14 KiB
14 KiB
Identification
- Introduction
- Identification of the Micro-Station
- Modal Analysis of the Micro-Station
- Compare with measurements at the CoM of each element
- Other analysis
Introduction ignore
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.
In order to do so:
- Decide where to virtually excite the station and where to measure its motion
- Extract transfer functions from the excitation forces to the measured motion
- Compare those transfer functions with the modal analysis
For the excitation, we can choose the same excitation points as the one used for the modal test. For the measurement points, we can choose the Center of Mass of each solid body. The center of mass of each solid body is not easily defined using Simscape. Indeed, we can define the center of mass of any solid body but not of multiple solid bodies. However, one solid body is composed of multiple STEP files. One solution could be to use one STEP file for one solid body. However, the position of the center of mass can be exported using simulink and then defined on Simscape.
Identification of the Micro-Station
Introduction ignore
Compute the transfer functions
We first define some parameters for the identification.
The simulink file for the identification is sim_micro_station_id.slx.
open('identification/matlab/sim_micro_station_id.slx')%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'sim_micro_station_id';%% Micro-Hexapod
% Input/Output definition
io(1) = linio([mdl, '/Micro-Station/Fm_ext'],1,'openinput');
io(2) = linio([mdl, '/Micro-Station/Fg_ext'],1,'openinput');
io(3) = linio([mdl, '/Micro-Station/Dm_inertial'],1,'output');
io(4) = linio([mdl, '/Micro-Station/Ty_inertial'],1,'output');
io(5) = linio([mdl, '/Micro-Station/Ry_inertial'],1,'output');
io(6) = linio([mdl, '/Micro-Station/Dg_inertial'],1,'output');% Run the linearization
G_ms = linearize(mdl, io, 0);
% Input/Output names
G_ms.InputName = {'Fmx', 'Fmy', 'Fmz',...
'Fgx', 'Fgy', 'Fgz'};
G_ms.OutputName = {'Dmx', 'Dmy', 'Dmz', ...
'Tyx', 'Tyy', 'Tyz', ...
'Ryx', 'Ryy', 'Ryz', ...
'Dgx', 'Dgy', 'Dgz'};%% Save the obtained transfer functions
save('./mat/id_micro_station.mat', 'G_ms');Plots the transfer functions
Compare with the measurements
Modal Analysis of the Micro-Station
Simscape Model
open('identification/matlab/sim_micro_station_modal_analysis.slx')%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'sim_micro_station_modal_analysis';%% Micro-Hexapod
% Input/Output definition
io(1) = linio([mdl, '/Micro-Station/F_hammer'],1,'openinput');
io(2) = linio([mdl, '/Micro-Station/acc9'],1,'output');
io(3) = linio([mdl, '/Micro-Station/acc10'],1,'output');
io(4) = linio([mdl, '/Micro-Station/acc11'],1,'output');
io(5) = linio([mdl, '/Micro-Station/acc12'],1,'output'); % Run the linearization
G_ms = linearize(mdl, io, 0);
% Input/Output names
G_ms.InputName = {'Fx', 'Fy', 'Fz'};
G_ms.OutputName = {'x9', 'y9', 'z9', ...
'x10', 'y10', 'z10', ...
'x11', 'y11', 'z11', ...
