Merge few figures
This commit is contained in:
@@ -70,13 +70,13 @@ The control configuration are compare in section [[sec:comparison]].
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#+end_src
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** Control Schematic
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The control architecture is shown in Figure [[fig:control_measure_rotating_2dof]].
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The control architecture is shown in Figure [[fig:decentralized_reference_tracking_L]].
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The required leg length $\bm{r}_\mathcal{L}$ is computed from the reference path $\bm{r}_\mathcal{X}$ using the inverse kinematics.
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Then, a diagonal (decentralized) controller $\bm{K}_\mathcal{L}$ is used such that each leg lengths stays close to its required length.
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#+begin_src latex :file control_measure_rotating_2dof.pdf
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#+begin_src latex :file decentralized_reference_tracking_L.pdf
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\begin{tikzpicture}
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% Blocs
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\node[block, align=center] (J) at (0, 0) {Inverse\\Kinematics};
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@@ -93,10 +93,10 @@ Then, a diagonal (decentralized) controller $\bm{K}_\mathcal{L}$ is used such th
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\end{tikzpicture}
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#+end_src
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#+name: fig:control_measure_rotating_2dof
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#+name: fig:decentralized_reference_tracking_L
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#+caption: Decentralized control for reference tracking
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#+RESULTS:
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[[file:figs/control_measure_rotating_2dof.png]]
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[[file:figs/decentralized_reference_tracking_L.png]]
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** Initialize the Stewart platform
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#+begin_src matlab :noweb yes
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@@ -121,49 +121,9 @@ Let's identify the transfer function from $\bm{\tau}$ to $\bm{\mathcal{L}}$.
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#+end_src
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** Plant Analysis
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The diagonal terms of the plant is shown in Figure [[fig:plant_decentralized_diagonal]].
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The diagonal and off-diagonal terms of the plant are shown in Figure [[fig:plant_decentralized_L]].
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All the diagonal terms are equal.
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#+begin_src matlab :exports none
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freqs = logspace(1, 4, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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for i = 1:6
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plot(freqs, abs(squeeze(freqresp(G(i, i), freqs, 'Hz'))));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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ax2 = subplot(2, 1, 2);
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hold on;
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for i = 1:6
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plot(freqs, 180/pi*angle(squeeze(freqresp(G(i, i), freqs, 'Hz'))));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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linkaxes([ax1,ax2],'x');
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#+end_src
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#+header: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/plant_decentralized_diagonal.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+name: fig:plant_decentralized_diagonal
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#+caption: Diagonal Elements of the Plant ([[./figs/plant_decentralized_diagonal.png][png]], [[./figs/plant_decentralized_diagonal.pdf][pdf]])
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[[file:figs/plant_decentralized_diagonal.png]]
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The off-diagonal terms are shown in Figure [[fig:plant_decentralized_off_diagonal]].
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We see that the plant is decoupled at low frequency which indicate that decentralized control may be a good idea.
