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A1-nass-uniaxial-model/mat/ground_motion_measurement.mat
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A1-nass-uniaxial-model/mat/ground_motion_measurement.mat
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A1-nass-uniaxial-model/mat/meas_microstation_frf.mat
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A1-nass-uniaxial-model/mat/meas_microstation_frf.mat
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A1-nass-uniaxial-model/mat/meas_spindle_off.mat
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A1-nass-uniaxial-model/mat/meas_spindle_off.mat
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A1-nass-uniaxial-model/mat/meas_spindle_on.mat
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A1-nass-uniaxial-model/mat/meas_spindle_on.mat
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A1-nass-uniaxial-model/mat/uniaxial_active_damping_controllers.mat
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A1-nass-uniaxial-model/mat/uniaxial_active_damping_controllers.mat
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A1-nass-uniaxial-model/mat/uniaxial_damped_plants.mat
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A1-nass-uniaxial-model/mat/uniaxial_damped_plants.mat
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A1-nass-uniaxial-model/mat/uniaxial_disturbance_psd.mat
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A1-nass-uniaxial-model/mat/uniaxial_disturbance_psd.mat
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A1-nass-uniaxial-model/mat/uniaxial_high_authority_controllers.mat
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A1-nass-uniaxial-model/mat/uniaxial_high_authority_controllers.mat
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A1-nass-uniaxial-model/mat/uniaxial_micro_station_parameters.mat
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A1-nass-uniaxial-model/mat/uniaxial_micro_station_parameters.mat
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A1-nass-uniaxial-model/mat/uniaxial_plants.mat
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A1-nass-uniaxial-model/mat/uniaxial_plants.mat
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A1-nass-uniaxial-model/nass_uniaxial_model.slx
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A1-nass-uniaxial-model/nass_uniaxial_model.slx
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A1-nass-uniaxial-model/uniaxial_1_micro_station_model.m
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A1-nass-uniaxial-model/uniaxial_1_micro_station_model.m
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% 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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%% Uniaxial Simscape model name
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mdl = 'nass_uniaxial_model';
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%% Frequency Vector [Hz]
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freqs = logspace(0, 3, 1000);
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%% Load measured FRF
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load('meas_microstation_frf.mat');
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%% Parameters - Mass
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mh = 15; % Micro Hexapod [kg]
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mt = 1200; % Ty + Ry + Rz [kg]
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mg = 2500; % Granite [kg]
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%% Parameters - Stiffnesses
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kh = 6.11e+07; % [N/m]
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kt = 5.19e+08; % [N/m]
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kg = 9.50e+08; % [N/m]
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%% Parameters - damping
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ch = 2*0.05*sqrt(kh*mh); % [N/(m/s)]
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ct = 2*0.05*sqrt(kt*mt); % [N/(m/s)]
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cg = 2*0.08*sqrt(kg*mg); % [N/(m/s)]
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%% Save model parameters
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save('./mat/uniaxial_micro_station_parameters.mat', 'mh', 'mt', 'mg', 'ch', 'ct', 'cg', 'kh', 'kt', 'kg')
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%% Disable the Nano-Hexpod for now
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model_config = struct();
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model_config.nhexa = "none";
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model_config.controller = "open_loop";
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%% Identify the transfer function from u to taum
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/micro_station/Fg'], 1, 'openinput'); io_i = io_i + 1; % Hammer on Granite
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io(io_i) = linio([mdl, '/micro_station/Fh'], 1, 'openinput'); io_i = io_i + 1; % Hammer on Hexapod
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io(io_i) = linio([mdl, '/micro_station/xg'], 1, 'openoutput'); io_i = io_i + 1; % Absolute motion of Granite
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io(io_i) = linio([mdl, '/micro_station/xh'], 1, 'openoutput'); io_i = io_i + 1; % Absolute motion of Hexapod
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%% Perform the model extraction
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G_id = linearize(mdl, io, 0.0);
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G_id.InputName = {'Fg', 'Fh'};
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G_id.OutputName = {'Dg', 'Dh'};
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%% Comparison of the measured FRF and identified ones from the uniaxial model
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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(f(f>20), abs(frf_Fhz_to_Dhz(f>20)), '-', 'color', colors(1,:), 'DisplayName', '$x_{h,z}/F_{h,z}$');
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plot(f(f>20), abs(frf_Fgz_to_Dhz(f>20)), '-', 'color', colors(2,:), 'DisplayName', '$x_{h,z}/F_{g,z}$');
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plot(f(f>20), abs(frf_Fgz_to_Dgz(f>20)), '-', 'color', colors(3,:), 'DisplayName', '$x_{g,z}/F_{g,z}$');
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plot(freqs, abs(squeeze(freqresp(G_id('Dh', 'Fh'), freqs, 'Hz'))), '--', 'color', colors(1,:), 'DisplayName', '$x_{h,z}/F_{h,z}$ (model)');
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plot(freqs, abs(squeeze(freqresp(G_id('Dh', 'Fg'), freqs, 'Hz'))), '--', 'color', colors(2,:), 'DisplayName', '$x_{h,z}/F_{g,z}$ (model)');
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plot(freqs, abs(squeeze(freqresp(G_id('Dg', 'Fg'), freqs, 'Hz'))), '--', 'color', colors(3,:), 'DisplayName', '$x_{g,z}/F_{g,z}$ (model)');
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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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ylim([1e-10, 2e-7]);
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legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 2);
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ax2 = nexttile;
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hold on;
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_id('Dh', 'Fh'), freqs, 'Hz')))), '--', 'color', colors(1,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_id('Dh', 'Fg'), freqs, 'Hz')))), '--', 'color', colors(2,:));
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plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_id('Dg', 'Fg'), freqs, 'Hz')))), '--', 'color', colors(3,:));
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plot(f(f>20), 180/pi*unwrap(angle(frf_Fhx_to_Dhx(f>20))), '-', 'color', colors(1,:));
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plot(f(f>30), 180/pi*unwrap(angle(frf_Fgx_to_Dhx(f>30))), '-', 'color', colors(2,:));
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plot(f(f>20), 180/pi*unwrap(angle(frf_Fgx_to_Dgx(f>20))), '-', '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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hold off;
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yticks(-360:90:360);
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ylim([-360, 90]);
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linkaxes([ax1,ax2],'x');
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xlim([1, 500]);
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191
A1-nass-uniaxial-model/uniaxial_2_nano_hexapod_model.m
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191
A1-nass-uniaxial-model/uniaxial_2_nano_hexapod_model.m
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% 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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%% Uniaxial Simscape model name
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mdl = 'nass_uniaxial_model';
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%% Frequency Vector [Hz]
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freqs = logspace(0, 3, 1000);
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%% Load the micro-station parameters
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load('uniaxial_micro_station_parameters.mat')
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%% Nano-Hexapod Parameters
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mn = 15; % [kg]
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kn = 1e7; % [N/m]
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cn = 2*0.01*sqrt(mn*kn); % [N/(m/s)]
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%% Sample Mass
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ms = 10; % [kg]
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%% Use 1DoF Nano-Hexpod model
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model_config = struct();
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model_config.nhexa = "1dof";
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model_config.controller = "open_loop";
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%% Identify the transfer function from disturbances and force actuator to d
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/controller'], 1, 'openinput'); io_i = io_i + 1; % Force Actuator
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io(io_i) = linio([mdl, '/fs'], 1, 'openinput'); io_i = io_i + 1; % Force applied on the sample
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io(io_i) = linio([mdl, '/micro_station/xf'], 1, 'openinput'); io_i = io_i + 1; % Floor Motion
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io(io_i) = linio([mdl, '/micro_station/ft'], 1, 'openinput'); io_i = io_i + 1; % Stage disturbances
