Simulation of Scientific Experiments

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 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
Compare with experiments when control is applied

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

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

load('mat/conf_simulink.mat');
set_param(conf_simulink, 'StopTime', '2');

We first initialize all the stages. The nano-hexapod is considered to be a rigid body.

initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeNanoHexapod('type', 'rigid');
initializeSample('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('Rz_type', 'rotating', 'Rz_period', 1);

No controller is used (Open Loop).

initializeController('type', 'open-loop');

And we put some gravity.

initializeSimscapeConfiguration('gravity', true);

We log the signals for further analysis.

initializeLoggingConfiguration('log', 'all');

2 Tomography Experiment with no disturbances

In this section, a tomography experiment is performed with the sample aligned with the rotation axis. No disturbance is included.

2.1 Simulation Setup

And we initialize the disturbances to be equal to zero.

initializeDisturbances(...
    '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
    );

We simulate the model.

sim('nass_model');

And we save the obtained data.

tomo_align_no_dist = simout;
save('./mat/experiment_tomography.mat', 'tomo_align_no_dist', '-append');

2.2 Analysis

load('./mat/experiment_tomography.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

In this section, we also perform a tomography experiment with the sample’s center of mass aligned with the rotation axis. However this time, we include perturbations such as ground motion and stage vibrations.

3.1 Simulation Setup

We now activate the disturbances.

initializeDisturbances(...
    '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
    );

We simulate the model.

sim('nass_model');

And we save the obtained data.

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

3.2 Analysis

load('./mat/experiment_tomography.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

In this section, the sample’s center of mass is not aligned with the rotation axis anymore. This is due to the fact that the micro-hexapod has performed some displacement.

No disturbances are included.

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

We initialize the stages.

initializeMicroHexapod('AP', P_micro_hexapod);

And we initialize the disturbances to zero.

initializeDisturbances(...
    '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
    );

We simulate the model.

sim('nass_model');

And we save the obtained data.

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

4.2 Analysis

load('./mat/experiment_tomography.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

In this section, scans with the translation stage are performed.

5.1 Simulation Setup

We set the reference path.

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

We initialize the stages.

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

And we initialize the disturbances to zero.

initializeDisturbances(...
    '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
    );

We simulate the model.

sim('nass_model');

And we save the obtained data.

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

5.2 Analysis

load('./mat/experiment_tomography.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.

Simulation of Scientific Experiments

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