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Update active damping analysis: add IFF + HPF

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Thomas Dehaeze 2020-01-20 17:20:50 +01:00
parent c5bb46c184
commit fe26a724f1
31 changed files with 715 additions and 288 deletions
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@ -265,7 +265,7 @@ And we save them for further analysis.
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [(m/s)/N]'); set(gca, 'XTickLabel',[]); ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]);
ax2 = subplot(2, 1, 2); ax2 = subplot(2, 1, 2);
hold on; hold on;
@ -510,6 +510,63 @@ We save the controller for further analysis.
save('./active_damping/mat/K_iff.mat', 'K_iff'); save('./active_damping/mat/K_iff.mat', 'K_iff');
#+end_src #+end_src
*** IFF with High Pass Filter
#+begin_src matlab
w_hpf = 2*pi*10; % Cut-off frequency for the high pass filter [rad/s]
w_lpf = 2*pi*200; % Cut-off frequency for the low pass filter [rad/s]
K_iff = 2*pi*200/s * (s/w_hpf)/(s/w_hpf + 1) * 1/(s/w_lpf + 1);
#+end_src
The corresponding loop gains are shown in figure [[fig:iff_hpf_open_loop]].
#+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(K_iff*G_iff(['Fnlm', num2str(i)], ['Fnl', num2str(i)]), freqs, 'Hz'))));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
ax2 = subplot(2, 1, 2);
hold on;
for i=1:6
plot(freqs, 180/pi*angle(squeeze(freqresp(K_iff*G_iff(['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
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/iff_hpf_open_loop.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:iff_hpf_open_loop
#+CAPTION: Loop Gain for the Integral Force Feedback with an High pass filter ([[./figs/iff_hpf_open_loop.png][png]], [[./figs/iff_hpf_open_loop.pdf][pdf]])
[[file:figs/iff_hpf_open_loop.png]]
We create the diagonal controller and we add a minus sign as we have a positive
feedback architecture.
#+begin_src matlab
K_iff = -K_iff*eye(6);
#+end_src
We save the controller for further analysis.
#+begin_src matlab
save('./active_damping/mat/K_iff_hpf.mat', 'K_iff');
#+end_src
** TODO Identification of the damped plant :noexport: ** TODO Identification of the damped plant :noexport:
*** Initialize the Simulation *** Initialize the Simulation
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -768,7 +825,7 @@ However, it increases coupling at low frequency (figure [[fig:plant_iff_coupling
[[file:figs/plant_iff_coupling.png]] [[file:figs/plant_iff_coupling.png]]
** Tomography Experiment ** Tomography Experiment
*** Initialize the Simulation *** Simulation with IFF Controller
We initialize elements for the tomography experiment. We initialize elements for the tomography experiment.
#+begin_src matlab #+begin_src matlab
prepareTomographyExperiment(); prepareTomographyExperiment();
@ -780,7 +837,6 @@ We set the IFF controller.
save('./mat/controllers.mat', 'K_iff', '-append'); save('./mat/controllers.mat', 'K_iff', '-append');
#+end_src #+end_src
*** Simulation
We change the simulation stop time. We change the simulation stop time.
#+begin_src matlab #+begin_src matlab
load('mat/conf_simscape.mat'); load('mat/conf_simscape.mat');
@ -799,29 +855,86 @@ Finally, we save the simulation results for further analysis
save('./active_damping/mat/tomo_exp.mat', 'En_iff', 'Eg_iff', '-append'); save('./active_damping/mat/tomo_exp.mat', 'En_iff', 'Eg_iff', '-append');
#+end_src #+end_src
*** Simulation with IFF Controller with added High Pass Filter
We initialize elements for the tomography experiment.
#+begin_src matlab
prepareTomographyExperiment();
#+end_src
We set the IFF controller with the High Pass Filter.
#+begin_src matlab
load('./active_damping/mat/K_iff_hpf.mat', 'K_iff');
save('./mat/controllers.mat', 'K_iff', '-append');
#+end_src
We change the simulation stop time.
#+begin_src matlab
load('mat/conf_simscape.mat');
set_param(conf_simscape, 'StopTime', '3');
#+end_src
And we simulate the system.
#+begin_src matlab
sim('sim_nass_active_damping');
#+end_src
Finally, we save the simulation results for further analysis
#+begin_src matlab
En_iff_hpf = En;
Eg_iff_hpf = Eg;
save('./active_damping/mat/tomo_exp.mat', 'En_iff_hpf', 'Eg_iff_hpf', '-append');
#+end_src
*** Compare with Undamped system *** Compare with Undamped system
We load the results of tomography experiments. We load the results of tomography experiments.
