78 lines
2.7 KiB
Mathematica
78 lines
2.7 KiB
Mathematica
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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freqs = logspace(0, 3, 1000);
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% Load Plant
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load('mat/plant.mat', 'sys', 'Gi', 'Zc', 'Ga', 'Gc', 'Gn', 'Gd');
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% Diagonal Controller
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% Using =SISOTOOL=, a diagonal controller is designed.
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% The two SISO loop gains are shown in Fig. [[fig:diag_contr_loop_gain]].
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Kh = -0.25598*(s+112)*(s^2 + 15.93*s + 6.686e06)/((s^2*(s+352.5)*(1+s/2/pi/2000)));
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Kv = 10207*(s+55.15)*(s^2 + 17.45*s + 2.491e06)/(s^2*(s+491.2)*(s+7695));
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K = blkdiag(Kh, Kv);
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K.InputName = {'Rh', 'Rv'};
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K.OutputName = {'Uch', 'Ucv'};
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figure;
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% Magnitude
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ax1 = subaxis(2,1,1);
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hold on;
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plot(freqs, abs(squeeze(freqresp(Kh*sys('Rh', 'Uch'), freqs, 'Hz'))), 'DisplayName', '$L_h = K_h G_{d,h}^{-1} G_{\frac{V_{p,h}}{\tilde{U}_{c,h}}} G_{i,h} $');
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plot(freqs, abs(squeeze(freqresp(Kv*sys('Rv', 'Ucv'), freqs, 'Hz'))), 'DisplayName', '$L_v = K_v G_{d,v}^{-1} G_{\frac{V_{p,v}}{\tilde{U}_{c,v}}} G_{i,v} $');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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set(gca, 'XTickLabel',[]);
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ylabel('Magnitude [dB]');
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hold off;
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legend('location', 'northeast');
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% Phase
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ax2 = subaxis(2,1,2);
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(Kh*sys('Rh', 'Uch'), freqs, 'Hz'))));
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plot(freqs, 180/pi*angle(squeeze(freqresp(Kv*sys('Rv', 'Ucv'), freqs, 'Hz'))));
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set(gca,'xscale','log');
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yticks(-180:90:180);
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ylim([-180 180]);
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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hold off;
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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% #+NAME: fig:diag_contr_loop_gain
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% #+CAPTION: Loop Gain using the Decentralized Diagonal Controller ([[./figs/diag_contr_loop_gain.png][png]], [[./figs/diag_contr_loop_gain.pdf][pdf]])
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% [[file:figs/diag_contr_loop_gain.png]]
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% We then close the loop and we look at the transfer function from the Newport rotation signal to the beam angle (Fig. [[fig:diag_contr_effect_newport]]).
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inputs = {'Uch', 'Ucv', 'Unh', 'Unv'};
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outputs = {'Vch', 'Vcv', 'Ich', 'Icv', 'Rh', 'Rv', 'Vph', 'Vpv'};
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sys_cl = connect(sys, -K, inputs, outputs);
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figure;
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hold on;
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(sys('Rh', 'Unh'), freqs, 'Hz'))), '-', 'DisplayName', 'OL - $R_h/U_{n,h}$');
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(sys_cl('Rh', 'Unh'), freqs, 'Hz'))), '--', 'DisplayName', 'CL - $R_h/U_{n,h}$');
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set(gca,'ColorOrderIndex',2);
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plot(freqs, abs(squeeze(freqresp(sys('Rv', 'Unv'), freqs, 'Hz'))), '-', 'DisplayName', 'OL - $R_v/U_{n,v}$');
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set(gca,'ColorOrderIndex',2);
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plot(freqs, abs(squeeze(freqresp(sys_cl('Rv', 'Unv'), freqs, 'Hz'))), '--', 'DisplayName', 'CL - $R_v/U_{n,v}$');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Magnitude [dB]');
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hold off;
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xlim([freqs(1), freqs(end)]);
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legend('location', 'southeast');
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