%% Clear Workspace and Close figures clear; close all; clc; %% Intialize Laplace variable s = zpk('s'); %% Path for functions, data and scripts addpath('./mat/'); % Path for data %% Colors for the figures colors = colororder; %% Frequency Vector [Hz] freqs = logspace(0, 3, 1000); %% Load the PSD of disturbances load('uniaxial_disturbance_psd.mat', 'f', 'psd_ft', 'psd_xf'); %% Load Plants Dynamics load('uniaxial_plants.mat', 'G_vc_light', 'G_md_light', 'G_pz_light', ... 'G_vc_mid', 'G_md_mid', 'G_pz_mid', ... 'G_vc_heavy', 'G_md_heavy', 'G_pz_heavy'); %% Damped plants for three considered payload masses - Comparison of active damping techniques % Integral Force Feedback figure; tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); ax1 = nexttile([2,1]); hold on; plot(freqs, abs(squeeze(freqresp(G_vc_light('fm', 'f'), freqs, 'Hz'))), '-', 'color', colors(1,:), 'DisplayName', '$m_s = 1\,kg$'); plot(freqs, abs(squeeze(freqresp(G_vc_mid( 'fm', 'f'), freqs, 'Hz'))), '-.', 'color', colors(1,:), 'DisplayName', '$m_s = 25\,kg$'); plot(freqs, abs(squeeze(freqresp(G_vc_heavy('fm', 'f'), freqs, 'Hz'))), '--', 'color', colors(1,:), 'DisplayName', '$m_s = 50\,kg$'); plot(freqs, abs(squeeze(freqresp(G_md_light('fm', 'f'), freqs, 'Hz'))), '-', 'color', colors(2,:), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(G_md_mid( 'fm', 'f'), freqs, 'Hz'))), '-.', 'color', colors(2,:), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(G_md_heavy('fm', 'f'), freqs, 'Hz'))), '--', 'color', colors(2,:), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(G_pz_light('fm', 'f'), freqs, 'Hz'))), '-', 'color', colors(3,:), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(G_pz_mid( 'fm', 'f'), freqs, 'Hz'))), '-.', 'color', colors(3,:), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(G_pz_heavy('fm', 'f'), freqs, 'Hz'))), '--', 'color', colors(3,:), 'HandleVisibility', 'off'); hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); ldg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1); ldg.ItemTokenSize = [20, 1]; ax1b = nexttile(); hold on; plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_light('fm', 'f'), freqs, 'Hz')))), '-', 'color', colors(1,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_mid( 'fm', 'f'), freqs, 'Hz')))), '-.', 'color', colors(1,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_heavy('fm', 'f'), freqs, 'Hz')))), '--', 'color', colors(1,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_light('fm', 'f'), freqs, 'Hz')))), '-', 'color', colors(2,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_mid( 'fm', 'f'), freqs, 'Hz')))), '-.', 'color', colors(2,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_heavy('fm', 'f'), freqs, 'Hz')))), '--', 'color', colors(2,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_light('fm', 'f'), freqs, 'Hz')))), '-', 'color', colors(3,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_mid( 'fm', 'f'), freqs, 'Hz')))), '-.', 'color', colors(3,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_heavy('fm', 'f'), freqs, 'Hz')))), '--', 'color', colors(3,:)); hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); xticks([1e0, 1e1, 1e2]); yticks(-360:90:360); ylim([-200, 20]); linkaxes([ax1,ax1b],'x'); xlim([1, 1000]); % Relative Motion Control figure; tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); ax2 = nexttile([2,1]); hold on; plot(freqs, abs(squeeze(freqresp(G_vc_light('dL', 'f'), freqs, 'Hz'))), '-', 'color', colors(1,:)); plot(freqs, abs(squeeze(freqresp(G_vc_mid( 'dL', 