MATLAB: Linear-Quadratic Regulator Design for State Space Systems

Berikut ini adalah script MATLAB untuk LQR (Linear-Quadratic Regulator) controller.

clear all, close all, clc;

%% Define the system

A = [1 0 2;
    2 3 0;
    1 2 3]
% the state matrix

B = [1; 0; 0]
% the input vector

eig(A)
% the eigenvalues are
% 4.7511 + 0.0000i
% 1.1244 + 1.0251i
% 1.1244 - 1.0251i
% it is not stable

%% LQR design

Q = eye(size(A))

R = 1

K = lqr(A,B,Q,R)
% K =
%    14.5461   24.4004   41.9475

%% State feedback controller

sys = ss(A-B*K, eye(size(A)), eye(size(A)), eye(size(A)))

eig(sys.a)
% the eigenvalues are
% -4.7742 + 0.0000i
% -1.3860 + 1.1477i
% -1.3860 - 1.1477i
% it is stable

x0 = [5; 5; 5]
% initial state

t = 0:0.01:5;
% the time duration

x = initial(sys,x0,t);
% response of the state-space
% with initial condition x0
% and time duration t

x1 = [1 0 0]*x';
x2 = [0 1 0]*x';
x3 = [0 0 1]*x';
% the state variables

%% Plot the state variables

subplot(3,1,1); plot(t,x1), grid
title('Response to initial condition')
ylabel('x1')

subplot(3,1,2); plot(t,x2), grid
ylabel('x2')

subplot(3,1,3); plot(t,x3), grid
ylabel('x3')
xlabel('t (seconds)')

Berikut ini ialah plot response dari state variable.

Lihat juga tentang.

Kendali state space MATLAB.