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# Stewart Platform - Active Damping

## Table of Contents

- 1. Inertial Control
  - 1.1. Simscape Model
  - 1.2. Initialize the Stewart model
  - 1.3. Identification of the Dynamics
  - 1.4. Analysis
  - 1.5. Conclusion

## 1 Inertial Control

### 1.1 Simscape Model

    open('simulink/stewart_active_damping.slx')

### 1.2 Initialize the Stewart model

    stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3);
    stewart = generateCubicConfiguration(stewart, 'Hc', 40e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3);
    stewart = computeJointsPose(stewart);
    stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1));
    stewart = computeJacobian(stewart);

### 1.3 Identification of the Dynamics

    %% Options for Linearized
    options = linearizeOptions;
    options.SampleTime = 0;

    %% Name of the Simulink File
    mdl = 'stewart_active_damping';

    %% Input/Output definition
    clear io; io_i = 1;
    io(io_i) = linio([mdl, '/F'],   1, 'openinput');  io_i = io_i + 1;
    io(io_i) = linio([mdl, '/WVB'], 1, 'openoutput'); io_i = io_i + 1;
    io(io_i) = linio([mdl, '/Dm'],  1, 'openoutput'); io_i = io_i + 1;

    %% Run the linearization
    G = linearize(mdl, io, options);
    G.InputName  = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
    G.OutputName = {'Vx', 'Vy', 'Vz', 'Wx', 'Wy', 'Wz', ...
                    'D1', 'D2', 'D3', 'D4', 'D5', 'D6'};

### 1.4 Analysis

    freqs = 2*pi*logspace(1, 4, 1000);

    figure;
    bode(G({'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}), freqs)

    figure;
    bode(stewart.J*G({'Vx', 'Vy', 'Vz', 'Wx', 'Wy', 'Wz'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}), freqs)

    figure;
    bode(G({'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}), stewart.J*G({'Vx', 'Vy', 'Vz', 'Wx', 'Wy', 'Wz'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}), freqs)

### 1.5 Conclusion

It is similar to use:

- one 6dof inertial sensor and the Jacobian the have the velocity of each lim
- 6 1dof inertial sensor in each top part of the limbs

Author: Dehaeze Thomas

Created: 2020-01-22 mer. 16:31