Initial Commit
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commit
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.gitignore
vendored
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.gitignore
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auto/
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*.tex
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*.blg
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*-blx.bib
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*.bbl
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*.aux
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*.bcf
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*.fdb_latexmk
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*.log
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*.out
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*.pyg
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*.toc
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*.fls
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*.synctex.gz
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.auctex-auto/
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_minted*
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# Emacs
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auto/
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# Simulink Real Time
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*bio.m
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*pt.m
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*ref.m
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*ri.m
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*xcp.m
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*.mldatx
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*.slxc
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*.xml
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*_slrt_rtw/
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# data
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data/
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# Windows default autosave extension
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*.asv
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# OSX / *nix default autosave extension
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*.m~
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# Compiled MEX binaries (all platforms)
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*.mex*
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# Packaged app and toolbox files
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*.mlappinstall
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*.mltbx
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# Generated helpsearch folders
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helpsearch*/
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# Simulink code generation folders
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slprj/
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sccprj/
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# Matlab code generation folders
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codegen/
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# Simulink autosave extension
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*.autosave
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# Octave session info
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octave-workspace
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43
dcm-simscape.matlab
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dcm-simscape.matlab
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% Initialize Path
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% #+NAME: m-init-path
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%% Path for functions, data and scripts
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addpath('./matlab/mat/'); % Path for data
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addpath('./matlab/'); % Path for scripts
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%% Simscape Model - Nano Hexapod
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addpath('./matlab/STEPS/')
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% #+NAME: m-init-path-tangle
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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%% Simscape Model - Nano Hexapod
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addpath('./STEPS/')
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% Initialize Simscape Model
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% #+NAME: m-init-simscape
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%% Initialize Parameters for Simscape model
