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A1-nass-uniaxial-model/uniaxial_7_support_compliance.m

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+%% 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;
+
+%% Load the micro-station parameters
+load('uniaxial_micro_station_parameters.mat')
+
+%% Frequency Vector [Hz]
+freqs = logspace(0, 3, 1000);
+
+%% Nano-Hexapod Parameters
+m = 20; % Mass [kg]
+
+% "Soft" Nano-Hexapod
+k_soft = m*(2*pi*10)^2; % Stiffness [N/m]
+c_soft = 0.1*2*sqrt(m*k_soft); % Damping [N/(m/s)]
+
+% "Mid" Nano-Hexapod
+k_mid = m*(2*pi*70)^2; % Stiffness [N/m]
+c_mid = 0.1*2*sqrt(m*k_mid); % Damping [N/(m/s)]
+
+% "Stiff" Nano-Hexapod
+k_stiff = m*(2*pi*350)^2; % Stiffness [N/m]
+c_stiff = 0.1*2*sqrt(m*k_stiff); % Damping [N/(m/s)]
+
+%% Compute the transfer functions for considered nano-hexapods - From F to L'
+% "Soft" Nano-Hexapod
+G_soft_a = 1/(m*s^2 + c_soft*s + k_soft); % Transfer function from F to L'
+
+% "Mid" Nano-Hexapod
+G_mid_a = 1/(m*s^2 + c_mid*s + k_mid); % Transfer function from F to L'
+
+% "Stiff" Nano-Hexapod
+G_stiff_a = 1/(m*s^2 + c_stiff*s + k_stiff); % Transfer function from F to L'
+
+%% Obtained transfer functions from F to L when neglecting support compliance
+freqs = logspace(0, 3, 1000);
+
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_soft_a, freqs, 'Hz'))), '-', 'color', colors(1,:));
+text(50, 5e-5, '$\omega_n =$ 10Hz', 'horizontalalignment', 'center');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Magnitude [m/N]');
+xlim([freqs(1), freqs(end)]);
+xticks([1e0, 1e1, 1e2]);
+ylim([1e-9, 1e-4]);
+yticks([1e-9, 1e-7, 1e-5]);
+
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_mid_a, freqs, 'Hz'))), '-', 'color', colors(1,:));
+text(70, 3e-6, '$\omega_n =$ 70Hz', 'horizontalalignment', 'center');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
+xlim([freqs(1), freqs(end)]);
+xticks([1e0, 1e1, 1e2]);
+ylim([1e-9, 1e-4]);
+yticks([1e-9, 1e-7, 1e-5]);
+
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_stiff_a, freqs, 'Hz'))), '-', 'color', colors(1,:), ...
+     'DisplayName', '$L^\prime/F$');
+text(200, 8e-8, '$\omega_n =$ 400Hz', 'horizontalalignment', 'center');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
+legend('location', 'northeast');
+xlim([freqs(1), freqs(end)]);
+xticks([1e0, 1e1, 1e2]);
+ylim([1e-9, 1e-4]);
+yticks([1e-9, 1e-7, 1e-5]);
+
+%% Parameters of the support compliance
+w0h = 2*pi*70; % [rad/s]
+xih = 0.1; % [-]
+
+mh = 20; % [kg]
+kh = mh*w0h^2;
+ch = xih*2*sqrt(kh*mh);
+
+%% Compute the transfer functions from F to L and from F to d for considered Nano-Hexapods
+% "Soft" Nano-Hexapod
+G_soft = (mh*s^2 + ch*s + kh)/(m*s^2*(c_soft*s + k_soft) + (m*s^2 + c_soft*s + k_soft)*(mh*s^2 + ch*s + kh)); % d/F
+G_soft_r = (1 - m*s^2*G_soft)/(c_soft*s + k_soft); % L/F
+
+% "Mid" Nano-Hexapod
+G_mid = (mh*s^2 + ch*s + kh)/(m*s^2*(c_mid*s + k_mid) + (m*s^2 + c_mid*s + k_mid)*(mh*s^2 + ch*s + kh)); % d/F
+G_mid_r = (1 - m*s^2*G_mid)/(c_mid*s + k_mid); % L/F
+
+% "Stiff" Nano-Hexapod
+G_stiff = (mh*s^2 + ch*s + kh)/(m*s^2*(c_stiff*s + k_stiff) + (m*s^2 + c_stiff*s + k_stiff)*(mh*s^2 + ch*s + kh)); % d/F
+G_stiff_r = (1 - m*s^2*G_stiff)/(c_stiff*s + k_stiff); % L/F
+
+%% Effect of the support compliance on the transfer functions from F to L and from F to d
+freqs = logspace(0, 3, 1000);
+
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_soft_a, freqs, 'Hz'))), '-', 'color', colors(1,:));
+plot(freqs, abs(squeeze(freqresp(G_soft_r, freqs, 'Hz'))), '-', 'color', colors(2,:));
+loglog(10.^(0.3*cos(0:0.01:2*pi)+log10(60)), ...