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io(io_i) = linio([mdl, '/d'] , 1, 'openoutput'); io_i = io_i + 1; % Metrology
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%% Perform the model extraction
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G_ol = linearize(mdl, io, 0.0);
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G_ol.InputName = {'f', 'fs', 'xf', 'ft'};
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G_ol.OutputName = {'d'};
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%% Sensitivity to disturbances - Fs
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figure;
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plot(freqs, abs(squeeze(freqresp(G_ol('d', 'fs'), freqs, 'Hz'))));
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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 - Ft
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figure;
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plot(freqs, abs(squeeze(freqresp(G_ol('d', 'ft'), freqs, 'Hz'))));
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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 - xf
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figure;
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plot(freqs, abs(squeeze(freqresp(G_ol('d', 'xf'), freqs, 'Hz'))));
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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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xlim([1, 500]);
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ylim([1e-2, 1e2]);
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%% Bode Plot of the transfer function from actuator forces to measured displacement by the metrology
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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_ol('d', 'f'), 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 $d/f$ [m/N]'); set(gca, 'XTickLabel',[]);
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ax2 = nexttile;
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(G_ol('d', 'f'), freqs, 'Hz'))));
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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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hold off;
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yticks(-360:90:360);
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ylim([-180, 0]);
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linkaxes([ax1,ax2],'x');
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xlim([1, 500]);
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%% Use 1DoF Nano-Hexpod model
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model_config = struct();
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model_config.nhexa = "1dof";
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model_config.controller = "open_loop";
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%% Nano-Hexapod Mass
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mn = 15; % Nano-Hexapod mass [kg]
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%% Identification of all combination of stiffnesses / masses
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force
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io(io_i) = linio([mdl, '/micro_station/xf'], 1, 'openinput'); io_i = io_i + 1; % Floor Motion
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io(io_i) = linio([mdl, '/micro_station/ft'], 1, 'openinput'); io_i = io_i + 1; % Stage vibrations
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io(io_i) = linio([mdl, '/fs'], 1, 'openinput'); io_i = io_i + 1; % Direct sample forces
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io(io_i) = linio([mdl, '/dL'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Sensor
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io(io_i) = linio([mdl, '/fm'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensor
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io(io_i) = linio([mdl, '/vn'] , 1, 'openoutput'); io_i = io_i + 1; % Geophone
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io(io_i) = linio([mdl, '/d'] , 1, 'openoutput'); io_i = io_i + 1; % Metrology Output
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%% Light Sample
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ms = 1; % Sample Mass [kg]
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% Voice Coil (i.e. soft) Nano-Hexapod
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kn = 1e4; % Nano-Hexapod Stiffness [N/m]
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cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
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G_vc_light = linearize(mdl, io, 0.0);
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G_vc_light.InputName = {'f', 'xf', 'ft', 'fs'};
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G_vc_light.OutputName = {'dL', 'fm', 'vn', 'd'};
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% APA (i.e. relatively stiff) Nano-Hexapod
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kn = 1e6; % Nano-Hexapod Stiffness [N/m]
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cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
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G_md_light = linearize(mdl, io, 0.0);
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G_md_light.InputName = {'f', 'xf', 'ft', 'fs'};
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G_md_light.OutputName = {'dL', 'fm', 'vn', 'd'};
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% Piezoelectric (i.e. stiff) Nano-Hexapod
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kn = 1e8; % Nano-Hexapod Stiffness [N/m]
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cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
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G_pz_light = linearize(mdl, io, 0.0);
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G_pz_light.InputName = {'f', 'xf', 'ft', 'fs'};
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G_pz_light.OutputName = {'dL', 'fm', 'vn', 'd'};
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%% Mid Sample
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ms = 25; % Sample Mass [kg]
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% Voice Coil (i.e. soft) Nano-Hexapod
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kn = 1e4; % Nano-Hexapod Stiffness [N/m]
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cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
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G_vc_mid = linearize(mdl, io, 0.0);
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G_vc_mid.InputName = {'f', 'xf', 'ft', 'fs'};
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G_vc_mid.OutputName = {'dL', 'fm', 'vn', 'd'};
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% APA (i.e. relatively stiff) Nano-Hexapod
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kn = 1e6; % Nano-Hexapod Stiffness [N/m]
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cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
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G_md_mid = linearize(mdl, io, 0.0);
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G_md_mid.InputName = {'f', 'xf', 'ft', 'fs'};
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G_md_mid.OutputName = {'dL', 'fm', 'vn', 'd'};
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% Piezoelectric (i.e. stiff) Nano-Hexapod
|
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kn = 1e8; % Nano-Hexapod Stiffness [N/m]
|
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cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
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G_pz_mid = linearize(mdl, io, 0.0);
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G_pz_mid.InputName = {'f', 'xf', 'ft', 'fs'};
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G_pz_mid.OutputName = {'dL', 'fm', 'vn', 'd'};
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%% Heavy Sample
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ms = 50; % Sample Mass [kg]
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% Voice Coil (i.e. soft) Nano-Hexapod
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kn = 1e4; % Nano-Hexapod Stiffness [N/m]
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cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
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G_vc_heavy = linearize(mdl, io, 0.0);
|
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G_vc_heavy.InputName = {'f', 'xf', 'ft', 'fs'};
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G_vc_heavy.OutputName = {'dL', 'fm', 'vn', 'd'};
|
||||
|
||||
% APA (i.e. relatively stiff) Nano-Hexapod
|
||||
kn = 1e6; % Nano-Hexapod Stiffness [N/m]
|
||||
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
||||
G_md_heavy = linearize(mdl, io, 0.0);
|
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G_md_heavy.InputName = {'f', 'xf', 'ft', 'fs'};
|
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G_md_heavy.OutputName = {'dL', 'fm', 'vn', 'd'};
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||||
|
||||
% Piezoelectric (i.e. stiff) Nano-Hexapod
|
||||
kn = 1e8; % Nano-Hexapod Stiffness [N/m]
|
||||
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
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G_pz_heavy = linearize(mdl, io, 0.0);
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G_pz_heavy.InputName = {'f', 'xf', 'ft', 'fs'};
|
||||
G_pz_heavy.OutputName = {'dL', 'fm', 'vn', 'd'};
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|
||||
%% Save All Identified Plants
|
||||
save('./mat/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', ...
|
||||
'G_vc_heavy', 'G_md_heavy', 'G_pz_heavy');
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A1-nass-uniaxial-model/uniaxial_3_disturbances.m
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A1-nass-uniaxial-model/uniaxial_3_disturbances.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;
|
||||
|
||||
%% Uniaxial Simscape model name
|
||||
mdl = 'nass_uniaxial_model';
|
||||
|
||||
%% Frequency Vector [Hz]
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
%% Load the micro-station parameters
|
||||
load('uniaxial_micro_station_parameters.mat');
|
||||
|
||||
%% Compute Floor Motion Spectral Density
|
||||
% Load floor motion data
|
||||
% t: time in [s]
|
||||
% V: measured voltage genrated by the geophone and amplified by a 60dB gain voltage amplifier [V]
|
||||
load('ground_motion_measurement.mat', 't', 'V');
|
||||
|
||||
% Geophone Transfer Function
|
||||
Tg = 88; % Sensitivity [V/(m/s)]
|
||||
w0 = 2*2*pi; % Cut-off frequency [rad/s]
|
||||
xi = 0.7; % Damping ratio
|
||||
|
||||
G_geo = Tg*s*s^2/(s^2 + 2*xi*w0*s + w0^2); % Geophone's transfer function [V/m]
|
||||
|
||||
% Voltage amplifier transfer function
|
||||
g0 = 10^(60/20); % [abs]
|
||||
