637 lines
31 KiB
Matlab
637 lines
31 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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%% Damped plants for three considered payload masses - Comparison of active damping techniques
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% Integral Force Feedback
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
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ax1 = nexttile([2,1]);
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hold on;
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plot(freqs, abs(squeeze(freqresp(G_vc_light('fm', 'f'), freqs, 'Hz'))), '-', 'color', colors(1,:), 'DisplayName', '$m_s = 1\,kg$');
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plot(freqs, abs(squeeze(freqresp(G_vc_mid( 'fm', 'f'), freqs, 'Hz'))), '-.', 'color', colors(1,:), 'DisplayName', '$m_s = 25\,kg$');
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plot(freqs, abs(squeeze(freqresp(G_vc_heavy('fm', 'f'), freqs, 'Hz'))), '--', 'color', colors(1,:), 'DisplayName', '$m_s = 50\,kg$');
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plot(freqs, abs(squeeze(freqresp(G_md_light('fm', 'f'), freqs, 'Hz'))), '-', 'color', colors(2,:), 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_md_mid( 'fm', 'f'), freqs, 'Hz'))), '-.', 'color', colors(2,:), 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_md_heavy('fm', 'f'), freqs, 'Hz'))), '--', 'color', colors(2,:), 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_pz_light('fm', 'f'), freqs, 'Hz'))), '-', 'color', colors(3,:), 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_pz_mid( 'fm', 'f'), freqs, 'Hz'))), '-.', 'color', colors(3,:), 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_pz_heavy('fm', 'f'), freqs, 'Hz'))), '--', 'color', colors(3,:), 'HandleVisibility', 'off');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
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ldg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
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ldg.ItemTokenSize = [20, 1];
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ax1b = nexttile();
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hold on;
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_light('fm', 'f'), freqs, 'Hz')))), '-', 'color', colors(1,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_mid( 'fm', 'f'), freqs, 'Hz')))), '-.', 'color', colors(1,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_heavy('fm', 'f'), freqs, 'Hz')))), '--', 'color', colors(1,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_light('fm', 'f'), freqs, 'Hz')))), '-', 'color', colors(2,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_mid( 'fm', 'f'), freqs, 'Hz')))), '-.', 'color', colors(2,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_heavy('fm', 'f'), freqs, 'Hz')))), '--', 'color', colors(2,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_light('fm', 'f'), freqs, 'Hz')))), '-', 'color', colors(3,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_mid( 'fm', 'f'), freqs, 'Hz')))), '-.', 'color', colors(3,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_heavy('fm', 'f'), freqs, 'Hz')))), '--', 'color', colors(3,:));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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xticks([1e0, 1e1, 1e2]);
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yticks(-360:90:360);
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ylim([-200, 20]);
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linkaxes([ax1,ax1b],'x');
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xlim([1, 1000]);
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% Relative Motion Control
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
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ax2 = nexttile([2,1]);
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hold on;
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plot(freqs, abs(squeeze(freqresp(G_vc_light('dL', 'f'), freqs, 'Hz'))), '-', 'color', colors(1,:));
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plot(freqs, abs(squeeze(freqresp(G_vc_mid( 'dL', 'f'), freqs, 'Hz'))), '-.', 'color', colors(1,:));
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plot(freqs, abs(squeeze(freqresp(G_vc_heavy('dL', 'f'), freqs, 'Hz'))), '--', 'color', colors(1,:));
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plot(freqs, abs(squeeze(freqresp(G_md_light('dL', 'f'), freqs, 'Hz'))), '-', 'color', colors(2,:));
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plot(freqs, abs(squeeze(freqresp(G_md_mid( 'dL', 'f'), freqs, 'Hz'))), '-.', 'color', colors(2,:));
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plot(freqs, abs(squeeze(freqresp(G_md_heavy('dL', 'f'), freqs, 'Hz'))), '--', 'color', colors(2,:));
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plot(freqs, abs(squeeze(freqresp(G_pz_light('dL', 'f'), freqs, 'Hz'))), '-', 'color', colors(3,:));
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plot(freqs, abs(squeeze(freqresp(G_pz_mid( 'dL', 'f'), freqs, 'Hz'))), '-.', 'color', colors(3,:));
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plot(freqs, abs(squeeze(freqresp(G_pz_heavy('dL', 'f'), freqs, 'Hz'))), '--', 'color', colors(3,:));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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ax2b = nexttile();
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hold on;
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_light('dL', 'f'), freqs, 'Hz')))), '-', 'color', colors(1,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_mid( 'dL', 'f'), freqs, 'Hz')))), '-.', 'color', colors(1,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_heavy('dL', 'f'), freqs, 'Hz')))), '--', 'color', colors(1,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_light('dL', 'f'), freqs, 'Hz')))), '-', 'color', colors(2,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_mid( 'dL', 'f'), freqs, 'Hz')))), '-.', 'color', colors(2,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_heavy('dL', 'f'), freqs, 'Hz')))), '--', 'color', colors(2,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_light('dL', 'f'), freqs, 'Hz')))), '-', 'color', colors(3,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_mid( 'dL', 'f'), freqs, 'Hz')))), '-.', 'color', colors(3,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_heavy('dL', 'f'), freqs, 'Hz')))), '--', 'color', colors(3,:));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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xticks([1e0, 1e1, 1e2]);
