Modify labels and legends
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bb0a89ba25
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45b4752831
@ -125,7 +125,7 @@ The system becomes unstable for $\Omega > \omega_0$.
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end
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plot(Ws, zeros(size(Ws)), 'k--')
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hold off;
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xlabel('Rotation Frequency [rad/s]'); ylabel('Pole Real Part');
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xlabel('Rotation Frequency [rad/s]'); ylabel('Real Part');
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ax2 = subplot(1,2,2);
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hold on;
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@ -134,7 +134,7 @@ The system becomes unstable for $\Omega > \omega_0$.
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plot(Ws, -imag(p_ws(p_i, :)), 'k-')
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end
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hold off;
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xlabel('Rotation Frequency [rad/s]'); ylabel('Pole Imaginary Part');
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xlabel('Rotation Frequency [rad/s]'); ylabel('Imaginary Part');
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#+end_src
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** Simscape Model
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@ -184,7 +184,8 @@ No controller for now.
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plot(freqs, abs(squeeze(freqresp(G_th(1,1), freqs))), '--')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]); ylabel('Amplitude [m/N]');
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set(gca, 'XTickLabel',[]); ylabel('Magnitude [m/N]');
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title('$d_u/F_u$, $d_v/F_v$');
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ax3 = subplot(2, 2, 3);
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hold on;
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@ -202,21 +203,24 @@ No controller for now.
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plot(freqs, abs(squeeze(freqresp(G_th(1,2), freqs))), '--')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]); ylabel('Amplitude [m/N]');
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set(gca, 'XTickLabel',[]); ylabel('Magnitude [m/N]');
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title('$d_u/F_v$, $d_v/F_u$');
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ax4 = subplot(2, 2, 4);
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(G(1,2), freqs))), '-')
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plot(freqs, 180/pi*angle(squeeze(freqresp(G_th(1,2), freqs))), '--')
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plot(freqs, 180/pi*angle(squeeze(freqresp(G(1,2), freqs))), '-', ...
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'DisplayName', 'Simscape')
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plot(freqs, 180/pi*angle(squeeze(freqresp(G_th(1,2), freqs))), '--', ...
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'DisplayName', 'Analytical')
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [rad/s]'); ylabel('Phase [deg]');
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yticks(-180:90:180);
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ylim([-180 180]);
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hold off;
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legend('location', 'northeast');
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linkaxes([ax1,ax2,ax3,ax4],'x');
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xlim([freqs(1), freqs(end)]);
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linkaxes([ax1,ax2],'y');
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#+end_src
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@ -370,7 +374,8 @@ No controller for now.
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plot(freqs, abs(squeeze(freqresp(Giff_th(1,1), freqs))), '--')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]); ylabel('Amplitude [N/N]');
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set(gca, 'XTickLabel',[]); ylabel('Magnitude [N/N]');
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title('$f_u/F_u$, $f_v/F_v$');
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ax3 = subplot(2, 2, 3);
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hold on;
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@ -388,21 +393,24 @@ No controller for now.
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plot(freqs, abs(squeeze(freqresp(Giff_th(1,2), freqs))), '--')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]); ylabel('Amplitude [N/N]');
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set(gca, 'XTickLabel',[]); ylabel('Magnitude [N/N]');
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title('$f_u/F_v$, $f_v/F_u$');
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ax4 = subplot(2, 2, 4);
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(Giff(1,2), freqs))), '-')
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plot(freqs, 180/pi*angle(squeeze(freqresp(Giff_th(1,2), freqs))), '--')
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plot(freqs, 180/pi*angle(squeeze(freqresp(Giff(1,2), freqs))), '-', ...
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'DisplayName', 'Simscape')
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plot(freqs, 180/pi*angle(squeeze(freqresp(Giff_th(1,2), freqs))), '--', ...
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'DisplayName', 'Analytical')
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [rad/s]'); ylabel('Phase [deg]');
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yticks(-180:90:180);
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ylim([-180 180]);
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hold off;
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legend('location', 'northeast');
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linkaxes([ax1,ax2,ax3,ax4],'x');
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xlim([freqs(1), freqs(end)]);
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linkaxes([ax1,ax2],'y');
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#+end_src
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@ -436,7 +444,7 @@ No controller for now.
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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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set(gca, 'XTickLabel',[]); ylabel('Amplitude [N/N]');
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set(gca, 'XTickLabel',[]); ylabel('Magnitude [N/N]');
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legend('location', 'northwest');
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ylim([0, 1e3]);
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@ -631,7 +639,7 @@ Let's take the integral feedback controller as a low pass filter (pseudo integra
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plot(freqs, abs(squeeze(freqresp(Giff(1,1)*Kiff(1,1), freqs))))
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]); ylabel('Amplitude [N/N]');
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set(gca, 'XTickLabel',[]); ylabel('Loop Gain');
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ax2 = subplot(2, 1, 2);
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hold on;
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@ -795,17 +803,20 @@ Root Locus that shows the maximum damping attainable.
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plot(freqs, abs(squeeze(freqresp(Giff_cl(1,1), freqs))))
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]); ylabel('Amplitude [N/N]');
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set(gca, 'XTickLabel',[]); ylabel('Magnitude [N/N]');
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(Giff(1,1), freqs))))
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plot(freqs, 180/pi*angle(squeeze(freqresp(Giff_cl(1,1), freqs))))
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plot(freqs, 180/pi*angle(squeeze(freqresp(Giff(1,1), freqs))), ...