|
||||
% Compute measured voltage PSD
|
||||
Ts = (t(2)-t(1)); % Sampling Time [s]
|
||||
Nfft = floor(2/Ts);
|
||||
win = hanning(Nfft);
|
||||
Noverlap = floor(Nfft/2);
|
||||
|
||||
[psd_V, f] = pwelch(V, win, Noverlap, Nfft, 1/Ts); % [V^2/Hz]
|
||||
|
||||
% Ground Motion ASD
|
||||
psd_xf = psd_V./abs(squeeze(freqresp(G_geo*g0, f, 'Hz'))).^2; % [m^2/Hz]
|
||||
|
||||
%% Amplitude Spectral Density of the measured Floor motion on ID31
|
||||
figure;
|
||||
plot(f, sqrt(psd_xf), 'DisplayName', '$\Gamma_{x_{f}}$');
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Ampl. Spectral Density $\left[\frac{m}{\sqrt{Hz}}\right]$')
|
||||
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
xlim([1, 500]);
|
||||
xticks([1e0, 1e1, 1e2]);
|
||||
|
||||
%% Estimation of the Spectral density of the stage vibrations
|
||||
|
||||
% Measured velocity of granite and hexapod during spindle rotation
|
||||
% t: time in [s]
|
||||
% vg: measured granite velocity [m/s]
|
||||
% vg: measured micro-hexapod's top platform velocity [m/s]
|
||||
load('meas_spindle_on.mat', 't', 'vg', 'vh');
|
||||
spindle_off = load('meas_spindle_off.mat', 't', 'vg', 'vh'); % No Rotation
|
||||
|
||||
% Compute Power Spectral Density of the relative velocity between granite and hexapod during spindle rotation
|
||||
Fs = 1/(t(2)-t(1)); % Sampling Frequency [Hz]
|
||||
win = hanning(ceil(2*Fs)); % Hanning window
|
||||
|
||||
[psd_vft, f] = pwelch(vh-vg, win, [], [], Fs); % [(m/s)^2/Hz]
|
||||
[psd_off, ~] = pwelch(spindle_off.vh-spindle_off.vg, win, [], [], Fs); % [(m/s)^2/Hz]
|
||||
|
||||
% Disable the Nano-Hexpod for now
|
||||
model_config = struct();
|
||||
model_config.nhexa = "none";
|
||||
model_config.controller = "open_loop";
|
||||
|
||||
% Identify the transfer function from u to taum
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/micro_station/ft'], 1, 'openinput'); io_i = io_i + 1; % Stage Disturbance Force
|
||||
io(io_i) = linio([mdl, '/micro_station/xg'], 1, 'openoutput'); io_i = io_i + 1; % Absolute motion of Granite
|
||||
io(io_i) = linio([mdl, '/micro_station/xh'], 1, 'openoutput'); io_i = io_i + 1; % Absolute motion of Hexapod
|
||||
|
||||
% Perform the model extraction
|
||||
G = linearize(mdl, io, 0.0);
|
||||
G.InputName = {'ft'};
|
||||
G.OutputName = {'Dg', 'Dh'};
|
||||
|
||||
% Power Spectral Density of the equivalent force ft [N/Hz^2]
|
||||
psd_ft = (psd_vft./(2*pi*f).^2)./abs(squeeze(freqresp(G('Dh', 'ft') - G('Dg', 'ft'), f, 'Hz'))).^2;
|
||||
|
||||
%% Amplitude Spectral Density of the relative motion measured between the granite and the micro-hexapod's top platform during Spindle rotating
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(psd_vft)./(2*pi*f), 'DisplayName', '6rpm');
|
||||
plot(f, sqrt(psd_off)./(2*pi*f), 'DisplayName', '0rpm');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Ampl. Spectral Density $\left[\frac{m}{\sqrt{Hz}}\right]$')
|
||||
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
xlim([1, 500]); ylim([1e-12, 1e-7])
|
||||
|
||||
%% Estimated disturbance force ft from measurement and uniaxial model
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(psd_ft), 'DisplayName', '$\Gamma_{f_{t}}$');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Ampl. Spectral Density $\left[\frac{N}{\sqrt{Hz}}\right]$')
|
||||
xlim([1, 500]);
|
||||
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
|
||||
%% Save PSD of disturbances
|
||||
save('./mat/uniaxial_disturbance_psd.mat', 'f', 'psd_ft', 'psd_xf');
|
||||
110
A1-nass-uniaxial-model/uniaxial_4_dynamic_noise_budget.m
Normal file
110
A1-nass-uniaxial-model/uniaxial_4_dynamic_noise_budget.m
Normal file
@@ -0,0 +1,110 @@
|
||||
%% 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');
|
||||
|
||||
%% Sensitivity to disturbances for three different nano-hexpod stiffnesses
|
||||
figure;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_vc_light('d', 'fs'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(G_md_light('d', 'fs'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz_light('d', 'fs'), freqs, 'Hz'))));
|
||||
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]);
|
||||
|
||||
%% Sensitivity to disturbances for three different nano-hexpod stiffnesses
|
||||
figure;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_vc_light('d', 'ft'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(G_md_light('d', 'ft'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz_light('d', 'ft'), freqs, 'Hz'))));
|
||||
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]);
|
||||
|
||||
%% Sensitivity to disturbances for three different nano-hexpod stiffnesses
|
||||
figure;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_vc_light('d', 'xf'), freqs, 'Hz'))), 'DisplayName', '$k_n = 0.01\,N/\mu m$');
|
||||
plot(freqs, abs(squeeze(freqresp(G_md_light('d', 'xf'), freqs, 'Hz'))), 'DisplayName', '$k_n = 1 \,N/\mu m$');
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz_light('d', 'xf'), freqs, 'Hz'))), 'DisplayName', '$k_n = 100 \,N/\mu m$');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $d/x_{f}$ [m/m]'); xlabel('Frequency [Hz]');
|
||||
xticks([1e0, 1e1, 1e2]);
|
||||
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15
|
||||
xlim([1, 500]);
|
||||
|
||||
%% Cumulative Amplitude Spectrum of the relative motion d, due to both the floor motion and the stage vibrations
|
||||
figure;
|
||||
hold on;
|
||||
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', '$f_t$');
|
||||
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', '$f_t$');
|
||||
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', '$f_t$');
|
||||
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', '$x_f$ ($k_n = 0.01\,N/\mu m$)');
|
||||
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', '$x_f$ ($k_n = 1 \,N/\mu m$)');
|
||||
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', '$x_f$ ($k_n = 100 \,N/\mu m$)');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('CAS [m]'); xlabel('Frequency [Hz]');
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
|
||||
leg.ItemTokenSize(1) = 15
|
||||
|
||||
xlim([1, 500]);
|
||||
ylim([1e-12, 3e-6])
|
||||
|
||||
%% Cumulative Amplitude Spectrum of the relative motion d due to all disturbances, for two sample masses
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_vc_light('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_vc_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', colors(1,:), 'DisplayName', '$m_s = 1\,kg$, $k_n = 0.01\,N/\mu m$');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_md_light('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_md_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', colors(2,:), 'DisplayName', '$m_s = 1\,kg$, $k_n = 1\,N/\mu m$');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_pz_light('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_pz_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', colors(3,:), 'DisplayName', '$m_s = 1\,kg$, $k_n = 100\,N/\mu m$');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_vc_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_vc_heavy('d', 'xf'), f, 'Hz'))).^2)))), '--', ...
|
||||
'color', colors(1,:), 'DisplayName', '$m_s = 50\,kg$, $k_n = 0.01\,N/\mu m$');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_md_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_md_heavy('d', 'xf'), f, 'Hz'))).^2)))), '--', ...
|
||||
'color', colors(2,:), 'DisplayName', '$m_s = 50\,kg$, $k_n = 1\,N/\mu m$');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_pz_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_pz_heavy('d', 'xf'), f, 'Hz'))).^2)))), '--', ...
|
||||
'color', colors(3,:), 'DisplayName', '$m_s = 50\,kg$, $k_n = 100\,N/\mu m$');
|
||||
plot([1, 1e3], [20e-9, 20e-9], 'k--', 'HandleVisibility', 'off');
|
||||
text(4, 1e-8, '20 nm RMS', 'horizontalalignment', 'center');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('CAS [m]'); xlabel('Frequency [Hz]');
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15
|
||||
|
||||
xlim([1, 500]);
|
||||
ylim([1e-12, 3e-6])
|
||||
630
A1-nass-uniaxial-model/uniaxial_5_active_damping.m
Normal file
630
A1-nass-uniaxial-model/uniaxial_5_active_damping.m
Normal file
@@ -0,0 +1,630 @@
|
||||
%% 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
|
||||
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)
|
||||
|
||||
% RDC
|
||||
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)
|
||||
|
||||
% DVF
|
||||
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)
|
||||
|
||||
%% 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])
|
||||
565
A1-nass-uniaxial-model/uniaxial_6_hac_lac.m
Normal file
565
A1-nass-uniaxial-model/uniaxial_6_hac_lac.m
Normal file
@@ -0,0 +1,565 @@
|
||||
%% 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');
|
||||
|
||||
%% Load Damped Plants
|
||||
load('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');
|
||||
|
||||
%% Damped plant - Robustness to change of sample's mass
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_vc_light('d', 'f'), freqs, 'Hz'))), 'color', [colors(1,:), 0.5]);
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff_vc_light('d', 'f'), freqs, 'Hz'))), 'color', colors(1,:));
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff_vc_mid( 'd', 'f'), freqs, 'Hz'))), 'color', colors(2,:));
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff_vc_heavy('d', 'f'), freqs, 'Hz'))), 'color', colors(3,:));
|
||||
loglog(10.^(0.4*cos([0:0.01:2*pi])+log10(100)), ...
|
||||
10.^(0.8*sin([0:0.01:2*pi]-pi/4)+log10(8e-8)), 'k--');
|
||||
text(20, 4e-8, sprintf('Small\nInteraction'), 'horizontalalignment', 'center');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
ylim([5e-10, 1e-3]);
|
||||
|
||||
ax1b = nexttile();
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_light('d', 'f'), freqs, 'Hz')))), 'color', [colors(1,:), 0.5]);
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_iff_vc_light('d', 'f'), freqs, 'Hz')))), 'color', colors(1,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_iff_vc_mid( 'd', 'f'), freqs, 'Hz')))), 'color', colors(2,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_iff_vc_heavy('d', 'f'), freqs, 'Hz')))), 'color', colors(3,:));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
xticks([1e0, 1e1, 1e2]);
|
||||
yticks(-360:90:360);
|
||||
ylim([-200, 20]);
|
||||
|
||||
linkaxes([ax1,ax1b],'x');
|
||||
xlim([1, 1e3]);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
ax2 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_md_light('d', 'f'), freqs, 'Hz'))), 'color', [colors(1,:), 0.5]);
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff_md_light('d', 'f'), freqs, 'Hz'))), 'color', colors(1,:));
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff_md_mid( 'd', 'f'), freqs, 'Hz'))), 'color', colors(2,:));
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff_md_heavy('d', 'f'), freqs, 'Hz'))), 'color', colors(3,:));
|
||||
loglog(10.^(0.4*cos([0:0.01:2*pi])+log10(200)), ...