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yticks(-360:90:360);
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ylim([-200, 20]);
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linkaxes([ax2,ax2b],'x');
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xlim([1, 1000]);
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% Direct Velocity Feedback
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
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ax3 = nexttile([2,1]);
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hold on;
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plot(freqs, abs(squeeze(freqresp(G_vc_light('vn', 'f'), freqs, 'Hz'))), '-', 'color', colors(1,:), 'DisplayName', '$k_n = 0.01\,N/\mu m$');
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plot(freqs, abs(squeeze(freqresp(G_vc_mid( 'vn', 'f'), freqs, 'Hz'))), '-.', 'color', colors(1,:), 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_vc_heavy('vn', 'f'), freqs, 'Hz'))), '--', 'color', colors(1,:), 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_md_light('vn', 'f'), freqs, 'Hz'))), '-', 'color', colors(2,:), 'DisplayName', '$k_n = 1\,N/\mu m$');
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plot(freqs, abs(squeeze(freqresp(G_md_mid( 'vn', 'f'), freqs, 'Hz'))), '-.', 'color', colors(2,:), 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_md_heavy('vn', 'f'), freqs, 'Hz'))), '--', 'color', colors(2,:), 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_pz_light('vn', 'f'), freqs, 'Hz'))), '-', 'color', colors(3,:), 'DisplayName', '$k_n = 100\,N/\mu m$');
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plot(freqs, abs(squeeze(freqresp(G_pz_mid( 'vn', 'f'), freqs, 'Hz'))), '-.', 'color', colors(3,:), 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_pz_heavy('vn', 'f'), freqs, 'Hz'))), '--', 'color', colors(3,:), 'HandleVisibility', 'off');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/s/N]'); set(gca, 'XTickLabel',[]);
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ldg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
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ldg.ItemTokenSize = [20, 1];
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ax3b = nexttile();
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hold on;
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_light('vn', 'f'), freqs, 'Hz')))), '-', 'color', colors(1,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_mid( 'vn', 'f'), freqs, 'Hz')))), '-.', 'color', colors(1,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_heavy('vn', 'f'), freqs, 'Hz')))), '--', 'color', colors(1,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_light('vn', 'f'), freqs, 'Hz')))), '-', 'color', colors(2,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_mid( 'vn', 'f'), freqs, 'Hz')))), '-.', 'color', colors(2,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_heavy('vn', 'f'), freqs, 'Hz')))), '--', 'color', colors(2,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_light('vn', 'f'), freqs, 'Hz')))), '-', 'color', colors(3,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_mid( 'vn', 'f'), freqs, 'Hz')))), '-.', 'color', colors(3,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_heavy('vn', 'f'), freqs, 'Hz')))), '--', 'color', colors(3,:));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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xticks([1e0, 1e1, 1e2]);
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yticks(-360:90:360);
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ylim([-110, 110]);
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linkaxes([ax3,ax3b],'x');
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xlim([1, 1000]);
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%% Design of Active Damping controllers to have reasonable damping
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% IFF
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K_iff_vc = 20/(s + 2*pi*0.01);
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K_iff_vc.InputName = {'fm'};
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K_iff_vc.OutputName = {'f'};
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K_iff_md = 200/(s + 2*pi*0.01);
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K_iff_md.InputName = {'fm'};
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K_iff_md.OutputName = {'f'};
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K_iff_pz = 4000/(s + 2*pi*0.01);
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K_iff_pz.InputName = {'fm'};
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K_iff_pz.OutputName = {'f'};
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% RDC
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K_rdc_vc = -1e3*s;
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K_rdc_vc.InputName = {'dL'};
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K_rdc_vc.OutputName = {'f'};
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K_rdc_md = -1e4*s;
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K_rdc_md.InputName = {'dL'};
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K_rdc_md.OutputName = {'f'};
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K_rdc_pz = -1e5*s;
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K_rdc_pz.InputName = {'dL'};
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K_rdc_pz.OutputName = {'f'};
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% DVF
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K_dvf_vc = -tf(1e3);
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K_dvf_vc.InputName = {'vn'};
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K_dvf_vc.OutputName = {'f'};
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K_dvf_md = -tf(8e3);
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K_dvf_md.InputName = {'vn'};
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K_dvf_md.OutputName = {'f'};
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K_dvf_pz = -tf(2e5);
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K_dvf_pz.InputName = {'vn'};
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K_dvf_pz.OutputName = {'f'};
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%% Save Active Damping Controller
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save('./mat/uniaxial_active_damping_controllers.mat', 'K_iff_vc', 'K_iff_md', 'K_iff_pz', ...
