cp3_1.m

离散控制系统设计的MATLAB 代码

%%%%%%%%%%% Comprehensive Problem 3.1 %%%%%%%%%%%
%   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                 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Ball and Beam System              
% System has 4 states, 1 input, and 2 outputs
% 4 states : ball's position and velocity, and
%            wheel's angular position and velocity
% 1 input  : motor voltage (u)
% 2 output : ball's position (xi), and 
%            wheel's angular position (theta)

disp('CP3.1: Ball and Beam')

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

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

Ts = 0.02;  % in dbbeam already

disp('*******>'); pause; disp(' ')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part B : Km(z) Proportional Control
% Kb(z) Proportional Control
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Km(z) prop. control - Kb(z) prop. control'); disp(' ')

for Kp1 = 0.5:0.5:5,
    t  = [0:1:100]*Ts;
    Km = Kp1;
    disp(['Closed-loop system with Km = ',num2str(Kp1),' is : ']);
    G_Kmcl = feedback(Gztf*Km,1,1,2,-1) % servo CL
    y = step(G_Kmcl,t);
    figure, plot(t,0.2*y(:,2)*180/pi,'o'),grid
    title(['Step Response - Km = ',num2str(Kp1)]);
    ylabel('Wheel angle (deg)')
    xlabel('Time (s)')
    disp('*******>');pause
end
disp('Select Km = 3, giving a fast response')

Km = 3;
disp(['G_Kmcl with Km = ',num2str(Km),' is : ']);
G_Kmcl = feedback(Gztf*Km,1,1,2,-1) % servo CL
disp('*******>');pause
figure
for Kp2 = 0.5:0.5:5,
    t  = [0:1:1000]*Ts;
    Kb = Kp2;
    disp(['G_Kbcl with Kb = ',num2str(Kp2),' is : ']);
    G_Kbcl = feedback(G_Kmcl(1,1)*Kb,1,1,1) % b&b CL
    y_Kbcl = step(G_Kbcl,t);
    plot(t,0.1*y_Kbcl,'.','markersize',5),grid
    title(['Step Response - Kb = ',num2str(Kp2)]);
    ylabel('Ball position (m)')
    xlabel('Time (s)')
    disp('*******>');pause
end
disp('Note that with small proportional control gain, the')
disp('response of the ball is damped but slow. At higher gain,')
disp('the oscillation becomes unstable.')

disp('*******>');pause; disp(' ')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part C : Km(z) proportional control 
% Kb(z) proportional-and-derivative control
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Km(z) prop. control - Kb(z) prop-deriv. control'); 
disp(' ')

Km = 3;
disp(['G_Kmcl with Km = ',num2str(Km),' is : ']);
G_Kmcl = feedback(Gztf*Km,1,1,2,-1) % servo CL
disp('*******>');pause
Kp2 = 1;
Kd  = 1;
disp('PD controller')
KbPD = tf(Kp2*[(1+Kd/Ts) -Kd/Ts],[1 0],Ts) % PD controller
t  = [0:1:1000]*Ts;
G_PDcl = feedback(G_Kmcl(1,1)*KbPD,1,1,1) % b&b CL
y_PDcl = step(G_PDcl,t);
figure, plot(t,0.1*y_PDcl,'.','markersize',5), grid
title(['Step Response using PD controller']);
ylabel('Ball position (m)')
xlabel('Time (s)')
disp('The PD controller improves the response time and damping.')
disp('*******>');pause

disp('End of Comprehensive Problem CP3.1')
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