135 lines
5.0 KiB
Matlab
135 lines
5.0 KiB
Matlab
%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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%% Colors for the figures
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colors = colororder;
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%% 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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% #+name: fig:micro_station_uniaxial_model
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% #+caption: Schematic of the Micro-Station measurement setup and uniaxial model.
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% #+begin_figure
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% #+attr_latex: :caption \subcaption{\label{fig:uniaxial_ustation_meas_dynamics_schematic}Measurement setup - Schematic}
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% #+attr_latex: :options {0.69\textwidth}
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% #+begin_subfigure
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% #+attr_latex: :scale 1
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% [[file:figs/uniaxial_ustation_meas_dynamics_schematic.png]]
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% #+end_subfigure
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% #+attr_latex: :caption \subcaption{\label{fig:uniaxial_model_micro_station}Uniaxial model of the micro-station}
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% #+attr_latex: :options {0.29\textwidth}
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% #+begin_subfigure
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% #+attr_latex: :scale 1
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% [[file:figs/uniaxial_model_micro_station.png]]
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% #+end_subfigure
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% #+end_figure
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% Due to the bad coherence at low frequency, the frequency response functions will only be shown between 20 and 200Hz (solid lines in Figure ref:fig:uniaxial_comp_frf_meas_model).
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%% Load measured FRF
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load('meas_microstation_frf.mat');
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% Masses are estimated from the CAD.
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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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% And stiffnesses from the data-sheet of stage manufacturers.
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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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% The damping coefficients are tuned to match the identified damping from the measurements.
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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 model and measurements
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% The comparison between the measurements and the model is shown in Figure ref:fig:uniaxial_comp_frf_meas_model.
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% Only three modes are modelled with frequencies at 70Hz, 140Hz and 320Hz.
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% As the model is simplistic, the goal is not to match exactly the measurement but to have a first approximation.
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% More accurate models will be used later on.
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%% Comparison of the measured FRF and identified ones from the uni-axial 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', '$D_{h,z}/F_{h,z}$');
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plot(f(f>20), abs(frf_Fgz_to_Dhz(f>20)), '-', 'color', colors(2,:), 'DisplayName', '$D_{h,z}/F_{g,z}$');
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plot(f(f>20), abs(frf_Fgz_to_Dgz(f>20)), '-', 'color', colors(3,:), 'DisplayName', '$D_{g,z}/F_{g,z}$');
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plot(freqs, abs(squeeze(freqresp(G_id('Dh', 'Fh'), freqs, 'Hz'))), '--', 'color', colors(1,:), 'DisplayName', '$D_{h,z}/F_{h,z}$ (model)');
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plot(freqs, abs(squeeze(freqresp(G_id('Dh', 'Fg'), freqs, 'Hz'))), '--', 'color', colors(2,:), 'DisplayName', '$D_{h,z}/F_{g,z}$ (model)');
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plot(freqs, abs(squeeze(freqresp(G_id('Dg', 'Fg'), freqs, 'Hz'))), '--', 'color', colors(3,:), 'DisplayName', '$D_{g,z}/F_{g,z}$ (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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