ex3_2.m

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%%%%%%%%%%%%%%%%%% Example 3.2 %%%%%%%%%%%%%%%%%%
%   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                 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   ---- Parallel connection of two systems ----
%
clear
disp('Example 3.2')
Ts = 1;                             % unity sampling period

H1 = tf([1 0.5],[1 0.75],Ts)        % H1 in TF form

%---- use convolution cmd to multiply 3 polynomials in denominator of H2
denH2 = conv([1 -0.9],conv([1 -0.8],[1 0.8]))
H2 = tf([0.15 0],denH2,Ts)          % H2(z) in TF form
disp('******>'), pause 

%---- parallel combination will be in TF form -----------
T = H1 + H2                         
[zT,pT,kT] = zpkdata(T,'v')         % zeros, poles, and gain of T(z)
disp('******>'), pause 
xy2p(zT);                           % zeros of T(z) in polar form
pH1 = pole(H1)                      % poles of H1
pH2 = pole(H2)                      % poles of H2

figure
[y,k] = step(T);                    % step reponse of T(z)
stem(k,y,':','filled');grid         % plot with stem option
title('Step response for Example 3.2')
xlabel('Time (s)')
%%%%%%%%%%