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'DisplayName', 'Open Loop')
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plot(freqs, 180/pi*angle(squeeze(freqresp(Giff_cl(1,1), freqs))), ...
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'DisplayName', 'Closed Loop')
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [rad/s]'); ylabel('Phase [deg]');
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yticks(-180:90:180);
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ylim([-180 180]);
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hold off;
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legend('location', 'northeast');
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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@ -946,7 +957,7 @@ And the IFF plant is identified in three different cases:
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plot(freqs, abs(squeeze(freqresp(Giff_l(1,1), freqs))), 'k:')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]); ylabel('Amplitude [N/N]');
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set(gca, 'XTickLabel',[]); ylabel('Magnitude [N/N]');
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ax2 = subplot(2, 1, 2);
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hold on;
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@ -1109,16 +1120,16 @@ Let's take $k_p = 2 m \Omega^2$ and find the optimal IFF control gain.
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gains = logspace(-2, 4, 100);
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hold on;
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plot(real(pole(Giff)), imag(pole(Giff)), 'kx', 'HandleVisibility', 'off');
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plot(real(tzero(Giff)), imag(tzero(Giff)), 'ko', 'HandleVisibility', 'off');
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plot(real(pole(Giff)), imag(pole(Giff)), 'kx');
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plot(real(tzero(Giff)), imag(tzero(Giff)), 'ko');
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for g = gains
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clpoles = pole(feedback(Giff, (g/s)*eye(2)));
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plot(real(clpoles), imag(clpoles), 'k.', 'HandleVisibility', 'off');
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plot(real(clpoles), imag(clpoles), 'k.');
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end
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% Optimal Gain
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clpoles = pole(feedback(Giff, (opt_gain/s)*eye(2)));
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set(gca,'ColorOrderIndex',1);
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plot(real(clpoles), imag(clpoles), 'x', 'HandleVisibility', 'off');
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plot(real(clpoles), imag(clpoles), 'x');
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hold off;
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axis square;
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xlim([-1.2, 0.05]); ylim([0, 1.25]);
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@ -1141,12 +1152,14 @@ Let's take $k_p = 2 m \Omega^2$ and find the optimal IFF control gain.
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plot(freqs, abs(squeeze(freqresp(Giff_cl(1,1), freqs))))
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]); ylabel('Amplitude [N/N]');
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set(gca, 'XTickLabel',[]); ylabel('Magnitude [N/N]');
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(Giff(1,1), freqs))))
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plot(freqs, 180/pi*angle(squeeze(freqresp(Giff_cl(1,1), freqs))))
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plot(freqs, 180/pi*angle(squeeze(freqresp(Giff(1,1), freqs))), ...
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'DisplayName', 'Open Loop')
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plot(freqs, 180/pi*angle(squeeze(freqresp(Giff_cl(1,1), freqs))), ...
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'DisplayName', 'Closed Loop')
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [rad/s]'); ylabel('Phase [deg]');
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yticks(-180:90:180);
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@ -1155,6 +1168,8 @@ Let's take $k_p = 2 m \Omega^2$ and find the optimal IFF control gain.
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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legend('location', 'southwest');
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#+end_src
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* Direct Velocity Feedback
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@ -1257,7 +1272,8 @@ The DVF plant is identified from the Simscape model and compared with the analyt
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plot(freqs, abs(squeeze(freqresp(Gdvf_th(1,1), freqs))), '--')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]); ylabel('Amplitude [m/s/N]');
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set(gca, 'XTickLabel',[]); ylabel('Magnitude [$\frac{m/s}{N}$]');
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title('$v_u/F_u$, $v_v/F_v$');
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ax3 = subplot(2, 2, 3);
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hold on;
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@ -1275,7 +1291,8 @@ The DVF plant is identified from the Simscape model and compared with the analyt
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plot(freqs, abs(squeeze(freqresp(Gdvf_th(1,2), freqs))), '--')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]); ylabel('Amplitude [m/s/N]');
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set(gca, 'XTickLabel',[]); ylabel('Magnitude [$\frac{m/s}{N}$]');
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title('$v_u/F_v$, $v_v/F_u$');
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ax4 = subplot(2, 2, 4);
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hold on;
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@ -1499,7 +1516,7 @@ The rotation speed is set to $\Omega = 0.1 \omega_0$.
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set(gca,'ColorOrderIndex',3);
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plot(real(tzero(Gdvf)), imag(tzero(Gdvf)), 'o', ...
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'HandleVisibility', 'off');
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for g = gains
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for g_i = gains
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Kdvf = g*eye(2);
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cl_poles = pole(feedback(Gdvf, Kdvf));
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set(gca,'ColorOrderIndex',3);
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@ -1708,7 +1725,7 @@ DVF:
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'DisplayName', 'IFF Pseudo int')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Frequency [rad/s]'); ylabel('Amplitude [m/m]');
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ylabel('Frequency [rad/s]'); ylabel('Transmissibility [m/m]');
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legend('location', 'northwest');
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#+end_src
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