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'K_rdc_vc', 'K_rdc_md', 'K_rdc_pz', ...
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'K_dvf_vc', 'K_dvf_md', 'K_dvf_pz');
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%% Compute Damped Plants
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% IFF
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G_iff_vc_light = feedback(G_vc_light, K_iff_vc, 'name', +1);
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G_iff_vc_mid = feedback(G_vc_mid , K_iff_vc, 'name', +1);
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G_iff_vc_heavy = feedback(G_vc_heavy, K_iff_vc, 'name', +1);
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G_iff_md_light = feedback(G_md_light, K_iff_md, 'name', +1);
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G_iff_md_mid = feedback(G_md_mid , K_iff_md, 'name', +1);
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G_iff_md_heavy = feedback(G_md_heavy, K_iff_md, 'name', +1);
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G_iff_pz_light = feedback(G_pz_light, K_iff_pz, 'name', +1);
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G_iff_pz_mid = feedback(G_pz_mid , K_iff_pz, 'name', +1);
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G_iff_pz_heavy = feedback(G_pz_heavy, K_iff_pz, 'name', +1);
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% RDC
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G_rdc_vc_light = feedback(G_vc_light, K_rdc_vc, 'name', +1);
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G_rdc_vc_mid = feedback(G_vc_mid , K_rdc_vc, 'name', +1);
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G_rdc_vc_heavy = feedback(G_vc_heavy, K_rdc_vc, 'name', +1);
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G_rdc_md_light = feedback(G_md_light, K_rdc_md, 'name', +1);
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G_rdc_md_mid = feedback(G_md_mid , K_rdc_md, 'name', +1);
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G_rdc_md_heavy = feedback(G_md_heavy, K_rdc_md, 'name', +1);
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G_rdc_pz_light = feedback(G_pz_light, K_rdc_pz, 'name', +1);
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G_rdc_pz_mid = feedback(G_pz_mid , K_rdc_pz, 'name', +1);
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G_rdc_pz_heavy = feedback(G_pz_heavy, K_rdc_pz, 'name', +1);
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% DVF
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G_dvf_vc_light = feedback(G_vc_light, K_dvf_vc, 'name', +1);
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G_dvf_vc_mid = feedback(G_vc_mid , K_dvf_vc, 'name', +1);
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G_dvf_vc_heavy = feedback(G_vc_heavy, K_dvf_vc, 'name', +1);
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G_dvf_md_light = feedback(G_md_light, K_dvf_md, 'name', +1);
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G_dvf_md_mid = feedback(G_md_mid , K_dvf_md, 'name', +1);
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G_dvf_md_heavy = feedback(G_md_heavy, K_dvf_md, 'name', +1);
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G_dvf_pz_light = feedback(G_pz_light, K_dvf_pz, 'name', +1);
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G_dvf_pz_mid = feedback(G_pz_mid , K_dvf_pz, 'name', +1);
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G_dvf_pz_heavy = feedback(G_pz_heavy, K_dvf_pz, 'name', +1);
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%% Verify Stability
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% IFF
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if not(isstable(G_iff_vc_light) && isstable(G_iff_vc_mid) && isstable(G_iff_vc_heavy) && ...
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isstable(G_iff_md_light) && isstable(G_iff_md_mid) && isstable(G_iff_md_heavy) && ...
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isstable(G_iff_pz_light) && isstable(G_iff_pz_mid) && isstable(G_iff_pz_heavy))
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warning("One of the damped plant with decentralized IFF is not stable.");
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end
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% RDC
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if not(isstable(G_rdc_vc_light) && isstable(G_rdc_vc_mid) && isstable(G_rdc_vc_heavy) && ...
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isstable(G_rdc_md_light) && isstable(G_rdc_md_mid) && isstable(G_rdc_md_heavy) && ...
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isstable(G_rdc_pz_light) && isstable(G_rdc_pz_mid) && isstable(G_rdc_pz_heavy))
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warning("One of the damped plant with decentralized RDC is not stable.");
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end
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% DVF
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if not(isstable(G_dvf_vc_light) && isstable(G_dvf_vc_mid) && isstable(G_dvf_vc_heavy) && ...
