Example of Minimal Realization in Control Systems Using MATLAB

To cancel the controllable poles and zeros of the control system and eliminate unnecessary states, the minreal() function can be used for this processing.

% System minimal realization

% minreal()

% ss2tf()

%%%%%%%%%%%

clear all;

clc;

close all;

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

%%%% Example 1

A1=[-3.9 -1.303 0 0

1.304 0 0 0

1.0 2.608 -11.22 -5.503

0 0 5.503 0];

B1=[1; 0; 0; 0];

C1=[1.0 2.6 -1.2 -1.0];

D1=0;

[A2,B2,C2,D2]=minreal(A1,B1,C1,D1,1.0e-5);

disp(‘ Original system transfer function: A1=’)

disp(A1)

disp(‘ New system transfer function: A2=’)

disp(A2)

%%%% Example 2

num1=[1.0 10.2 33.47 35.19];

den1=[1.0 12.1 48.781 75.586 35.035];

[num2,den2]=minreal(num1,den1,1.0e-3);

disp(‘ Original system transfer function: G1=’)

printsys(num1,den1);

disp(‘ New system transfer function: G2=’)

printsys(num2,den2);

%%%%%%%%

disp(‘ End.’);