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controller.type = 0; % Open Loop Control
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%% Options for Linearization
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options = linearizeOptions;
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options.SampleTime = 0;
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%% Open Simulink Model
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mdl = 'simscape_dcm';
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open(mdl)
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% Initialize other elements
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% #+NAME: m-init-other
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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(1, 3, 1000);
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dcm-simscape.org
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After Width: | Height: | Size: 22 KiB |
BIN
matlab/Fast_Jack.slx
Normal file
BIN
matlab/Fast_Jack.slx
Normal file
Binary file not shown.
1844
matlab/STEPS/00221283.STEP
Normal file
1844
matlab/STEPS/00221283.STEP
Normal file
File diff suppressed because it is too large
Load Diff
132819
matlab/STEPS/00221401_schematic.STEP
Normal file
132819
matlab/STEPS/00221401_schematic.STEP
Normal file
File diff suppressed because it is too large
Load Diff
114141
matlab/STEPS/00221450_schematic.STEP
Normal file
114141
matlab/STEPS/00221450_schematic.STEP
Normal file
File diff suppressed because one or more lines are too long
112479
matlab/STEPS/00221610_schematic.STEP
Normal file
112479
matlab/STEPS/00221610_schematic.STEP
Normal file
File diff suppressed because one or more lines are too long
112951
matlab/STEPS/00221611.STEP
Normal file
112951
matlab/STEPS/00221611.STEP
Normal file
File diff suppressed because one or more lines are too long
26683
matlab/STEPS/00221612.STEP
Normal file
26683
matlab/STEPS/00221612.STEP
Normal file
File diff suppressed because one or more lines are too long
15562
matlab/STEPS/00221613.STEP
Normal file
15562
matlab/STEPS/00221613.STEP
Normal file
File diff suppressed because it is too large
Load Diff
24327
matlab/STEPS/00221614.STEP
Normal file
24327
matlab/STEPS/00221614.STEP
Normal file
File diff suppressed because one or more lines are too long
46219
matlab/STEPS/00221615.STEP
Normal file
46219
matlab/STEPS/00221615.STEP
Normal file
File diff suppressed because one or more lines are too long
5339
matlab/STEPS/00221639.STEP
Normal file
5339
matlab/STEPS/00221639.STEP
Normal file
File diff suppressed because it is too large
Load Diff
139005
matlab/STEPS/00221700_schematic.STEP
Normal file
139005
matlab/STEPS/00221700_schematic.STEP
Normal file
File diff suppressed because one or more lines are too long
42339
matlab/STEPS/00221702.STEP
Normal file
42339
matlab/STEPS/00221702.STEP
Normal file
File diff suppressed because one or more lines are too long
9286
matlab/STEPS/00221714.STEP
Normal file
9286
matlab/STEPS/00221714.STEP
Normal file
File diff suppressed because it is too large
Load Diff
40869
matlab/STEPS/00221720.STEP
Normal file
40869
matlab/STEPS/00221720.STEP
Normal file
File diff suppressed because one or more lines are too long
4663
matlab/STEPS/00221724.STEP
Normal file
4663
matlab/STEPS/00221724.STEP
Normal file
File diff suppressed because it is too large
Load Diff
2284
matlab/STEPS/00221729.STEP
Normal file
2284
matlab/STEPS/00221729.STEP
Normal file
File diff suppressed because it is too large
Load Diff
24868
matlab/STEPS/fast_jack_fixed.STEP
Normal file
24868
matlab/STEPS/fast_jack_fixed.STEP
Normal file
File diff suppressed because it is too large
Load Diff
6857
matlab/STEPS/fast_jack_moving.STEP
Normal file
6857
matlab/STEPS/fast_jack_moving.STEP
Normal file
File diff suppressed because it is too large
Load Diff
10149
matlab/STEPS/fast_jack_top_piezo.STEP
Normal file
10149
matlab/STEPS/fast_jack_top_piezo.STEP
Normal file
File diff suppressed because it is too large
Load Diff
5439
matlab/STEPS/flex_bot.STEP
Normal file
5439
matlab/STEPS/flex_bot.STEP
Normal file
File diff suppressed because it is too large
Load Diff
5670
matlab/STEPS/flex_top.STEP
Normal file
5670
matlab/STEPS/flex_top.STEP
Normal file
File diff suppressed because it is too large
Load Diff
225
matlab/dcm_active_damping_iff.m
Normal file
225
matlab/dcm_active_damping_iff.m
Normal file
@ -0,0 +1,225 @@
|
||||
% Matlab Init :noexport:ignore:
|
||||
|
||||
%% dcm_active_damping_iff.m
|
||||
% Test of Integral Force Feedback Strategy
|
||||
|
||||
%% 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
|
||||
|
||||
%% Simscape Model - Nano Hexapod
|
||||
addpath('./STEPS/')
|
||||
|
||||
%% Initialize Parameters for Simscape model
|
||||
