reinf2_19.m

离散控制系统设计的MATLAB 代码

%%%%%%%%%%% Reinforcement Problem 2.19 %%%%%%%%%%
%   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                 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --- Sinusoidal input sequence ---
%
clear
disp('Reinforcement Problem 2.19')
z1 = exp(j*pi/10);
zz = [z1; conj(z1)]
pp = [0.2; 0.4; 0.6; 0.8]
gn = 2
G = zpk(zz,pp,gn,1)         % build G(z) as ZPK object with Ts = 1
[magzG,thetazG] = xy2p(zz)  % magnitude and angle of system zeros 
k = 0:40;                   % discrete time  
u = 10*sin(pi*k/10);        % discrete input sequence              
y = lsim(G,u,k);            % system response due to u(k)
figure
stem(k,y,'filled');grid     % plot response
hold on
plot(k,u,'o')               % plot input
hold off
text(26,11,'input')
text(10,13,'output')
title('Response for Reinforcement Problem 2.19')
xlabel('Discrete time k')

%-- verify that poles of input transform are same as zeros of G(z) --
%  transform of input: per #18 in Franklin, Powell, Workman
%  numU(z) = z*sin(pi/10)
%  denU(z) = z^2 -2*cos(pi/10)*z  + 1
numU = sin(pi/10);
denU = [1 -2*cos(pi/10)  1]
pU = roots(denU)	            
[magpU,thetapU] = xy2p(pU)    % magnitude & angle of input poles
%%%%%%%%%%