify that be imposing the error motion on the nano-hexapod, we indeed have zero error at the end
We now keep the wanted pose but we impose a displacement of the nano hexapod corresponding to the measured position error.
#+begin_src matlab
opts.Dn_pos = [Edx, Edy, Edz, Erx, Ery, Erz]';
initializeReferences(opts);
initializeReferences(...
'Ts', 1e-3, ... % Sampling Frequency [s]
'Dy_type', 'constant', ... % Either "constant" / "triangular" / "sinusoidal"
'Dy_amplitude', 0, ... % Amplitude of the displacement [m]
'Ry_type', 'constant', ... % Either "constant" / "triangular" / "sinusoidal"
'Ry_amplitude', 0, ... % Amplitude [rad]
'Rz_type', 'constant', ... % Either "constant" / "rotating"
'Rz_amplitude', 0*pi/180, ... % Initial angle [rad]
'Dh_type', 'constant', ... % For now, only constant is implemented
'Dh_pos', [0; 0; 0; 0; 0; 0], ... % Initial position [m,m,m,rad,rad,rad] of the top platform
'Rm_type', 'constant', ... % For now, only constant is implemented
'Rm_pos', [0, pi]', ... % Initial position of the two masses
'Dn_type', 'constant', ... % For now, only constant is implemented
'Dn_pos', [Edx, Edy, Edz, Erx, Ery, Erz]' ... % Initial position [m,m,m,rad,rad,rad] of the top platform
);
#+end_src
And we run the simulation.