controller.type = 0; % Open Loop Control
|
||||
|
||||
%% Options for Linearization
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
%% Open Simulink Model
|
||||
mdl = 'simscape_dcm';
|
||||
|
||||
open(mdl)
|
||||
|
||||
%% Colors for the figures
|
||||
colors = colororder;
|
||||
|
||||
%% Frequency Vector
|
||||
freqs = logspace(1, 3, 1000);
|
||||
|
||||
% Identification
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
|
||||
%% Inputs
|
||||
% Control Input {3x1} [N]
|
||||
io(io_i) = linio([mdl, '/control_system'], 1, 'openinput'); io_i = io_i + 1;
|
||||
|
||||
%% Outputs
|
||||
% Force Sensor {3x1} [m]
|
||||
io(io_i) = linio([mdl, '/DCM'], 3, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
%% Extraction of the dynamics
|
||||
G_fs = linearize(mdl, io);
|
||||
|
||||
G_fs.InputName = {'u_ur', 'u_uh', 'u_d'};
|
||||
G_fs.OutputName = {'fs_ur', 'fs_uh', 'fs_d'};
|
||||
|
||||
|
||||
|
||||
% #+RESULTS:
|
||||
% | -1.4113e-13 | 1.0339e-13 | 3.774e-14 |
|
||||
% | 1.0339e-13 | -1.4113e-13 | 3.774e-14 |
|
||||
% | 3.7792e-14 | 3.7792e-14 | -7.5585e-14 |
|
||||
|
||||
|
||||
%% Bode plot for the plant
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_fs(1,1), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'd');
|
||||
plot(freqs, abs(squeeze(freqresp(G_fs(2,2), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'uh');
|
||||
plot(freqs, abs(squeeze(freqresp(G_fs(3,3), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'ur');
|
||||
plot(freqs, abs(squeeze(freqresp(G_fs(1,2), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||
'DisplayName', 'off-diag');
|
||||
for i = 1:2
|
||||
for j = i+1:3
|
||||
plot(freqs, abs(squeeze(freqresp(G_fs(i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 2);
|
||||
ylim([1e-13, 1e-7]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_fs(1,1), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_fs(2,2), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_fs(3,3), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360);
|
||||
ylim([-180, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
|
||||
% Controller - Root Locus
|
||||
|
||||
Kiff_g1 = eye(3)*1/(1 + s/2/pi/20);
|
||||
|
||||
%% Root Locus for IFF
|
||||
gains = logspace(9, 12, 200);
|
||||
|
||||
figure;
|
||||
|
||||
hold on;
|
||||
plot(real(pole(G_fs)), imag(pole(G_fs)), 'x', 'color', colors(1,:), ...
|
||||
'DisplayName', '$g = 0$');
|
||||
plot(real(tzero(G_fs)), imag(tzero(G_fs)), 'o', 'color', colors(1,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
|
||||
for g = gains
|
||||
clpoles = pole(feedback(G_fs, g*Kiff_g1, +1));
|
||||
plot(real(clpoles), imag(clpoles), '.', 'color', colors(1,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
|
||||
% Optimal gain
|
||||
g = 8e10;
|
||||
clpoles = pole(feedback(G_fs, g*Kiff_g1, +1));
|
||||
plot(real(clpoles), imag(clpoles), 'x', 'color', colors(2,:), ...
|
||||
'DisplayName', sprintf('$g=%.0e$', g));
|
||||
hold off;
|
||||
axis square;
|
||||
xlim([-2700, 0]); ylim([0, 2700]);
|
||||
xlabel('Real Part'); ylabel('Imaginary Part');
|
||||
legend('location', 'northwest');
|
||||
|
||||
|
||||
|
||||
% #+name: fig:iff_root_locus
|
||||
% #+caption: Root Locus plot for the IFF Control strategy
|
||||
% #+RESULTS:
|
||||
% [[file:figs/iff_root_locus.png]]
|
||||
|
||||
|
||||
%% Integral Force Feedback Controller
|
||||
Kiff = g*Kiff_g1;
|
||||
|
||||
% Damped Plant
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
|
||||
%% Inputs
|
||||
% Control Input {3x1} [N]
|
||||
io(io_i) = linio([mdl, '/control_system'], 1, 'input'); io_i = io_i + 1;
|
||||
|
||||
%% Outputs
|
||||
% Force Sensor {3x1} [m]
|
||||
io(io_i) = linio([mdl, '/DCM'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
%% DCM Kinematics
|
||||
load('mat/dcm_kinematics.mat');
|
||||
|
||||
%% Identification of the Open Loop plant
|
||||
controller.type = 0; % Open Loop
|
||||
G_ol = J_a_111*inv(J_s_111)*linearize(mdl, io);
|
||||
G_ol.InputName = {'u_ur', 'u_uh', 'u_d'};
|
||||
G_ol.OutputName = {'d_ur', 'd_uh', 'd_d'};
|
||||
|
||||
%% Identification of the damped plant with IFF
|
||||
controller.type = 1; % IFF
|
||||
G_dp = J_a_111*inv(J_s_111)*linearize(mdl, io);
|
||||
G_dp.InputName = {'u_ur', 'u_uh', 'u_d'};
|
||||
G_dp.OutputName = {'d_ur', 'd_uh', 'd_d'};
|
||||
|
||||
%% Comparison of the damped and undamped plant
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_ol(1,1), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'd - OL');
|
||||
plot(freqs, abs(squeeze(freqresp(G_ol(2,2), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'uh - OL');
|
||||
plot(freqs, abs(squeeze(freqresp(G_ol(3,3), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'ur - OL');
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(G_dp(1,1), freqs, 'Hz'))), '--', ...