#+begin_src matlab #+begin_src matlab
load('./active_damping/mat/tomo_exp.mat', 'En', 'En_iff'); load('./active_damping/mat/tomo_exp.mat', 'En', 'En_iff', 'En_iff_hpf');
#+end_src
#+begin_src matlab
t = linspace(0, 3, length(En(:,1))); t = linspace(0, 3, length(En(:,1)));
#+end_src #+end_src
#+begin_src matlab :exports none #+begin_src matlab :exports none
figure; figure;
hold on; hold on;
plot(t, En(:,1), 'DisplayName', '$\epsilon_{x}$') plot(En(:,1), En(:,2), 'DisplayName', '$\epsilon_{x,y}$ - OL')
plot(t, En(:,2), 'DisplayName', '$\epsilon_{y}$') plot(En_iff(:,1), En_iff(:,2), 'DisplayName', '$\epsilon_{x,y}$ - IFF')
plot(t, En(:,3), 'DisplayName', '$\epsilon_{z}$') plot(En_iff_hpf(:,1), En_iff_hpf(:,2), 'DisplayName', '$\epsilon_{x,y}$ - IFF + HPF')
set(gca,'ColorOrderIndex',1); xlabel('X Motion [m]'); ylabel('Y Motion [m]');
plot(t, En_iff(:,1), '--', 'DisplayName', '$\epsilon_{x}$ - IFF')
plot(t, En_iff(:,2), '--', 'DisplayName', '$\epsilon_{y}$ - IFF')
plot(t, En_iff(:,3), '--', 'DisplayName', '$\epsilon_{z}$ - IFF')
hold off;
legend('location', 'northwest'); legend('location', 'northwest');
xlabel('Time [s]'); ylabel('Position Error [m]'); #+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/nass_act_damp_iff_sim_tomo_xy.pdf" :var figsize="small-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:nass_act_damp_iff_sim_tomo_xy
#+CAPTION: Position Error during tomography experiment - XY Motion ([[./figs/nass_act_damp_iff_sim_tomo_xy.png][png]], [[./figs/nass_act_damp_iff_sim_tomo_xy.pdf][pdf]])
[[file:figs/nass_act_damp_iff_sim_tomo_xy.png]]
#+begin_src matlab :exports none
figure;
ax1 = subplot(3, 1, 1);
hold on;
plot(t, En(:,1), 'DisplayName', '$\epsilon_{x}$')
plot(t, En_iff(:,1), 'DisplayName', '$\epsilon_{x}$ - IFF')
plot(t, En_iff_hpf(:,1), 'DisplayName', '$\epsilon_{x}$ - IFF + HPF')
legend('location', 'southwest');
ax2 = subplot(3, 1, 2);
hold on;
plot(t, En(:,2), 'DisplayName', '$\epsilon_{y}$')
plot(t, En_iff(:,2), 'DisplayName', '$\epsilon_{y}$ - IFF')
plot(t, En_iff_hpf(:,2), 'DisplayName', '$\epsilon_{y}$ - IFF + HPF')
legend('location', 'southwest');
ylabel('Position Error [m]');
ax3 = subplot(3, 1, 3);
hold on;
plot(t, En(:,3), 'DisplayName', '$\epsilon_{z}$')
plot(t, En_iff(:,3), 'DisplayName', '$\epsilon_{z}$ - IFF')
plot(t, En_iff_hpf(:,3), 'DisplayName', '$\epsilon_{z}$ - IFF + HPF')
legend('location', 'northwest');
xlabel('Time [s]');
#+end_src #+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes #+HEADER: :tangle no :exports results :results none :noweb yes
@ -835,18 +948,30 @@ We load the results of tomography experiments.