361
simscape_subsystems/index.org
View File

@ -53,60 +53,81 @@
This Matlab function is accessible [[file:../src/initializeInputs.m][here]].
*** Function Declaration and Documentation
#+begin_src matlab
function [ref] = initializeReferences(opts_param)
%% Default values for opts
opts = struct( ...
'Ts', 1e-3, ... % Sampling Frequency [s]
'Tmax', 100, ... % Maximum simulation time [s]
'Dy_type', 'constant', ... % Either "constant" / "triangular" / "sinusoidal"
'Dy_amplitude', 0, ... % Amplitude of the displacement [m]
'Dy_period', 1, ... % Period of the displacement [s]
'Ry_type', 'constant', ... % Either "constant" / "triangular" / "sinusoidal"
'Ry_amplitude', 0, ... % Amplitude [rad]
'Ry_period', 1, ... % Period of the displacement [s]
'Rz_type', 'constant', ... % Either "constant" / "rotating"
'Rz_amplitude', 0, ... % Initial angle [rad]
'Rz_period', 1, ... % Period of the rotating [s]
'Dh_type', 'constant', ... % For now, only constant is implemented
'Dh_pos', zeros(6, 1), ... % Initial position [m,m,m,rad,rad,rad] of the top platform (Pitch-Roll-Yaw Euler angles)
'Rm_type', 'constant', ... % For now, only constant is implemented
'Rm_pos', [0; pi], ... % Initial position of the two masses
'Dn_type', 'constant', ... % For now, only constant is implemented
'Dn_pos', zeros(6,1) ... % Initial position [m,m,m,rad,rad,rad] of the top platform
);
function [ref] = initializeReferences(args)
#+end_src
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
*** Optional Parameters
#+begin_src matlab
arguments
% Sampling Frequency [s]
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3
% Maximum simulation time [s]
args.Tmax (1,1) double {mustBeNumeric, mustBePositive} = 100
% Either "constant" / "triangular" / "sinusoidal"
args.Dy_type char {mustBeMember(args.Dy_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
% Amplitude of the displacement [m]
args.Dy_amplitude (1,1) double {mustBeNumeric} = 0
% Period of the displacement [s]
args.Dy_period (1,1) double {mustBeNumeric, mustBePositive} = 1
% Either "constant" / "triangular" / "sinusoidal"
args.Ry_type char {mustBeMember(args.Ry_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
% Amplitude [rad]
args.Ry_amplitude (1,1) double {mustBeNumeric} = 0
% Period of the displacement [s]
args.Ry_period (1,1) double {mustBeNumeric, mustBePositive} = 1
% Either "constant" / "rotating"
args.Rz_type char {mustBeMember(args.Rz_type,{'constant', 'rotating'})} = 'constant'
% Initial angle [rad]
args.Rz_amplitude (1,1) double {mustBeNumeric} = 0
% Period of the rotating [s]
args.Rz_period (1,1) double {mustBeNumeric, mustBePositive} = 1
% For now, only constant is implemented
args.Dh_type char {mustBeMember(args.Dh_type,{'constant'})} = 'constant'
% Initial position [m,m,m,rad,rad,rad] of the top platform (Pitch-Roll-Yaw Euler angles)
args.Dh_pos (6,1) double {mustBeNumeric} = zeros(6, 1), ...
% For now, only constant is implemented
args.Rm_type char {mustBeMember(args.Rm_type,{'constant'})} = 'constant'
% Initial position of the two masses
args.Rm_pos (2,1) double {mustBeNumeric} = [0; pi]
% For now, only constant is implemented
args.Dn_type char {mustBeMember(args.Dn_type,{'constant'})} = 'constant'
% Initial position [m,m,m,rad,rad,rad] of the top platform
args.Dn_pos (6,1) double {mustBeNumeric} = zeros(6,1)
end
#+end_src
*** Initialize Parameters
#+begin_src matlab
%% Set Sampling Time
Ts = opts.Ts;
Tmax = opts.Tmax;
Ts = args.Ts;
Tmax = args.Tmax;
%% Low Pass Filter to filter out the references
s = zpk('s');
w0 = 2*pi*100;
xi = 1;
H_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2);
#+end_src
*** Translation Stage
#+begin_src matlab
%% Translation stage - Dy
t = 0:Ts:Tmax; % Time Vector [s]
Dy = zeros(length(t), 1);
Dyd = zeros(length(t), 1);
Dydd = zeros(length(t), 1);
switch opts.Dy_type
switch args.Dy_type
case 'constant'
Dy(:) = opts.Dy_amplitude;
Dy(:) = args.Dy_amplitude;
Dyd(:) = 0;
Dydd(:) = 0;
case 'triangular'
% This is done to unsure that we start with no displacement
Dy_raw = opts.Dy_amplitude*sawtooth(2*pi*t/opts.Dy_period,1/2);
i0 = find(t>=opts.Dy_period/4,1);
Dy_raw = args.Dy_amplitude*sawtooth(2*pi*t/args.Dy_period,1/2);
i0 = find(t>=args.Dy_period/4,1);
Dy(1:end-i0+1) = Dy_raw(i0:end);
Dy(end-i0+2:end) = Dy_raw(end); % we fix the last value
@ -115,29 +136,32 @@ This Matlab function is accessible [[file:../src/initializeInputs.m][here]].
Dyd = lsim(H_lpf*s, Dy, t);
Dydd = lsim(H_lpf*s^2, Dy, t);
case 'sinusoidal'
Dy(:) = opts.Dy_amplitude*sin(2*pi/opts.Dy_period*t);
Dyd = opts.Dy_amplitude*2*pi/opts.Dy_period*cos(2*pi/opts.Dy_period*t);
Dydd = -opts.Dy_amplitude*(2*pi/opts.Dy_period)^2*sin(2*pi/opts.Dy_period*t);
Dy(:) = args.Dy_amplitude*sin(2*pi/args.Dy_period*t);
Dyd = args.Dy_amplitude*2*pi/args.Dy_period*cos(2*pi/args.Dy_period*t);
Dydd = -args.Dy_amplitude*(2*pi/args.Dy_period)^2*sin(2*pi/args.Dy_period*t);
otherwise
warning('Dy_type is not set correctly');
end
Dy = struct('time', t, 'signals', struct('values', Dy), 'deriv', Dyd, 'dderiv', Dydd);
#+end_src
*** Tilt Stage
#+begin_src matlab
%% Tilt Stage - Ry
t = 0:Ts:Tmax; % Time Vector [s]
Ry = zeros(length(t), 1);
Ryd = zeros(length(t), 1);
Rydd = zeros(length(t), 1);
switch opts.Ry_type
switch args.Ry_type
case 'constant'
Ry(:) = opts.Ry_amplitude;
Ry(:) = args.Ry_amplitude;
Ryd(:) = 0;
Rydd(:) = 0;
case 'triangular'
Ry_raw = opts.Ry_amplitude*sawtooth(2*pi*t/opts.Ry_period,1/2);
i0 = find(t>=opts.Ry_period/4,1);
Ry_raw = args.Ry_amplitude*sawtooth(2*pi*t/args.Ry_period,1/2);
i0 = find(t>=args.Ry_period/4,1);
Ry(1:end-i0+1) = Ry_raw(i0:end);
Ry(end-i0+2:end) = Ry_raw(end); % we fix the last value
@ -146,29 +170,32 @@ This Matlab function is accessible [[file:../src/initializeInputs.m][here]].
Ryd = lsim(H_lpf*s, Ry, t);
Rydd = lsim(H_lpf*s^2, Ry, t);
case 'sinusoidal'
Ry(:) = opts.Ry_amplitude*sin(2*pi/opts.Ry_period*t);
Ry(:) = args.Ry_amplitude*sin(2*pi/args.Ry_period*t);
Ryd = opts.Ry_amplitude*2*pi/opts.Ry_period*cos(2*pi/opts.Ry_period*t);
Rydd = -opts.Ry_amplitude*(2*pi/opts.Ry_period)^2*sin(2*pi/opts.Ry_period*t);
Ryd = args.Ry_amplitude*2*pi/args.Ry_period*cos(2*pi/args.Ry_period*t);
Rydd = -args.Ry_amplitude*(2*pi/args.Ry_period)^2*sin(2*pi/args.Ry_period*t);
otherwise
warning('Ry_type is not set correctly');
end
Ry = struct('time', t, 'signals', struct('values', Ry), 'deriv', Ryd, 'dderiv', Rydd);
#+end_src
*** Spindle
#+begin_src matlab
%% Spindle - Rz
t = 0:Ts:Tmax; % Time Vector [s]
Rz = zeros(length(t), 1);
Rzd = zeros(length(t), 1);
Rzdd = zeros(length(t), 1);
switch opts.Rz_type
switch args.Rz_type
case 'constant'
Rz(:) = opts.Rz_amplitude;
Rz(:) = args.Rz_amplitude;
Rzd(:) = 0;
Rzdd(:) = 0;
case 'rotating'
Rz(:) = opts.Rz_amplitude+2*pi/opts.Rz_period*t;
Rz(:) = args.Rz_amplitude+2*pi/args.Rz_period*t;
% The signal is filtered out
Rz = lsim(H_lpf, Rz, t);
@ -179,23 +206,26 @@ This Matlab function is accessible [[file:../src/initializeInputs.m][here]].
end
Rz = struct('time', t, 'signals', struct('values', Rz), 'deriv', Rzd, 'dderiv', Rzdd);
#+end_src
*** Micro Hexapod
#+begin_src matlab