|
||||
'DisplayName', 'd - IFF');
|
||||
plot(freqs, abs(squeeze(freqresp(G_dp(2,2), freqs, 'Hz'))), '--', ...
|
||||
'DisplayName', 'uh - IFF');
|
||||
plot(freqs, abs(squeeze(freqresp(G_dp(3,3), freqs, 'Hz'))), '--', ...
|
||||
'DisplayName', 'ur - IFF');
|
||||
for i = 1:2
|
||||
for j = i+1:3
|
||||
plot(freqs, abs(squeeze(freqresp(G_dp(i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
|
||||
ylim([1e-12, 1e-6]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_ol(1,1), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_ol(2,2), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_ol(3,3), freqs, 'Hz'))));
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dp(1,1), freqs, 'Hz'))), '--');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dp(2,2), freqs, 'Hz'))), '--');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dp(3,3), freqs, 'Hz'))), '--');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360);
|
||||
ylim([-180, 0]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
|
||||
save('mat/Kiff.mat', 'Kiff');
|
||||
101
matlab/dcm_active_damping_strain_gauges.m
Normal file
101
matlab/dcm_active_damping_strain_gauges.m
Normal file
@ -0,0 +1,101 @@
|
||||
% Matlab Init :noexport:ignore:
|
||||
|
||||
%% dcm_active_damping_strain_gauges.m
|
||||
% Active Damping using relative motion sensors (strain gauges)
|
||||
|
||||
%% 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
|
||||
|
||||
%% Simscape Model - Nano Hexapod
|
||||
addpath('./STEPS/')
|
||||
|
||||
%% Initialize Parameters for Simscape model
|
||||
controller.type = 0; % Open Loop Control
|
||||
|
||||
%% Options for Linearization
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
%% Open Simulink Model
|
||||
mdl = 'simscape_dcm';
|
||||
|
||||
open(mdl)
|
||||
|
||||
%% Colors for the figures
|
||||
colors = colororder;
|
||||
|
||||
%% Frequency Vector
|
||||
freqs = logspace(1, 3, 1000);
|
||||
|
||||
% Identification
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
|
||||
%% Inputs
|
||||
% Control Input {3x1} [N]
|
||||
io(io_i) = linio([mdl, '/u'], 1, 'openinput'); io_i = io_i + 1;
|
||||
% % Stepper Displacement {3x1} [m]
|
||||
% io(io_i) = linio([mdl, '/d'], 1, 'openinput'); io_i = io_i + 1;
|
||||
|
||||
%% Outputs
|
||||
% Strain Gauges {3x1} [m]
|
||||
io(io_i) = linio([mdl, '/sg'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
%% Extraction of the dynamics
|
||||
G_sg = linearize(mdl, io);
|
||||
|
||||
G_sg.InputName = {'u_ur', 'u_uh', 'u_d'};
|
||||
G_sg.OutputName = {'sg_ur', 'sg_uh', 'sg_d'};
|
||||
|
||||
|
||||
|
||||
% #+RESULTS:
|
||||
% | -1.4113e-13 | 1.0339e-13 | 3.774e-14 |
|
||||
% | 1.0339e-13 | -1.4113e-13 | 3.774e-14 |
|
||||
% | 3.7792e-14 | 3.7792e-14 | -7.5585e-14 |
|
||||
|
||||
|
||||
%% Bode plot for the plant
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_sg(1,1), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'd');
|
||||
plot(freqs, abs(squeeze(freqresp(G_sg(2,2), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'uh');
|
||||
plot(freqs, abs(squeeze(freqresp(G_sg(3,3), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'ur');
|
||||
for i = 1:2
|
||||
for j = i+1:3
|
||||
plot(freqs, abs(squeeze(freqresp(G_sg(i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_sg(1,1), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_sg(2,2), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_sg(3,3), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360);
|
||||