|
||||
10.^(0.8*sin([0:0.01:2*pi]-pi/4)+log10(2e-8)), 'k--');
|
||||
text(40, 1e-8, sprintf('Small\nInteraction'), 'horizontalalignment', 'center');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
|
||||
ylim([5e-10, 1e-3]);
|
||||
|
||||
ax2b = nexttile();
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_md_light('d', 'f'), freqs, 'Hz')))), 'color', [colors(1,:), 0.5]);
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_iff_md_light('d', 'f'), freqs, 'Hz')))), 'color', colors(1,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_iff_md_mid( 'd', 'f'), freqs, 'Hz')))), 'color', colors(2,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_iff_md_heavy('d', 'f'), freqs, 'Hz')))), 'color', colors(3,:));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
||||
xticks([1e0, 1e1, 1e2]);
|
||||
yticks(-360:90:360);
|
||||
ylim([-200, 20]);
|
||||
|
||||
linkaxes([ax2,ax2b],'x');
|
||||
xlim([1, 1e3]);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
ax3 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz_light('d', 'f'), freqs, 'Hz'))), 'color', [colors(1,:), 0.5], 'DisplayName', '$m_s = 1\,kg$, OL');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff_pz_light('d', 'f'), freqs, 'Hz'))), 'color', colors(1,:), 'DisplayName', '$m_s = 1\,kg$, IFF');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff_pz_mid( 'd', 'f'), freqs, 'Hz'))), 'color', colors(2,:), 'DisplayName', '$m_s = 25\,kg$, IFF');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff_pz_heavy('d', 'f'), freqs, 'Hz'))), 'color', colors(3,:), 'DisplayName', '$m_s = 50\,kg$, IFF');
|
||||
loglog(10.^(0.8*cos([0:0.01:2*pi])+log10(350)), ...
|
||||
10.^(1.2*sin([0:0.01:2*pi])+log10(8e-9)), 'k--', 'HandleVisibility', 'off');
|
||||
text(200, 5e-7, sprintf('$\\mu$ Station\nCoupling'), 'horizontalalignment', 'center');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
|
||||
ylim([5e-10, 1e-3]);
|
||||
ldg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
ldg.ItemTokenSize = [20, 1];
|
||||
|
||||
ax3b = nexttile();
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_light('d', 'f'), freqs, 'Hz')))), 'color', [colors(1,:), 0.5]);
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_iff_pz_light('d', 'f'), freqs, 'Hz')))), 'color', colors(1,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_iff_pz_mid( 'd', 'f'), freqs, 'Hz')))), 'color', colors(2,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_iff_pz_heavy('d', 'f'), freqs, 'Hz')))), 'color', colors(3,:));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
||||
xticks([1e0, 1e1, 1e2]);
|
||||
yticks(-360:90:360);
|
||||
ylim([-200, 20]);
|
||||
|
||||
linkaxes([ax3,ax3b],'x');
|
||||
xlim([1, 1e3]);
|
||||
|
||||
%% High Authority Controller - Soft Nano-Hexapod
|
||||
% Lead to increase phase margin
|
||||
a = 5; % Amount of phase lead / width of the phase lead / high frequency gain
|
||||
wc = 2*pi*20; % Frequency with the maximum phase lead [rad/s]
|
||||
H_lead = (1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a)));
|
||||
|
||||
% Lag at low frequency
|
||||
H_lag = (s + 2*pi*5)/(s + 2*pi*0.01);
|
||||
|
||||
% Low Pass filter to increase robustness
|
||||
H_lpf = 1/(1 + s/2/pi/200);
|
||||
|
||||
% High Authority Controller
|
||||
K_hac_vc = 4e5 * ... % Gain
|
||||
H_lead * ... % Lead
|
||||
H_lag * ... % Lag
|
||||
H_lpf; % LPF
|
||||
K_hac_vc.InputName = {'d'};
|
||||
K_hac_vc.OutputName = {'f'};
|
||||
|
||||
%% High Authority Controller - Mid Stiffness Nano-Hexapod
|
||||
% Lead to increase phase margin
|
||||
a = 4; % Amount of phase lead / width of the phase lead / high frequency gain
|
||||
wc = 2*pi*70; % Frequency with the maximum phase lead [rad/s]
|
||||
|
||||
H_lead = (1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a)));
|
||||
|
||||
% Lag at low frequency
|
||||
H_lag = ((s + 2*pi*15)/(s + 2*pi*0.01))^2;
|
||||
|
||||
% Low Pass filter to increase robustness
|
||||
H_lpf = 1/(1 + s/2/pi/300);
|
||||
|
||||
% High Authority Controller
|
||||
K_hac_md = 3e6 * ... % Gain
|
||||
H_lead * ... % Lead
|
||||
H_lag * ... % Lag
|
||||
H_lpf; % LPF
|
||||
K_hac_md.InputName = {'d'};
|
||||
K_hac_md.OutputName = {'f'};
|
||||
|
||||
%% High Authority Controller - Stiff Nano-Hexapod
|
||||
% Lead to increase phase margin
|
||||
a = 5; % Amount of phase lead / width of the phase lead / high frequency gain
|
||||
wc = 2*pi*100; % Frequency with the maximum phase lead [rad/s]
|
||||
H_lead = ((1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a))))^2;
|
||||
|
||||
% Integrator
|
||||
H_int = 1/(s + 2*pi*0.01)^2;
|
||||
|
||||
% Low Pass filter to increase robustness
|
||||
H_lpf = 1/(1 + s/2/pi/500);
|
||||
|
||||
% High Authority Controller
|
||||
K_hac_pz = 6e12 * ... % Gain
|
||||
H_lead * ... % Lead
|
||||
H_int * ... % Lag
|
||||
H_lpf; % LPF
|
||||
K_hac_pz.InputName = {'d'};
|
||||
K_hac_pz.OutputName = {'f'};
|
||||
|
||||
%% Save High Authority Controllers
|
||||
save('./mat/uniaxial_high_authority_controllers.mat', ...