'f'), freqs, 'Hz'))), '-.', 'color', colors(1,:)); plot(freqs, abs(squeeze(freqresp(G_vc_heavy('dL', 'f'), freqs, 'Hz'))), '--', 'color', colors(1,:)); plot(freqs, abs(squeeze(freqresp(G_md_light('dL', 'f'), freqs, 'Hz'))), '-', 'color', colors(2,:)); plot(freqs, abs(squeeze(freqresp(G_md_mid( 'dL', 'f'), freqs, 'Hz'))), '-.', 'color', colors(2,:)); plot(freqs, abs(squeeze(freqresp(G_md_heavy('dL', 'f'), freqs, 'Hz'))), '--', 'color', colors(2,:)); plot(freqs, abs(squeeze(freqresp(G_pz_light('dL', 'f'), freqs, 'Hz'))), '-', 'color', colors(3,:)); plot(freqs, abs(squeeze(freqresp(G_pz_mid( 'dL', 'f'), freqs, 'Hz'))), '-.', 'color', colors(3,:)); plot(freqs, abs(squeeze(freqresp(G_pz_heavy('dL', 'f'), freqs, 'Hz'))), '--', 'color', colors(3,:)); hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); ax2b = nexttile(); hold on; plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_light('dL', 'f'), freqs, 'Hz')))), '-', 'color', colors(1,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_mid( 'dL', 'f'), freqs, 'Hz')))), '-.', 'color', colors(1,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_heavy('dL', 'f'), freqs, 'Hz')))), '--', 'color', colors(1,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_light('dL', 'f'), freqs, 'Hz')))), '-', 'color', colors(2,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_mid( 'dL', 'f'), freqs, 'Hz')))), '-.', 'color', colors(2,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_heavy('dL', 'f'), freqs, 'Hz')))), '--', 'color', colors(2,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_light('dL', 'f'), freqs, 'Hz')))), '-', 'color', colors(3,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_mid( 'dL', 'f'), freqs, 'Hz')))), '-.', 'color', colors(3,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_heavy('dL', 'f'), freqs, 'Hz')))), '--', 'color', colors(3,:)); hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); xticks([1e0, 1e1, 1e2]); yticks(-360:90:360); ylim([-200, 20]); linkaxes([ax2,ax2b],'x'); xlim([1, 1000]); % Direct Velocity Feedback figure; tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); ax3 = nexttile([2,1]); hold on; plot(freqs, abs(squeeze(freqresp(G_vc_light('vn', 'f'), freqs, 'Hz'))), '-', 'color', colors(1,:), 'DisplayName', '$k_n = 0.01\,N/\mu m$'); plot(freqs, abs(squeeze(freqresp(G_vc_mid( 'vn', 'f'), freqs, 'Hz'))), '-.', 'color', colors(1,:), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(G_vc_heavy('vn', 'f'), freqs, 'Hz'))), '--', 'color', colors(1,:), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(G_md_light('vn', 'f'), freqs, 'Hz'))), '-', 'color', colors(2,:), 'DisplayName', '$k_n = 1\,N/\mu m$'); plot(freqs, abs(squeeze(freqresp(G_md_mid( 'vn', 'f'), freqs, 'Hz'))), '-.', 'color', colors(2,:), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(G_md_heavy('vn', 'f'), freqs, 'Hz'))), '--', 'color', colors(2,:), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(G_pz_light('vn', 'f'), freqs, 'Hz'))), '-', 'color', colors(3,:), 'DisplayName', '$k_n = 100\,N/\mu m$'); plot(freqs, abs(squeeze(freqresp(G_pz_mid( 'vn', 'f'), freqs, 'Hz'))), '-.', 'color', colors(3,:), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(G_pz_heavy('vn', 'f'), freqs, 'Hz'))), '--', 'color', colors(3,:), 'HandleVisibility', 'off'); hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); ylabel('Amplitude [m/s/N]'); set(gca, 'XTickLabel',[]); ldg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1); ldg.ItemTokenSize = [20, 1]; ax3b = nexttile(); hold on; plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_light('vn', 'f'), freqs, 'Hz')))), '-', 'color', colors(1,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_mid( 'vn', 'f'), freqs, 'Hz')))), '-.', 'color', colors(1,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_heavy('vn', 'f'), freqs, 'Hz')))), '--', 'color', colors(1,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_light('vn', 'f'), freqs, 'Hz')))), '-', 'color', colors(2,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_mid( 'vn', 'f'), freqs, 'Hz')))), '-.', 'color', colors(2,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_heavy('vn', 'f'), freqs, 'Hz')))), '--', 'color', colors(2,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_light('vn', 'f'), freqs, 'Hz')))), '-', 'color', colors(3,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_mid( 'vn', 'f'), freqs, 'Hz')))), '-.', 'color', colors(3,:)); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_heavy('vn', 'f'), freqs, 'Hz')))), '--', 'color', colors(3,:)); hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); xticks([1e0, 1e1, 1e2]); yticks(-360:90:360); ylim([-110, 110]); linkaxes([ax3,ax3b],'x'); xlim([1, 1000]); %% Design of Active Damping controllers to have reasonable damping % IFF K_iff_vc = 20/(s + 2*pi*0.01); K_iff_vc.InputName = {'fm'}; K_iff_vc.OutputName = {'f'}; K_iff_md = 200/(s + 2*pi*0.01); K_iff_md.InputName = {'fm'}; K_iff_md.OutputName = {'f'}; K_iff_pz = 4000/(s + 2*pi*0.01); K_iff_pz.InputName = {'fm'}; K_iff_pz.OutputName = {'f'}; % RDC K_rdc_vc = -1e3*s; K_rdc_vc.InputName = {'dL'}; K_rdc_vc.OutputName = {'f'}; K_rdc_md = -1e4*s; K_rdc_md.InputName = {'dL'}; K_rdc_md.OutputName = {'f'}; K_rdc_pz = -1e5*s; K_rdc_pz.InputName = {'dL'}; K_rdc_pz.OutputName = {'f'}; % DVF K_dvf_vc = -tf(1e3); K_dvf_vc.InputName = {'vn'}; K_dvf_vc.OutputName = {'f'}; K_dvf_md = -tf(8e3); K_dvf_md.InputName = {'vn'}; K_dvf_md.OutputName = {'f'}; K_dvf_pz = -tf(2e5); K_dvf_pz.InputName = {'vn'}; K_dvf_pz.OutputName = {'f'}; %% Save Active Damping Controller save('./mat/uniaxial_active_damping_controllers.mat', 'K_iff_vc', 'K_iff_md', 'K_iff_pz', ... 'K_rdc_vc', 'K_rdc_md', 'K_rdc_pz', ... 'K_dvf_vc', 'K_dvf_md', 'K_dvf_pz'); %% Compute Damped Plants % IFF G_iff_vc_light = feedback(G_vc_light, K_iff_vc, 'name', +1); G_iff_vc_mid = feedback(G_vc_mid , K_iff_vc, 'name', +1); G_iff_vc_heavy = feedback(G_vc_heavy, K_iff_vc, 'name', +1); G_iff_md_light = feedback(G_md_light, K_iff_md, 'name', +1); G_iff_md_mid = feedback(G_md_mid , K_iff_md, 'name', +1); G_iff_md_heavy = feedback(G_md_heavy, K_iff_md, 'name', +1); G_iff_pz_light = feedback(G_pz_light, K_iff_pz, 'name', +1); G_iff_pz_mid = feedback(G_pz_mid , K_iff_pz, 'name', +1); G_iff_pz_heavy = feedback(G_pz_heavy, K_iff_pz, 'name', +1); % RDC G_rdc_vc_light = feedback(G_vc_light, K_rdc_vc, 'name', +1); G_rdc_vc_mid = feedback(G_vc_mid , K_rdc_vc, 'name', +1); G_rdc_vc_heavy = feedback(G_vc_heavy, K_rdc_vc, 'name', +1); G_rdc_md_light = feedback(G_md_light, K_rdc_md, 'name', +1); G_rdc_md_mid = feedback(G_md_mid , K_rdc_md, 'name', +1); G_rdc_md_heavy = feedback(G_md_heavy, K_rdc_md, 'name', +1); G_rdc_pz_light = feedback(G_pz_light, K_rdc_pz, 'name', +1); G_rdc_pz_mid = feedback(G_pz_mid , K_rdc_pz, 'name', +1); G_rdc_pz_heavy = feedback(G_pz_heavy, K_rdc_pz, 'name', +1); % DVF G_dvf_vc_light = feedback(G_vc_light, K_dvf_vc, 'name', +1); G_dvf_vc_mid = feedback(G_vc_mid , K_dvf_vc, 'name', +1); G_dvf_vc_heavy = feedback(G_vc_heavy, K_dvf_vc, 'name', +1); G_dvf_md_light = feedback(G_md_light, K_dvf_md, 'name', +1); G_dvf_md_mid = feedback(G_md_mid , K_dvf_md, 'name', +1); G_dvf_md_heavy = feedback(G_md_heavy, K_dvf_md, 'name', +1); G_dvf_pz_light = feedback(G_pz_light, K_dvf_pz, 'name', +1); G_dvf_pz_mid = feedback(G_pz_mid , K_dvf_pz, 'name', +1); G_dvf_pz_heavy = feedback(G_pz_heavy, K_dvf_pz, 'name', +1); %% Verify Stability % IFF if not(isstable(G_iff_vc_light) && isstable(G_iff_vc_mid) && isstable(G_iff_vc_heavy) && ... isstable(G_iff_md_light) && isstable(G_iff_md_mid) && isstable(G_iff_md_heavy) && ... isstable(G_iff_pz_light) && isstable(G_iff_pz_mid) && isstable(G_iff_pz_heavy)) warning("One of the damped plant with decentralized IFF is not stable."); end % RDC if not(isstable(G_rdc_vc_light) && isstable(G_rdc_vc_mid) && isstable(G_rdc_vc_heavy) && ... isstable(G_rdc_md_light) && isstable(G_rdc_md_mid) && isstable(G_rdc_md_heavy) && ... isstable(G_rdc_pz_light) && isstable(G_rdc_pz_mid) && isstable(G_rdc_pz_heavy)) warning("One of the damped plant with decentralized RDC is not stable."); end % DVF if not(isstable(G_dvf_vc_light) && isstable(G_dvf_vc_mid) && isstable(G_dvf_vc_heavy) && ... isstable(G_dvf_md_light) && isstable(G_dvf_md_mid) && isstable(G_dvf_md_heavy) && ... isstable(G_dvf_pz_light) && isstable(G_dvf_pz_mid) && isstable(G_dvf_pz_heavy)) warning("One of the damped plant with decentralized DVF is not stable."); end %% Save Damped Plants save('./mat/uniaxial_damped_plants.mat', 'G_iff_vc_light', 'G_iff_md_light', 'G_iff_pz_light', ... 'G_rdc_vc_light', 'G_rdc_md_light', 'G_rdc_pz_light', ... 'G_dvf_vc_light', 'G_dvf_md_light', 'G_dvf_pz_light', ... 'G_iff_vc_mid', 'G_iff_md_mid', 'G_iff_pz_mid', ... 'G_rdc_vc_mid', 'G_rdc_md_mid', 'G_rdc_pz_mid', ... 'G_dvf_vc_mid', 'G_dvf_md_mid', 'G_dvf_pz_mid', ... 'G_iff_vc_heavy', 'G_iff_md_heavy', 'G_iff_pz_heavy', ... 'G_rdc_vc_heavy', 'G_rdc_md_heavy', 'G_rdc_pz_heavy', ... 'G_dvf_vc_heavy', 'G_dvf_md_heavy', 'G_dvf_pz_heavy'); %% Active Damping Robustness to change of sample's mass - Root Locus for all three damping techniques with 3 different sample's masses % Soft Nano-Hexapod figure; hold on; % IFF plot(real(pole(G_vc_light('fm', 'f'))), imag(pole(G_vc_light('fm', 'f'))), 'x', 'color', colors(1,:), ... 'HandleVisibility', 'off'); plot(real(zero(G_vc_light('fm', 'f'))), imag(zero(G_vc_light('fm', 'f'))), 'o', 'color', colors(1,:), ... 'DisplayName', 'IFF'); for g = logspace(0,2,400) clpoles = pole(feedback(G_vc_light('fm', 'f'), g/s, +1)); plot(real(clpoles), imag(clpoles), '.', 'color', colors(1,:), ... 'HandleVisibility', 'off'); end % RDC plot(real(pole(G_vc_light('dL', 'f'))), imag(pole(G_vc_light('dL', 'f'))), 'x', 'color', colors(2,:), ... 'HandleVisibility', 'off'); plot(real(zero(G_vc_light('dL', 'f'))), imag(zero(G_vc_light('dL', 'f'))), 'o', 'color', colors(2,:), ... '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]'); 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_md_mid('d', 'ft'), f, 'Hz'))).^2 + ... psd_xf.*abs(squeeze(freqresp(G_md_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_md_mid('d', 'ft'), f, 'Hz'))).^2 + ... psd_xf.*abs(squeeze(freqresp(G_iff_md_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_md_mid('d', 'ft'), f, 'Hz'))).^2 + ... psd_xf.*abs(squeeze(freqresp(G_rdc_md_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_md_mid('d', 'ft'), f, 'Hz'))).^2 + ... psd_xf.*abs(squeeze(freqresp(G_dvf_md_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]); 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])