EE443: USING MATLAB TO TEST CONTROLLABILITY AND OBSERVABILITY AS WELL AS SIMULATE SYSTEM REGULATION ABOUT ZERO

%
% Filename:  example6.m
%
% Description: Example using matlab to check state feedback design for
%              system regulation.
%

clear; clf;
x0 = [pi/2; 0.3];						% ICs: theta=pi/2 rad, thetadot=0.3rad/sec
	
A = [0 1;0 0];							% system matrices
B = [0; 0.2];
C = [1 0];

K = [205 40];							% state feedback controller gains

Pc = ctrb(A,B);                  % construct controllability matrix
if(abs(det(Pc)) > eps)           % test for controllability
   disp('System Is Controllable');
else
   disp('System Is NOT Controllable');
end;

Q = obsv(A,C);                   % construct observability matrix
if(abs(det(Q)) > eps)           	% test for controllability
   disp('System Is Observable');
else
   disp('System Is NOT Observable');
end;

initial((A-B*K),[0;0],C,[0],x0);	% compute and plot response
title('Regulation Response of Satellite Orientation Angle');