cp4_2.m

离散控制系统设计的MATLAB 代码

%%%%%%%%%%% Comprehensive Problem 4.2 %%%%%%%%%%%
%   Discrete-Time Control Problems using        %
%       MATLAB and the Control System Toolbox   %
%   by J.H. Chow, D.K. Frederick, & N.W. Chbat  %
%         Brooks/Cole Publishing Company        %
%                September 2002                 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Inverted Pendulum
% System has 4 states, 1 input, and 2 outputs
% 4 states : pendulum's angular position and velocity, and
%            cart's position and velocity
% 1 input  : motor voltage (u)
% 2 outputs: pendulum's angular position (theta)
%            cart's position (x) 

disp('CP4.2: Inverted Pendulum')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part A : Load model
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear; close all

% Load continuous and discrete-time systems
if ~exist('stick.mat'), 
    dstick
elseif exist('stick.mat') == 2,
    load stick
end

Ts = 0.01;  % in dstick already
disp('*******>'); pause; disp(' ');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part B : Compute Poles
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp(['The matrices of the state-space model Gz(z) are :'])
[A,B,C,D] =ssdata(Gz)
disp('*******>');pause; disp(' ');

disp('System eigenvalues:')
disp('  one at z = 1 - position of cart without a reference point')
disp('  one outside of the unit circle - unstable motion of pendulum')
disp('  two inside the unit circle - stable motion of pendulum and ')
disp('    cart.')
eig(A)
disp('*******>');pause; disp(' ');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part C : Simulation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

disp('initial conditions')
x0 = [0.1 -0.6002 0 0]'
dtime = [0:Ts:1]';
y = lsim(Gz,0*dtime,dtime,x0);

figure
stem(dtime,y), grid
title('Initial Condition Response to 0.1 rad pendulum angle');
ylabel('Pendulum angle (rad) and cart position (m)')
xlabel('Time (s)')
legend('pendulum angle','cart position')
disp('*******>');pause

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part D : Modal form
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

disp('Modal form')
Gzm = canon(Gz,'modal')
disp('The eigenvalues are on the diagonal of the modal form A matrix')

disp('End of Comprehensive Problem CP4.2')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%