Identification

1. Identification of the Micro-Station
2. Modal Analysis of the Micro-Station
3. Compare with measurements at the CoM of each element
4. Other analysis

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.

1 Identification of the Micro-Station

1.1 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');

1.2 Plots the transfer functions

1.3 Compare with the measurements

2 Modal Analysis of the Micro-Station

2.1 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'};

2.2 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;

2.3 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;

3 Compare with measurements at the CoM of each element

3.1 Init

initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();

3.2 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')

3.3 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'};

3.4 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

Figure 1: caption (png, pdf)

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

Figure 2: caption (png, pdf)

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