|
||||
'K_hac_vc', 'K_hac_md', 'K_hac_pz');
|
||||
|
||||
%% Compute Loop gain for Nyquist Plot
|
||||
L_vc_light = squeeze(freqresp(K_hac_vc*G_iff_vc_light('d', 'f'), freqs, 'Hz'));
|
||||
L_vc_mid = squeeze(freqresp(K_hac_vc*G_iff_vc_mid( 'd', 'f'), freqs, 'Hz'));
|
||||
L_vc_heavy = squeeze(freqresp(K_hac_vc*G_iff_vc_heavy('d', 'f'), freqs, 'Hz'));
|
||||
|
||||
L_md_light = squeeze(freqresp(K_hac_md*G_iff_md_light('d', 'f'), freqs, 'Hz'));
|
||||
L_md_mid = squeeze(freqresp(K_hac_md*G_iff_md_mid( 'd', 'f'), freqs, 'Hz'));
|
||||
L_md_heavy = squeeze(freqresp(K_hac_md*G_iff_md_heavy('d', 'f'), freqs, 'Hz'));
|
||||
|
||||
L_pz_light = squeeze(freqresp(K_hac_pz*G_iff_pz_light('d', 'f'), freqs, 'Hz'));
|
||||
L_pz_mid = squeeze(freqresp(K_hac_pz*G_iff_pz_mid( 'd', 'f'), freqs, 'Hz'));
|
||||
L_pz_heavy = squeeze(freqresp(K_hac_pz*G_iff_pz_heavy('d', 'f'), freqs, 'Hz'));
|
||||
|
||||
%% Nyquist Plot - Hight Authority Controller for all three nano-hexapod stiffnesses and all sample masses
|
||||
figure;
|
||||
hold on;
|
||||
plot(real(L_vc_light), +imag(L_vc_light), '-', 'color', [colors(1,:), 0.5], 'DisplayName', '$k_n = 0.01\,N/\mu m$')
|
||||
plot(real(L_vc_light), -imag(L_vc_light), '-', 'color', [colors(1,:), 0.5], 'HandleVisibility', 'off')
|
||||
plot(real(L_vc_mid ), +imag(L_vc_mid ), '-', 'color', [colors(1,:), 0.5], 'HandleVisibility', 'off')
|
||||
plot(real(L_vc_mid ), -imag(L_vc_mid ), '-', 'color', [colors(1,:), 0.5], 'HandleVisibility', 'off')
|
||||
plot(real(L_vc_heavy), +imag(L_vc_heavy), '-', 'color', [colors(1,:), 0.5], 'HandleVisibility', 'off')
|
||||
plot(real(L_vc_heavy), -imag(L_vc_heavy), '-', 'color', [colors(1,:), 0.5], 'HandleVisibility', 'off')
|
||||
|
||||
plot(real(L_md_light), +imag(L_md_light), '-', 'color', [colors(2,:), 0.5], 'DisplayName', '$k_n = 1\,N/\mu m$')
|
||||
plot(real(L_md_light), -imag(L_md_light), '-', 'color', [colors(2,:), 0.5], 'HandleVisibility', 'off')
|
||||
plot(real(L_md_mid ), +imag(L_md_mid ), '-', 'color', [colors(2,:), 0.5], 'HandleVisibility', 'off')
|
||||
plot(real(L_md_mid ), -imag(L_md_mid ), '-', 'color', [colors(2,:), 0.5], 'HandleVisibility', 'off')
|
||||
plot(real(L_md_heavy), +imag(L_md_heavy), '-', 'color', [colors(2,:), 0.5], 'HandleVisibility', 'off')
|
||||
plot(real(L_md_heavy), -imag(L_md_heavy), '-', 'color', [colors(2,:), 0.5], 'HandleVisibility', 'off')
|
||||
|
||||
plot(real(L_pz_light), +imag(L_pz_light), '-', 'color', [colors(3,:), 0.5], 'DisplayName', '$k_n = 100\,N/\mu m$')
|
||||
plot(real(L_pz_light), -imag(L_pz_light), '-', 'color', [colors(3,:), 0.5], 'HandleVisibility', 'off')
|
||||
plot(real(L_pz_mid ), +imag(L_pz_mid ), '-', 'color', [colors(3,:), 0.5], 'HandleVisibility', 'off')
|
||||
plot(real(L_pz_mid ), -imag(L_pz_mid ), '-', 'color', [colors(3,:), 0.5], 'HandleVisibility', 'off')
|
||||
plot(real(L_pz_heavy), +imag(L_pz_heavy), '-', 'color', [colors(3,:), 0.5], 'HandleVisibility', 'off')
|
||||
plot(real(L_pz_heavy), -imag(L_pz_heavy), '-', 'color', [colors(3,:), 0.5], 'HandleVisibility', 'off')
|
||||
plot(-1, 0, 'kx', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Real'); ylabel('Imag');
|
||||
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
xlim([-3.8, 0.2]); ylim([-2, 2]);
|
||||
axis square;
|
||||
|
||||
%% Nyquist Plot - Hight Authority Controller - Soft Nano-Hexapod
|
||||
figure;
|
||||
hold on;
|
||||
plot(real(L_vc_light), +imag(L_vc_light), '-', 'color', colors(1,:), 'DisplayName', '$m_s = 1\,$kg')
|
||||
plot(real(L_vc_light), -imag(L_vc_light), '-', 'color', colors(1,:), 'HandleVisibility', 'off')
|
||||
plot(real(L_vc_mid ), +imag(L_vc_mid ), '-', 'color', colors(2,:), 'DisplayName', '$m_s = 25\,$kg')
|
||||
plot(real(L_vc_mid ), -imag(L_vc_mid ), '-', 'color', colors(2,:), 'HandleVisibility', 'off')
|
||||
plot(real(L_vc_heavy), +imag(L_vc_heavy), '-', 'color', colors(3,:), 'DisplayName', '$m_s = 50\,$kg')
|
||||
plot(real(L_vc_heavy), -imag(L_vc_heavy), '-', 'color', colors(3,:), 'HandleVisibility', 'off')
|
||||
% Minimum modul margin
|
||||
vc_mod_margin = min([min(abs(L_vc_light + 1)), min(abs(L_vc_mid + 1)), min(abs(L_vc_heavy + 1))]);
|
||||
plot(-1 + vc_mod_margin*cos(linspace(0,2*pi,100)), vc_mod_margin*sin(linspace(0,2*pi,100)), 'k-', 'DisplayName', sprintf('$r = %.2f$', vc_mod_margin))
|
||||
plot(-1, 0, 'kx', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Real'); ylabel('Imag');
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15
|
||||
xlim([-3.8, 0.2]); ylim([-2, 2]);
|
||||
axis square;
|
||||
|
||||
%% Nyquist Plot - Hight Authority Controller - Soft Nano-Hexapod
|
||||
figure;
|
||||
hold on;
|
||||
plot(real(L_md_light), +imag(L_md_light), '-', 'color', colors(1,:), 'DisplayName', '$m_s = 1\,$kg')
|
||||
plot(real(L_md_light), -imag(L_md_light), '-', 'color', colors(1,:), 'HandleVisibility', 'off')
|
||||
plot(real(L_md_mid ), +imag(L_md_mid ), '-', 'color', colors(2,:), 'DisplayName', '$m_s = 25\,$kg')
|
||||
plot(real(L_md_mid ), -imag(L_md_mid ), '-', 'color', colors(2,:), 'HandleVisibility', 'off')
|
||||
plot(real(L_md_heavy), +imag(L_md_heavy), '-', 'color', colors(3,:), 'DisplayName', '$m_s = 50\,$kg')
|
||||
plot(real(L_md_heavy), -imag(L_md_heavy), '-', 'color', colors(3,:), 'HandleVisibility', 'off')
|
||||
% Minimum modul margin
|
||||
md_mod_margin = min([min(abs(L_md_light + 1)), min(abs(L_md_mid + 1)), min(abs(L_md_heavy + 1))]);
|
||||
plot(-1 + md_mod_margin*cos(linspace(0,2*pi,100)), md_mod_margin*sin(linspace(0,2*pi,100)), 'k-', 'DisplayName', sprintf('$r = %.2f$', md_mod_margin))
|
||||
plot(-1, 0, 'kx', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Real'); ylabel('Imag');
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15
|
||||
xlim([-3.8, 0.2]); ylim([-2, 2]);
|
||||
axis square;
|
||||
|
||||
%% Nyquist Plot - Hight Authority Controller - Soft Nano-Hexapod
|
||||
figure;
|
||||
hold on;
|
||||
plot(real(L_pz_light), +imag(L_pz_light), '-', 'color', colors(1,:), 'DisplayName', '$m_s = 1\,$kg')
|
||||
plot(real(L_pz_light), -imag(L_pz_light), '-', 'color', colors(1,:), 'HandleVisibility', 'off')
|
||||
plot(real(L_pz_mid ), +imag(L_pz_mid ), '-', 'color', colors(2,:), 'DisplayName', '$m_s = 25\,$kg')
|
||||
plot(real(L_pz_mid ), -imag(L_pz_mid ), '-', 'color', colors(2,:), 'HandleVisibility', 'off')
|
||||
plot(real(L_pz_heavy), +imag(L_pz_heavy), '-', 'color', colors(3,:), 'DisplayName', '$m_s = 50\,$kg')
|
||||
plot(real(L_pz_heavy), -imag(L_pz_heavy), '-', 'color', colors(3,:), 'HandleVisibility', 'off')
|
||||
% Minimum modul margin
|
||||
pz_mod_margin = min([min(abs(L_pz_light + 1)), min(abs(L_pz_mid + 1)), min(abs(L_pz_heavy + 1))]);
|
||||
plot(-1 + pz_mod_margin*cos(linspace(0,2*pi,100)), pz_mod_margin*sin(linspace(0,2*pi,100)), 'k-', 'DisplayName', sprintf('$r = %.2f$', pz_mod_margin))
|
||||
plot(-1, 0, 'kx', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Real'); ylabel('Imag');
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15
|
||||
xlim([-3.8, 0.2]); ylim([-2, 2]);
|
||||
axis square;
|
||||
|
||||
%% Loop Gain - High Authority Controller - Relatively soft nano-hexapod
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(L_vc_light), 'color', colors(1,:), 'DisplayName', '$m_s = 1\,$kg');
|
||||
plot(freqs, abs(L_vc_mid), 'color', colors(2,:), 'DisplayName', '$m_s = 25\,$kg');
|
||||
plot(freqs, abs(L_vc_heavy), 'color', colors(3,:), 'DisplayName', '$m_s = 50\,$kg');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Loop Gain'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-3, 1e3]);
|
||||
yticks([1e-2, 1, 1e2])
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(L_vc_light)), 'color', colors(1,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(L_vc_mid )), 'color', colors(2,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(L_vc_heavy)), 'color', colors(3,:));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-225, -90]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([1, 500]);
|
||||
xticks([1, 10, 100]);
|
||||
|
||||
%% Loop Gain - High Authority Controller - Relatively stiff nano-hexapod
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(L_md_light), 'color', colors(1,:), 'DisplayName', '$m_s = 1\,$kg');