ylim([-180, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
34
matlab/dcm_hac_iff.m
Normal file
34
matlab/dcm_hac_iff.m
Normal file
@ -0,0 +1,34 @@
|
||||
% Matlab Init :noexport:ignore:
|
||||
|
||||
%% dcm_hac_iff.m
|
||||
% Development of the HAC-IFF control strategy
|
||||
|
||||
%% 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
|
||||
|
||||
%% Simscape Model - Nano Hexapod
|
||||
addpath('./STEPS/')
|
||||
|
||||
%% Initialize Parameters for Simscape model
|
||||
controller.type = 0; % Open Loop Control
|
||||
|
||||
%% Options for Linearization
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
%% Open Simulink Model
|
||||
mdl = 'simscape_dcm';
|
||||
|
||||
open(mdl)
|
||||
|
||||
%% Colors for the figures
|
||||
colors = colororder;
|
||||
|
||||
%% Frequency Vector
|
||||
freqs = logspace(1, 3, 1000);
|
||||
202
matlab/dcm_identification.m
Normal file
202
matlab/dcm_identification.m
Normal file
@ -0,0 +1,202 @@
|
||||
% Matlab Init :noexport:ignore:
|
||||
|
||||
%% dcm_identification.m
|
||||
% Extraction of system dynamics using Simscape model
|
||||
|
||||
%% 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
|
||||
|
||||
%% Simscape Model - Nano Hexapod
|
||||
addpath('./STEPS/')
|
||||
|
||||
%% Initialize Parameters for Simscape model
|
||||
controller.type = 0; % Open Loop Control
|
||||
|
||||
%% Options for Linearization
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
%% Open Simulink Model
|
||||
mdl = 'simscape_dcm';
|
||||
|
||||
open(mdl)
|
||||
|
||||
%% Colors for the figures
|
||||
colors = colororder;
|
||||
|
||||
%% Frequency Vector
|
||||
freqs = logspace(1, 3, 1000);
|
||||
|
||||
|
||||
|
||||
% #+name: fig:schematic_system_inputs_outputs
|
||||
% #+caption: Dynamical system with inputs and outputs
|
||||
% #+RESULTS:
|
||||
% [[file:figs/schematic_system_inputs_outputs.png]]
|
||||
|
||||
% The system is identified from the Simscape model.
|
||||
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
|
||||
%% Inputs
|
||||
% Control Input {3x1} [N]
|
||||
io(io_i) = linio([mdl, '/control_system'], 1, 'openinput'); io_i = io_i + 1;
|
||||
|
||||
%% Outputs
|
||||
% Interferometers {3x1} [m]
|
||||
io(io_i) = linio([mdl, '/DCM'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
%% Extraction of the dynamics
|
||||
G = linearize(mdl, io);
|
||||
|
||||
%% Input and Output names
|
||||
G.InputName = {'u_ur', 'u_uh', 'u_d'};
|
||||
G.OutputName = {'int_111_1', 'int_111_2', 'int_111_3'};
|
||||
|
||||
% Plant in the frame of the fastjacks
|
||||
|
||||
load('mat/dcm_kinematics.mat');
|
||||
|
||||
|
||||
|
||||
% #+name: fig:schematic_jacobian_frame_fastjack
|
||||
% #+caption: Use of Jacobian matrices to obtain the system in the frame of the fastjacks
|
||||
% #+RESULTS:
|
||||
% [[file:figs/schematic_jacobian_frame_fastjack.png]]
|
||||
|
||||
|
||||
|
||||
%% Compute the system in the frame of the fastjacks
|
||||
G_pz = J_a_111*inv(J_s_111)*G;
|
||||
|
||||
|
||||
|
||||
% #+name: tab:dc_gain_plan_fj
|
||||
% #+caption: DC gain of the plant in the frame of the fast jacks $\bm{G}_{\text{fj}}$
|
||||
% #+attr_latex: :environment tabularx :width 0.5\linewidth :align ccc
|
||||
% #+attr_latex: :center t :booktabs t
|
||||
% #+RESULTS:
|
||||
% | 4.4407e-09 | 2.7656e-12 | 1.0132e-12 |
|
||||
% | 2.7656e-12 | 4.4407e-09 | 1.0132e-12 |
|
||||
% | 1.0109e-12 | 1.0109e-12 | 4.4424e-09 |
|
||||
|
||||
% The bode plot of $\bm{G}_{\text{fj}}(s)$ is shown in Figure [[fig:bode_plot_plant_fj]].
