Add tilt flexibility to granite
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cdbd62b3ee
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3745bbebee
@ -0,0 +1,2 @@
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<?xml version='1.0' encoding='UTF-8'?>
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<Info Ref="simscape" Type="Relative" />
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@ -1,2 +0,0 @@
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<?xml version='1.0' encoding='UTF-8'?>
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<Info Ref="identification" Type="Relative" />
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@ -42,7 +42,7 @@
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:END:
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* Introduction :ignore:
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The goal here is to make an identification of the micro-station in order to compare the model with the measurements on the real micro-station.
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The goal here is to make an identification of the *micro-station* in order to compare the model with the measurements on the real micro-station.
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In order to do so:
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- Decide where to virtually excite the station and where to measure its motion
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@ -56,6 +56,356 @@ Indeed, we can define the center of mass of any solid body but not of multiple s
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One solution could be to use one STEP file for one solid body.
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However, the position of the center of mass can be exported using simulink and then defined on Simscape.
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* Identification of the Micro-Station
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** Introduction :ignore:
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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#+begin_src matlab :tangle no
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simulinkproject('../');
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#+end_src
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** Compute the transfer functions
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We first define some parameters for the identification.
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The simulink file for the identification is =sim_micro_station_id.slx=.
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#+begin_src matlab
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open 'simscape/sim_micro_station_id.slx'
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#+end_src
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#+begin_src matlab
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%% Options for Linearized
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options = linearizeOptions;
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options.SampleTime = 0;
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%% Name of the Simulink File
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mdl = 'sim_micro_station_id';
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#+end_src
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#+begin_src matlab
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%% Micro-Hexapod
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% Input/Output definition
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io(1) = linio([mdl, '/Micro-Station/Fm_ext'],1,'openinput');
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io(2) = linio([mdl, '/Micro-Station/Fg_ext'],1,'openinput');
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io(3) = linio([mdl, '/Micro-Station/Dm_inertial'],1,'output');
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io(4) = linio([mdl, '/Micro-Station/Ty_inertial'],1,'output');
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io(5) = linio([mdl, '/Micro-Station/Ry_inertial'],1,'output');
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io(6) = linio([mdl, '/Micro-Station/Dg_inertial'],1,'output');
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#+end_src
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#+begin_src matlab
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% Run the linearization
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G_ms = linearize(mdl, io, 0);
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% Input/Output names
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G_ms.InputName = {'Fmx', 'Fmy', 'Fmz',...
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'Fgx', 'Fgy', 'Fgz'};
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G_ms.OutputName = {'Dmx', 'Dmy', 'Dmz', ...
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'Tyx', 'Tyy', 'Tyz', ...
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'Ryx', 'Ryy', 'Ryz', ...
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'Dgx', 'Dgy', 'Dgz'};
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#+end_src
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#+begin_src matlab
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%% Save the obtained transfer functions
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save('./mat/id_micro_station.mat', 'G_ms');
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#+end_src
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** Plots the transfer functions
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** Compare with the measurements
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* Modal Analysis of the Micro-Station
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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#+begin_src matlab :tangle no
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simulinkproject('../');
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#+end_src
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** Simscape Model
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#+begin_src matlab
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open 'simscape/sim_micro_station_modal_analysis.slx'
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#+end_src
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#+begin_src matlab
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%% Options for Linearized
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options = linearizeOptions;
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options.SampleTime = 0;
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%% Name of the Simulink File
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mdl = 'sim_micro_station_modal_analysis';
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#+end_src
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#+begin_src matlab
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%% Micro-Hexapod
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% Input/Output definition
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io(1) = linio([mdl, '/Micro-Station/F_hammer'],1,'openinput');
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io(2) = linio([mdl, '/Micro-Station/acc9'],1,'output');
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io(3) = linio([mdl, '/Micro-Station/acc10'],1,'output');
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io(4) = linio([mdl, '/Micro-Station/acc11'],1,'output');
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io(5) = linio([mdl, '/Micro-Station/acc12'],1,'output');
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#+end_src
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#+begin_src matlab
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% Run the linearization
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G_ms = linearize(mdl, io, 0);
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% Input/Output names
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G_ms.InputName = {'Fx', 'Fy', 'Fz'};
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G_ms.OutputName = {'x9', 'y9', 'z9', ...