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#+begin_src matlab :exports none
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@@ -171,7 +131,29 @@ We see that the plant is decoupled at low frequency which indicate that decentra
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figure;
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ax1 = subplot(2, 1, 1);
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ax1 = subplot(2, 2, 1);
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hold on;
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for i = 1:6
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plot(freqs, abs(squeeze(freqresp(G(i, i), freqs, 'Hz'))));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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title('Diagonal elements of the Plant');
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ax2 = subplot(2, 2, 3);
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hold on;
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for i = 1:6
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plot(freqs, 180/pi*angle(squeeze(freqresp(G(i, i), freqs, 'Hz'))), 'DisplayName', sprintf('$d\\mathcal{L}_%i/\\tau_%i$', i, i));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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legend('location', 'northwest');
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ax3 = subplot(2, 2, 2);
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hold on;
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for i = 1:5
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for j = i+1:6
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@@ -183,8 +165,9 @@ We see that the plant is decoupled at low frequency which indicate that decentra
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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title('Off-Diagonal elements of the Plant');
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ax2 = subplot(2, 1, 2);
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ax4 = subplot(2, 2, 4);
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hold on;
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for i = 1:5
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for j = i+1:6
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@@ -199,17 +182,17 @@ We see that the plant is decoupled at low frequency which indicate that decentra
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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linkaxes([ax1,ax2],'x');
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linkaxes([ax1,ax2,ax3,ax4],'x');
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#+end_src
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#+header: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/plant_decentralized_off_diagonal.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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#+begin_src matlab :var filepath="figs/plant_decentralized_L.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+name: fig:plant_decentralized_off_diagonal
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#+caption: Diagonal Elements of the Plant ([[./figs/plant_decentralized_off_diagonal.png][png]], [[./figs/plant_decentralized_off_diagonal.pdf][pdf]])
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[[file:figs/plant_decentralized_off_diagonal.png]]
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#+name: fig:plant_decentralized_L
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#+caption: Obtain Diagonal and off diagonal dynamics ([[./figs/plant_decentralized_L.png][png]], [[./figs/plant_decentralized_L.pdf][pdf]])
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[[file:figs/plant_decentralized_L.png]]
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** Controller Design
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The controller consists of:
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@@ -558,12 +541,16 @@ We now multiply the plant by the Jacobian matrix as shown in Figure [[fig:centra
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Gl.OutputName = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6'};
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#+end_src
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The bode plot of the plant is shown in Figure [[fig:plant_centralized_L]].
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We can see that the diagonal elements are identical.
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This will simplify the design of the controller as all the elements of the diagonal controller can be made identical.
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#+begin_src matlab :exports none
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freqs = logspace(1, 4, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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ax1 = subplot(2, 2, 1);
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hold on;
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for i = 1:6
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plot(freqs, abs(squeeze(freqresp(Gl(i, i), freqs, 'Hz'))));
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@@ -571,42 +558,21 @@ We now multiply the plant by the Jacobian matrix as shown in Figure [[fig:centra
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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title('Diagonal elements of the Plant');
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ax2 = subplot(2, 1, 2);
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ax2 = subplot(2, 2, 3);
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hold on;
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for i = 1:6
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gl(i, i), freqs, 'Hz'))), 'DisplayName', ['$d\mathcal{L}_' num2str(i) '/\tau_' num2str(i) '$']);
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gl(i, i), freqs, 'Hz'))), 'DisplayName', sprintf('$\\epsilon_{\\mathcal{L}_%i}/\\tau_%i$', i, i));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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legend();
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legend('location', 'northwest');
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linkaxes([ax1,ax2],'x');
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#+end_src
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#+header: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/plant_centralized_diagonal_L.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+name: fig:plant_centralized_diagonal_L
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#+caption: Diagonal Elements of the plant $\bm{J} \bm{G}$ ([[./figs/plant_centralized_diagonal_L.png][png]], [[./figs/plant_centralized_diagonal_L.pdf][pdf]])
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[[file:figs/plant_centralized_diagonal_L.png]]
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All the diagonal elements are identical.
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This will simplify the design of the controller as all the elements of the diagonal controller can be made identical.
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The off-diagonal terms of the controller are shown in Figure [[fig:plant_centralized_off_diagonal_L]].
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#+begin_src matlab :exports none
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freqs = logspace(1, 4, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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ax3 = subplot(2, 2, 2);
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hold on;
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for i = 1:5
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for j = i+1:6
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@@ -618,8 +584,9 @@ The off-diagonal terms of the controller are shown in Figure [[fig:plant_central
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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title('Off-Diagonal elements of the Plant');
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ax2 = subplot(2, 1, 2);
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ax4 = subplot(2, 2, 4);
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hold on;
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for i = 1:5
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for j = i+1:6
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@@ -634,17 +601,17 @@ The off-diagonal terms of the controller are shown in Figure [[fig:plant_central
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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linkaxes([ax1,ax2],'x');
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linkaxes([ax1,ax2,ax3,ax4],'x');
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#+end_src
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#+header: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/plant_centralized_off_diagonal_L.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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#+begin_src matlab :var filepath="figs/plant_centralized_L.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+name: fig:plant_centralized_off_diagonal_L
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#+caption: Off Diagonal Elements of the plant $\bm{J} \bm{G}$ ([[./figs/plant_centralized_off_diagonal_L.png][png]], [[./figs/plant_centralized_off_diagonal_L.pdf][pdf]])
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[[file:figs/plant_centralized_off_diagonal_L.png]]
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#+name: fig:plant_centralized_L
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#+caption: Diagonal and off-diagonal elements of the plant $\bm{K}\bm{G}$ ([[./figs/plant_centralized_L.png][png]], [[./figs/plant_centralized_L.pdf][pdf]])
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[[file:figs/plant_centralized_L.png]]
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We can see that this *totally decouples the system at low frequency*.