|
||||
|
||||
|
||||
%% Bode plot for the plant
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz(1,1), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'd');
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz(2,2), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'uh');
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz(3,3), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'ur');
|
||||
for i = 1:2
|
||||
for j = i+1:3
|
||||
plot(freqs, abs(squeeze(freqresp(G_pz(i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 3);
|
||||
ylim([1e-13, 1e-6]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_pz(1,1), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_pz(2,2), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_pz(3,3), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360);
|
||||
ylim([-180, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
|
||||
|
||||
|
||||
% #+name: fig:schematic_jacobian_frame_crystal
|
||||
% #+caption: Use of Jacobian matrices to obtain the system in the frame of the crystal
|
||||
% #+RESULTS:
|
||||
% [[file:figs/schematic_jacobian_frame_crystal.png]]
|
||||
|
||||
|
||||
G_mr = inv(J_s_111)*G*inv(J_a_111');
|
||||
|
||||
|
||||
|
||||
% #+RESULTS:
|
||||
% | 1.9978e-09 | 3.9657e-09 | 7.7944e-09 |
|
||||
% | 3.9656e-09 | 8.4979e-08 | -1.5135e-17 |
|
||||
% | 7.7944e-09 | -3.9252e-17 | 1.834e-07 |
|
||||
|
||||
|
||||
%% Bode plot for the plant
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_mr(1,1), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'd');
|
||||
plot(freqs, abs(squeeze(freqresp(G_mr(2,2), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'uh');
|
||||
plot(freqs, abs(squeeze(freqresp(G_mr(3,3), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'ur');
|
||||
for i = 1:2
|
||||
for j = i+1:3
|
||||
plot(freqs, abs(squeeze(freqresp(G_mr(i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_mr(1,1), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_mr(2,2), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_mr(3,3), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360);
|
||||
ylim([-180, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
|
||||
%% Bode plot for the plant
|
||||
fig = figure;
|
||||
tiledlayout(3, 3, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
for i_out = 1:3
|
||||
for i_in = 1:3
|
||||
ax = nexttile;
|
||||
plot(freqs, abs(squeeze(freqresp(G_mr(i_out, i_in), freqs, 'Hz'))));
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
end
|
||||
end
|
||||
|
||||
linkaxes(findall(fig, 'type', 'axes'),'xy');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
98
matlab/dcm_kinematics.m
Normal file
98
matlab/dcm_kinematics.m
Normal file
@ -0,0 +1,98 @@
|
||||
% Matlab Init :noexport:ignore:
|
||||
|
||||
%% dcm_kinematics.m
|
||||
% Computation of the DCM kinematics
|
||||
|
||||
%% 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
|
||||
|
||||
%% Simscape Model - Nano Hexapod
|
||||
addpath('./STEPS/')
|
||||
|
||||
%% Colors for the figures
|
||||
colors = colororder;
|
||||
|
||||
%% Frequency Vector
|
||||
