Modern Control Engineering

Example Problems and Solutions 841

MATLAB Program 10–29

% Response to initial condition ---- full-order observer

A = [0 1;0 -2];

B = [0;4];

C = [1 0];

K = [4 0.5];

Ke = [14;36];

AA = [A-BK BK; zeros(2,2) A-Ke*C];

sys = ss(AA, eye(4), eye(4), eye(4));

t = 0:0.01:8;

x = initial(sys, [1;0;1;0],t);

x1 = [1 0 0 0]*x';

x2 = [0 1 0 0]*x';

e1 = [0 0 1 0]*x';

e2 = [0 0 0 1]*x';

subplot(2,2,1); plot(t,x1); grid

xlabel('t (sec)'); ylabel('x1')

subplot(2,2,2); plot(t,x2); grid

xlabel('t (sec)'); ylabel('x2')

subplot(2,2,3); plot(t,e1); grid

xlabel('t (sec)'); ylabel('e1')

subplot(2,2,4); plot(t,e2); grid

xlabel('t (sec)'); ylabel('e2')

x^1 x^2

e^1 e^2

0.4

0.6

0.8

1

0.2 0 −0.2

02468

−0.4

0.6

0.8

1

1.2

0.4 0.2 0 −0.2

0

1

− 1

− 2

−0.5

0