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@@ -774,7 +741,7 @@ We now multiply the plant by the Jacobian matrix as shown in Figure [[fig:centra
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figure;
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ax1 = subplot(2, 1, 1);
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ax1 = subplot(2, 2, 1);
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hold on;
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for i = 1:6
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plot(freqs, abs(squeeze(freqresp(Gx(i, i), freqs, 'Hz'))));
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@@ -782,8 +749,9 @@ We now multiply the plant by the Jacobian matrix as shown in Figure [[fig:centra
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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title('Diagonal elements of the Plant');
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ax2 = subplot(2, 1, 2);
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ax2 = subplot(2, 2, 3);
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hold on;
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for i = 1:6
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gx(i, i), freqs, 'Hz'))), 'DisplayName', labels{i});
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@@ -793,30 +761,9 @@ We now multiply the plant by the Jacobian matrix as shown in Figure [[fig:centra
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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legend();
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legend('location', 'northwest');
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linkaxes([ax1,ax2],'x');
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#+end_src
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#+header: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/plant_centralized_diagonal_X.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+name: fig:plant_centralized_diagonal_X
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#+caption: Diagonal Elements of the plant $\bm{G} \bm{J}^{-T}$ ([[./figs/plant_centralized_diagonal_X.png][png]], [[./figs/plant_centralized_diagonal_X.pdf][pdf]])
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[[file:figs/plant_centralized_diagonal_X.png]]
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The diagonal terms are not the same.
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The resonances of the system are "decoupled".
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For instance, the vertical resonance of the system is only present on the diagonal term corresponding to $D_z/\mathcal{F}_z$.
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#+begin_src matlab :exports none
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freqs = logspace(1, 4, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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ax3 = subplot(2, 2, 2);
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hold on;
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for i = 1:5
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for j = i+1:6
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@@ -828,8 +775,9 @@ For instance, the vertical resonance of the system is only present on the diagon
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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title('Off-Diagonal elements of the Plant');
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ax2 = subplot(2, 1, 2);
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ax4 = subplot(2, 2, 4);
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hold on;
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for i = 1:5
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for j = i+1:6
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@@ -844,17 +792,21 @@ For instance, the vertical resonance of the system is only present on the diagon
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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linkaxes([ax1,ax2],'x');
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linkaxes([ax1,ax2,ax3,ax4],'x');
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#+end_src
|
||||
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#+header: :tangle no :exports results :results none :noweb yes
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||||
#+begin_src matlab :var filepath="figs/plant_centralized_off_diagonal_X.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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#+begin_src matlab :var filepath="figs/plant_centralized_X.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+name: fig:plant_centralized_off_diagonal_X
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#+caption: Off Diagonal Elements of the plant $\bm{G} \bm{J}^{-T}$ ([[./figs/plant_centralized_off_diagonal_X.png][png]], [[./figs/plant_centralized_off_diagonal_X.pdf][pdf]])
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||||
[[file:figs/plant_centralized_off_diagonal_X.png]]
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#+name: fig:plant_centralized_X
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||||
#+caption: Diagonal and off-diagonal elements of the plant $\bm{G} \bm{J}^{-T}$ ([[./figs/plant_centralized_X.png][png]], [[./figs/plant_centralized_X.pdf][pdf]])
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[[file:figs/plant_centralized_X.png]]
|
||||
|
||||
The diagonal terms are not the same.
|
||||
The resonances of the system are "decoupled".
|
||||
For instance, the vertical resonance of the system is only present on the diagonal term corresponding to $D_z/\mathcal{F}_z$.
|
||||
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||||
Here the system is almost decoupled at all frequencies except for the transfer functions $\frac{R_y}{\mathcal{F}_x}$ and $\frac{R_x}{\mathcal{F}_y}$.