#+begin_src matlab :exports none #+begin_src matlab :exports none
figure; figure;
ax1 = subplot(3, 1, 1);
hold on; hold on;
plot(t, En(:,4), 'DisplayName', '$\epsilon_{\theta_x}$') plot(t, En(:,4), 'DisplayName', '$\epsilon_{\theta_x}$')
plot(t, En_iff(:,4), 'DisplayName', '$\epsilon_{\theta_x}$ - IFF')
plot(t, En_iff_hpf(:,4), 'DisplayName', '$\epsilon_{\theta_x}$ - IFF + HPF')
legend('location', 'northwest');
ax2 = subplot(3, 1, 2);
hold on;
plot(t, En(:,5), 'DisplayName', '$\epsilon_{\theta_y}$') plot(t, En(:,5), 'DisplayName', '$\epsilon_{\theta_y}$')
plot(t, En_iff(:,5), 'DisplayName', '$\epsilon_{\theta_y}$ - IFF')
plot(t, En_iff_hpf(:,5), 'DisplayName', '$\epsilon_{\theta_y}$ - IFF + HPF')
legend('location', 'southwest');
ylabel('Position Error [rad]');
ax3 = subplot(3, 1, 3);
hold on;
plot(t, En(:,6), 'DisplayName', '$\epsilon_{\theta_z}$') plot(t, En(:,6), 'DisplayName', '$\epsilon_{\theta_z}$')
set(gca,'ColorOrderIndex',1); plot(t, En_iff(:,6), 'DisplayName', '$\epsilon_{\theta_z}$ - IFF')
plot(t, En_iff(:,4), '--', 'DisplayName', '$\epsilon_{\theta_x}$ - IFF') plot(t, En_iff_hpf(:,6), 'DisplayName', '$\epsilon_{\theta_z}$ - IFF + HPF')
plot(t, En_iff(:,5), '--', 'DisplayName', '$\epsilon_{\theta_y}$ - IFF')
plot(t, En_iff(:,6), '--', 'DisplayName', '$\epsilon_{\theta_z}$ - IFF')
hold off;
xlim([0.5,inf]);
legend(); legend();
xlabel('Time [s]'); ylabel('Position Error [rad]'); xlabel('Time [s]');
linkaxes([ax1,ax2,ax3],'x');
#+end_src #+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes #+HEADER: :tangle no :exports results :results none :noweb yes
@ -1261,16 +1386,42 @@ We load the results of tomography experiments.
#+begin_src matlab :exports none #+begin_src matlab :exports none
figure; figure;
hold on; hold on;
plot(t, En(:,1), 'DisplayName', '$\epsilon_{x}$') plot(En(:,1), En(:,2), 'DisplayName', '$\epsilon_{x,y}$ - OL')
plot(t, En(:,2), 'DisplayName', '$\epsilon_{y}$') plot(En_dvf(:,1), En_dvf(:,2), 'DisplayName', '$\epsilon_{x,y}$ - DVF')
plot(t, En(:,3), 'DisplayName', '$\epsilon_{z}$') xlabel('X Motion [m]'); ylabel('Y Motion [m]');
set(gca,'ColorOrderIndex',1);
plot(t, En_dvf(:,1), '--', 'DisplayName', '$\epsilon_{x}$ - DVF')
plot(t, En_dvf(:,2), '--', 'DisplayName', '$\epsilon_{y}$ - DVF')
plot(t, En_dvf(:,3), '--', 'DisplayName', '$\epsilon_{z}$ - DVF')
hold off;
legend(); legend();
xlabel('Time [s]'); ylabel('Position Error [m]'); #+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/nass_act_damp_dvf_sim_tomo_xy.pdf" :var figsize="small-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:nass_act_damp_dvf_sim_tomo_xy
#+CAPTION: Position Error during tomography experiment - XY Motion ([[./figs/nass_act_damp_dvf_sim_tomo_xy.png][png]], [[./figs/nass_act_damp_dvf_sim_tomo_xy.pdf][pdf]])
[[file:figs/nass_act_damp_dvf_sim_tomo_xy.png]]
#+begin_src matlab :exports none
figure;
ax1 = subplot(3, 1, 1);
hold on;
plot(t, En(:,1), 'DisplayName', '$\epsilon_{x}$')
plot(t, En_dvf(:,1), 'DisplayName', '$\epsilon_{x}$ - DVF')
legend();
ax2 = subplot(3, 1, 2);
hold on;
plot(t, En(:,2), 'DisplayName', '$\epsilon_{y}$')
plot(t, En_dvf(:,2), 'DisplayName', '$\epsilon_{y}$ - DVF')
legend();
ylabel('Position Error [m]');
ax3 = subplot(3, 1, 3);
hold on;
plot(t, En(:,3), 'DisplayName', '$\epsilon_{z}$')
plot(t, En_dvf(:,3), 'DisplayName', '$\epsilon_{z}$ - DVF')
legend();
xlabel('Time [s]');
#+end_src #+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes #+HEADER: :tangle no :exports results :results none :noweb yes
@ -1284,18 +1435,27 @@ We load the results of tomography experiments.
