cp2_2.m

离散控制系统设计的MATLAB 代码

%%%%%%%%%%% Comprehensive Problem 2.2 %%%%%%%%%%%
%   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('CP2.2: 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 : System Orders
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display Gp first
disp('Transfer Function Gp(z) from u to theta')
Gp = tf(dnump,ddenp,Ts)
disp('Order of Gp(z)')
oGp = length(ddenp)-1
disp('*******>'); pause
% display Gc first
disp('Transfer Function Gc(z) from u to cart''s position')
Gc = tf(dnumc,ddenc,Ts)
disp('Order of Gc(z)')
oGc = length(ddenc)-1
disp('*******>'); pause

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part C : Poles
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Poles of Gp(z) are')
pole(Gp)  
disp('*******>'); pause
disp('Poles of Gc(z) are')
pole(Gc)
disp('Gp(z) and Gc(z) differ by a pole at z = 1.0')
disp('This is because pendulum dynamics are not affected by ')
disp('the relative position of the cart. ')
disp('*******>'); pause; disp(' ');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part D : Zeros
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Zeros of Gp(z) are')
tzero(Gp) 
disp('Zeros of Gc(z) are')
tzero(Gc)
disp('Gp(z) and Gc(z) have a common zero at -0.9453')
disp('*******>'); pause; disp(' ');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part E : Residues
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Residues at the poles of Gp(z) are')
[resp,ppp,otherp] = residue(dnump,ddenp)
disp('*******>');pause
disp('Residues at the poles of Gc(z) are')
[resc,ppc,otherc] = residue(dnumc,ddenc)
disp('*******>'); pause
disp('ppp are the poles of Gp(z)')
disp('ppc are the poles of Gc(z)')
disp('Residues resp & resc are the weights of ppp & ppc.')
disp('*******>'); pause; disp(' ');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part F :  step response
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[y,k] = step(Gztf);
y = y*[180/pi 0; 0 100];
figure, stem(k,y)
xlabel('Time (s)'); 
ylabel('Amplitude (deg and cm)'); grid; title('Step Response')
legend('pendulum angle','cart position',3)
disp('A step voltage input to the motor moves the cart') 
disp('(green curve) forward. As a result, the pendulum (blue')
disp('curve) falls backward or rotates in the negative direction.')
disp('*******>'); pause; disp(' ');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part G :  impulse response 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[y,k] = impulse(Gztf);
y = y*[180/pi 0; 0 100];
figure, stem(k,y)
xlabel('Time (s)'); 
ylabel('Amplitude (deg and cm)'); grid; title('Impulse Response')
legend('pendulum angle','cart position',3)
disp('An impulse voltage input to the motor moves the cart') 
disp('(green curve) forward. As a result, the pendulum (blue')
disp('curve) falls backward or rotates in the negative direction.')
disp('The motion is less than that due to the step input.')
disp('*******>'); pause; disp(' ');

disp('End of Comprehensive Problem CP2.2')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%