|
||||
plot(freqs, abs(L_md_mid), 'color', colors(2,:), 'DisplayName', '$m_s = 25\,$kg');
|
||||
plot(freqs, abs(L_md_heavy), 'color', colors(3,:), 'DisplayName', '$m_s = 50\,$kg');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Loop Gain'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-3, 1e3]);
|
||||
yticks([1e-2, 1, 1e2])
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(L_md_light)), 'color', colors(1,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(L_md_mid )), 'color', colors(2,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(L_md_heavy)), 'color', colors(3,:));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-225, -90]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([1, 500]);
|
||||
xticks([1, 10, 100]);
|
||||
|
||||
%% Loop Gain - High Authority Controller - Stiff nano-hexapod
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(L_pz_light), 'color', colors(1,:), 'DisplayName', '$m_s = 1\,$kg');
|
||||
plot(freqs, abs(L_pz_mid), 'color', colors(2,:), 'DisplayName', '$m_s = 25\,$kg');
|
||||
plot(freqs, abs(L_pz_heavy), 'color', colors(3,:), 'DisplayName', '$m_s = 50\,$kg');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Loop Gain'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-3, 1e3]);
|
||||
yticks([1e-2, 1, 1e2])
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(L_pz_light)), 'color', colors(1,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(L_pz_mid )), 'color', colors(2,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(L_pz_heavy)), 'color', colors(3,:));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-225, -90]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([1, 500]);
|
||||
xticks([1, 10, 100]);
|
||||
|
||||
%% Compute Closed Loop Systems
|
||||
G_hac_iff_vc_light = feedback(G_iff_vc_light, K_hac_vc, 'name', -1);
|
||||
G_hac_iff_vc_mid = feedback(G_iff_vc_mid , K_hac_vc, 'name', -1);
|
||||
G_hac_iff_vc_heavy = feedback(G_iff_vc_heavy, K_hac_vc, 'name', -1);
|
||||
|
||||
G_hac_iff_md_light = feedback(G_iff_md_light, K_hac_md, 'name', -1);
|
||||
G_hac_iff_md_mid = feedback(G_iff_md_mid , K_hac_md, 'name', -1);
|
||||
G_hac_iff_md_heavy = feedback(G_iff_md_heavy, K_hac_md, 'name', -1);
|
||||
|
||||
G_hac_iff_pz_light = feedback(G_iff_pz_light, K_hac_pz, 'name', -1);
|
||||
G_hac_iff_pz_mid = feedback(G_iff_pz_mid , K_hac_pz, 'name', -1);
|
||||
G_hac_iff_pz_heavy = feedback(G_iff_pz_heavy, K_hac_pz, 'name', -1);
|
||||
|
||||
%% Verify Stability
|
||||
isstable(G_hac_iff_vc_light) && isstable(G_hac_iff_vc_mid) && isstable(G_hac_iff_vc_heavy)
|
||||
|
||||
isstable(G_hac_iff_md_light) && isstable(G_hac_iff_md_mid) && isstable(G_hac_iff_md_heavy)
|
||||
|
||||
isstable(G_hac_iff_pz_light) && isstable(G_hac_iff_pz_mid) && isstable(G_hac_iff_pz_heavy)
|
||||
|
||||
%% Change of sensitivity to disturbances with LAC and with HAC-LAC
|
||||
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_hac_iff_md_mid('d', 'fs'), freqs, 'Hz'))), 'color', colors(2,:));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xticks([1e0, 1e1, 1e2]);
|
||||
ylabel('Amplitude $d/f_{s}$ [m/N]'); xlabel('Frequency [Hz]');
|
||||
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_hac_iff_md_mid('d', 'ft'), freqs, 'Hz'))), 'color', colors(2,:));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xticks([1e0, 1e1, 1e2]);
|
||||
ylabel('Amplitude $d/f_{t}$ [m/N]'); xlabel('Frequency [Hz]');
|
||||
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_hac_iff_md_mid('d', 'xf'), freqs, 'Hz'))), 'color', colors(2,:), 'DisplayName', 'HAC-IFF');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xticks([1e0, 1e1, 1e2]);
|
||||
ylabel('Amplitude $d/x_{f}$ [m/m]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
xlim([1, 500]);
|
||||
|
||||
%% Cumulative Amplitude Spectrum for all three nano-hexapod stiffnesses - Comparison of OL, IFF and HAC-LAC cases
|
||||
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', [0,0,0,0.5], 'DisplayName', 'OL');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_vc_light('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_vc_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [0,0,0,0.5], 'HandleVisibility', 'off');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_vc_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_vc_heavy('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [0,0,0,0.5], 'HandleVisibility', 'off');
|
||||
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,:), 0.5], 'DisplayName', 'IFF');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_iff_vc_light('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_iff_vc_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(1,:), 0.5], 'HandleVisibility', 'off');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_iff_vc_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_iff_vc_heavy('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(1,:), 0.5], 'HandleVisibility', 'off');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_vc_mid('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_vc_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(2,:), 0.5], 'DisplayName', 'HAC-IFF');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_vc_light('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_vc_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(2,:), 0.5], 'HandleVisibility', 'off');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_vc_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_vc_heavy('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(2,:), 0.5], 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xticks([1e0, 1e1, 1e2]);
|
||||
ylabel('CAS of $d$ [m]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
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', [0,0,0,0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_md_light('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_md_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [0,0,0,0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_md_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_md_heavy('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [0,0,0,0.5]);
|
||||
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,:), 0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_iff_md_light('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_iff_md_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(1,:), 0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_iff_md_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_iff_md_heavy('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(1,:), 0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_md_mid('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_md_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(2,:), 0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_md_light('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_md_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(2,:), 0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_md_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_md_heavy('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(2,:), 0.5]);
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xticks([1e0, 1e1, 1e2]);
|
||||
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
||||
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', [0,0,0,0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_pz_light('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_pz_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [0,0,0,0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_pz_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_pz_heavy('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [0,0,0,0.5]);
|
||||
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,:), 0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_iff_pz_light('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_iff_pz_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(1,:), 0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_iff_pz_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_iff_pz_heavy('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(1,:), 0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_pz_mid('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_pz_mid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(2,:), 0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_pz_light('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_pz_light('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(2,:), 0.5]);