'x12', 'y12', 'z12'};Plot Results
figure;
hold on;
plot(freqs, abs(squeeze(freqresp(G_ms('x9', 'Fx'), freqs, 'Hz'))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]');
hold off;Compare with measurements
load('../meas/modal-analysis/mat/frf_coh_matrices.mat', 'FRFs', 'COHs', 'freqs'); dirs = {'x', 'y', 'z'};
n_acc = 9;
n_dir = 1; % x, y, z
n_exc = 1; % x, y, z
figure;
hold on;
plot(freqs, abs(squeeze(FRFs(3*(n_acc-1) + n_dir, n_exc, :)))./((2*pi*freqs).^2)');
plot(freqs, abs(squeeze(freqresp(G_ms([dirs{n_dir}, num2str(n_acc)], ['F', dirs{n_dir}]), freqs, 'Hz'))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]');
hold off;Compare with measurements at the CoM of each element
Init
initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();TODO Center of Mass of each solid body
- Verify that this is coherent with the simscape and with the measurements
| granite bot | granite top | ty | ry | rz | hexa | |
|---|---|---|---|---|---|---|
| X [mm] | 45 | 52 | 0 | 0 | 0 | -4 |
| Y [mm] | 144 | 258 | 14 | -5 | 0 | 6 |
| Z [mm] | -1251 | -778 | -600 | -628 | -580 | -319 |
open('identification/matlab/sim_micro_station_modal_analysis_com.slx')Simscape Model
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'sim_micro_station_modal_analysis_com'; %% Micro-Hexapod
% Input/Output definition
io(1) = linio([mdl, '/Micro-Station/F_hammer'],1,'openinput');
io(2) = linio([mdl, '/Micro-Station/acc_gtop'],1,'output');
io(3) = linio([mdl, '/Micro-Station/acc_ty'],1,'output');
io(4) = linio([mdl, '/Micro-Station/acc_ry'],1,'output');
io(5) = linio([mdl, '/Micro-Station/acc_rz'],1,'output');
io(6) = linio([mdl, '/Micro-Station/acc_hexa'],1,'output'); % Run the linearization
G_ms = linearize(mdl, io, 0);
% Input/Output names
G_ms.InputName = {'Fx', 'Fy', 'Fz'};
G_ms.OutputName = {'gtop_x', 'gtop_y', 'gtop_z', 'gtop_rx', 'gtop_ry', 'gtop_rz', ...
'ty_x', 'ty_y', 'ty_z', 'ty_rx', 'ty_ry', 'ty_rz', ...
'ry_x', 'ry_y', 'ry_z', 'ry_rx', 'ry_ry', 'ry_rz', ...
'rz_x', 'rz_y', 'rz_z', 'rz_rx', 'rz_ry', 'rz_rz', ...
'hexa_x', 'hexa_y', 'hexa_z', 'hexa_rx', 'hexa_ry', 'hexa_rz'};Compare with measurements
load('../meas/modal-analysis/mat/frf_coh_matrices.mat', 'freqs');
load('../meas/modal-analysis/mat/frf_com.mat', 'FRFs_CoM'); dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
stages = {'gbot', 'gtop', 'ty', 'ry', 'rz', 'hexa'}
n_stg = 2;
n_dir = 5; % x, y, z, Rx, Ry, Rz
n_exc = 2; % x, y, z
f = logspace(0, 3, 1000);
figure;
hold on;
plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg-1) + n_dir, n_exc, :)))./((2*pi*freqs).^2)');
plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_exc}]), f, 'Hz'))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]');
hold off;
xlim([1, 200]); dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
stages = {'gtop', 'ty', 'ry', 'rz', 'hexa'}
f = logspace(1, 3, 1000);
figure;
for n_stg = 1:2
for n_dir = 1:3
subplot(3, 2, (n_dir-1)*2 + n_stg);
title(['F ', dirs{n_dir}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
hold on;
plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg) + n_dir, n_dir, :)))./((2*pi*freqs).^2)');
plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_dir}]), f, 'Hz'))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]');
if n_dir == 3
xlabel('Frequency [Hz]');
end
hold off;
xlim([10, 1000]);
ylim([1e-12, 1e-6]);
end
end <<plt-matlab>>
dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
stages = {'ry', 'rz', 'hexa'}
f = logspace(1, 3, 1000);
figure;
for n_stg = 1:2
for n_dir = 1:3
subplot(3, 2, (n_dir-1)*2 + n_stg);
title(['F ', dirs{n_dir}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
hold on;
plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg+2) + n_dir, n_dir, :)))./((2*pi*freqs).^2)');
plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_dir}]), f, 'Hz'))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]');
if n_dir == 3
xlabel('Frequency [Hz]');
end
hold off;
xlim([10, 1000]);
ylim([1e-12, 1e-6]);
end
end <<plt-matlab>>
dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
stages = {'hexa'}
f = logspace(1, 3, 1000);
figure;
for n_stg = 1
for n_dir = 1:3
subplot(3, 1, (n_dir-1)*2 + n_stg);
title(['F ', dirs{n_dir}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
hold on;
plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg+4) + n_dir, n_dir, :)))./((2*pi*freqs).^2)');
plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_dir}]), f, 'Hz'))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]');
if n_dir == 3
xlabel('Frequency [Hz]');
end
hold off;
xlim([10, 1000]);
ylim([1e-12, 1e-6]);
end
end <<plt-matlab>>