Stewart Platform - Tracking Control

1. First Control Architecture

1 First Control Architecture

1.1 Control Schematic

1.2 Initialize the Stewart platform

stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
stewart = initializeInertialSensor(stewart, 'type', 'accelerometer', 'freq', 5e3);

ground = initializeGround('type', 'none');
payload = initializePayload('type', 'none');

1.3 Identification of the plant

Let’s identify the transfer function from \(\bm{\tau}\) to \(\bm{L}\).

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

%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'],        1, 'openinput');  io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Stewart Platform'],  1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]

%% Run the linearization
G = linearize(mdl, io);
G.InputName  = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
G.OutputName = {'L1', 'L2', 'L3', 'L4', 'L5', 'L6'};

1.4 Plant Analysis

Diagonal terms Compare to off-diagonal terms

1.5 Controller Design

One integrator should be present in the controller.

A lead is added around the crossover frequency which is set to be around 500Hz.

% wint = 2*pi*100; % Integrate until [rad]
% wlead = 2*pi*500; % Location of the lead [rad]
% hlead = 2; % Lead strengh

% Kl = 1e6 * ... % Gain
%      (s + wint)/(s) * ... % Integrator until 100Hz
%      (1 + s/(wlead/hlead)/(1 + s/(wlead*hlead))); % Lead

wc = 2*pi*100;
Kl = 1/abs(freqresp(G(1,1), wc)) * wc/s * 1/(1 + s/(3*wc));
Kl = Kl * eye(6);