%% Micro-Hexapod
t = [0, Ts];
Dh = zeros(length(t), 6);
Dhl = zeros(length(t), 6);
switch opts.Dh_type
switch args.Dh_type
case 'constant'
Dh = [opts.Dh_pos, opts.Dh_pos];
Dh = [args.Dh_pos, args.Dh_pos];
load('./mat/stages.mat', 'micro_hexapod');
load('mat/stages.mat', 'micro_hexapod');
AP = [opts.Dh_pos(1) ; opts.Dh_pos(2) ; opts.Dh_pos(3)];
AP = [args.Dh_pos(1) ; args.Dh_pos(2) ; args.Dh_pos(3)];
tx = opts.Dh_pos(4);
ty = opts.Dh_pos(5);
tz = opts.Dh_pos(6);
tx = args.Dh_pos(4);
ty = args.Dh_pos(5);
tz = args.Dh_pos(6);
ARB = [cos(tz) -sin(tz) 0;
sin(tz) cos(tz) 0;
@ -215,28 +245,37 @@ This Matlab function is accessible [[file:../src/initializeInputs.m][here]].
Dh = struct('time', t, 'signals', struct('values', Dh));
Dhl = struct('time', t, 'signals', struct('values', Dhl));
#+end_src
*** Axis Compensation
#+begin_src matlab
%% Axis Compensation - Rm
t = [0, Ts];
Rm = [opts.Rm_pos, opts.Rm_pos];
Rm = [args.Rm_pos, args.Rm_pos];
Rm = struct('time', t, 'signals', struct('values', Rm));
#+end_src
*** Nano Hexapod
#+begin_src matlab
%% Nano-Hexapod
t = [0, Ts];
Dn = zeros(length(t), 6);
switch opts.Dn_type
switch args.Dn_type
case 'constant'
Dn = [opts.Dn_pos, opts.Dn_pos];
Dn = [args.Dn_pos, args.Dn_pos];
otherwise
warning('Dn_type is not set correctly');
end
Dn = struct('time', t, 'signals', struct('values', Dn));
#+end_src
*** Save
#+begin_src matlab
%% Save
save('./mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'Rm', 'Dn', 'Ts');
save('mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'Rm', 'Dn', 'Ts');
end
#+end_src
@ -252,36 +291,35 @@ This Matlab function is accessible [[file:src/initDisturbances.m][here]].
*** Function Declaration and Documentation
#+begin_src matlab
function [] = initDisturbances(opts_param)
function [] = initDisturbances(args)
% initDisturbances - Initialize the disturbances
%
% Syntax: [] = initDisturbances(opts_param)
% Syntax: [] = initDisturbances(args)
%
% Inputs:
% - opts_param -
% - args -
#+end_src
*** Default values for the Options
*** Optional Parameters
#+begin_src matlab
%% Default values for opts
opts = struct(...
'Dwx', true, ... % Ground Motion - X direction
'Dwy', true, ... % Ground Motion - Y direction
'Dwz', true, ... % Ground Motion - Z direction
'Fty_x', true, ... % Translation Stage - X direction
'Fty_z', true, ... % Translation Stage - Z direction
'Frz_z', true ... % Spindle - Z direction
);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
arguments
% Ground Motion - X direction
args.Dwx logical {mustBeNumericOrLogical} = true
% Ground Motion - Y direction
args.Dwy logical {mustBeNumericOrLogical} = true
% Ground Motion - Z direction
args.Dwz logical {mustBeNumericOrLogical} = true
% Translation Stage - X direction
args.Fty_x logical {mustBeNumericOrLogical} = true
% Translation Stage - Z direction
args.Fty_z logical {mustBeNumericOrLogical} = true
% Spindle - Z direction
args.Frz_z logical {mustBeNumericOrLogical} = true
end
#+end_src
*** Load Data
#+begin_src matlab
load('./disturbances/mat/dist_psd.mat', 'dist_f');
@ -317,7 +355,7 @@ We define some parameters that will be used in the algorithm.
#+end_src
#+begin_src matlab
if opts.Dwx
if args.Dwx
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
@ -328,7 +366,7 @@ We define some parameters that will be used in the algorithm.
#+end_src
#+begin_src matlab
if opts.Dwy
if args.Dwy
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
@ -339,7 +377,7 @@ We define some parameters that will be used in the algorithm.
#+end_src
#+begin_src matlab
if opts.Dwy
if args.Dwy
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
@ -351,7 +389,7 @@ We define some parameters that will be used in the algorithm.
*** Translation Stage - X direction
#+begin_src matlab
if opts.Fty_x
if args.Fty_x
phi = dist_f.psd_ty; % TODO - we take here the vertical direction which is wrong but approximate
C = zeros(N/2,1);
for i = 1:N/2
@ -369,7 +407,7 @@ We define some parameters that will be used in the algorithm.
*** Translation Stage - Z direction
#+begin_src matlab
if opts.Fty_z
if args.Fty_z
phi = dist_f.psd_ty;
C = zeros(N/2,1);
for i = 1:N/2
@ -387,7 +425,7 @@ We define some parameters that will be used in the algorithm.
*** Spindle - Z direction
#+begin_src matlab
if opts.Frz_z
if args.Frz_z
phi = dist_f.psd_rz;
C = zeros(N/2,1);
for i = 1:N/2
@ -421,7 +459,7 @@ We define some parameters that will be used in the algorithm.
*** Save
#+begin_src matlab
save('./mat/nass_disturbances.mat', 'Dwx', 'Dwy', 'Dwz', 'Fty_x', 'Fty_z', 'Frz_z', 'Fd', 'Ts', 't');
save('mat/nass_disturbances.mat', 'Dwx', 'Dwy', 'Dwz', 'Fty_x', 'Fty_z', 'Frz_z', 'Fd', 'Ts', 't');
#+end_src
* Initialize Elements
@ -462,15 +500,9 @@ end
This Matlab function is accessible [[file:../src/initializeGranite.m][here]].
#+begin_src matlab
function [granite] = initializeGranite(opts_param)
%% Default values for opts
opts = struct('rigid', false);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [granite] = initializeGranite(args)
arguments
args.rigid logical {mustBeNumericOrLogical} = false
end
%%
@ -486,7 +518,7 @@ This Matlab function is accessible [[file:../src/initializeGranite.m][here]].
granite.mass_top = 4000; % [kg] TODO
%% Dynamical Properties
if opts.rigid
if args.rigid
granite.k.x = 1e12; % [N/m]
granite.k.y = 1e12; % [N/m]
granite.k.z = 1e12; % [N/m]
@ -527,15 +559,9 @@ This Matlab function is accessible [[file:../src/initializeGranite.m][here]].
This Matlab function is accessible [[file:../src/initializeTy.m][here]].
#+begin_src matlab
function [ty] = initializeTy(opts_param)
%% Default values for opts
opts = struct('rigid', false);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [ty] = initializeTy(args)
arguments
args.rigid logical {mustBeNumericOrLogical} = false
end
%%
@ -582,7 +608,7 @@ This Matlab function is accessible [[file:../src/initializeTy.m][here]].
ty.m = 1000; % TODO [kg]
%% Y-Translation - Dynamicals Properties
if opts.rigid
if args.rigid
ty.k.ax = 1e12; % Axial Stiffness for each of the 4 guidance (y) [N/m]
ty.k.rad = 1e12; % Radial Stiffness for each of the 4 guidance (x-z) [N/m]
else
@ -608,15 +634,9 @@ This Matlab function is accessible [[file:../src/initializeTy.m][here]].
This Matlab function is accessible [[file:../src/initializeRy.m][here]].
#+begin_src matlab
function [ry] = initializeRy(opts_param)
%% Default values for opts
opts = struct('rigid', false);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [ry] = initializeRy(args)
arguments
args.rigid logical {mustBeNumericOrLogical} = false
end
%%
@ -643,7 +663,7 @@ This Matlab function is accessible [[file:../src/initializeRy.m][here]].
ry.m = 800; % TODO [kg]
%% Tilt Stage - Dynamical Properties
if opts.rigid
if args.rigid
ry.k.tilt = 1e10; % Rotation stiffness around y [N*m/deg]
ry.k.h = 1e12; % Stiffness in the direction of the guidance [N/m]
ry.k.rad = 1e12; % Stiffness in the top direction [N/m]
@ -678,15 +698,9 @@ This Matlab function is accessible [[file:../src/initializeRy.m][here]].
This Matlab function is accessible [[file:../src/initializeRz.m][here]].
#+begin_src matlab
