Stewart Platform - Control Study
Table of Contents
1 First Control Architecture
1.1 Control Schematic
\begin{tikzpicture} % Blocs \node[block] (J) at (0, 0) {$J$}; \node[addb={+}{}{}{}{-}, right=1 of J] (subr) {}; \node[block, right=0.8 of subr] (K) {$K_{L}$}; \node[block, right=1 of K] (G) {$G_{L}$}; % Connections and labels \draw[<-] (J.west)node[above left]{$\bm{r}_{n}$} -- ++(-1, 0); \draw[->] (J.east) -- (subr.west) node[above left]{$\bm{r}_{L}$}; \draw[->] (subr.east) -- (K.west) node[above left]{$\bm{\epsilon}_{L}$}; \draw[->] (K.east) -- (G.west) node[above left]{$\bm{\tau}$}; \draw[->] (G.east) node[above right]{$\bm{L}$} -| ($(G.east)+(1, -1)$) -| (subr.south); \end{tikzpicture}
1.2 Initialize the Stewart platform
stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3); % stewart = generateCubicConfiguration(stewart, 'Hc', 60e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3); stewart = generateGeneralConfiguration(stewart); stewart = computeJointsPose(stewart); stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1)); stewart = computeJacobian(stewart);
1.3 Initialize the Simulation
load('mat/conf_simscape.mat');
1.4 Identification of the plant
Let’s identify the transfer function from \(\bm{\tau}}\) to \(\bm{L}\).
%% Options for Linearized options = linearizeOptions; options.SampleTime = 0; %% Name of the Simulink File mdl = 'stewart_platform_control'; %% Input/Output definition clear io; io_i = 1; io(io_i) = linio([mdl, '/tau'], 1, 'openinput'); io_i = io_i + 1; io(io_i) = linio([mdl, '/L'], 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 = {'L1', 'L2', 'L3', 'L4', 'L5', 'L6'};
1.5 Plant Analysis
Diagonal terms Compare to off-diagonal terms
1.6 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);