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isstable(G_dvf_md_light) && isstable(G_dvf_md_mid) && isstable(G_dvf_md_heavy) && ...
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isstable(G_dvf_pz_light) && isstable(G_dvf_pz_mid) && isstable(G_dvf_pz_heavy))
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warning("One of the damped plant with decentralized DVF is not stable.");
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end
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%% Save Damped Plants
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save('./mat/uniaxial_damped_plants.mat', 'G_iff_vc_light', 'G_iff_md_light', 'G_iff_pz_light', ...
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'G_rdc_vc_light', 'G_rdc_md_light', 'G_rdc_pz_light', ...
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'G_dvf_vc_light', 'G_dvf_md_light', 'G_dvf_pz_light', ...
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'G_iff_vc_mid', 'G_iff_md_mid', 'G_iff_pz_mid', ...
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'G_rdc_vc_mid', 'G_rdc_md_mid', 'G_rdc_pz_mid', ...
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'G_dvf_vc_mid', 'G_dvf_md_mid', 'G_dvf_pz_mid', ...
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'G_iff_vc_heavy', 'G_iff_md_heavy', 'G_iff_pz_heavy', ...
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'G_rdc_vc_heavy', 'G_rdc_md_heavy', 'G_rdc_pz_heavy', ...
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'G_dvf_vc_heavy', 'G_dvf_md_heavy', 'G_dvf_pz_heavy');
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%% Active Damping Robustness to change of sample's mass - Root Locus for all three damping techniques with 3 different sample's masses
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% Soft Nano-Hexapod
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figure;
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hold on;
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% IFF
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plot(real(pole(G_vc_light('fm', 'f'))), imag(pole(G_vc_light('fm', 'f'))), 'x', 'color', colors(1,:), ...
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'HandleVisibility', 'off');
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plot(real(zero(G_vc_light('fm', 'f'))), imag(zero(G_vc_light('fm', 'f'))), 'o', 'color', colors(1,:), ...
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'DisplayName', 'IFF');
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for g = logspace(0,2,400)
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clpoles = pole(feedback(G_vc_light('fm', 'f'), g/s, +1));
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plot(real(clpoles), imag(clpoles), '.', 'color', colors(1,:), ...
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'HandleVisibility', 'off');
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end
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% RDC
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plot(real(pole(G_vc_light('dL', 'f'))), imag(pole(G_vc_light('dL', 'f'))), 'x', 'color', colors(2,:), ...
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'HandleVisibility', 'off');
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plot(real(zero(G_vc_light('dL', 'f'))), imag(zero(G_vc_light('dL', 'f'))), 'o', 'color', colors(2,:), ...
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'DisplayName', 'RDC');
|
|
for g = logspace(1,3,400)
|
|
clpoles = pole(feedback(G_vc_light('dL', 'f'), -g*s, +1));
|
|
plot(real(clpoles), imag(clpoles), '.', 'color', colors(2,:), ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
|
|
% DVF
|
|
plot(real(pole(G_vc_light('vn', 'f'))), imag(pole(G_vc_light('vn', 'f'))), 'x', 'color', colors(3,:), ...
|
|
'HandleVisibility', 'off');
|
|
plot(real(zero(G_vc_light('vn', 'f'))), imag(zero(G_vc_light('vn', 'f'))), 'o', 'color', colors(3,:), ...
|
|
'DisplayName', 'DVF');
|
|
for g = logspace(1,3,400)
|
|
clpoles = pole(feedback(G_vc_light('vn', 'f'), -g, +1));
|
|
plot(real(clpoles), imag(clpoles), '.', 'color', colors(3,:), ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
hold off;
|
|
axis square;
|
|
xlabel('Real Part'); ylabel('Imaginary Part');
|
|
ldg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
|
ldg.ItemTokenSize = [10, 1];
|
|
xlim([-30, 0]); ylim([0, 30]);
|
|
ytickangle(90)
|
|
|
|
% Medium-Stiff Nano-Hexapod
|
|
figure;
|
|
hold on;
|
|
% IFF
|
|
plot(real(pole(G_md_light('fm', 'f'))), imag(pole(G_md_light('fm', 'f'))), 'x', 'color', colors(1,:), ...
|
|
'HandleVisibility', 'off');
|
|
plot(real(zero(G_md_light('fm', 'f'))), imag(zero(G_md_light('fm', 'f'))), 'o', 'color', colors(1,:), ...
|
|
'HandleVisibility', 'off');
|
|
for g = logspace(0,3,400)
|
|
clpoles = pole(feedback(G_md_light('fm', 'f'), g/s, +1));
|
|
plot(real(clpoles), imag(clpoles), '.', 'color', colors(1,:), ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
|
|
% RDC
|
|
plot(real(pole(G_md_light('dL', 'f'))), imag(pole(G_md_light('dL', 'f'))), 'x', 'color', colors(2,:), ...