function [rz] = initializeRz(opts_param)
%% Default values for opts
opts = struct('rigid', false);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [rz] = initializeRz(args)
arguments
args.rigid logical {mustBeNumericOrLogical} = false
end
%%
@ -711,7 +725,7 @@ This Matlab function is accessible [[file:../src/initializeRz.m][here]].
%% Spindle - Dynamical Properties
if opts.rigid
if args.rigid
rz.k.rot = 1e10; % Rotational Stiffness (Rz) [N*m/deg]
rz.k.tilt = 1e10; % Rotational Stiffness (Rx, Ry) [N*m/deg]
rz.k.ax = 1e12; % Axial Stiffness (Z) [N/m]
@ -744,19 +758,11 @@ This Matlab function is accessible [[file:../src/initializeRz.m][here]].
This Matlab function is accessible [[file:../src/initializeMicroHexapod.m][here]].
#+begin_src matlab
function [micro_hexapod] = initializeMicroHexapod(opts_param)
%% Default values for opts
opts = struct(...
'rigid', false, ...
'AP', zeros(3, 1), ... % Wanted position in [m] of OB with respect to frame {A}
'ARB', eye(3) ... % Rotation Matrix that represent the wanted orientation of frame {B} with respect to frame {A}
);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [micro_hexapod] = initializeMicroHexapod(args)
arguments
args.rigid logical {mustBeNumericOrLogical} = false
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
end
%% Stewart Object
@ -792,7 +798,7 @@ This Matlab function is accessible [[file:../src/initializeMicroHexapod.m][here]
Leg = struct();
Leg.stroke = 10e-3; % Maximum Stroke of each leg [m]
if opts.rigid
if args.rigid
Leg.k.ax = 1e12; % Stiffness of each leg [N/m]
else
Leg.k.ax = 2e7; % Stiffness of each leg [N/m]
@ -844,7 +850,7 @@ This Matlab function is accessible [[file:../src/initializeMicroHexapod.m][here]
micro_hexapod = initializeParameters(micro_hexapod);
%% Setup equilibrium position of each leg
micro_hexapod.L0 = inverseKinematicsHexapod(micro_hexapod, opts.AP, opts.ARB);
micro_hexapod.L0 = inverseKinematicsHexapod(micro_hexapod, args.AP, args.ARB);
%% Save
save('./mat/stages.mat', 'micro_hexapod', '-append');
@ -1003,18 +1009,10 @@ This Matlab function is accessible [[file:../src/initializeAxisc.m][here]].
This Matlab function is accessible [[file:../src/initializeMirror.m][here]].
#+begin_src matlab
function [] = initializeMirror(opts_param)
%% Default values for opts
opts = struct(...
'shape', 'spherical', ... % spherical or conical
'angle', 45 ...
);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [] = initializeMirror(args)
arguments
args.shape char {mustBeMember(args.shape,{'spherical', 'conical'})} = 'spherical'
args.angle (1,1) double {mustBeNumeric, mustBePositive} = 45
end
%%
@ -1029,7 +1027,7 @@ This Matlab function is accessible [[file:../src/initializeMirror.m][here]].
mirror.density = 2400; % Density of the mirror [kg/m3]
mirror.color = [0.4 1.0 1.0]; % Color of the mirror
mirror.cone_length = mirror.rad*tand(opts.angle)+mirror.h+mirror.jacobian; % Distance from Apex point of the cone to jacobian point
mirror.cone_length = mirror.rad*tand(args.angle)+mirror.h+mirror.jacobian; % Distance from Apex point of the cone to jacobian point
%% Shape
mirror.shape = [...
@ -1039,14 +1037,14 @@ This Matlab function is accessible [[file:../src/initializeMirror.m][here]].
mirror.rad 0 ...
];
if strcmp(opts.shape, 'spherical')
if strcmp(args.shape, 'spherical')
mirror.sphere_radius = sqrt((mirror.jacobian+mirror.h)^2+mirror.rad^2); % Radius of the sphere [mm]
for z = linspace(0, mirror.h, 101)
mirror.shape = [mirror.shape; sqrt(mirror.sphere_radius^2-(z-mirror.jacobian-mirror.h)^2) z];
end
elseif strcmp(opts.shape, 'conical')
mirror.shape = [mirror.shape; mirror.rad+mirror.h/tand(opts.angle) mirror.h];
elseif strcmp(args.shape, 'conical')
mirror.shape = [mirror.shape; mirror.rad+mirror.h/tand(args.angle) mirror.h];
else
error('Shape should be either conical or spherical');
end
@ -1068,22 +1066,17 @@ This Matlab function is accessible [[file:../src/initializeMirror.m][here]].
This Matlab function is accessible [[file:../src/initializeNanoHexapod.m][here]].
#+begin_src matlab
function [nano_hexapod] = initializeNanoHexapod(opts_param)
%% Default values for opts
opts = struct('actuator', 'piezo');
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [nano_hexapod] = initializeNanoHexapod(args)
arguments
args.actuator char {mustBeMember(args.actuator,{'piezo', 'lorentz'})} = 'piezo'
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
end
%% Stewart Object
nano_hexapod = struct();
nano_hexapod.h = 90; % Total height of the platform [mm]
nano_hexapod.jacobian = 175; % Point where the Jacobian is computed => Center of rotation [mm]
% nano_hexapod.jacobian = 174.26; % Point where the Jacobian is computed => Center of rotation [mm]
%% Bottom Plate
BP = struct();
@ -1113,12 +1106,12 @@ This Matlab function is accessible [[file:../src/initializeNanoHexapod.m][here]]
Leg = struct();
Leg.stroke = 80e-6; % Maximum Stroke of each leg [m]
if strcmp(opts.actuator, 'piezo')
if strcmp(args.actuator, 'piezo')
Leg.k.ax = 1e7; % Stiffness of each leg [N/m]
elseif strcmp(opts.actuator, 'lorentz')
elseif strcmp(args.actuator, 'lorentz')
Leg.k.ax = 1e4; % Stiffness of each leg [N/m]
else
error('opts.actuator should be piezo or lorentz');
error('args.actuator should be piezo or lorentz');
end
Leg.ksi.ax = 10; % Maximum amplification at resonance []
Leg.rad.bottom = 12; % Radius of the cylinder of the bottom part [mm]
@ -1167,6 +1160,9 @@ This Matlab function is accessible [[file:../src/initializeNanoHexapod.m][here]]
%%
nano_hexapod = initializeParameters(nano_hexapod);
%% Setup equilibrium position of each leg
nano_hexapod.L0 = inverseKinematicsHexapod(nano_hexapod, args.AP, args.ARB);
%% Save
save('./mat/stages.mat', 'nano_hexapod', '-append');
@ -1284,17 +1280,7 @@ This Matlab function is accessible [[file:../src/initializeNanoHexapod.m][here]]
This Matlab function is accessible [[file:../src/initializeCedratPiezo.m][here]].
#+begin_src matlab
function [cedrat] = initializeCedratPiezo(opts_param)
%% Default values for opts
opts = struct();
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
end
function [cedrat] = initializeCedratPiezo()
%% Stewart Object
cedrat = struct();
cedrat.k = 10e7; % Linear Stiffness of each "blade" [N/m]
@ -1323,20 +1309,13 @@ This Matlab function is accessible [[file:../src/initializeCedratPiezo.m][here]]
This Matlab function is accessible [[file:../src/initializeSample.m][here]].
#+begin_src matlab
function [sample] = initializeSample(opts_param)
%% Default values for opts
sample = struct('radius', 100, ...
'height', 300, ...
'mass', 50, ...
'offset', 0, ...
'color', [0.45, 0.45, 0.45] ...
);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
sample.(opt{1}) = opts_param.(opt{1});
end
function [sample] = initializeSample(sample)
arguments
sample.radius (1,1) double {mustBeNumeric, mustBePositive} = 100
sample.height (1,1) double {mustBeNumeric, mustBePositive} = 300
sample.mass (1,1) double {mustBeNumeric, mustBePositive} = 50
sample.offset (1,1) double {mustBeNumeric} = 0
sample.color (1,3) double {mustBeNumeric} = [0.45, 0.45, 0.45]
end
%%

