tdehaeze/svd-control
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Update Stewart Platform figures

Browse Source
This commit is contained in:
Thomas Dehaeze
2020-11-06 12:22:37 +01:00
parent 8425c1d613
commit f4d9fe6f66
14 changed files with 84788 additions and 1257 deletions
Download Patch File Download Diff File Expand all files Collapse all files

73
index.org
View File

@@ -945,7 +945,7 @@ The real approximation is computed as follows:
| 220.6 | -220.6 | 220.6 | -220.6 | 220.6 | -220.6 |
Please not that the plant $G$ at $\omega_c$ is already an almost real matrix.
Note that the plant $G$ at $\omega_c$ is already an almost real matrix.
This can be seen on the Bode plots where the phase is close to 1.
This can be verified below where only the real value of $G(\omega_c)$ is shown
@@ -1031,10 +1031,11 @@ Gershgorin Radii for the decoupled plant using the Jacobian:
hold off;
xlabel('Frequency (Hz)'); ylabel('Gershgorin Radii')
legend('location', 'northeast');
ylim([1e-3, 1e3]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/simscape_model_gershgorin_radii.pdf', 'width', 'full', 'height', 'full');
exportFig('figs/simscape_model_gershgorin_radii.pdf', 'eps', true, 'width', 'wide', 'height', 'tall');
#+end_src
#+name: fig:simscape_model_gershgorin_radii
@@ -1066,11 +1067,12 @@ Let's see the bode plot of the decoupled plant $G_d(s)$.
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude'); xlabel('Frequency [Hz]');
legend('location', 'southeast');
legend('location', 'northwest');
ylim([1e-3, 1e5]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/simscape_model_decoupled_plant_svd.pdf', 'width', 'full', 'height', 'full');
exportFig('figs/simscape_model_decoupled_plant_svd.pdf', 'eps', true, 'width', 'wide', 'height', 'tall');
#+end_src
#+name: fig:simscape_model_decoupled_plant_svd
@@ -1096,11 +1098,12 @@ Let's see the bode plot of the decoupled plant $G_d(s)$.
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude'); xlabel('Frequency [Hz]');
legend('location', 'southeast');
legend('location', 'northwest');
ylim([1e-3, 1e6]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/simscape_model_decoupled_plant_jacobian.pdf', 'width', 'full', 'height', 'full');
exportFig('figs/simscape_model_decoupled_plant_jacobian.pdf', 'eps', true, 'width', 'wide', 'height', 'tall');
#+end_src
#+name: fig:simscape_model_decoupled_plant_jacobian
@@ -1212,71 +1215,73 @@ Let's first verify the stability of the closed-loop systems:
The obtained transmissibility in Open-loop, for the centralized control as well as for the SVD control are shown in Figure [[fig:stewart_platform_simscape_cl_transmissibility]].
#+begin_src matlab :exports results
freqs = logspace(-3, 3, 1000);
freqs = logspace(-2, 2, 1000);
figure
figure;
tiledlayout(2, 2, 'TileSpacing', 'None', 'Padding', 'None');
ax1 = subplot(2, 3, 1);
ax1 = nexttile;
hold on;
plot(freqs, abs(squeeze(freqresp(G( 'Ax', 'Dwx')/s^2, freqs, 'Hz'))), 'DisplayName', 'Open-Loop');
plot(freqs, abs(squeeze(freqresp(G_cen('Ax', 'Dwx')/s^2, freqs, 'Hz'))), 'DisplayName', 'Centralized');
plot(freqs, abs(squeeze(freqresp(G_svd('Ax', 'Dwx')/s^2, freqs, 'Hz'))), 'DisplayName', 'SVD');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Transmissibility - $D_x/D_{w,x}$'); xlabel('Frequency [Hz]');
ylabel('$D_x/D_{w,x}$, $D_y/D_{w, y}$'); set(gca, 'XTickLabel',[]);