|
|
'HandleVisibility', 'off');
|
|
plot(real(zero(G_md_light('dL', 'f'))), imag(zero(G_md_light('dL', 'f'))), 'o', 'color', colors(2,:), ...
|
|
'HandleVisibility', 'off');
|
|
for g = logspace(2,4,400)
|
|
clpoles = pole(feedback(G_md_light('dL', 'f'), -g*s, +1));
|
|
plot(real(clpoles), imag(clpoles), '.', 'color', colors(2,:), ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
|
|
% DVF
|
|
plot(real(pole(G_md_light('vn', 'f'))), imag(pole(G_md_light('vn', 'f'))), 'x', 'color', colors(3,:), ...
|
|
'HandleVisibility', 'off');
|
|
plot(real(zero(G_md_light('vn', 'f'))), imag(zero(G_md_light('vn', 'f'))), 'o', 'color', colors(3,:), ...
|
|
'HandleVisibility', 'off');
|
|
for g = logspace(2,4,400)
|
|
clpoles = pole(feedback(G_md_light('vn', 'f'), -g, +1));
|
|
plot(real(clpoles), imag(clpoles), '.', 'color', colors(3,:), ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
hold off;
|
|
axis square;
|
|
xlabel('Real Part'); ylabel('Imaginary Part');
|
|
xlim([-300, 0]); ylim([0, 300]);
|
|
ytickangle(90)
|
|
|
|
% Stiff Nano Hexapod
|
|
figure;
|
|
hold on;
|
|
% IFF
|
|
plot(real(pole(G_pz_light('fm', 'f'))), imag(pole(G_pz_light('fm', 'f'))), 'x', 'color', colors(1,:), ...
|
|
'HandleVisibility', 'off');
|
|
plot(real(zero(G_pz_light('fm', 'f'))), imag(zero(G_pz_light('fm', 'f'))), 'o', 'color', colors(1,:), ...
|
|
'HandleVisibility', 'off');
|
|
for g = logspace(2,5,400)
|
|
clpoles = pole(feedback(G_pz_light('fm', 'f'), g/s, +1));
|
|
plot(real(clpoles), imag(clpoles), '.', 'color', colors(1,:), ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
|
|
% RDC
|
|
plot(real(pole(G_pz_light('dL', 'f'))), imag(pole(G_pz_light('dL', 'f'))), 'x', 'color', colors(2,:), ...
|
|
'HandleVisibility', 'off');
|
|
plot(real(zero(G_pz_light('dL', 'f'))), imag(zero(G_pz_light('dL', 'f'))), 'o', 'color', colors(2,:), ...
|
|
'HandleVisibility', 'off');
|
|
for g = logspace(3,6,400)
|
|
clpoles = pole(feedback(G_pz_light('dL', 'f'), -g*s, +1));
|
|
plot(real(clpoles), imag(clpoles), '.', 'color', colors(2,:), ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
|
|
% DVF
|
|
plot(real(pole(G_pz_light('vn', 'f'))), imag(pole(G_pz_light('vn', 'f'))), 'x', 'color', colors(3,:), ...
|
|
'HandleVisibility', 'off');
|
|
plot(real(zero(G_pz_light('vn', 'f'))), imag(zero(G_pz_light('vn', 'f'))), 'o', 'color', colors(3,:), ...
|
|
'HandleVisibility', 'off');
|
|
for g = logspace(3,6,400)
|
|
clpoles = pole(feedback(G_pz_light('vn', 'f'), -g, +1));
|
|
plot(real(clpoles), imag(clpoles), '.', 'color', colors(3,:), ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
hold off;
|
|
axis square;
|
|
xlabel('Real Part'); ylabel('Imaginary Part');
|
|
xlim([-4000, 0]); ylim([0, 4000]);
|
|
ytickangle(90)
|
|
|
|
%% Root Locus for the three damping techniques
|
|
|
|
figure;
|
|
|
|
hold on;
|
|
% IFF
|
|
plot(real(pole(G_md_mid('fm', 'f'))), imag(pole(G_md_mid('fm', 'f'))), 'x', 'color', colors(1,:), ...
|
|
'DisplayName', 'IFF');
|
|
plot(real(zero(G_md_mid('fm', 'f'))), imag(zero(G_md_mid('fm', 'f'))), 'o', 'color', colors(1,:), ...
|
|
'HandleVisibility', 'off');
|
|
for g = logspace(1,4,500)
|
|
clpoles = pole(feedback(G_md_mid('fm', 'f'), g/s, +1));
|
|
plot(real(clpoles), imag(clpoles), '.', 'color', colors(1,:), ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
|
|
% RDC
|
|
plot(real(pole(G_md_mid('dL', 'f'))), imag(pole(G_md_mid('dL', 'f'))), 'x', 'color', colors(2,:), ...