#+begin_src matlab :exports none #+begin_src matlab :exports none
figure; figure;
ax1 = subplot(3, 1, 1);
hold on; hold on;
plot(t, En(:,4), 'DisplayName', '$\epsilon_{\theta_x}$') plot(t, En(:,4), 'DisplayName', '$\epsilon_{\theta_x}$')
plot(t, En(:,5), 'DisplayName', '$\epsilon_{\theta_y}$') plot(t, En_dvf(:,4), 'DisplayName', '$\epsilon_{\theta_x}$ - DVF')
plot(t, En(:,6), 'DisplayName', '$\epsilon_{\theta_z}$')
set(gca,'ColorOrderIndex',1);
plot(t, En_dvf(:,4), '--', 'DisplayName', '$\epsilon_{\theta_x}$ - DVF')
plot(t, En_dvf(:,5), '--', 'DisplayName', '$\epsilon_{\theta_y}$ - DVF')
plot(t, En_dvf(:,6), '--', 'DisplayName', '$\epsilon_{\theta_z}$ - DVF')
hold off;
xlim([0.5,inf]);
legend(); legend();
xlabel('Time [s]'); ylabel('Position Error [rad]');
ax2 = subplot(3, 1, 2);
hold on;
plot(t, En(:,5), 'DisplayName', '$\epsilon_{\theta_y}$')
plot(t, En_dvf(:,5), 'DisplayName', '$\epsilon_{\theta_y}$ - DVF')
legend();
ylabel('Position Error [rad]');
ax3 = subplot(3, 1, 3);
hold on;
plot(t, En(:,6), 'DisplayName', '$\epsilon_{\theta_z}$')
plot(t, En_dvf(:,6), 'DisplayName', '$\epsilon_{\theta_z}$ - DVF')
legend();
xlabel('Time [s]');
linkaxes([ax1,ax2,ax3],'x');
#+end_src #+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes #+HEADER: :tangle no :exports results :results none :noweb yes
@ -1336,7 +1496,7 @@ Direct Velocity Feedback:
#+end_note #+end_note
** Introduction :ignore: ** Introduction :ignore:
In Inertial Control, a feedback is applied between the measured *absolute* velocity of the platform to the actuator force input. In Inertial Control, a feedback is applied between the measured *absolute* motion (velocity or acceleration) of the platform to the actuator force input.
** Matlab Init :noexport: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) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
@ -1380,7 +1540,7 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); ylabel('Amplitude [$\frac{m/s^2}{N}$]'); set(gca, 'XTickLabel',[]);
ax2 = subplot(2, 1, 2); ax2 = subplot(2, 1, 2);
hold on; hold on;
@ -1409,7 +1569,7 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
The controller is defined below and the obtained loop gain is shown in figure [[fig:ine_open_loop_gain]]. The controller is defined below and the obtained loop gain is shown in figure [[fig:ine_open_loop_gain]].
#+begin_src matlab #+begin_src matlab
K_ine = 1e3/(1+s/(2*pi*100)); K_ine = 1e4/(1+s/(2*pi*100));
#+end_src #+end_src
#+begin_src matlab :exports none #+begin_src matlab :exports none
@ -1688,19 +1848,46 @@ We load the results of tomography experiments.