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'x10', 'y10', 'z10', ...
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'x11', 'y11', 'z11', ...
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'x12', 'y12', 'z12'};
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#+end_src
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** Plot Results
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#+begin_src matlab
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G_ms('x9', 'Fx'), freqs, 'Hz'))));
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]');
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hold off;
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#+end_src
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** Compare with measurements
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#+begin_src matlab
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load('../meas/modal-analysis/mat/frf_coh_matrices.mat', 'FRFs', 'COHs', 'freqs');
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#+end_src
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#+begin_src matlab
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dirs = {'x', 'y', 'z'};
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n_acc = 9;
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n_dir = 1; % x, y, z
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n_exc = 1; % x, y, z
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figure;
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hold on;
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plot(freqs, abs(squeeze(FRFs(3*(n_acc-1) + n_dir, n_exc, :)))./((2*pi*freqs).^2)');
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plot(freqs, abs(squeeze(freqresp(G_ms([dirs{n_dir}, num2str(n_acc)], ['F', dirs{n_dir}]), freqs, 'Hz'))));
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]');
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hold off;
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#+end_src
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* Compare with measurements at the CoM of each element
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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#+begin_src matlab :tangle no
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simulinkproject('../');
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#+end_src
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** Init
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#+begin_src matlab :results none
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%% Initialize Ground
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initializeGround();
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%% Initialize Granite
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initializeGranite();
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%% Initialize Translation stage
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initializeTy();
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%% Initialize Tilt Stage
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initializeRy();
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%% Initialize Spindle
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initializeRz();
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%% Initialize Hexapod Symétrie
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initializeMicroHexapod();
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#+end_src
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** Center of Mass of each solid body
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| | granite bot | granite top | ty | ry | rz | hexa |
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|--------+-------------+-------------+------+------+------+------|
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| X [mm] | 45 | 52 | 0 | 0 | 0 | -4 |
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| Y [mm] | 144 | 258 | 14 | -5 | 0 | 6 |
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| Z [mm] | -1251 | -778 | -600 | -628 | -580 | -319 |
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#+begin_src matlab
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open 'simscape/sim_micro_station_modal_analysis_com.slx'
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#+end_src
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** Simscape Model
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#+begin_src matlab
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%% Options for Linearized
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options = linearizeOptions;
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options.SampleTime = 0;
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%% Name of the Simulink File
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mdl = 'sim_micro_station_modal_analysis_com';
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#+end_src
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#+begin_src matlab
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%% Micro-Hexapod
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% Input/Output definition
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io(1) = linio([mdl, '/Micro-Station/F_hammer'],1,'openinput');
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io(2) = linio([mdl, '/Micro-Station/acc_gtop'],1,'output');
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io(3) = linio([mdl, '/Micro-Station/acc_ty'],1,'output');
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io(4) = linio([mdl, '/Micro-Station/acc_ry'],1,'output');
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io(5) = linio([mdl, '/Micro-Station/acc_rz'],1,'output');
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io(6) = linio([mdl, '/Micro-Station/acc_hexa'],1,'output');
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#+end_src
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#+begin_src matlab
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% Run the linearization
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G_ms = linearize(mdl, io, 0);
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% Input/Output names
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G_ms.InputName = {'Fx', 'Fy', 'Fz'};
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G_ms.OutputName = {'gtop_x', 'gtop_y', 'gtop_z', 'gtop_rx', 'gtop_ry', 'gtop_rz', ...
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'ty_x', 'ty_y', 'ty_z', 'ty_rx', 'ty_ry', 'ty_rz', ...
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'ry_x', 'ry_y', 'ry_z', 'ry_rx', 'ry_ry', 'ry_rz', ...
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'rz_x', 'rz_y', 'rz_z', 'rz_rx', 'rz_ry', 'rz_rz', ...
