Implementing Feedback Connection Between Two Systems Using MATLAB

First, write out the four matrices of the state-space model for the two systems separately, then call feedback() to establish the feedback connection, and finally call step() to test the step response curve of the overall system.

%% Feedback connection between two state-space systems

%% feedback();

%% step();

%%%%%%%%%%%

clear all;

clc;

close all;

%%%%%%%%%%%%%

%% System 1

A1=[-1.03 -1.05;

0.42 -1.08];

B1=[1;0];

C1=[1.1 1.2];

D1=[0.5];

%%% System 2

A2=[-1.06 0.31;

-1.52 -1.08];

B2=[0;1];

C2=[1.2 0.4];

D2=[0.4];

[A3,B3,C3,D3]=feedback(A1,B1,C1,D1,A2,B2,C2,D2);

sys3=ss(A3,B3,C3,D3);

t1=0:0.01:40;

[y3,t3]=step(sys3,t1);

figure(1);

plot(t3,y3,’b-‘);

title(‘Feedback Connection Output’);

xlabel(‘t(s)’);

ylabel(‘y’);

legend(‘Feedback Connection Output’);

grid on;

grid on;

%%%%

disp(‘End.’);