#+begin_src matlab :exports none #+begin_src matlab :exports none
figure; figure;
hold on; hold on;
plot(t, En(:,1), 'DisplayName', '$\epsilon_{x}$') plot(En(:,1), En(:,2), 'DisplayName', '$\epsilon_{x,y}$ - OL')
plot(t, En(:,2), 'DisplayName', '$\epsilon_{y}$') plot(En_ine(:,1), En_ine(:,2), 'DisplayName', '$\epsilon_{x,y}$ - Inertial')
plot(t, En(:,3), 'DisplayName', '$\epsilon_{z}$') xlabel('X Motion [m]'); ylabel('Y Motion [m]');
set(gca,'ColorOrderIndex',1);
plot(t, En_ine(:,1), '--', 'DisplayName', '$\epsilon_{x}$ - Inertial')
plot(t, En_ine(:,2), '--', 'DisplayName', '$\epsilon_{y}$ - Inertial')
plot(t, En_ine(:,3), '--', 'DisplayName', '$\epsilon_{z}$ - Inertial')
hold off;
legend(); legend();
#+end_src #+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes #+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/nass_act_damp_ine_sim_tomo_trans.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png") #+begin_src matlab :var filepath="figs/nass_act_damp_ine_sim_tomo_xy.pdf" :var figsize="small-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:nass_act_damp_ine_sim_tomo_xy
#+CAPTION: Position Error during tomography experiment - XY Motion ([[./figs/nass_act_damp_ine_sim_tomo_xy.png][png]], [[./figs/nass_act_damp_ine_sim_tomo_xy.pdf][pdf]])
[[file:figs/nass_act_damp_ine_sim_tomo_xy.png]]
#+begin_src matlab :exports none
figure;
ax1 = subplot(3, 1, 1);
hold on;
plot(t, En(:,1), 'DisplayName', '$\epsilon_{x}$')
plot(t, En_ine(:,1), 'DisplayName', '$\epsilon_{x}$ - Inertial')
legend();
ax2 = subplot(3, 1, 2);
hold on;
plot(t, En(:,2), 'DisplayName', '$\epsilon_{y}$')
plot(t, En_ine(:,2), 'DisplayName', '$\epsilon_{y}$ - Inertial')
legend();
ylabel('Position Error [m]');
ax3 = subplot(3, 1, 3);
hold on;
plot(t, En(:,3), 'DisplayName', '$\epsilon_{z}$')
plot(t, En_ine(:,3), 'DisplayName', '$\epsilon_{z}$ - Inertial')
legend();
xlabel('Time [s]');
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/nass_act_damp_ine_sim_tomo_trans.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>> <<plt-matlab>>
#+end_src #+end_src
@ -1710,21 +1897,31 @@ We load the results of tomography experiments.
#+begin_src matlab :exports none #+begin_src matlab :exports none
figure; figure;
ax1 = subplot(3, 1, 1);
hold on; hold on;
plot(t, En(:,4), 'DisplayName', '$\epsilon_{\theta_x}$') plot(t, En(:,4), 'DisplayName', '$\epsilon_{\theta_x}$')
plot(t, En(:,5), 'DisplayName', '$\epsilon_{\theta_y}$') plot(t, En_ine(:,4), 'DisplayName', '$\epsilon_{\theta_x}$ - Inertial')
plot(t, En(:,6), 'DisplayName', '$\epsilon_{\theta_z}$')
set(gca,'ColorOrderIndex',1);
plot(t, En_ine(:,4), '--', 'DisplayName', '$\epsilon_{\theta_x}$ - Inertial')
plot(t, En_ine(:,5), '--', 'DisplayName', '$\epsilon_{\theta_y}$ - Inertial')
plot(t, En_ine(:,6), '--', 'DisplayName', '$\epsilon_{\theta_z}$ - Inertial')
hold off;
xlim([0.5,inf]);
legend(); legend();
ax2 = subplot(3, 1, 2);
hold on;
plot(t, En(:,5), 'DisplayName', '$\epsilon_{\theta_y}$')
plot(t, En_ine(:,5), 'DisplayName', '$\epsilon_{\theta_y}$ - Inertial')
legend();
ylabel('Position Error [rad]');
ax3 = subplot(3, 1, 3);
hold on;
plot(t, En(:,6), 'DisplayName', '$\epsilon_{\theta_z}$')
plot(t, En_ine(:,6), 'DisplayName', '$\epsilon_{\theta_z}$ - Inertial')
legend();
xlabel('Time [s]');
linkaxes([ax1,ax2,ax3],'x');
#+end_src #+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes #+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/nass_act_damp_ine_sim_tomo_rot.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png") #+begin_src matlab :var filepath="figs/nass_act_damp_ine_sim_tomo_rot.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>> <<plt-matlab>>
#+end_src #+end_src
@ -2017,12 +2214,70 @@ Inertial Control:
