142 lines
3.0 KiB
Mathematica
142 lines
3.0 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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% Load Plant
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load('mat/plant.mat', 'Gi', 'Zc', 'Ga', 'Gc', 'Gn', 'Gd');
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% Test
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bodeFig({Ga*Zc*Gi}, struct('phase', true));
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% TODO Huddle Test
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% We load the data taken during the Huddle Test.
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load('mat/data_huddle_test.mat', ...
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't', 'Uch', 'Ucv', ...
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'Unh', 'Unv', ...
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'Vph', 'Vpv', ...
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'Vch', 'Vcv', ...
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'Vnh', 'Vnv', ...
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'Va');
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% We remove the first second of data where everything is settling down.
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t0 = 1;
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Uch(t<t0) = [];
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Ucv(t<t0) = [];
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Unh(t<t0) = [];
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Unv(t<t0) = [];
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Vph(t<t0) = [];
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Vpv(t<t0) = [];
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Vch(t<t0) = [];
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Vcv(t<t0) = [];
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Vnh(t<t0) = [];
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Vnv(t<t0) = [];
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Va(t<t0) = [];
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t(t<t0) = [];
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t = t - t(1); % We start at t=0
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figure;
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hold on;
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plot(t, Vph, 'DisplayName', '$Vp_h$');
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plot(t, Vpv, 'DisplayName', '$Vp_v$');
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hold off;
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xlabel('Time [s]');
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ylabel('Amplitude [V]');
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xlim([t(1), t(end)]);
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legend();
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% We compute the Power Spectral Density of the horizontal and vertical positions of the beam as measured by the 4 quadrant diode.
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[psd_Vph, f] = pwelch(Vph, hanning(ceil(1*fs)), [], [], fs);
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[psd_Vpv, ~] = pwelch(Vpv, hanning(ceil(1*fs)), [], [], fs);
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figure;
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hold on;
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plot(f, sqrt(psd_Vph), 'DisplayName', '$\Gamma_{Vp_h}$');
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plot(f, sqrt(psd_Vpv), 'DisplayName', '$\Gamma_{Vp_v}$');
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hold off;
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{V}{\sqrt{Hz}}\right]$')
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legend('Location', 'southwest');
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xlim([1, 1000]);
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figure;
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hold on;
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plot(t, Vch, 'DisplayName', '$Vc_h$');
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plot(t, Vcv, 'DisplayName', '$Vc_v$');
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hold off;
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xlabel('Time [s]');
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ylabel('Amplitude [V]');
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xlim([t(1), t(end)]);
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legend();
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% We compute the Power Spectral Density of the voltage across the inductance used for horizontal and vertical positioning of the Cercalo.
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[psd_Vch, f] = pwelch(Vch, hanning(ceil(1*fs)), [], [], fs);
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[psd_Vcv, ~] = pwelch(Vcv, hanning(ceil(1*fs)), [], [], fs);
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figure;
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hold on;
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plot(f, sqrt(psd_Vch), 'DisplayName', '$\Gamma_{Vc_h}$');
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plot(f, sqrt(psd_Vcv), 'DisplayName', '$\Gamma_{Vc_v}$');
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hold off;
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{V}{\sqrt{Hz}}\right]$')
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legend('Location', 'southwest');
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xlim([1, 1000]);
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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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% Load Plant
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load('mat/plant.mat', 'G');
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% RGA-Number
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freqs = logspace(2, 4, 1000);
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G_resp = freqresp(G, freqs, 'Hz');
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A = zeros(size(G_resp));
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RGAnum = zeros(1, length(freqs));
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for i = 1:length(freqs)
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A(:, :, i) = G_resp(:, :, i).*inv(G_resp(:, :, i))';
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RGAnum(i) = sum(sum(abs(A(:, :, i)-eye(2))));
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end
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% RGA = G0.*inv(G0)';
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figure;
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plot(freqs, RGAnum);
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set(gca, 'xscale', 'log');
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U = zeros(2, 2, length(freqs));
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S = zeros(2, 2, length(freqs))
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V = zeros(2, 2, length(freqs));
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for i = 1:length(freqs)
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[Ui, Si, Vi] = svd(G_resp(:, :, i));
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U(:, :, i) = Ui;
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S(:, :, i) = Si;
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V(:, :, i) = Vi;
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end
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% Rotation Matrix
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G0 = freqresp(G, 0);
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