|
|
'DisplayName', 'RDC');
|
|
plot(real(zero(G_md_mid('dL', 'f'))), imag(zero(G_md_mid('dL', 'f'))), 'o', 'color', colors(2,:), ...
|
|
'HandleVisibility', 'off');
|
|
% Estimate the maximum damping added by RDC
|
|
gs = logspace(2,5,500);
|
|
phis = zeros(size(gs));
|
|
for i = 1:length(gs)
|
|
g = gs(i);
|
|
clpoles = pole(feedback(G_md_mid('dL', 'f'), -g*s, +1));
|
|
plot(real(clpoles), imag(clpoles), '.', 'color', colors(2,:), ...
|
|
'HandleVisibility', 'off');
|
|
% Estimate damping of u-station mode
|
|
ustation_pole = clpoles(imag(clpoles)>1000);
|
|
phis(i) = atan2(abs(real(ustation_pole)), abs(imag(ustation_pole)));
|
|
end
|
|
[~, i_max] = max(phis);
|
|
plot([0, -5e3*sin(phis(i_max))], [0, 5e3*cos(phis(i_max))], 'k--', 'HandleVisibility', 'off');
|
|
clpoles_max = pole(feedback(G_md_mid('dL', 'f'), -gs(i_max)*s, +1));
|
|
ustation_pole = clpoles_max(imag(clpoles_max)>1000);
|
|
plot(real(ustation_pole), imag(ustation_pole), 'kx', ...
|
|
'HandleVisibility', 'off');
|
|
% Plot angle
|
|
plot(-8e2*sin(0:0.01:max(phis)), 8e2*cos(sin(0:0.01:max(phis))), 'k-', 'HandleVisibility', 'off')
|
|
text(-200, 850, '$\phi$', 'horizontalalignment', 'center');
|
|
text(real(ustation_pole)-100, imag(ustation_pole), '$\xi = \sin(\phi)$', 'horizontalalignment', 'right');
|
|
|
|
% DVF
|
|
plot(real(pole(G_md_mid('vn', 'f'))), imag(pole(G_md_mid('vn', 'f'))), 'x', 'color', colors(3,:), ...
|
|
'DisplayName', 'DVF');
|
|
plot(real(zero(G_md_mid('vn', 'f'))), imag(zero(G_md_mid('vn', 'f'))), 'o', 'color', colors(3,:), ...
|
|
'HandleVisibility', 'off');
|
|
for g = logspace(2,5,500)
|
|
clpoles = pole(feedback(G_md_mid('vn', 'f'), -tf(g), +1));
|
|
plot(real(clpoles), imag(clpoles), '.', 'color', colors(3,:), ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
hold off;
|
|
xlim([-2100, 0]); ylim([0, 2100]);
|
|
axis square;
|
|
xlabel('Real Part'); ylabel('Imaginary Part');
|
|
ldg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
|
ldg.ItemTokenSize = [10, 1];
|
|
|
|
%% Obtained damped transfer function from f to d for the three damping techniques
|
|
figure;
|
|
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
|
|
|
ax1 = nexttile([2,1]);
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_vc_mid('d', 'f'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL');
|
|
plot(freqs, abs(squeeze(freqresp(G_iff_vc_mid('d', 'f'), freqs, 'Hz'))), 'color', colors(1,:), 'DisplayName', 'IFF');
|
|
plot(freqs, abs(squeeze(freqresp(G_rdc_vc_mid('d', 'f'), freqs, 'Hz'))), 'color', colors(2,:), 'DisplayName', 'RDC');
|
|
plot(freqs, abs(squeeze(freqresp(G_dvf_vc_mid('d', 'f'), freqs, 'Hz'))), 'color', colors(3,:), 'DisplayName', 'DVF');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude $d/f$ [m/N]'); set(gca, 'XTickLabel',[]);
|
|
|
|
ax2 = nexttile();
|
|
hold on;
|
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_mid('d', 'f'), freqs, 'Hz')))), 'k-');
|
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_iff_vc_mid('d', 'f'), freqs, 'Hz')))), 'color', colors(1,:));
|
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_rdc_vc_mid('d', 'f'), freqs, 'Hz')))), 'color', colors(2,:));
|
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_dvf_vc_mid('d', 'f'), freqs, 'Hz')))), 'color', colors(3,:));
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
|
yticks(-360:90:360);
|
|
ylim([-270, 90]);
|
|
xticks([1e0, 1e1, 1e2]);
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([1, 500]);
|
|
|
|
%% Obtained damped transfer function from f to d for the three damping techniques
|
|
figure;
|
|
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
|
|
|
ax1 = nexttile([2,1]);
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_md_mid('d', 'f'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL');
|
|
plot(freqs, abs(squeeze(freqresp(G_iff_md_mid('d', 'f'), freqs, 'Hz'))), 'color', colors(1,:), 'DisplayName', 'IFF');
|
|
plot(freqs, abs(squeeze(freqresp(G_rdc_md_mid('d', 'f'), freqs, 'Hz'))), 'color', colors(2,:), 'DisplayName', 'RDC');
|
|
plot(freqs, abs(squeeze(freqresp(G_dvf_md_mid('d', 'f'), freqs, 'Hz'))), 'color', colors(3,:), 'DisplayName', 'DVF');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude $d/f$ [m/N]'); set(gca, 'XTickLabel',[]);
|
|
|
|
ax2 = nexttile();
|
|
hold on;
|