46
src/initDisturbances.m
View File

@ -1,26 +1,24 @@
function [] = initDisturbances(opts_param)
function [] = initDisturbances(args)
% initDisturbances - Initialize the disturbances
%
% Syntax: [] = initDisturbances(opts_param)
% Syntax: [] = initDisturbances(args)
%
% Inputs:
% - opts_param -
% - args -
%% Default values for opts
opts = struct(...
'Dwx', true, ... % Ground Motion - X direction
'Dwy', true, ... % Ground Motion - Y direction
'Dwz', true, ... % Ground Motion - Z direction
'Fty_x', true, ... % Translation Stage - X direction
'Fty_z', true, ... % Translation Stage - Z direction
'Frz_z', true ... % Spindle - Z direction
);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
arguments
% Ground Motion - X direction
args.Dwx logical {mustBeNumericOrLogical} = true
% Ground Motion - Y direction
args.Dwy logical {mustBeNumericOrLogical} = true
% Ground Motion - Z direction
args.Dwz logical {mustBeNumericOrLogical} = true
% Translation Stage - X direction
args.Fty_x logical {mustBeNumericOrLogical} = true
% Translation Stage - Z direction
args.Fty_z logical {mustBeNumericOrLogical} = true
% Spindle - Z direction
args.Frz_z logical {mustBeNumericOrLogical} = true
end
load('./disturbances/mat/dist_psd.mat', 'dist_f');
@ -44,7 +42,7 @@ for i = 1:N/2
C(i) = sqrt(phi(i)*df);
end
if opts.Dwx
if args.Dwx
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
@ -53,7 +51,7 @@ else
Dwx = zeros(length(t), 1);
end
if opts.Dwy
if args.Dwy
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
@ -62,7 +60,7 @@ else
Dwy = zeros(length(t), 1);
end
if opts.Dwy
if args.Dwy
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
@ -71,7 +69,7 @@ else
Dwz = zeros(length(t), 1);
end
if opts.Fty_x
if args.Fty_x
phi = dist_f.psd_ty; % TODO - we take here the vertical direction which is wrong but approximate
C = zeros(N/2,1);
for i = 1:N/2
@ -86,7 +84,7 @@ else
Fty_x = zeros(length(t), 1);
end
if opts.Fty_z
if args.Fty_z
phi = dist_f.psd_ty;
C = zeros(N/2,1);
for i = 1:N/2
@ -101,7 +99,7 @@ else
Fty_z = zeros(length(t), 1);
end
if opts.Frz_z
if args.Frz_z
phi = dist_f.psd_rz;
C = zeros(N/2,1);
for i = 1:N/2

12
src/initializeCedratPiezo.m
View File

@ -1,14 +1,4 @@
function [cedrat] = initializeCedratPiezo(opts_param)
%% Default values for opts
opts = struct();
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
end
function [cedrat] = initializeCedratPiezo()
%% Stewart Object
cedrat = struct();
cedrat.k = 10e7; % Linear Stiffness of each "blade" [N/m]

14
src/initializeGranite.m
View File

@ -1,12 +1,6 @@
function [granite] = initializeGranite(opts_param)
%% Default values for opts
opts = struct('rigid', false);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [granite] = initializeGranite(args)
arguments
args.rigid logical {mustBeNumericOrLogical} = false
end
%%
@ -22,7 +16,7 @@ function [granite] = initializeGranite(opts_param)
granite.mass_top = 4000; % [kg] TODO
%% Dynamical Properties
if opts.rigid
if args.rigid
granite.k.x = 1e12; % [N/m]
granite.k.y = 1e12; % [N/m]
granite.k.z = 1e12; % [N/m]

