Tomography Experiment

1. Simscape Model
2. Tomography Experiment with no disturbances
3. Tomography Experiment with included perturbations
4. Tomography when the micro-hexapod is not centered
5. Raster Scans with the translation stage

The goal here is to simulate some scientific experiments with the tuned Simscape model when no control is applied to the nano-hexapod.

This has several goals:

Validate the model
Estimate the expected error motion for the experiments
Estimate the stroke that we may need for the nano-hexapod

The document in organized as follow:

In section 1 the Simscape model is initialized
In section 2 a tomography experiment is performed where the sample is aligned with the rotation axis. No disturbance is included
In section 3, the same is done but with disturbance included
In section 4 the micro-hexapod translate the sample such that its center of mass is no longer aligned with the rotation axis. No disturbance is included
In section 5, scans with the translation stage are simulated with no perturbation included

1 Simscape Model

The simulink file to do tomography experiments is sim_nano_station_tomo.slx.

open('experiment_tomography/matlab/sim_nano_station_tomo.slx')

We load the shared simulink configuration and we set the StopTime.

load('mat/conf_simscape.mat');
set_param(conf_simscape, 'StopTime', '5');

We first initialize all the stages.

initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 1));

We initialize the reference path for all the stages. All stage is set to its zero position except the Spindle which is rotating at 60rpm.

initializeReferences(struct('Rz_type', 'rotating', 'Rz_period', 1));

2 Tomography Experiment with no disturbances

2.1 Simulation Setup

And we initialize the disturbances to be equal to zero.

opts = struct(...
    'Dwx', false, ... % Ground Motion - X direction
    'Dwy', false, ... % Ground Motion - Y direction
    'Dwz', false, ... % Ground Motion - Z direction
    'Fty_x', false, ... % Translation Stage - X direction
    'Fty_z', false, ... % Translation Stage - Z direction
    'Frz_z', false  ... % Spindle - Z direction
);
initDisturbances(opts);

We simulate the model.

sim('sim_nano_station_tomo');

And we save the obtained data.

tomo_align_no_dist = struct('t', t, 'MTr', MTr);
save('experiment_tomography/mat/experiment.mat', 'tomo_align_no_dist', '-append');

2.2 Analysis

load('experiment_tomography/mat/experiment.mat', 'tomo_align_no_dist');
t = tomo_align_no_dist.t;
MTr = tomo_align_no_dist.MTr;

Edx = squeeze(MTr(1, 4, :));
Edy = squeeze(MTr(2, 4, :));
Edz = squeeze(MTr(3, 4, :));
% The angles obtained are u-v-w Euler angles (rotations in the moving frame)
Ery = atan2( squeeze(MTr(1, 3, :)),           squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));

Figure 1: X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (png, pdf)

Figure 2: X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances (png, pdf)

2.3 Conclusion

When everything is aligned, the resulting error motion is very small (nm range) and is quite negligible with respect to the error when disturbances are included. This residual error motion probably comes from a small misalignment somewhere.

3 Tomography Experiment with included perturbations

3.1 Simulation Setup

We now activate the disturbances.

opts = struct(...
    'Dwx', true, ... % Ground Motion - X direction
    'Dwy', true, ... % Ground Motion - Y direction
    'Dwz', true, ... % Ground Motion - Z direction
    'Fty_x', true, ... % Translation Stage - X direction
    'Fty_z', true, ... % Translation Stage - Z direction
    'Frz_z', true  ... % Spindle - Z direction
);
initDisturbances(opts);

We simulate the model.

sim('sim_nano_station_tomo');

And we save the obtained data.

tomo_align_dist = struct('t', t, 'MTr', MTr);
save('experiment_tomography/mat/experiment.mat', 'tomo_align_dist', '-append');

3.2 Analysis

load('experiment_tomography/mat/experiment.mat', 'tomo_align_dist');
t = tomo_align_dist.t;
MTr = tomo_align_dist.MTr;

Edx = squeeze(MTr(1, 4, :));
Edy = squeeze(MTr(2, 4, :));
Edz = squeeze(MTr(3, 4, :));
% The angles obtained are u-v-w Euler angles (rotations in the moving frame)
Ery = atan2( squeeze(MTr(1, 3, :)),           squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));

Figure 3: X-Y-Z translation of the sample w.r.t. the granite when performing tomography experiment with disturbances (png, pdf)

Figure 4: X-Y-Z rotations of the sample w.r.t. the granite when performing tomography experiment with disturbances (png, pdf)

3.3 Conclusion

Error motion is what expected from the disturbance measurements.

