Section 10–6 / Design of Regulator Systems with Observers 783
The error equation for the minimum-order observer is
(10–111)
By combining Equations (10–110) and (10–111), we get
with the initial condition
MATLAB Program 10–15 produces the response to the given initial condition. The
response curves are shown in Figure 10–21.They seem to be acceptable.
B
x( 0 )
e( 0 )
R = E
1
0
0
1
0
U
B
x
e
#R = B
A-BK
0
BKb
Abb-Ke Aab
RB
x
e
R
e
=AAbb-Ke AabBe
MATLAB Program 10–15
% Response to initial condition.
A = [0 1 0;0 0 1;0 -24 -10];
B = [0;10;-80];
K = [1.25 1.25 0.19375];
Kb = [1.25 0.19375];
Ke = [-1;6.25];
Aab = [1 0]; Abb = [0 1;-24 -10];
AA = [A-BK BKb; zeros(2,3) Abb-Ke*Aab];
sys = ss(AA,eye(5),eye(5),eye(5));
t = 0:0.01:8;
x = initial(sys,[1;0;0;1;0],t);
x1 = [1 0 0 0 0]*x';
x2 = [0 1 0 0 0]*x';
x3 = [0 0 1 0 0]*x';
e1 = [0 0 0 1 0]*x';
e2 = [0 0 0 0 1]*x';
subplot(3,2,1); plot(t,x1); grid
xlabel ('t (sec)'); ylabel('x1')
subplot(3,2,2); plot(t,x2); grid
xlabel ('t (sec)'); ylabel('x2')
subplot(3,2,3); plot(t,x3); grid
xlabel ('t (sec)'); ylabel('x3')
subplot(3,2,4); plot(t,e1); grid
xlabel('t (sec)'); ylabel('e1')
subplot(3,2,5); plot(t,e2); grid
xlabel('t (sec)'); ylabel('e2')