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@@ -985,7 +937,7 @@ The control architecture is shown in Figure [[fig:centralized_reference_tracking
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||||
|
||||
*** Plant Analysis
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The plant is pre-multiplied by $\bm{G}^{-1}(\omega = 0)$.
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||||
The diagonal elements of the shaped plant are shown in Figure [[fig:plant_centralized_diagonal_SD]].
|
||||
The diagonal and off-diagonal elements of the shaped plant are shown in Figure [[fig:plant_centralized_SD]].
|
||||
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#+begin_src matlab
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G0 = G*inv(freqresp(G, 0));
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@@ -996,7 +948,7 @@ The diagonal elements of the shaped plant are shown in Figure [[fig:plant_centra
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||||
|
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figure;
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||||
|
||||
ax1 = subplot(2, 1, 1);
|
||||
ax1 = subplot(2, 2, 1);
|
||||
hold on;
|
||||
for i = 1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G0(i, i), freqs, 'Hz'))));
|
||||
@@ -1004,37 +956,21 @@ The diagonal elements of the shaped plant are shown in Figure [[fig:plant_centra
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
title('Diagonal elements of the Plant');
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
ax2 = subplot(2, 2, 3);
|
||||
hold on;
|
||||
for i = 1:6
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G0(i, i), freqs, 'Hz'))), 'DisplayName', ['$G_0(' num2str(i) ',' num2str(i) ')$']);
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||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G0(i, i), freqs, 'Hz'))), 'DisplayName', sprintf('$G_0(%i,%i)$', i, i));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
legend();
|
||||
legend('location', 'northwest');
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
#+header: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/plant_centralized_diagonal_SD.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+name: fig:plant_centralized_diagonal_SD
|
||||
#+caption: Diagonal Elements of the plant $\bm{G} \bm{G}^{-1}(\omega = 0)$ ([[./figs/plant_centralized_diagonal_SD.png][png]], [[./figs/plant_centralized_diagonal_SD.pdf][pdf]])
|
||||
[[file:figs/plant_centralized_diagonal_SD.png]]
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 4, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
ax1 = subplot(2, 1, 1);
|
||||
ax3 = subplot(2, 2, 2);
|
||||
hold on;
|
||||
for i = 1:5
|
||||
for j = i+1:6
|
||||
@@ -1046,8 +982,9 @@ The diagonal elements of the shaped plant are shown in Figure [[fig:plant_centra
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
title('Off-Diagonal elements of the Plant');
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
ax4 = subplot(2, 2, 4);
|
||||
hold on;
|
||||
for i = 1:5
|
||||
for j = i+1:6
|
||||
@@ -1062,17 +999,17 @@ The diagonal elements of the shaped plant are shown in Figure [[fig:plant_centra
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
linkaxes([ax1,ax2,ax3,ax4],'x');
|
||||
#+end_src
|
||||
|
||||
#+header: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/plant_centralized_off_diagonal_SD.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
#+begin_src matlab :var filepath="figs/plant_centralized_SD.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+name: fig:plant_centralized_off_diagonal_SD
|
||||
#+caption: Off Diagonal Elements of the plant $\bm{G} \bm{J}^{-T}$ ([[./figs/plant_centralized_off_diagonal_SD.png][png]], [[./figs/plant_centralized_off_diagonal_SD.pdf][pdf]])
|
||||
[[file:figs/plant_centralized_off_diagonal_SD.png]]
|
||||
#+name: fig:plant_centralized_SD
|
||||
#+caption: Diagonal and off-diagonal elements of the plant $\bm{G} \bm{G}^{-1}(\omega = 0)$ ([[./figs/plant_centralized_SD.png][png]], [[./figs/plant_centralized_SD.pdf][pdf]])
|
||||
[[file:figs/plant_centralized_SD.png]]
|
||||
|
||||
*** Controller Design
|
||||
We have that:
|
||||
@@ -1296,14 +1233,14 @@ Let's identify the transfer function from $\bm{\tau}$ to $\bm{L}$.