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'hexa_x', 'hexa_y', 'hexa_z', 'hexa_rx', 'hexa_ry', 'hexa_rz'};
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#+end_src
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** Compare with measurements
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#+begin_src matlab
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load('../meas/modal-analysis/mat/frf_coh_matrices.mat', 'freqs');
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load('../meas/modal-analysis/mat/frf_com.mat', 'FRFs_CoM');
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#+end_src
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#+begin_src matlab
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dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
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stages = {'gbot', 'gtop', 'ty', 'ry', 'rz', 'hexa'}
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n_stg = 2;
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n_dir = 2; % x, y, z, Rx, Ry, Rz
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n_exc = 2; % x, y, z
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f = logspace(1, 3, 1000);
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figure;
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hold on;
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plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg-1) + n_dir, n_exc, :)))./((2*pi*freqs).^2)');
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plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_exc}]), f, 'Hz'))));
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]');
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hold off;
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xlim([10, 1000]);
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#+end_src
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#+begin_src matlab
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dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
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stages = {'gtop', 'ty', 'ry', 'rz', 'hexa'}
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f = logspace(1, 3, 1000);
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figure;
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for n_stg = 1:2
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for n_dir = 1:3
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subplot(3, 2, (n_dir-1)*2 + n_stg);
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title(['F ', dirs{n_dir}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
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hold on;
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plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg) + n_dir, n_dir, :)))./((2*pi*freqs).^2)');
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plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_dir}]), f, 'Hz'))));
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]');
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hold off;
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xlim([10, 1000]);
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ylim([1e-12, 1e-6]);
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end
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end
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#+end_src
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#+begin_src matlab
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dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
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stages = {'ry', 'rz', 'hexa'}
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f = logspace(1, 3, 1000);
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figure;
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for n_stg = 1:2
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for n_dir = 1:3
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subplot(3, 2, (n_dir-1)*2 + n_stg);
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title(['F ', dirs{n_dir}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
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hold on;
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plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg+2) + n_dir, n_dir, :)))./((2*pi*freqs).^2)');
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plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_dir}]), f, 'Hz'))));
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]');
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hold off;
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xlim([10, 1000]);
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ylim([1e-12, 1e-6]);
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end
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end
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#+end_src
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#+begin_src matlab
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dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
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stages = {'hexa'}
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f = logspace(1, 3, 1000);
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figure;
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for n_stg = 1
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for n_dir = 1:3
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subplot(3, 2, (n_dir-1)*2 + n_stg);
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title(['F ', dirs{n_dir}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
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hold on;
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plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg+4) + n_dir, n_dir, :)))./((2*pi*freqs).^2)');
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plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_dir}]), f, 'Hz'))));
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]');
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hold off;
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xlim([10, 1000]);
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ylim([1e-12, 1e-6]);
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end
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end
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#+end_src
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For Granite Fx to Tx/Ty/Tz/Rx/Ry/Rz
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#+begin_src matlab
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dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
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stages = {'gtop', 'ty', 'ry', 'rz', 'hexa'}
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n_stg = 2;
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n_exc = 2;
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f = logspace(1, 3, 1000);
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figure;
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for n_dir = 1:6
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subplot(2, 3, n_dir);
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title(['F', dirs{n_exc}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
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hold on;
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plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg) + n_dir, n_exc, :)))./((2*pi*freqs).^2)');
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plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_exc}]), f, 'Hz'))));
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]');
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hold off;
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xlim([10, 1000]);
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ylim([1e-12, 1e-6]);
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end
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#+end_src
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* ZIP file containing the data and matlab files :ignore:
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#+begin_src bash :exports none :results none
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if [ matlab/identification_micro_station.m -nt data/identification_micro_station.zip ]; then
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3075
simscape/index.html
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simscape/index.html
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Load Diff
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simscape/index.org
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simscape/index.org
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Load Diff
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simscape/sim_micro_station_id.slx
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simscape/sim_micro_station_id.slx
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simscape/sim_micro_station_modal_analysis.slx
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simscape/sim_micro_station_modal_analysis.slx
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simscape/sim_micro_station_modal_analysis_com.slx
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simscape/sim_micro_station_modal_analysis_com.slx
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