165 lines
6.4 KiB
Matlab
165 lines
6.4 KiB
Matlab
% Matlab Init :noexport:ignore:
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%% ustation_4_experiments.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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addpath('./src/'); % Path for functions
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addpath('./STEPS/'); % Path for STEPS
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addpath('./subsystems/'); % Path for Subsystems Simulink files
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% Simulink Model name
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mdl = 'ustation_simscape';
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load('nass_model_conf_simulink.mat');
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%% Colors for the figures
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colors = colororder;
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%% Frequency Vector
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freqs = logspace(log10(10), log10(2e3), 1000);
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% Tomography Experiment
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% <<sec:ustation_experiments_tomography>>
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% To simulate a tomography experiment, the setpoint of the Spindle is configured to perform a constant rotation with a rotational velocity of 60rpm.
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% Both ground motion and spindle vibration disturbances were simulated based on what was computed in Section ref:sec:ustation_disturbances.
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% A radial offset of $\approx 1\,\mu m$ between the "point-of-interest" and the spindle's rotation axis is introduced to represent what is experimentally observed.
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% During the 10 second simulation (i.e. 10 spindle turns), the position of the "point-of-interest" with respect to the granite was recorded.
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% Results are shown in Figure ref:fig:ustation_errors_model_spindle.
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% A good correlation with the measurements is observed both for radial errors (Figure ref:fig:ustation_errors_model_spindle_radial) and axial errors (Figure ref:fig:ustation_errors_model_spindle_axial).
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%% Tomography experiment
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% Sample is not centered with the rotation axis
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% This is done by offsetfing the micro-hexapod by 0.9um
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P_micro_hexapod = [0.9e-6; 0; 0]; % [m]
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set_param(conf_simulink, 'StopTime', '10');
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initializeGround();
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initializeGranite();
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initializeTy();
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initializeRy();
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initializeRz();
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initializeMicroHexapod('AP', P_micro_hexapod);
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initializeSimscapeConfiguration('gravity', false);
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initializeLoggingConfiguration('log', 'all');
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initializeDisturbances(...
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'Dw_x', true, ... % Ground Motion - X direction
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'Dw_y', true, ... % Ground Motion - Y direction
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'Dw_z', true, ... % Ground Motion - Z direction
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'Fdy_x', false, ... % Translation Stage - X direction
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'Fdy_z', false, ... % Translation Stage - Z direction
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'Frz_x', true, ... % Spindle - X direction
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'Frz_y', true, ... % Spindle - Y direction
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'Frz_z', true); % Spindle - Z direction
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initializeReferences(...
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'Rz_type', 'rotating', ...
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'Rz_period', 1, ...
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'Dh_pos', [P_micro_hexapod; 0; 0; 0]);
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sim(mdl);
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exp_tomography = simout;
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%% Compare with the measurements
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spindle_errors = load('ustation_errors_spindle.mat');
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%% Measured radial errors of the Spindle
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figure;
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hold on;
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plot(1e6*spindle_errors.Dx(1:100:end), 1e6*spindle_errors.Dy(1:100:end), 'DisplayName', 'Measurements')
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plot(1e6*exp_tomography.y.x.Data, 1e6*exp_tomography.y.y.Data, 'DisplayName', 'Simulation')
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hold off;
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xlabel('X displacement [$\mu$m]'); ylabel('Y displacement [$\mu$m]');
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axis equal
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xlim([-1, 1]); ylim([-1, 1]);
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xticks([-1, -0.5, 0, 0.5, 1]);
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yticks([-1, -0.5, 0, 0.5, 1]);
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leg = legend('location', 'none', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15;
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%% Measured axial errors of the Spindle
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figure;
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hold on;
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plot(spindle_errors.deg(1:100:end)/360, detrend(1e9*spindle_errors.Dz(1:100:end), 0), 'DisplayName', 'Measurements')
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plot(exp_tomography.y.z.Time, detrend(1e9*exp_tomography.y.z.Data, 0), 'DisplayName', 'Simulation')
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hold off;
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xlabel('Rotation [turn]'); ylabel('Z displacement [nm]');
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axis square
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xlim([0,2]); ylim([-40, 40]);
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leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15;
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% Raster Scans with the translation stage
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% <<sec:ustation_experiments_ty_scans>>
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% A second experiment was performed in which the translation stage was scanned at constant velocity.
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% The translation stage setpoint is configured to have a "triangular" shape with stroke of $\pm 4.5\, mm$.
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% Both ground motion and translation stage vibrations were included in the simulation.
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% Similar to what was performed for the tomography simulation, the PoI position with respect to the granite was recorded and compared with the experimental measurements in Figure ref:fig:ustation_errors_model_dy_vertical.
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% A similar error amplitude was observed, thus indicating that the multi-body model with the included disturbances accurately represented the micro-station behavior in typical scientific experiments.
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%% Translation stage latteral scans
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set_param(conf_simulink, 'StopTime', '2');
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initializeGround();
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initializeGranite();
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initializeTy();
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initializeRy();
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initializeRz();
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initializeMicroHexapod();
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initializeSimscapeConfiguration('gravity', false);
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initializeLoggingConfiguration('log', 'all');
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initializeDisturbances(...
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'Dw_x', true, ... % Ground Motion - X direction
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'Dw_y', true, ... % Ground Motion - Y direction
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'Dw_z', true, ... % Ground Motion - Z direction
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'Fdy_x', true, ... % Translation Stage - X direction
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'Fdy_z', true, ... % Translation Stage - Z direction
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'Frz_x', false, ... % Spindle - X direction
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'Frz_y', false, ... % Spindle - Y direction
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'Frz_z', false); % Spindle - Z direction
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initializeReferences(...
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'Dy_type', 'triangular', ...
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'Dy_amplitude', 4.5e-3, ...
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'Dy_period', 2);
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sim(mdl);
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exp_latteral_scans = simout;
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% Load the experimentally measured errors
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ty_errors = load('ustation_errors_ty.mat');
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% Compute best straight line to remove it from data
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average_error = mean(ty_errors.ty_z')';
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straight_line = average_error - detrend(average_error, 1);
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% Only plot data for the scan from -4.5mm to 4.5mm
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dy_setpoint = 1e3*exp_latteral_scans.y.y.Data(exp_latteral_scans.y.y.time > 0.5 & exp_latteral_scans.y.y.time < 1.5);
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dz_error = detrend(1e6*exp_latteral_scans.y.z.Data(exp_latteral_scans.y.y.time > 0.5 & exp_latteral_scans.y.y.time < 1.5), 0);
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figure;
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hold on;
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plot(ty_errors.setpoint, detrend(ty_errors.ty_z(:,1) - straight_line, 0), 'color', colors(1,:), 'DisplayName', 'Measurement')
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% plot(ty_errors.setpoint, detrend(ty_errors.ty_z(:,[4,6]) - straight_line, 0), 'color', colors(1,:), 'HandleVisibility', 'off')
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plot(dy_setpoint, dz_error, 'color', colors(2,:), 'DisplayName', 'Simulation')
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hold off;
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xlabel('$D_y$ position [mm]'); ylabel('Vertical error [$\mu$m]');
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xlim([-5, 5]); ylim([-0.4, 0.4]);
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leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15;
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