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_pz_heavy('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_pz_heavy('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'color', [colors(2,:), 0.5]);
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xticks([1e0, 1e1, 1e2]);
|
||||
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
||||
xlim([1, 500]);
|
||||
ylim([2e-10, 3e-6])
|
||||
202
A1-nass-uniaxial-model/uniaxial_7_support_compliance.m
Normal file
202
A1-nass-uniaxial-model/uniaxial_7_support_compliance.m
Normal file
@@ -0,0 +1,202 @@
|
||||
%% 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]);
|
||||
397
A1-nass-uniaxial-model/uniaxial_8_payload_dynamics.m
Normal file
397
A1-nass-uniaxial-model/uniaxial_8_payload_dynamics.m
Normal file
@@ -0,0 +1,397 @@
|
||||
%% 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;
|
||||
|
||||
%% Uniaxial Simscape model name
|
||||
mdl = 'nass_uniaxial_model';
|
||||
|
||||
%% Load the micro-station parameters
|
||||
load('uniaxial_micro_station_parameters.mat')
|
||||
|
||||
%% Load the PSD of disturbances
|
||||
load('uniaxial_disturbance_psd.mat', 'f', 'psd_ft', 'psd_xf');
|
||||
|
||||
%% Load Active Damping Controller
|
||||
load('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');
|
||||
|
||||
%% Load High Authority Controllers
|
||||
load('uniaxial_high_authority_controllers.mat', 'K_hac_vc', 'K_hac_md', 'K_hac_pz');
|
||||
|
||||
%% Frequency Vector [Hz]
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
%% Soft Nano-Hexapod
|
||||
% Light payload mass
|
||||
mn = 15; % Nano-Hexapod mass [kg]
|
||||
ms = 1; % Sample Mass [kg]
|
||||
kn = 1e4; % Nano-Hexapod (soft) Stiffness [N/m]
|
||||
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
||||
|
||||
% Rigid sample
|
||||
G_vc_rigid_light = 1/((mn + ms)*s^2 + cn*s + kn);
|
||||
|
||||
% Soft Sample
|
||||
ws = 2*pi*20;
|
||||
ks = ms * ws^2;
|
||||
cs = 2*0.01*sqrt(ms*ks);
|
||||
G_vc_soft_light = (ms*s^2 + cs*s + ks)/((mn*s^2 + cn*s + kn)*(ms*s^2 + cs*s + ks) + ms*s^2*(cs*s + ks));
|
||||
|
||||
% Stiff Sample
|
||||
ws = 2*pi*200;
|
||||
ks = ms * ws^2;
|
||||
cs = 2*0.01*sqrt(ms*ks);
|
||||
G_vc_stiff_light = (ms*s^2 + cs*s + ks)/((mn*s^2 + cn*s + kn)*(ms*s^2 + cs*s + ks) + ms*s^2*(cs*s + ks));
|
||||
|
||||
% Heavy payload mass
|
||||
mn = 15; % Nano-Hexapod mass [kg]
|
||||
ms = 50; % Sample Mass [kg]
|
||||
kn = 1e4; % Nano-Hexapod (soft) Stiffness [N/m]
|
||||
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
||||
|
||||
% Rigid sample
|
||||
G_vc_rigid_heavy = 1/((mn + ms)*s^2 + cn*s + kn);
|
||||
|
||||
% Soft Sample
|
||||
ws = 2*pi*20;
|
||||
ks = ms * ws^2;
|
||||
cs = 2*0.01*sqrt(ms*ks);
|
||||
G_vc_soft_heavy = (ms*s^2 + cs*s + ks)/((mn*s^2 + cn*s + kn)*(ms*s^2 + cs*s + ks) + ms*s^2*(cs*s + ks));
|
||||
|
||||
% Stiff Sample
|
||||
ws = 2*pi*200;
|
||||
ks = ms * ws^2;
|
||||
cs = 2*0.01*sqrt(ms*ks);
|
||||
G_vc_stiff_heavy = (ms*s^2 + cs*s + ks)/((mn*s^2 + cn*s + kn)*(ms*s^2 + cs*s + ks) + ms*s^2*(cs*s + ks));
|
||||
|
||||
%% Effect of the payload dynamics on the soft Nano-Hexapod. Light sample on the right, and heavy sample on the left
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_vc_rigid_light, freqs, 'Hz'))), '-', 'color', colors(1,:), 'DisplayName', 'Rigid sample');
|
||||
plot(freqs, abs(squeeze(freqresp(G_vc_stiff_light, freqs, 'Hz'))), '-', 'color', colors(2,:), 'DisplayName', '$\omega_s = 200\,Hz$');
|
||||
plot(freqs, abs(squeeze(freqresp(G_vc_soft_light, freqs, 'Hz'))), '-', 'color', colors(3,:), 'DisplayName', '$\omega_s = 20\,Hz$');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-10, 1e-2])
|
||||
|
||||
ax1b = nexttile();
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_rigid_light, freqs, 'Hz')))), '-', 'color', colors(1,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_stiff_light, freqs, 'Hz')))), '-', 'color', colors(2,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_soft_light, 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]);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax2 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_vc_rigid_heavy, freqs, 'Hz'))), '-', 'color', colors(1,:), 'DisplayName', 'Rigid sample');
|
||||
plot(freqs, abs(squeeze(freqresp(G_vc_stiff_heavy, freqs, 'Hz'))), '-', 'color', colors(2,:), 'DisplayName', '$\omega_s = 200\,Hz$');
|
||||
plot(freqs, abs(squeeze(freqresp(G_vc_soft_heavy, freqs, 'Hz'))), '-', 'color', colors(3,:), 'DisplayName', '$\omega_s = 20\,Hz$');
|
||||
plot(freqs, abs(squeeze(freqresp(1/(mn*s^2), freqs, 'Hz'))), '-', 'color', [0,0,0,0.5], 'DisplayName', '$\frac{1}{m_n s^2}$');
|
||||
plot(freqs, abs(squeeze(freqresp(1/((mn + ms)*s^2), freqs, 'Hz'))), '--', 'color', [0,0,0,0.5], 'DisplayName', '$\frac{1}{(m_n + m_s) s^2}$');
|
||||
text(2.2, 2e-3, '$\omega_n = \sqrt{\frac{k_n}{m_n + m_s}}$', 'horizontalalignment', 'left');
|
||||
text(20, 1e-8, '$\omega_s = \sqrt{\frac{k_s}{m_s}}$', 'horizontalalignment', 'center');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
ldg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
ldg.ItemTokenSize = [20, 1];
|
||||
ylim([1e-10, 1e-2])
|
||||
|
||||
ax2b = nexttile();
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_rigid_heavy, freqs, 'Hz')))), '-', 'color', colors(1,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_stiff_heavy, freqs, 'Hz')))), '-', 'color', colors(2,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_vc_soft_heavy, 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]);
|
||||
|
||||
%% Stiff Nano-Hexapod
|
||||
% Light payload mass
|
||||
mn = 15; % Nano-Hexapod mass [kg]
|
||||
ms = 1; % Sample Mass [kg]
|
||||
kn = 1e8; % Nano-Hexapod (soft) Stiffness [N/m]
|
||||
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
||||
|
||||
% Rigid sample
|
||||
G_pz_rigid_light = 1/((mn + ms)*s^2 + cn*s + kn);
|
||||
|
||||
% Soft Sample
|
||||
ws = 2*pi*20;
|
||||
ks = ms * ws^2;
|
||||
cs = 2*0.01*sqrt(ms*ks);
|
||||
G_pz_soft_light = (ms*s^2 + cs*s + ks)/((mn*s^2 + cn*s + kn)*(ms*s^2 + cs*s + ks) + ms*s^2*(cs*s + ks));
|
||||
|
||||
% Stiff Sample
|
||||
ws = 2*pi*200;
|
||||
ks = ms * ws^2;
|
||||
cs = 2*0.01*sqrt(ms*ks);
|
||||
G_pz_stiff_light = (ms*s^2 + cs*s + ks)/((mn*s^2 + cn*s + kn)*(ms*s^2 + cs*s + ks) + ms*s^2*(cs*s + ks));
|
||||
|
||||
% Heavy payload mass
|
||||
mn = 15; % Nano-Hexapod mass [kg]
|
||||
ms = 50; % Sample Mass [kg]
|
||||
kn = 1e8; % Nano-Hexapod (soft) Stiffness [N/m]
|
||||
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
||||
|
||||
% Rigid sample
|
||||
G_pz_rigid_heavy = 1/((mn + ms)*s^2 + cn*s + kn);
|
||||
|
||||
% Soft Sample
|
||||
ws = 2*pi*20;
|
||||
ks = ms * ws^2;
|
||||
cs = 2*0.01*sqrt(ms*ks);
|
||||
G_pz_soft_heavy = (ms*s^2 + cs*s + ks)/((mn*s^2 + cn*s + kn)*(ms*s^2 + cs*s + ks) + ms*s^2*(cs*s + ks));
|
||||
|
||||
% Stiff Sample
|
||||
ws = 2*pi*200;
|
||||
ks = ms * ws^2;
|
||||
cs = 2*0.01*sqrt(ms*ks);
|
||||
G_pz_stiff_heavy = (ms*s^2 + cs*s + ks)/((mn*s^2 + cn*s + kn)*(ms*s^2 + cs*s + ks) + ms*s^2*(cs*s + ks));
|
||||
|
||||
%% Effect of the payload dynamics on the stiff Nano-Hexapod. Light sample on the right, and heavy sample on the left
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz_rigid_light, freqs, 'Hz'))), '-', 'color', colors(1,:));
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz_stiff_light, freqs, 'Hz'))), '-', 'color', colors(2,:));
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz_soft_light, freqs, 'Hz'))), '-', 'color', colors(3,:));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-10, 1e-6])
|
||||
|
||||
ax1b = nexttile();