22
src/initializeMicroHexapod.m
View File

@ -1,16 +1,8 @@
function [micro_hexapod] = initializeMicroHexapod(opts_param)
%% Default values for opts
opts = struct(...
'rigid', false, ...
'AP', zeros(3, 1), ... % Wanted position in [m] of OB with respect to frame {A}
'ARB', eye(3) ... % Rotation Matrix that represent the wanted orientation of frame {B} with respect to frame {A}
);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [micro_hexapod] = initializeMicroHexapod(args)
arguments
args.rigid logical {mustBeNumericOrLogical} = false
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
end
%% Stewart Object
@ -46,7 +38,7 @@ function [micro_hexapod] = initializeMicroHexapod(opts_param)
Leg = struct();
Leg.stroke = 10e-3; % Maximum Stroke of each leg [m]
if opts.rigid
if args.rigid
Leg.k.ax = 1e12; % Stiffness of each leg [N/m]
else
Leg.k.ax = 2e7; % Stiffness of each leg [N/m]
@ -98,7 +90,7 @@ function [micro_hexapod] = initializeMicroHexapod(opts_param)
micro_hexapod = initializeParameters(micro_hexapod);
%% Setup equilibrium position of each leg
micro_hexapod.L0 = inverseKinematicsHexapod(micro_hexapod, opts.AP, opts.ARB);
micro_hexapod.L0 = inverseKinematicsHexapod(micro_hexapod, args.AP, args.ARB);
%% Save
save('./mat/stages.mat', 'micro_hexapod', '-append');

24
src/initializeMirror.m
View File

@ -1,15 +1,7 @@
function [] = initializeMirror(opts_param)
%% Default values for opts
opts = struct(...
'shape', 'spherical', ... % spherical or conical
'angle', 45 ...
);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [] = initializeMirror(args)
arguments
args.shape char {mustBeMember(args.shape,{'spherical', 'conical'})} = 'spherical'
args.angle (1,1) double {mustBeNumeric, mustBePositive} = 45
end
%%
@ -24,7 +16,7 @@ function [] = initializeMirror(opts_param)
mirror.density = 2400; % Density of the mirror [kg/m3]
mirror.color = [0.4 1.0 1.0]; % Color of the mirror
mirror.cone_length = mirror.rad*tand(opts.angle)+mirror.h+mirror.jacobian; % Distance from Apex point of the cone to jacobian point
mirror.cone_length = mirror.rad*tand(args.angle)+mirror.h+mirror.jacobian; % Distance from Apex point of the cone to jacobian point
%% Shape
mirror.shape = [...
@ -34,14 +26,14 @@ function [] = initializeMirror(opts_param)
mirror.rad 0 ...
];
if strcmp(opts.shape, 'spherical')
if strcmp(args.shape, 'spherical')
mirror.sphere_radius = sqrt((mirror.jacobian+mirror.h)^2+mirror.rad^2); % Radius of the sphere [mm]
for z = linspace(0, mirror.h, 101)
mirror.shape = [mirror.shape; sqrt(mirror.sphere_radius^2-(z-mirror.jacobian-mirror.h)^2) z];
end
elseif strcmp(opts.shape, 'conical')
mirror.shape = [mirror.shape; mirror.rad+mirror.h/tand(opts.angle) mirror.h];
elseif strcmp(args.shape, 'conical')
mirror.shape = [mirror.shape; mirror.rad+mirror.h/tand(args.angle) mirror.h];
else
error('Shape should be either conical or spherical');
end

26
src/initializeNanoHexapod.m
View File

@ -1,16 +1,8 @@
function [nano_hexapod] = initializeNanoHexapod(opts_param)
%% Default values for opts
opts = struct(...
'actuator', 'piezo', ...
'AP', zeros(3, 1), ... % Wanted position in [m] of OB with respect to frame {A}
'ARB', eye(3) ... % Rotation Matrix that represent the wanted orientation of frame {B} with respect to frame {A}
);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [nano_hexapod] = initializeNanoHexapod(args)
arguments
args.actuator char {mustBeMember(args.actuator,{'piezo', 'lorentz'})} = 'piezo'
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
end
%% Stewart Object
@ -46,12 +38,12 @@ function [nano_hexapod] = initializeNanoHexapod(opts_param)
Leg = struct();
Leg.stroke = 80e-6; % Maximum Stroke of each leg [m]
if strcmp(opts.actuator, 'piezo')
if strcmp(args.actuator, 'piezo')
Leg.k.ax = 1e7; % Stiffness of each leg [N/m]
elseif strcmp(opts.actuator, 'lorentz')
elseif strcmp(args.actuator, 'lorentz')
Leg.k.ax = 1e4; % Stiffness of each leg [N/m]
else
error('opts.actuator should be piezo or lorentz');
error('args.actuator should be piezo or lorentz');
end
Leg.ksi.ax = 10; % Maximum amplification at resonance []
Leg.rad.bottom = 12; % Radius of the cylinder of the bottom part [mm]
@ -101,7 +93,7 @@ function [nano_hexapod] = initializeNanoHexapod(opts_param)
nano_hexapod = initializeParameters(nano_hexapod);
%% Setup equilibrium position of each leg
nano_hexapod.L0 = inverseKinematicsHexapod(nano_hexapod, opts.AP, opts.ARB);
nano_hexapod.L0 = inverseKinematicsHexapod(nano_hexapod, args.AP, args.ARB);
%% Save
save('./mat/stages.mat', 'nano_hexapod', '-append');