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_mid('d', 'f'), freqs, 'Hz')))), 'k-');
|
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_iff_md_mid('d', 'f'), freqs, 'Hz')))), 'color', colors(1,:));
|
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_rdc_md_mid('d', 'f'), freqs, 'Hz')))), 'color', colors(2,:));
|
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_dvf_md_mid('d', 'f'), freqs, 'Hz')))), 'color', colors(3,:));
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
|
yticks(-360:90:360);
|
|
ylim([-270, 90]);
|
|
xticks([1e0, 1e1, 1e2]);
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([1, 500]);
|
|
|
|
%% Obtained damped transfer function from f to d for the three damping techniques
|
|
figure;
|
|
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
|
|
|
ax1 = nexttile([2,1]);
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_pz_mid('d', 'f'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL');
|
|
plot(freqs, abs(squeeze(freqresp(G_iff_pz_mid('d', 'f'), freqs, 'Hz'))), 'color', colors(1,:), 'DisplayName', 'IFF');
|
|
plot(freqs, abs(squeeze(freqresp(G_rdc_pz_mid('d', 'f'), freqs, 'Hz'))), 'color', colors(2,:), 'DisplayName', 'RDC');
|
|
plot(freqs, abs(squeeze(freqresp(G_dvf_pz_mid('d', 'f'), freqs, 'Hz'))), 'color', colors(3,:), 'DisplayName', 'DVF');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude $d/f$ [m/N]'); set(gca, 'XTickLabel',[]);
|
|
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
|
leg.ItemTokenSize(1) = 15;
|
|
|
|
ax2 = nexttile();
|
|
hold on;
|
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_mid('d', 'f'), freqs, 'Hz')))), 'k-');
|
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_iff_pz_mid('d', 'f'), freqs, 'Hz')))), 'color', colors(1,:));
|
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_rdc_pz_mid('d', 'f'), freqs, 'Hz')))), 'color', colors(2,:));
|
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_dvf_pz_mid('d', 'f'), freqs, 'Hz')))), 'color', colors(3,:));
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
|
yticks(-360:90:360);
|
|
ylim([-270, 90]);
|
|
xticks([1e0, 1e1, 1e2]);
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([1, 500]);
|
|
|
|
%% Change of sensitivity to disturbance with all three active damping strategies
|
|
% FS
|
|
figure;
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_md_mid('d', 'fs'), freqs, 'Hz'))), 'k-');
|
|
plot(freqs, abs(squeeze(freqresp(G_iff_md_mid('d', 'fs'), freqs, 'Hz'))), 'color', colors(1,:));
|
|
plot(freqs, abs(squeeze(freqresp(G_rdc_md_mid('d', 'fs'), freqs, 'Hz'))), 'color', colors(2,:));
|
|
plot(freqs, abs(squeeze(freqresp(G_dvf_md_mid('d', 'fs'), freqs, 'Hz'))), 'color', colors(3,:));
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude $d/f_{s}$ [m/N]'); xlabel('Frequency [Hz]');
|
|
xticks([1e0, 1e1, 1e2]);
|
|
xlim([1, 500]);
|
|
|
|
figure;
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_md_mid('d', 'ft'), freqs, 'Hz'))), 'k-');
|
|
plot(freqs, abs(squeeze(freqresp(G_iff_md_mid('d', 'ft'), freqs, 'Hz'))), 'color', colors(1,:));
|
|
plot(freqs, abs(squeeze(freqresp(G_rdc_md_mid('d', 'ft'), freqs, 'Hz'))), 'color', colors(2,:));
|
|
plot(freqs, abs(squeeze(freqresp(G_dvf_md_mid('d', 'ft'), freqs, 'Hz'))), 'color', colors(3,:));
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude $d/f_{t}$ [m/N]'); xlabel('Frequency [Hz]');
|
|
xticks([1e0, 1e1, 1e2]);
|
|
xlim([1, 500]);
|
|
|
|
figure;
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_md_mid('d', 'xf'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL');
|
|
plot(freqs, abs(squeeze(freqresp(G_iff_md_mid('d', 'xf'), freqs, 'Hz'))), 'color', colors(1,:), 'DisplayName', 'IFF');
|
|
plot(freqs, abs(squeeze(freqresp(G_rdc_md_mid('d', 'xf'), freqs, 'Hz'))), 'color', colors(2,:), 'DisplayName', 'RDC');
|
|
plot(freqs, abs(squeeze(freqresp(G_dvf_md_mid('d', 'xf'), freqs, 'Hz'))), 'color', colors(3,:), 'DisplayName', 'DVF');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude $d/x_{f}$ [m/m]'); xlabel('Frequency [Hz]');
|
|
xticks([1e0, 1e1, 1e2]);
|
|
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
|
|
xlim([1, 500]);
|
|
|
|
%% Cumulative Amplitude Spectrum of the distance d with all three active damping techniques
|
|
figure;
|
|
hold on;
|
|
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_vc_mid('d', 'ft'), f, 'Hz'))).^2 + ...