|
||||
#+end_src
|
||||
|
||||
*** Obtained Plant
|
||||
The diagonal elements of the plant are shown in Figure [[fig:hybrid_control_Kl_plant_diagonal]] while the off diagonal terms are shown in Figure [[fig:hybrid_control_Kl_plant_off_diagonal]].
|
||||
The obtained plant is shown in Figure [[fig:hybrid_control_Kl_plant]].
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 4, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
ax1 = subplot(2, 1, 1);
|
||||
ax1 = subplot(2, 2, 1);
|
||||
hold on;
|
||||
for i = 1:6
|
||||
plot(freqs, abs(squeeze(freqresp(Gl(i, i), freqs, 'Hz'))));
|
||||
@@ -1311,36 +1248,21 @@ The diagonal elements of the plant are shown in Figure [[fig:hybrid_control_Kl_p
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
title('Diagonal elements of the Plant');
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
ax2 = subplot(2, 2, 3);
|
||||
hold on;
|
||||
for i = 1:6
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gl(i, i), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gl(i, i), freqs, 'Hz'))), 'DisplayName', sprintf('$\\epsilon_{\\mathcal{L}_%i}/\\tau_%i$', i, i));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
legend('location', 'northwest');
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
#+header: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/hybrid_control_Kl_plant_diagonal.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+name: fig:hybrid_control_Kl_plant_diagonal
|
||||
#+caption: Diagonal elements of the plant for the design of $\bm{K}_\mathcal{L}$ ([[./figs/hybrid_control_Kl_plant_diagonal.png][png]], [[./figs/hybrid_control_Kl_plant_diagonal.pdf][pdf]])
|
||||
[[file:figs/hybrid_control_Kl_plant_diagonal.png]]
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 4, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
ax1 = subplot(2, 1, 1);
|
||||
ax3 = subplot(2, 2, 2);
|
||||
hold on;
|
||||
for i = 1:5
|
||||
for j = i+1:6
|
||||
@@ -1352,8 +1274,9 @@ The diagonal elements of the plant are shown in Figure [[fig:hybrid_control_Kl_p
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
title('Off-Diagonal elements of the Plant');
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
ax4 = subplot(2, 2, 4);
|
||||
hold on;
|
||||
for i = 1:5
|
||||
for j = i+1:6
|
||||
@@ -1368,17 +1291,17 @@ The diagonal elements of the plant are shown in Figure [[fig:hybrid_control_Kl_p
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
linkaxes([ax1,ax2,ax3,ax4],'x');
|
||||
#+end_src
|
||||
|
||||
#+header: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/hybrid_control_Kl_plant_off_diagonal.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
#+begin_src matlab :var filepath="figs/hybrid_control_Kl_plant.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+name: fig:hybrid_control_Kl_plant_off_diagonal
|
||||
#+caption: Off-diagonal elements of the plant for the design of $\bm{K}_\mathcal{L}$ ([[./figs/hybrid_control_Kl_plant_off_diagonal.png][png]], [[./figs/hybrid_control_Kl_plant_off_diagonal.pdf][pdf]])
|
||||
[[file:figs/hybrid_control_Kl_plant_off_diagonal.png]]
|
||||
#+name: fig:hybrid_control_Kl_plant
|
||||
#+caption: Diagonal and off-diagonal elements of the plant for the design of $\bm{K}_\mathcal{L}$ ([[./figs/hybrid_control_Kl_plant.png][png]], [[./figs/hybrid_control_Kl_plant.pdf][pdf]])
|
||||
[[file:figs/hybrid_control_Kl_plant.png]]
|
||||
|
||||
*** Controller Design
|
||||
We apply a decentralized (diagonal) direct velocity feedback.
|
||||
|
||||
Reference in New Issue
Block a user