4 Tomography when the micro-hexapod is not centered

4.1 Simulation Setup

We first set the wanted translation of the Micro Hexapod.

P_micro_hexapod = [0.01; 0; 0]; % [m]

We initialize the reference path.

initializeReferences(struct('Dh_pos', [P_micro_hexapod; 0; 0; 0], 'Rz_type', 'rotating', 'Rz_period', 1));

We initialize the stages.

initializeMicroHexapod(struct('AP', P_micro_hexapod));

And we initialize the disturbances to zero.

opts = struct(...
    'Dwx', false, ... % Ground Motion - X direction
    'Dwy', false, ... % Ground Motion - Y direction
    'Dwz', false, ... % Ground Motion - Z direction
    'Fty_x', false, ... % Translation Stage - X direction
    'Fty_z', false, ... % Translation Stage - Z direction
    'Frz_z', false  ... % Spindle - Z direction
);
initDisturbances(opts);

We simulate the model.

sim('sim_nano_station_tomo');

And we save the obtained data.

tomo_not_align = struct('t', t, 'MTr', MTr);
save('experiment_tomography/mat/experiment.mat', 'tomo_not_align', '-append');

4.2 Analysis

load('experiment_tomography/mat/experiment.mat', 'tomo_not_align');
t = tomo_not_align.t;
MTr = tomo_not_align.MTr;

Edx = squeeze(MTr(1, 4, :));
Edy = squeeze(MTr(2, 4, :));
Edz = squeeze(MTr(3, 4, :));
% The angles obtained are u-v-w Euler angles (rotations in the moving frame)
Ery = atan2( squeeze(MTr(1, 3, :)),           squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));

Figure 5: X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (png, pdf)

Figure 6: X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances (png, pdf)

4.3 Conclusion

The main motions are translations in the X direction of the mobile platform (corresponds to the eccentricity of the micro-hexapod) and rotations along the rotating Y axis.

5 Raster Scans with the translation stage

5.1 Simulation Setup

We set the reference path.

initializeReferences(struct('Dy_type', 'triangular', 'Dy_amplitude', 10e-3, 'Dy_period', 1));

We initialize the stages.

initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod(struct('actuator', 'piezo'));
initializeSample(struct('mass', 1));

And we initialize the disturbances to zero.

opts = struct(...
    'Dwx', false, ... % Ground Motion - X direction
    'Dwy', false, ... % Ground Motion - Y direction
    'Dwz', false, ... % Ground Motion - Z direction
    'Fty_x', false, ... % Translation Stage - X direction
    'Fty_z', false, ... % Translation Stage - Z direction
    'Frz_z', false  ... % Spindle - Z direction
);
initDisturbances(opts);

We simulate the model.

sim('sim_nano_station_tomo');

And we save the obtained data.

ty_scan = struct('t', t, 'MTr', MTr);
save('experiment_tomography/mat/experiment.mat', 'ty_scan', '-append');

5.2 Analysis

load('experiment_tomography/mat/experiment.mat', 'ty_scan');
t = ty_scan.t;
MTr = ty_scan.MTr;

Edx = squeeze(MTr(1, 4, :));
Edy = squeeze(MTr(2, 4, :));
Edz = squeeze(MTr(3, 4, :));
% The angles obtained are u-v-w Euler angles (rotations in the moving frame)
Ery = atan2( squeeze(MTr(1, 3, :)),           squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));

Figure 7: X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (png, pdf)

Figure 8: X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances (png, pdf)

5.3 Conclusion

This is logic that the main error moving is translation along the Y axis and rotation along the X axis. In order to reduce the errors, we can make a smoother reference path for the translation stage.

Tomography Experiment

Table of Contents

1 Simscape Model

2 Tomography Experiment with no disturbances

2.1 Simulation Setup

2.2 Analysis

2.3 Conclusion

3 Tomography Experiment with included perturbations

3.1 Simulation Setup

3.2 Analysis

3.3 Conclusion

4 Tomography when the micro-hexapod is not centered

4.1 Simulation Setup

4.2 Analysis

4.3 Conclusion

5 Raster Scans with the translation stage

5.1 Simulation Setup

5.2 Analysis

5.3 Conclusion