|
|
psd_xf.*abs(squeeze(freqresp(G_vc_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
|
'color', 'black', 'DisplayName', 'OL');
|
|
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_iff_vc_mid('d', 'ft'), f, 'Hz'))).^2 + ...
|
|
psd_xf.*abs(squeeze(freqresp(G_iff_vc_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
|
'color', colors(1,:), 'DisplayName', 'IFF');
|
|
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_rdc_vc_mid('d', 'ft'), f, 'Hz'))).^2 + ...
|
|
psd_xf.*abs(squeeze(freqresp(G_rdc_vc_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
|
'color', colors(2,:), 'DisplayName', 'RDC');
|
|
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_dvf_vc_mid('d', 'ft'), f, 'Hz'))).^2 + ...
|
|
psd_xf.*abs(squeeze(freqresp(G_dvf_vc_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
|
'color', colors(3,:), 'DisplayName', 'DVF');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('CAS of $d$ [m]'); xlabel('Frequency [Hz]');
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xticks([1e0, 1e1, 1e2]);
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xlim([1, 500]);
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ylim([2e-10, 3e-6])
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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_md_mid('d', 'ft'), f, 'Hz'))).^2 + ...
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psd_xf.*abs(squeeze(freqresp(G_md_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
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'color', 'black', 'DisplayName', 'OL');
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plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_iff_md_mid('d', 'ft'), f, 'Hz'))).^2 + ...
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|
psd_xf.*abs(squeeze(freqresp(G_iff_md_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
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'color', colors(1,:), 'DisplayName', 'IFF');
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|
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_rdc_md_mid('d', 'ft'), f, 'Hz'))).^2 + ...
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|
psd_xf.*abs(squeeze(freqresp(G_rdc_md_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
|
'color', colors(2,:), 'DisplayName', 'RDC');
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|
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_dvf_md_mid('d', 'ft'), f, 'Hz'))).^2 + ...
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|
psd_xf.*abs(squeeze(freqresp(G_dvf_md_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
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|
'color', colors(3,:), 'DisplayName', 'DVF');
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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]'); set(gca, 'YTickLabel',[]);
|
|
xticks([1e0, 1e1, 1e2]);
|
|
xlim([1, 500]);
|
|
ylim([2e-10, 3e-6])
|
|
|
|
figure;
|
|
hold on;
|
|
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_pz_mid('d', 'ft'), f, 'Hz'))).^2 + ...
|
|
psd_xf.*abs(squeeze(freqresp(G_pz_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
|
'color', 'black', 'DisplayName', 'OL');
|
|
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_iff_pz_mid('d', 'ft'), f, 'Hz'))).^2 + ...
|
|
psd_xf.*abs(squeeze(freqresp(G_iff_pz_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
|
'color', colors(1,:), 'DisplayName', 'IFF');
|
|
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_rdc_pz_mid('d', 'ft'), f, 'Hz'))).^2 + ...
|
|
psd_xf.*abs(squeeze(freqresp(G_rdc_pz_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
|
'color', colors(2,:), 'DisplayName', 'RDC');
|
|
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_dvf_pz_mid('d', 'ft'), f, 'Hz'))).^2 + ...
|
|
psd_xf.*abs(squeeze(freqresp(G_dvf_pz_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
|
'color', colors(3,:), 'DisplayName', 'DVF');
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
|
xticks([1e0, 1e1, 1e2]);
|
|
legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
|
xlim([1, 500]);
|
|
ylim([2e-10, 3e-6])
|