788 Chapter 10 / Control Systems Design in State Spacewhere
Next, we choose the desired closed-loop poles for pole placement at
s=–1+j, s=–1-j, s=–8
and the desired observer poles at
s=–4, s=–4
The state feedback gain matrix Kand the observer gain matrix Kecan be obtained as
follows:
See MATLAB Program 10–16.
Ke= B
8
15
R
K=[16 17 10]
A= C
0
0
0
1
0
- 1
0
1
0
S, B= C
0
0
1
S, C=[1 0 0]
MATLAB Program 10–16
A = [0 1 0;0 0 1;0 -1 0];
B = [0;0;1];
J = [-1+j -1-j -8];
K = acker(A,B,J)
K =
16 17 10
Aab = [1 0];
Abb = [0 1;-1 0];
L = [-4 -4];
Ke = acker(Abb',Aab',L)'
Ke =
8
15
The transfer function of the observer controller is obtained by use of MATLAB
Program 10–17. The result is
=
302(s+0.5017+j0.772)(s+0.5017-j0.772)
(s+ 9 +j5.6569)(s+ 9 - j5.6569)
Gc(s)=
302s^2 +303s+ 256
s^2 +18s+ 113
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