+       10.^(0.6*sin(0:0.01:2*pi)+log10(4e-7)), 'k--');
+text(8, 3e-7, sprintf('Support\nDynamics'), 'horizontalalignment', 'center');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Magnitude [m/N]');
+xlim([freqs(1), freqs(end)]);
+xticks([1e0, 1e1, 1e2]);
+ylim([1e-9, 1e-4]);
+yticks([1e-9, 1e-7, 1e-5]);
+
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_mid_a, freqs, 'Hz'))), '-', 'color', colors(1,:));
+plot(freqs, abs(squeeze(freqresp(G_mid_r, freqs, 'Hz'))), '-', 'color', colors(2,:));
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]');
+set(gca, 'YTickLabel',[]);
+xlim([freqs(1), freqs(end)]);
+xticks([1e0, 1e1, 1e2]);
+ylim([1e-9, 1e-4]);
+yticks([1e-9, 1e-7, 1e-5]);
+
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_stiff_a, freqs, 'Hz'))), '-', 'color', colors(1,:), ...
+     'DisplayName', '$L^\prime/F$');
+plot(freqs, abs(squeeze(freqresp(G_stiff_r, freqs, 'Hz'))), '-', 'color', colors(2,:), ...
+     'DisplayName', '$L/F$');
+loglog(10.^(0.3*cos(0:0.01:2*pi)+log10(50)), ...
+       10.^(0.3*sin(0:0.01:2*pi)+log10(8e-9)), 'k--', 'HandleVisibility', 'off');
+text(50, 3e-8, 'No effect', 'horizontalalignment', 'center');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
+legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
+xlim([freqs(1), freqs(end)]);
+xticks([1e0, 1e1, 1e2]);
+ylim([1e-9, 1e-4]);
+yticks([1e-9, 1e-7, 1e-5]);
+
+%% Effect of the support compliance on the transfer functions from F to L and from F to d
+freqs = logspace(0, 3, 1000);
+
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_soft_a, freqs, 'Hz'))), '-', 'color', colors(1,:));
+plot(freqs, abs(squeeze(freqresp(G_soft,   freqs, 'Hz'))), '-', 'color', colors(3,:));
+loglog(10.^(0.3*cos(0:0.01:2*pi)+log10(60)), ...
+       10.^(0.6*sin(0:0.01:2*pi)+log10(4e-7)), 'k--');
+text(8, 3e-7, 'No effect', 'horizontalalignment', 'center');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Magnitude [m/N]');
+xlim([freqs(1), freqs(end)]);
+xticks([1e0, 1e1, 1e2]);
+ylim([1e-9, 1e-4]);
+yticks([1e-9, 1e-7, 1e-5]);
+
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_mid_a, freqs, 'Hz'))), '-', 'color', colors(1,:));
+plot(freqs, abs(squeeze(freqresp(G_mid,   freqs, 'Hz'))), '-', 'color', colors(3,:));
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]');
+set(gca, 'YTickLabel',[]);
+xlim([freqs(1), freqs(end)]);
+xticks([1e0, 1e1, 1e2]);
+ylim([1e-9, 1e-4]);
+yticks([1e-9, 1e-7, 1e-5]);
+
+figure;
+hold on;
+plot(freqs, abs(squeeze(freqresp(G_stiff_a, freqs, 'Hz'))), '-', 'color', colors(1,:), ...
+     'DisplayName', '$L^\prime/F$');
+plot(freqs, abs(squeeze(freqresp(G_stiff,   freqs, 'Hz'))), '-', 'color', colors(3,:), ...
+     'DisplayName', '$d/F$');
+loglog(10.^(0.4*cos(0:0.01:2*pi)+log10(50)), ...
+       10.^(0.8*sin(0:0.01:2*pi)+log10(8e-9)), 'k--', 'HandleVisibility', 'off');
+text(50, 2e-7, sprintf('Support\nDynamics'), 'horizontalalignment', 'center');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
+legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
+xlim([freqs(1), freqs(end)]);
+xticks([1e0, 1e1, 1e2]);
+ylim([1e-9, 1e-4]);
+yticks([1e-9, 1e-7, 1e-5]);