legend('location', 'southwest');
ax2 = subplot(2, 3, 2);
hold on;
plot(freqs, abs(squeeze(freqresp(G( 'Ay', 'Dwy')/s^2, freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(G_cen('Ay', 'Dwy')/s^2, freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(G_svd('Ay', 'Dwy')/s^2, freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Transmissibility - $D_y/D_{w,y}$'); xlabel('Frequency [Hz]');
% ax2 = nexttile;
% hold on;
% plot(freqs, abs(squeeze(freqresp(G( 'Ay', 'Dwy')/s^2, freqs, 'Hz'))));
% plot(freqs, abs(squeeze(freqresp(G_cen('Ay', 'Dwy')/s^2, freqs, 'Hz'))));
% plot(freqs, abs(squeeze(freqresp(G_svd('Ay', 'Dwy')/s^2, freqs, 'Hz'))));
% hold off;
% set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
% ylabel('Transmissibility - $D_y/D_{w,y}$'); xlabel('Frequency [Hz]');
ax3 = subplot(2, 3, 3);
ax3 = nexttile;
hold on;
plot(freqs, abs(squeeze(freqresp(G( 'Az', 'Dwz')/s^2, freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(G_cen('Az', 'Dwz')/s^2, freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(G_svd('Az', 'Dwz')/s^2, freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Transmissibility - $D_z/D_{w,z}$'); xlabel('Frequency [Hz]');
ylabel('$D_z/D_{w,z}$'); set(gca, 'XTickLabel',[]);
ax4 = subplot(2, 3, 4);
ax4 = nexttile;
hold on;
plot(freqs, abs(squeeze(freqresp(G( 'Arx', 'Rwx')/s^2, freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(G_cen('Arx', 'Rwx')/s^2, freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(G_svd('Arx', 'Rwx')/s^2, freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Transmissibility - $R_x/R_{w,x}$'); xlabel('Frequency [Hz]');
ylabel('$R_x/R_{w,x}$, $R_y/R_{w,y}$'); xlabel('Frequency [Hz]');
ax5 = subplot(2, 3, 5);
hold on;
plot(freqs, abs(squeeze(freqresp(G( 'Ary', 'Rwy')/s^2, freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(G_cen('Ary', 'Rwy')/s^2, freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(G_svd('Ary', 'Rwy')/s^2, freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Transmissibility - $R_y/R_{w,y}$'); xlabel('Frequency [Hz]');
% ax5 = nexttile;
% hold on;
% plot(freqs, abs(squeeze(freqresp(G( 'Ary', 'Rwy')/s^2, freqs, 'Hz'))));
% plot(freqs, abs(squeeze(freqresp(G_cen('Ary', 'Rwy')/s^2, freqs, 'Hz'))));
% plot(freqs, abs(squeeze(freqresp(G_svd('Ary', 'Rwy')/s^2, freqs, 'Hz'))));
% hold off;
% set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
% ylabel('Transmissibility - $R_y/R_{w,y}$'); xlabel('Frequency [Hz]');
ax6 = subplot(2, 3, 6);
ax6 = nexttile;
hold on;
plot(freqs, abs(squeeze(freqresp(G( 'Arz', 'Rwz')/s^2, freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(G_cen('Arz', 'Rwz')/s^2, freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(G_svd('Arz', 'Rwz')/s^2, freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Transmissibility - $R_z/R_{w,z}$'); xlabel('Frequency [Hz]');
ylabel('$R_z/R_{w,z}$'); xlabel('Frequency [Hz]');
linkaxes([ax1,ax2,ax3,ax4,ax5,ax6],'x');
linkaxes([ax1,ax2,ax3,ax4,ax5,ax6],'xy');
xlim([freqs(1), freqs(end)]);
ylim([1e-5, 1e2]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/stewart_platform_simscape_cl_transmissibility.pdf', 'width', 1600, 'height', 'full');
exportFig('figs/stewart_platform_simscape_cl_transmissibility.pdf', 'eps', true, 'width', 'wide', 'height', 'tall');
#+end_src
#+name: fig:stewart_platform_simscape_cl_transmissibility