111 lines
6.0 KiB
Matlab
111 lines
6.0 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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%% Colors for the figures
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colors = colororder;
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%% Frequency Vector [Hz]
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freqs = logspace(0, 3, 1000);
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%% Load the PSD of disturbances
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load('uniaxial_disturbance_psd.mat', 'f', 'psd_ft', 'psd_xf');
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%% Load Plants Dynamics
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load('uniaxial_plants.mat', 'G_vc_light', 'G_md_light', 'G_pz_light', ...
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'G_vc_mid', 'G_md_mid', 'G_pz_mid', ...
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'G_vc_heavy', 'G_md_heavy', 'G_pz_heavy');
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%% Sensitivity to disturbances for three different nano-hexpod stiffnesses
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G_vc_light('d', 'fs'), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G_md_light('d', 'fs'), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G_pz_light('d', 'fs'), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $d/f_{s}$ [m/N]'); xlabel('Frequency [Hz]');
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xticks([1e0, 1e1, 1e2]);
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xlim([1, 500]);
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%% Sensitivity to disturbances for three different nano-hexpod stiffnesses
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G_vc_light('d', 'ft'), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G_md_light('d', 'ft'), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G_pz_light('d', 'ft'), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $d/f_{t}$ [m/N]'); xlabel('Frequency [Hz]');
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xticks([1e0, 1e1, 1e2]);
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xlim([1, 500]);
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%% Sensitivity to disturbances for three different nano-hexpod stiffnesses
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G_vc_light('d', 'xf'), freqs, 'Hz'))), 'DisplayName', '$k_n = 0.01\,N/\mu m$');
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plot(freqs, abs(squeeze(freqresp(G_md_light('d', 'xf'), freqs, 'Hz'))), 'DisplayName', '$k_n = 1 \,N/\mu m$');
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plot(freqs, abs(squeeze(freqresp(G_pz_light('d', 'xf'), freqs, 'Hz'))), 'DisplayName', '$k_n = 100 \,N/\mu m$');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $d/x_{f}$ [m/m]'); xlabel('Frequency [Hz]');
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xticks([1e0, 1e1, 1e2]);
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leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15
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xlim([1, 500]);
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%% Cumulative Amplitude Spectrum of the relative motion d, due to both the floor motion and the stage vibrations
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figure;
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hold on;
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plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_vc_light('d', 'ft'), f, 'Hz'))).^2)))), '-', 'color', colors(1,:), 'DisplayName', '$f_t$');
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plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_md_light('d', 'ft'), f, 'Hz'))).^2)))), '-', 'color', colors(2,:), 'DisplayName', '$f_t$');
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plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_pz_light('d', 'ft'), f, 'Hz'))).^2)))), '-', 'color', colors(3,:), 'DisplayName', '$f_t$');
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plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_xf.*abs(squeeze(freqresp(G_vc_light('d', 'xf'), f, 'Hz'))).^2)))), '--', 'color', colors(1,:), 'DisplayName', '$x_f$ ($k_n = 0.01\,N/\mu m$)');
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plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_xf.*abs(squeeze(freqresp(G_md_light('d', 'xf'), f, 'Hz'))).^2)))), '--', 'color', colors(2,:), 'DisplayName', '$x_f$ ($k_n = 1 \,N/\mu m$)');
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plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_xf.*abs(squeeze(freqresp(G_pz_light('d', 'xf'), f, 'Hz'))).^2)))), '--', 'color', colors(3,:), 'DisplayName', '$x_f$ ($k_n = 100 \,N/\mu m$)');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('CAS [m]'); xlabel('Frequency [Hz]');
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leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
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leg.ItemTokenSize(1) = 15
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xlim([1, 500]);
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ylim([1e-12, 3e-6])
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%% Cumulative Amplitude Spectrum of the relative motion d due to all disturbances, for two sample masses
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figure;
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hold on;
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plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_vc_light('d', 'ft'), f, 'Hz'))).^2 + ...
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psd_xf.*abs(squeeze(freqresp(G_vc_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
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'color', colors(1,:), 'DisplayName', '$m_s = 1\,kg$, $k_n = 0.01\,N/\mu m$');
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plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_md_light('d', 'ft'), f, 'Hz'))).^2 + ...
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psd_xf.*abs(squeeze(freqresp(G_md_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
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'color', colors(2,:), 'DisplayName', '$m_s = 1\,kg$, $k_n = 1\,N/\mu m$');
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plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_pz_light('d', 'ft'), f, 'Hz'))).^2 + ...
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psd_xf.*abs(squeeze(freqresp(G_pz_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
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'color', colors(3,:), 'DisplayName', '$m_s = 1\,kg$, $k_n = 100\,N/\mu m$');
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plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_vc_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
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psd_xf.*abs(squeeze(freqresp(G_vc_heavy('d', 'xf'), f, 'Hz'))).^2)))), '--', ...
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'color', colors(1,:), 'DisplayName', '$m_s = 50\,kg$, $k_n = 0.01\,N/\mu m$');
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plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_md_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
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psd_xf.*abs(squeeze(freqresp(G_md_heavy('d', 'xf'), f, 'Hz'))).^2)))), '--', ...
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'color', colors(2,:), 'DisplayName', '$m_s = 50\,kg$, $k_n = 1\,N/\mu m$');
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plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_pz_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
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psd_xf.*abs(squeeze(freqresp(G_pz_heavy('d', 'xf'), f, 'Hz'))).^2)))), '--', ...
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'color', colors(3,:), 'DisplayName', '$m_s = 50\,kg$, $k_n = 100\,N/\mu m$');
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plot([1, 1e3], [20e-9, 20e-9], 'k--', 'HandleVisibility', 'off');
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text(4, 1e-8, '20 nm RMS', 'horizontalalignment', 'center');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('CAS [m]'); xlabel('Frequency [Hz]');
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leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15
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xlim([1, 500]);
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ylim([1e-12, 3e-6])
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