freqs = logspace(1, 3, 1000);
|
||||
|
||||
% Bragg Angle
|
||||
|
||||
%% Tested bragg angles
|
||||
bragg = linspace(5, 80, 1000); % Bragg angle [deg]
|
||||
d_off = 10.5e-3; % Wanted offset between x-rays [m]
|
||||
|
||||
%% Vertical Jack motion as a function of Bragg angle
|
||||
dz = d_off./(2*cos(bragg*pi/180));
|
||||
|
||||
%% Jack motion as a function of Bragg angle
|
||||
figure;
|
||||
plot(bragg, 1e3*dz)
|
||||
xlabel('Bragg angle [deg]'); ylabel('Jack Motion [mm]');
|
||||
|
||||
|
||||
|
||||
% #+name: fig:jack_motion_bragg_angle
|
||||
% #+caption: Jack motion as a function of Bragg angle
|
||||
% #+RESULTS:
|
||||
% [[file:figs/jack_motion_bragg_angle.png]]
|
||||
|
||||
|
||||
%% Required Jack stroke
|
||||
ans = 1e3*(dz(end) - dz(1))
|
||||
|
||||
|
||||
|
||||
% #+name: fig:schematic_sensor_jacobian_inverse_kinematics
|
||||
% #+caption: Inverse Kinematics - Interferometers
|
||||
% #+RESULTS:
|
||||
% [[file:figs/schematic_sensor_jacobian_inverse_kinematics.png]]
|
||||
|
||||
|
||||
% From the Figure [[fig:sensor_111_crystal_points]], the inverse kinematics can be solved as follow (for small motion):
|
||||
% \begin{equation}
|
||||
% \bm{J}_{s,111}
|
||||
% =
|
||||
% \begin{bmatrix}
|
||||
% 1 & 0.07 & -0.015 \\
|
||||
% 1 & 0 & 0.015 \\
|
||||
% 1 & -0.07 & -0.015
|
||||
% \end{bmatrix}
|
||||
% \end{equation}
|
||||
|
||||
|
||||
%% Sensor Jacobian matrix for 111 crystal
|
||||
J_s_111 = [1, 0.07, -0.015
|
||||
1, 0, 0.015
|
||||
1, -0.07, -0.015];
|
||||
|
||||
|
||||
|
||||
% #+name: fig:schematic_sensor_jacobian_inverse_kinematics
|
||||
% #+caption: Inverse Kinematics - Actuators
|
||||
% #+RESULTS:
|
||||
% [[file:figs/schematic_actuator_jacobian_inverse_kinematics.png]]
|
||||
|
||||
% Based on the geometry in Figure [[fig:actuator_jacobian_111_points]], we obtain:
|
||||
% \begin{equation}
|
||||
% \bm{J}_{a,111}
|
||||
% =
|
||||
% \begin{bmatrix}
|
||||
% 1 & 0.14 & -0.1525 \\
|
||||
% 1 & 0.14 & 0.0675 \\
|
||||
% 1 & -0.14 & -0.0425
|
||||
% \end{bmatrix}
|
||||
% \end{equation}
|
||||
|
||||
|
||||
%% Actuator Jacobian - 111 crystal
|
||||
J_a_111 = [1, 0.14, -0.1525
|
||||
1, 0.14, 0.0675
|
||||
1, -0.14, -0.0425];
|
||||
|
||||
save('mat/dcm_kinematics.mat', 'J_a_111', 'J_s_111')
|
||||
BIN
matlab/mat/Kiff.mat
Normal file
BIN
matlab/mat/Kiff.mat
Normal file
Binary file not shown.
BIN
matlab/mat/dcm_kinematics.mat
Normal file
BIN
matlab/mat/dcm_kinematics.mat
Normal file
Binary file not shown.
BIN
matlab/simscape_dcm.slx
Normal file
BIN
matlab/simscape_dcm.slx
Normal file
Binary file not shown.
11
ref.bib
Normal file
11
ref.bib
Normal file
@ -0,0 +1,11 @@
|
||||
@article{fleming10_integ_strain_force_feedb_high,
|
||||
author = {Fleming, Andrew J and Leang, Kam K},
|
||||
title = {Integrated Strain and Force Feedback for High-Performance
|
||||
Control of Piezoelectric Actuators},
|
||||
journal = {Sensors and Actuators A: Physical},
|
||||
volume = 161,
|
||||
number = {1-2},
|
||||
pages = {256--265},
|
||||
year = 2010,
|
||||
publisher = {Elsevier}
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user