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_rigid_light, freqs, 'Hz')))), '-', 'color', colors(1,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_stiff_light, freqs, 'Hz')))), '-', 'color', colors(2,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_soft_light, 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]);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax2 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz_rigid_heavy, freqs, 'Hz'))), '-', 'color', colors(1,:), 'DisplayName', 'Rigid sample');
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz_stiff_heavy, freqs, 'Hz'))), '-', 'color', colors(2,:), 'DisplayName', 'Stiff sample: $\omega_s = 200\,Hz$');
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz_soft_heavy, freqs, 'Hz'))), '-', 'color', colors(3,:), 'DisplayName', 'Soft sample: $\omega_s = 20\,Hz$');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-10, 1e-6])
|
||||
ldg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
ldg.ItemTokenSize = [20, 1];
|
||||
|
||||
ax2b = nexttile();
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_rigid_heavy, freqs, 'Hz')))), '-', 'color', colors(1,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_stiff_heavy, freqs, 'Hz')))), '-', 'color', colors(2,:));
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_pz_soft_heavy, 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]);
|
||||
|
||||
%% Nano-Hexpod model
|
||||
model_config = struct();
|
||||
model_config.controller = "open_loop";
|
||||
mn = 15; % Nano-Hexapod mass [kg]
|
||||
ms = 1; % Sample Mass [kg]
|
||||
|
||||
%% Identification
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force
|
||||
io(io_i) = linio([mdl, '/micro_station/xf'], 1, 'openinput'); io_i = io_i + 1; % Floor Motion
|
||||
io(io_i) = linio([mdl, '/micro_station/ft'], 1, 'openinput'); io_i = io_i + 1; % Stage vibrations
|
||||
io(io_i) = linio([mdl, '/fs'], 1, 'openinput'); io_i = io_i + 1; % Direct sample forces
|
||||
io(io_i) = linio([mdl, '/dL'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Sensor
|
||||
io(io_i) = linio([mdl, '/fm'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensor
|
||||
io(io_i) = linio([mdl, '/vn'] , 1, 'openoutput'); io_i = io_i + 1; % Geophone
|
||||
io(io_i) = linio([mdl, '/d'] , 1, 'openoutput'); io_i = io_i + 1; % Metrology Output
|
||||
io(io_i) = linio([mdl, '/y'] , 1, 'openoutput'); io_i = io_i + 1; % Sample's position
|
||||
|
||||
%% Soft Nano-Hexapod
|
||||
% Light payload mass
|
||||
kn = 1e4; % Nano-Hexapod (soft) Stiffness [N/m]
|
||||
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
||||
|
||||
% Rigid Sample
|
||||
model_config.nhexa = "1dof";
|
||||
G_vc_light_rigid = linearize(mdl, io, 0.0);
|
||||
G_vc_light_rigid.InputName = {'f', 'xf', 'ft', 'fs'};
|
||||
G_vc_light_rigid.OutputName = {'dL', 'fm', 'vn', 'd', 'y'};
|
||||
|
||||
% Soft Sample
|
||||
model_config.nhexa = "2dof";
|
||||
ws = 2*pi*20;
|
||||
ks = ms * ws^2;
|
||||
cs = 2*0.01*sqrt(ms*ks);
|
||||
|
||||
G_vc_light_soft = linearize(mdl, io, 0.0);
|
||||
G_vc_light_soft.InputName = {'f', 'xf', 'ft', 'fs'};
|
||||
G_vc_light_soft.OutputName = {'dL', 'fm', 'vn', 'd', 'y'};
|
||||
|
||||
% Rigid Sample
|
||||
model_config.nhexa = "2dof";
|
||||
ws = 2*pi*200;
|
||||
ks = ms * ws^2;
|
||||
cs = 2*0.01*sqrt(ms*ks);
|
||||
|
||||
G_vc_light_stiff = linearize(mdl, io, 0.0);
|
||||
G_vc_light_stiff.InputName = {'f', 'xf', 'ft', 'fs'};
|
||||
G_vc_light_stiff.OutputName = {'dL', 'fm', 'vn', 'd', 'y'};
|
||||
|
||||
%% Stiff Nano-Hexapod
|
||||
% Light payload mass
|
||||
kn = 1e8; % Nano-Hexapod (soft) Stiffness [N/m]
|
||||
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
||||
|
||||
% Rigid Sample
|
||||
model_config.nhexa = "1dof";
|
||||
G_pz_light_rigid = linearize(mdl, io, 0.0);
|
||||
G_pz_light_rigid.InputName = {'f', 'xf', 'ft', 'fs'};
|
||||
G_pz_light_rigid.OutputName = {'dL', 'fm', 'vn', 'd', 'y'};
|
||||
|
||||
% Soft Sample
|
||||
model_config.nhexa = "2dof";
|
||||
ws = 2*pi*20;
|
||||
ks = ms * ws^2;
|
||||
cs = 2*0.01*sqrt(ms*ks);
|
||||
|
||||
G_pz_light_soft = linearize(mdl, io, 0.0);
|
||||
G_pz_light_soft.InputName = {'f', 'xf', 'ft', 'fs'};
|
||||
G_pz_light_soft.OutputName = {'dL', 'fm', 'vn', 'd', 'y'};
|
||||
|
||||
% Rigid Sample
|
||||
model_config.nhexa = "2dof";
|
||||
ws = 2*pi*200;
|
||||
ks = ms * ws^2;
|
||||
cs = 2*0.01*sqrt(ms*ks);
|
||||
|
||||
G_pz_light_stiff = linearize(mdl, io, 0.0);
|
||||
G_pz_light_stiff.InputName = {'f', 'xf', 'ft', 'fs'};
|
||||
G_pz_light_stiff.OutputName = {'dL', 'fm', 'vn', 'd', 'y'};
|
||||
|
||||
%% Apply IFF and verify stability
|
||||
% Soft Nano-Hexapod
|
||||
G_iff_vc_light_rigid = feedback(G_vc_light_rigid, K_iff_vc, 'name', +1);
|
||||
G_iff_vc_light_soft = feedback(G_vc_light_soft , K_iff_vc, 'name', +1);
|
||||
G_iff_vc_light_stiff = feedback(G_vc_light_stiff, K_iff_vc, 'name', +1);
|
||||
|
||||
isstable(G_iff_vc_light_rigid)
|
||||
isstable(G_iff_vc_light_soft)
|
||||
isstable(G_iff_vc_light_stiff)
|
||||
|
||||
% Stiff Nano-Hexapod
|
||||
G_iff_pz_light_rigid = feedback(G_pz_light_rigid, K_iff_pz, 'name', +1);
|
||||
G_iff_pz_light_soft = feedback(G_pz_light_soft , K_iff_pz, 'name', +1);
|
||||
G_iff_pz_light_stiff = feedback(G_pz_light_stiff, K_iff_pz, 'name', +1);
|
||||
|
||||
isstable(G_iff_pz_light_rigid)
|
||||
isstable(G_iff_pz_light_soft)
|
||||
isstable(G_iff_pz_light_stiff)
|
||||
|
||||
%% Compute closed-loop plants and verify stability
|
||||
% Soft Nano-Hexapod
|
||||
G_hac_iff_vc_light_rigid = feedback(G_iff_vc_light_rigid, K_hac_vc, 'name', -1);
|
||||
G_hac_iff_vc_light_soft = feedback(G_iff_vc_light_soft , K_hac_vc, 'name', -1);
|
||||
G_hac_iff_vc_light_stiff = feedback(G_iff_vc_light_stiff, K_hac_vc, 'name', -1);
|
||||
|
||||
isstable(G_hac_iff_vc_light_rigid)
|
||||
isstable(G_hac_iff_vc_light_soft)
|
||||
isstable(G_hac_iff_vc_light_stiff)
|
||||
|
||||
% Stiff Nano-Hexapod
|
||||
G_hac_iff_pz_light_rigid = feedback(G_iff_pz_light_rigid, K_hac_pz, 'name', -1);
|
||||
G_hac_iff_pz_light_soft = feedback(G_iff_pz_light_soft , K_hac_pz, 'name', -1);
|
||||
G_hac_iff_pz_light_stiff = feedback(G_iff_pz_light_stiff, K_hac_pz, 'name', -1);
|
||||
|
||||
isstable(G_hac_iff_pz_light_rigid)
|
||||
isstable(G_hac_iff_pz_light_soft)
|
||||
isstable(G_hac_iff_pz_light_stiff)
|
||||
|
||||
%% Cumulative Amplitude Spectrum of d - Effect of Sample's flexibility
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_pz_light_rigid('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_pz_light_rigid('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'DisplayName', 'Rigid sample');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_pz_light_stiff('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_pz_light_stiff('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'DisplayName', '$\omega_s = 200\,$Hz');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_pz_light_soft('d', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_pz_light_soft('d', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'DisplayName', '$\omega_s = 20\,$Hz');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('CAS of $d$ [m]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
xlim([1, 500]);
|
||||
xticks([1e0, 1e1, 1e2]);
|
||||
ylim([2e-10, 2e-7])
|
||||
|
||||
%% Cumulative Amplitude Spectrum - Effect of Sample's flexibility
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_pz_light_rigid('y', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_pz_light_rigid('y', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'DisplayName', 'Rigid sample');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_pz_light_stiff('y', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_pz_light_stiff('y', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'DisplayName', '$\omega_s = 200\,$Hz');
|
||||
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(psd_ft.*abs(squeeze(freqresp(G_hac_iff_pz_light_soft('y', 'ft'), f, 'Hz'))).^2 + ...
|
||||
psd_xf.*abs(squeeze(freqresp(G_hac_iff_pz_light_soft('y', 'xf'), f, 'Hz'))).^2)))), '-', ...
|
||||
'DisplayName', '$\omega_s = 20\,$Hz');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('CAS of $y$ [m]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
xlim([1, 500]);
|
||||
xticks([1e0, 1e1, 1e2]);
|
||||
ylim([2e-10, 2e-7])
|
||||
Reference in New Issue
Block a user