nass-simscape/experiment_tomography/index.org

Tomography Experiment

• Introduction
• Simscape Model
• Tomography Experiment with no disturbances
  • Simulation Setup
  • Analysis
• With Perturbations
  • Simulation Setup
  • Analysis
• Tomography
  • Simulation Setup
  • Analysis

Introduction   ignore

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));

Tomography Experiment with no disturbances

Simulation Setup

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));

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.

  MTr_alig_no_dist = MTr;
  save('experiment_tomography/mat/experiment.mat', 'MTr_alig_no_dist', '-append');

Analysis

  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));

  <<plt-matlab>>

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

  <<plt-matlab>>

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

With Perturbations

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.

  MTr_alig_dist = MTr;
  save('experiment_tomography/mat/experiment.mat', 'MTr_alig_dist', '-append');

Analysis

  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));

  <<plt-matlab>>

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

  <<plt-matlab>>

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

Tomography

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.

  MTr_not_alig = MTr;
  save('experiment_tomography/mat/experiment.mat', 'MTr_not_alig', '-append');

Analysis

  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));

  <<plt-matlab>>

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

  <<plt-matlab>>

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