nass-simscape/org/compensation_gravity_forces.org

Compensating the gravity forces to start at steady state

• Introduction
• Initialization of the Experimental Conditions
• Without compensation
• Simulation to compute the required force in each joint
• New simulation with compensation of gravity forces

Introduction   ignore

In this file is shown a technique used to compensate the gravity forces at t=0.

The problem is that in presence of gravity, the system does not start at steady state and experience a transient phase (section sec:no_compensation).

In order to start the simulation at steady state in presence of gravity:

• section sec:compute_forces: first the stages are initialize in such a way that they are rigid, and the forces/torques applied at the location of their joints is measured
• section sec:compensation: Then, the equilibrium position of each joint is modified in such a way that at t=0, the forces in each joints exactly compensate the forces due to gravity forces

Initialization of the Experimental Conditions

We don't inject any perturbations and no reference tracking.

  initializeReferences();
  initializeDisturbances('enable', false);
  initializeController();

We include the gravity and log all the signals to display.

  initializeSimscapeConfiguration('gravity', true);
  initializeLoggingConfiguration('log', 'all');

Without compensation

<<sec:no_compensation>> Let's simulate the system without any compensation of gravity forces.

  initializeGround();
  initializeGranite();
  initializeTy();
  initializeRy();
  initializeRz();
  initializeMicroHexapod();
  initializeAxisc();
  initializeMirror();
  initializeNanoHexapod();
  initializeSample();

  load('mat/conf_simulink.mat');
  set_param(conf_simulink, 'StopTime', '0.5');

  sim('nass_model');
  sim_no_compensation = simout;

Verification that nothing is moving

<<plt-matlab>>

Motion of the sample at the start of the simulation in presence of gravity (png, pdf)

Simulation to compute the required force in each joint

<<sec:compute_forces>> We here wish to simulate the system in order to compute the required force in each joint to compensate the gravity forces.

  initializeGround();
  initializeGranite('type', 'init');
  initializeTy('type', 'init');
  initializeRy('type', 'init');
  initializeRz('type', 'init');
  initializeMicroHexapod('type', 'init');
  initializeAxisc();
  initializeMirror();
  initializeNanoHexapod('type', 'init');
  initializeSample('type', 'init');

We simulate for a short time period (all the bodies are solid, so nothing should move).

  load('mat/conf_simulink.mat');
  set_param(conf_simulink, 'StopTime', '0.1');

  sim('nass_model');

Verification that nothing is moving by looking at the maximum displacement of the sample:

  max(max(simout.Em.En.Data))

1.0681e-15

We here show the measured total force/torque applied at the location of each joint.

  data2orgtable([Fgm 0 0 0; Ftym; Fym; Fsm], {'Granite', 'Translation Stage', 'Tilt Stage', 'Sample'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}, ' %.1e ');

	Fx	Fy	Fz	Mx	My	Mz
Granite	-7.6e-12	1.2e-11	-34000.0	0.0	0.0	0.0
Translation Stage	-7.6e-12	1.2e-11	-12000.0	31.0	2.5	6.6e-13
Tilt Stage	-7.6e-12	1.2e-11	-8800.0	33.0	-0.52	6.6e-13
Sample	-5.7e-12	1.3e-11	-490.0	-2.5e-12	-8.1e-13	2.7e-13

  data2orgtable([Fhm; Fnm], {'Micro-Hexapod', 'Nano-Hexapod'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}, ' %.1e ');

	F1	F2	F3	F4	F5	F6
Micro-Hexapod	-180.0	-180.0	-180.0	-180.0	-180.0	-180.0
Nano-Hexapod	-160.0	-160.0	-160.0	-160.0	-160.0	-160.0

We save these forces in Foffset.mat.

  save('mat/Foffset.mat', 'Fgm', 'Ftym', 'Fym', 'Fzm', 'Fhm', 'Fnm', 'Fsm');

New simulation with compensation of gravity forces

<<sec:compensation>> We now initialize the stages with the option Foffset.

  initializeGround();
  initializeGranite('Foffset', true);
  initializeTy('Foffset', true);
  initializeRy('Foffset', true);
  initializeRz('Foffset', true);
  initializeMicroHexapod('Foffset', true);
  initializeAxisc();
  initializeMirror();
  initializeNanoHexapod('Foffset', true);
  initializeSample('Foffset', true);

And we simulate the system for 0.5 seconds.

  load('mat/conf_simulink.mat');
  set_param(conf_simulink, 'StopTime', '0.5');

  sim('nass_model');
  sim_compensation = simout;

Verification that nothing is moving

<<plt-matlab>>

Motion of the sample at the start of the simulation in presence of gravity when compensating the gravity forces (png, pdf)