119
src/initializeReferences.m
View File

@ -1,36 +1,45 @@
function [ref] = initializeReferences(opts_param)
function [ref] = initializeReferences(args)
%% Default values for opts
opts = struct( ...
'Ts', 1e-3, ... % Sampling Frequency [s]
'Tmax', 100, ... % Maximum simulation time [s]
'Dy_type', 'constant', ... % Either "constant" / "triangular" / "sinusoidal"
'Dy_amplitude', 0, ... % Amplitude of the displacement [m]
'Dy_period', 1, ... % Period of the displacement [s]
'Ry_type', 'constant', ... % Either "constant" / "triangular" / "sinusoidal"
'Ry_amplitude', 0, ... % Amplitude [rad]
'Ry_period', 1, ... % Period of the displacement [s]
'Rz_type', 'constant', ... % Either "constant" / "rotating"
'Rz_amplitude', 0, ... % Initial angle [rad]
'Rz_period', 1, ... % Period of the rotating [s]
'Dh_type', 'constant', ... % For now, only constant is implemented
'Dh_pos', zeros(6, 1), ... % Initial position [m,m,m,rad,rad,rad] of the top platform (Pitch-Roll-Yaw Euler angles)
'Rm_type', 'constant', ... % For now, only constant is implemented
'Rm_pos', [0; pi], ... % Initial position of the two masses
'Dn_type', 'constant', ... % For now, only constant is implemented
'Dn_pos', zeros(6,1) ... % Initial position [m,m,m,rad,rad,rad] of the top platform
);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
arguments
% Sampling Frequency [s]
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3
% Maximum simulation time [s]
args.Tmax (1,1) double {mustBeNumeric, mustBePositive} = 100
% Either "constant" / "triangular" / "sinusoidal"
args.Dy_type char {mustBeMember(args.Dy_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
% Amplitude of the displacement [m]
args.Dy_amplitude (1,1) double {mustBeNumeric} = 0
% Period of the displacement [s]
args.Dy_period (1,1) double {mustBeNumeric, mustBePositive} = 1
% Either "constant" / "triangular" / "sinusoidal"
args.Ry_type char {mustBeMember(args.Ry_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
% Amplitude [rad]
args.Ry_amplitude (1,1) double {mustBeNumeric} = 0
% Period of the displacement [s]
args.Ry_period (1,1) double {mustBeNumeric, mustBePositive} = 1
% Either "constant" / "rotating"
args.Rz_type char {mustBeMember(args.Rz_type,{'constant', 'rotating'})} = 'constant'
% Initial angle [rad]
args.Rz_amplitude (1,1) double {mustBeNumeric} = 0
% Period of the rotating [s]
args.Rz_period (1,1) double {mustBeNumeric, mustBePositive} = 1
% For now, only constant is implemented
args.Dh_type char {mustBeMember(args.Dh_type,{'constant'})} = 'constant'
% Initial position [m,m,m,rad,rad,rad] of the top platform (Pitch-Roll-Yaw Euler angles)
args.Dh_pos (6,1) double {mustBeNumeric} = zeros(6, 1), ...
% For now, only constant is implemented
args.Rm_type char {mustBeMember(args.Rm_type,{'constant'})} = 'constant'
% Initial position of the two masses
args.Rm_pos (2,1) double {mustBeNumeric} = [0; pi]
% For now, only constant is implemented
args.Dn_type char {mustBeMember(args.Dn_type,{'constant'})} = 'constant'
% Initial position [m,m,m,rad,rad,rad] of the top platform
args.Dn_pos (6,1) double {mustBeNumeric} = zeros(6,1)
end
%% Set Sampling Time
Ts = opts.Ts;
Tmax = opts.Tmax;
Ts = args.Ts;
Tmax = args.Tmax;
%% Low Pass Filter to filter out the references
s = zpk('s');
@ -43,15 +52,15 @@ t = 0:Ts:Tmax; % Time Vector [s]
Dy = zeros(length(t), 1);
Dyd = zeros(length(t), 1);
Dydd = zeros(length(t), 1);
switch opts.Dy_type
switch args.Dy_type
case 'constant'
Dy(:) = opts.Dy_amplitude;
Dy(:) = args.Dy_amplitude;
Dyd(:) = 0;
Dydd(:) = 0;
case 'triangular'
% This is done to unsure that we start with no displacement
Dy_raw = opts.Dy_amplitude*sawtooth(2*pi*t/opts.Dy_period,1/2);
i0 = find(t>=opts.Dy_period/4,1);
Dy_raw = args.Dy_amplitude*sawtooth(2*pi*t/args.Dy_period,1/2);
i0 = find(t>=args.Dy_period/4,1);
Dy(1:end-i0+1) = Dy_raw(i0:end);
Dy(end-i0+2:end) = Dy_raw(end); % we fix the last value
@ -60,9 +69,9 @@ switch opts.Dy_type
Dyd = lsim(H_lpf*s, Dy, t);
Dydd = lsim(H_lpf*s^2, Dy, t);
case 'sinusoidal'
Dy(:) = opts.Dy_amplitude*sin(2*pi/opts.Dy_period*t);
Dyd = opts.Dy_amplitude*2*pi/opts.Dy_period*cos(2*pi/opts.Dy_period*t);
Dydd = -opts.Dy_amplitude*(2*pi/opts.Dy_period)^2*sin(2*pi/opts.Dy_period*t);
Dy(:) = args.Dy_amplitude*sin(2*pi/args.Dy_period*t);
Dyd = args.Dy_amplitude*2*pi/args.Dy_period*cos(2*pi/args.Dy_period*t);
Dydd = -args.Dy_amplitude*(2*pi/args.Dy_period)^2*sin(2*pi/args.Dy_period*t);
otherwise
warning('Dy_type is not set correctly');
end
@ -75,14 +84,14 @@ Ry = zeros(length(t), 1);
Ryd = zeros(length(t), 1);
Rydd = zeros(length(t), 1);
switch opts.Ry_type
switch args.Ry_type
case 'constant'
Ry(:) = opts.Ry_amplitude;
Ry(:) = args.Ry_amplitude;
Ryd(:) = 0;
Rydd(:) = 0;
case 'triangular'
Ry_raw = opts.Ry_amplitude*sawtooth(2*pi*t/opts.Ry_period,1/2);
i0 = find(t>=opts.Ry_period/4,1);
Ry_raw = args.Ry_amplitude*sawtooth(2*pi*t/args.Ry_period,1/2);
i0 = find(t>=args.Ry_period/4,1);
Ry(1:end-i0+1) = Ry_raw(i0:end);
Ry(end-i0+2:end) = Ry_raw(end); % we fix the last value
@ -91,10 +100,10 @@ switch opts.Ry_type
Ryd = lsim(H_lpf*s, Ry, t);
Rydd = lsim(H_lpf*s^2, Ry, t);
case 'sinusoidal'
Ry(:) = opts.Ry_amplitude*sin(2*pi/opts.Ry_period*t);
Ry(:) = args.Ry_amplitude*sin(2*pi/args.Ry_period*t);
Ryd = opts.Ry_amplitude*2*pi/opts.Ry_period*cos(2*pi/opts.Ry_period*t);
Rydd = -opts.Ry_amplitude*(2*pi/opts.Ry_period)^2*sin(2*pi/opts.Ry_period*t);
Ryd = args.Ry_amplitude*2*pi/args.Ry_period*cos(2*pi/args.Ry_period*t);
Rydd = -args.Ry_amplitude*(2*pi/args.Ry_period)^2*sin(2*pi/args.Ry_period*t);
otherwise
warning('Ry_type is not set correctly');
end
@ -107,13 +116,13 @@ Rz = zeros(length(t), 1);
Rzd = zeros(length(t), 1);
Rzdd = zeros(length(t), 1);
switch opts.Rz_type
switch args.Rz_type
case 'constant'
Rz(:) = opts.Rz_amplitude;
Rz(:) = args.Rz_amplitude;
Rzd(:) = 0;
Rzdd(:) = 0;
case 'rotating'
Rz(:) = opts.Rz_amplitude+2*pi/opts.Rz_period*t;
Rz(:) = args.Rz_amplitude+2*pi/args.Rz_period*t;
% The signal is filtered out
Rz = lsim(H_lpf, Rz, t);
@ -130,17 +139,17 @@ t = [0, Ts];
Dh = zeros(length(t), 6);
Dhl = zeros(length(t), 6);
switch opts.Dh_type
switch args.Dh_type
case 'constant'
Dh = [opts.Dh_pos, opts.Dh_pos];
Dh = [args.Dh_pos, args.Dh_pos];
load('mat/stages.mat', 'micro_hexapod');
AP = [opts.Dh_pos(1) ; opts.Dh_pos(2) ; opts.Dh_pos(3)];
AP = [args.Dh_pos(1) ; args.Dh_pos(2) ; args.Dh_pos(3)];
tx = opts.Dh_pos(4);
ty = opts.Dh_pos(5);
tz = opts.Dh_pos(6);
tx = args.Dh_pos(4);
ty = args.Dh_pos(5);
tz = args.Dh_pos(6);
ARB = [cos(tz) -sin(tz) 0;
sin(tz) cos(tz) 0;
@ -164,16 +173,16 @@ Dhl = struct('time', t, 'signals', struct('values', Dhl));
%% Axis Compensation - Rm
t = [0, Ts];
Rm = [opts.Rm_pos, opts.Rm_pos];
Rm = [args.Rm_pos, args.Rm_pos];
Rm = struct('time', t, 'signals', struct('values', Rm));
%% Nano-Hexapod
t = [0, Ts];
Dn = zeros(length(t), 6);
switch opts.Dn_type
switch args.Dn_type
case 'constant'
Dn = [opts.Dn_pos, opts.Dn_pos];
Dn = [args.Dn_pos, args.Dn_pos];
otherwise
warning('Dn_type is not set correctly');
end