*** Frequency Domain *** Frequency Domain
#+begin_src matlab #+begin_src matlab
Ts = t(1); % Sample Time for the Data [s] Ts = t(2)-t(1); % Sample Time for the Data [s]
n_av = 8; n_av = 8;
han_win = hanning(ceil(length(En(:, 1))/n_av)); han_win = hanning(ceil(length(En(:, 1))/n_av));
[pdx, f] = pwelch(Ern(:, 1), han_win, [], [], 1/Ts); [pxx, f] = pwelch(En(:, 1), han_win, [], [], 1/Ts);
[pxx_ine, ~] = pwelch(En_ine(:, 1), han_win, [], [], 1/Ts);
[pxx_dvf, ~] = pwelch(En_dvf(:, 1), han_win, [], [], 1/Ts);
[pxx_iff, ~] = pwelch(En_iff(:, 1), han_win, [], [], 1/Ts);
[pyy, ~] = pwelch(En(:, 2), han_win, [], [], 1/Ts);
[pyy_ine, ~] = pwelch(En_ine(:, 2), han_win, [], [], 1/Ts);
[pyy_dvf, ~] = pwelch(En_dvf(:, 2), han_win, [], [], 1/Ts);
[pyy_iff, ~] = pwelch(En_iff(:, 2), han_win, [], [], 1/Ts);
[pzz, ~] = pwelch(En(:, 3), han_win, [], [], 1/Ts);
[pzz_ine, ~] = pwelch(En_ine(:, 3), han_win, [], [], 1/Ts);
[pzz_dvf, ~] = pwelch(En_dvf(:, 3), han_win, [], [], 1/Ts);
[pzz_iff, ~] = pwelch(En_iff(:, 3), han_win, [], [], 1/Ts);
[prx, ~] = pwelch(En(:, 4), han_win, [], [], 1/Ts);
[prx_ine, ~] = pwelch(En_ine(:, 4), han_win, [], [], 1/Ts);
[prx_dvf, ~] = pwelch(En_dvf(:, 4), han_win, [], [], 1/Ts);
[prx_iff, ~] = pwelch(En_iff(:, 4), han_win, [], [], 1/Ts);
[pry, ~] = pwelch(En(:, 5), han_win, [], [], 1/Ts);
[pry_ine, ~] = pwelch(En_ine(:, 5), han_win, [], [], 1/Ts);
[pry_dvf, ~] = pwelch(En_dvf(:, 5), han_win, [], [], 1/Ts);
[pry_iff, ~] = pwelch(En_iff(:, 5), han_win, [], [], 1/Ts);
[prz, ~] = pwelch(En(:, 6), han_win, [], [], 1/Ts);
[prz_ine, ~] = pwelch(En_ine(:, 6), han_win, [], [], 1/Ts);
[prz_dvf, ~] = pwelch(En_dvf(:, 6), han_win, [], [], 1/Ts);
[prz_iff, ~] = pwelch(En_iff(:, 6), han_win, [], [], 1/Ts);
#+end_src
#+begin_src matlab
figure;
hold on;
plot(f, prx_ine, 'DisplayName', 'Inertial')
plot(f, prx_dvf, 'DisplayName', 'DVF')
plot(f, prx_iff, 'DisplayName', 'IFF')
plot(f, prx, 'k--', 'DisplayName', 'Undamped')
hold off;
xlabel('Frequency [Hz]');
ylabel('Power Spectral Density [$m^2/Hz$]');
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
legend('location', 'northeast');
xlim([1, 500]);
#+end_src
#+begin_src matlab
figure;
hold on;
plot(f, pxx_ine, 'DisplayName', 'Inertial')
plot(f, pxx_dvf, 'DisplayName', 'DVF')
plot(f, pxx_iff, 'DisplayName', 'IFF')
plot(f, pxx, 'k--', 'DisplayName', 'Undamped')
hold off;
xlabel('Frequency [Hz]');
ylabel('Power Spectral Density [$m^2/Hz$]');
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
legend('location', 'northeast');
xlim([1, 500]);
#+end_src #+end_src
* Useful Functions * Useful Functions
@ -2036,11 +2291,18 @@ Inertial Control:
This Matlab function is accessible [[file:src/prepareTomographyExperiment.m][here]]. This Matlab function is accessible [[file:src/prepareTomographyExperiment.m][here]].
*** Function Description *** Function Description
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab #+begin_src matlab
function [] = prepareTomographyExperiment(args) function [] = prepareTomographyExperiment(args)
#+end_src #+end_src
*** Optional Parameters *** Optional Parameters
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab #+begin_src matlab
arguments arguments
args.nass_actuator char {mustBeMember(args.nass_actuator,{'piezo', 'lorentz'})} = 'piezo' args.nass_actuator char {mustBeMember(args.nass_actuator,{'piezo', 'lorentz'})} = 'piezo'
@ -2050,6 +2312,9 @@ This Matlab function is accessible [[file:src/prepareTomographyExperiment.m][her
#+end_src #+end_src
*** Initialize the Simulation *** Initialize the Simulation
:PROPERTIES:
:UNNUMBERED: t
:END:
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
#+begin_src matlab #+begin_src matlab
initializeGround(); initializeGround();

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