97 lines
3.2 KiB
Matlab
97 lines
3.2 KiB
Matlab
%% 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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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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addpath('./src/'); % Path for Functions
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%% Colors for the figures
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colors = colororder;
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%% Simscape model name
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mdl = 'rotating_model';
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%% Load "Generic" system dynamics
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load('rotating_generic_plants.mat', 'Gs', 'Wzs');
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%% Root Locus for Relative Damping Control
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Krdc = s*eye(2); % Relative damping controller
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gains = logspace(-2, 2, 300); % Tested gains
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Wz_i = [1,3,4];
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figure;
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hold on;
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for i = 1:length(Wz_i)
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plot(real(pole(Gs{Wz_i(i)}({'du', 'dv'}, {'Fu', 'Fv'})*Krdc)), imag(pole(Gs{Wz_i(i)}({'du', 'dv'}, {'Fu', 'Fv'})*Krdc)), 'x', 'color', colors(i,:), ...
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'DisplayName', sprintf('$\\Omega = %.1f \\omega_0 $', Wzs(Wz_i(i))),'MarkerSize',8);
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plot(real(tzero(Gs{Wz_i(i)}({'du', 'dv'}, {'Fu', 'Fv'})*Krdc)), imag(tzero(Gs{Wz_i(i)}({'du', 'dv'}, {'Fu', 'Fv'})*Krdc)), 'o', 'color', colors(i,:), ...
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'HandleVisibility', 'off','MarkerSize',8);
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for g = gains
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cl_poles = pole(feedback(Gs{Wz_i(i)}({'du', 'dv'}, {'Fu', 'Fv'}), g*Krdc, -1));
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plot(real(cl_poles), imag(cl_poles), '.', 'color', colors(i,:), ...
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'HandleVisibility', 'off','MarkerSize',4);
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end
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end
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hold off;
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axis square;
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xlim([-1.8, 0.2]); ylim([0, 2]);
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xticks([-1, 0])
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xticklabels({'-$\omega_0$', '$0$'})
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yticks([0, 1, 2])
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yticklabels({'$0$', '$\omega_0$', '$2 \omega_0$'})
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xlabel('Real Part'); ylabel('Imaginary Part');
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leg = legend('location', 'northwest', 'FontSize', 8);
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leg.ItemTokenSize(1) = 8;
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i = 2;
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%% Relative Damping Controller
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Krdc = 2*s*eye(2);
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Krdc.InputName = {'Du', 'Dv'};
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Krdc.OutputName = {'Fu', 'Fv'};
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%% Compute the damped plant
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G_cl_rdc = feedback(Gs{i}, Krdc, 'name');
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%% Damped plant using Relative Damping Control
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freqs = logspace(-3, 2, 1000);
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
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% Magnitude
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ax1 = nexttile([2, 1]);
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hold on;
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plot(freqs, abs(squeeze(freqresp(Gs{i}( 'Du', 'Fu'), freqs, 'rad/s'))), '-', 'color', zeros(1,3), ...
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'DisplayName', 'OL - $G_d(1,1)$')
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plot(freqs, abs(squeeze(freqresp(G_cl_rdc('Du', 'Fu'), freqs, 'rad/s'))), '-', 'color', colors(1,:), ...
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'DisplayName', 'RDC - $G_d(1,1)$')
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plot(freqs, abs(squeeze(freqresp(Gs{i}( 'Dv', 'Fu'), freqs, 'rad/s'))), '-', 'color', [zeros(1,3), 0.5], ...
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'DisplayName', 'OL - $G_d(2,1)$')
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plot(freqs, abs(squeeze(freqresp(G_cl_rdc('Dv', 'Fu'), freqs, 'rad/s'))), '-', 'color', [colors(1,:), 0.5], ...
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'DisplayName', 'RDC - $G_d(2,1)$')
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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('Magnitude [m/N]');
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ldg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
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ldg.ItemTokenSize(1) = 20;
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ylim([1e-4, 1e2]);
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ax2 = nexttile;
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gs{i}('Du', 'Fu'), freqs, 'rad/s'))), '-', 'color', zeros(1,3))
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plot(freqs, 180/pi*angle(squeeze(freqresp(G_cl_rdc('Du', 'Fu'), freqs, 'rad/s'))), '-', 'color', colors(1,:))
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hold off;
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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 0]);
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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