14
src/initializeRy.m
View File

@ -1,12 +1,6 @@
function [ry] = initializeRy(opts_param)
%% Default values for opts
opts = struct('rigid', false);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [ry] = initializeRy(args)
arguments
args.rigid logical {mustBeNumericOrLogical} = false
end
%%
@ -33,7 +27,7 @@ function [ry] = initializeRy(opts_param)
ry.m = 800; % TODO [kg]
%% Tilt Stage - Dynamical Properties
if opts.rigid
if args.rigid
ry.k.tilt = 1e10; % Rotation stiffness around y [N*m/deg]
ry.k.h = 1e12; % Stiffness in the direction of the guidance [N/m]
ry.k.rad = 1e12; % Stiffness in the top direction [N/m]

14
src/initializeRz.m
View File

@ -1,12 +1,6 @@
function [rz] = initializeRz(opts_param)
%% Default values for opts
opts = struct('rigid', false);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [rz] = initializeRz(args)
arguments
args.rigid logical {mustBeNumericOrLogical} = false
end
%%
@ -31,7 +25,7 @@ function [rz] = initializeRz(opts_param)
%% Spindle - Dynamical Properties
if opts.rigid
if args.rigid
rz.k.rot = 1e10; % Rotational Stiffness (Rz) [N*m/deg]
rz.k.tilt = 1e10; % Rotational Stiffness (Rx, Ry) [N*m/deg]
rz.k.ax = 1e12; % Axial Stiffness (Z) [N/m]

21
src/initializeSample.m
View File

@ -1,17 +1,10 @@
function [sample] = initializeSample(opts_param)
%% Default values for opts
sample = struct('radius', 100, ...
'height', 300, ...
'mass', 50, ...
'offset', 0, ...
'color', [0.45, 0.45, 0.45] ...
);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
sample.(opt{1}) = opts_param.(opt{1});
end
function [sample] = initializeSample(sample)
arguments
sample.radius (1,1) double {mustBeNumeric, mustBePositive} = 100
sample.height (1,1) double {mustBeNumeric, mustBePositive} = 300
sample.mass (1,1) double {mustBeNumeric, mustBePositive} = 50
sample.offset (1,1) double {mustBeNumeric} = 0
sample.color (1,3) double {mustBeNumeric} = [0.45, 0.45, 0.45]
end
%%

14
src/initializeTy.m
View File

@ -1,12 +1,6 @@
function [ty] = initializeTy(opts_param)
%% Default values for opts
opts = struct('rigid', false);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
function [ty] = initializeTy(args)
arguments
args.rigid logical {mustBeNumericOrLogical} = false
end
%%
@ -53,7 +47,7 @@ function [ty] = initializeTy(opts_param)
ty.m = 1000; % TODO [kg]
%% Y-Translation - Dynamicals Properties
if opts.rigid
if args.rigid
ty.k.ax = 1e12; % Axial Stiffness for each of the 4 guidance (y) [N/m]
ty.k.rad = 1e12; % Radial Stiffness for each of the 4 guidance (x-z) [N/m]
else

32
uniaxial/index.org
View File

@ -659,8 +659,8 @@ The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
All the controllers are set to 0 (Open Loop).
@ -1159,8 +1159,8 @@ Let's initialize the system prior to identification.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
All the controllers are set to 0.
@ -1586,8 +1586,8 @@ Let's initialize the system prior to identification.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
And initialize the controllers.
@ -2017,8 +2017,8 @@ Let's initialize the system prior to identification.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'piezo');
initializeSample('mass', 50);
#+end_src
And initialize the controllers.
@ -2250,9 +2250,9 @@ Let's initialize the system prior to identification.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeNanoHexapod('actuator', 'piezo');
initializeCedratPiezo();
initializeSample(struct('mass', 50));
initializeSample('mass', 50);
#+end_src
And initialize the controllers.
@ -2386,9 +2386,9 @@ Let's initialize the system prior to identification.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeNanoHexapod('actuator', 'piezo');
initializeCedratPiezo();
initializeSample(struct('mass', 50));
initializeSample('mass', 50);
#+end_src
All the controllers are set to 0.
@ -2847,8 +2847,8 @@ The nano-hexapod is an hexapod with voice coils and the sample has a mass of 50k
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'lorentz'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'lorentz');
initializeSample('mass', 50);
#+end_src
All the controllers are set to 0 (Open Loop).
@ -3118,8 +3118,8 @@ Let's initialize the system prior to identification.
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'lorentz'));
initializeSample(struct('mass', 50));
initializeNanoHexapod('actuator', 'lorentz');
initializeSample('mass', 50);
#+end_src
All the controllers are set to 0.