842 Chapter 10 / Control Systems Design in State SpaceMATLAB Program 10–31
% Obtaining Ke ---- minimum-order observer
Aab = [1];
Abb = [-2];
LL = [-8];
Ke = acker(Abb',Aab',LL)'
Ke =
6
MATLAB Program 10–30
% Determination of transfer function of observer controller ---- full-order observer
A = [0 1;0 -2];
B = [0;4];
C = [1 0];
K = [4 0.5];
Ke = [14;36];
[num,den] = ss2tf(A-KeC-BK, Ke,K,0)
num =
0 74.0000 256.0000
den =
1 18 108
To obtain the transfer function of the observer controller, we use MATLAB. MATLAB
Program 10–30 produces this transfer function. The result isnum
den=
74 s+ 256
s^2 + 18 s+ 108=
74 (s+3.4595)
(s+ 9 +j5.1962)(s+ 9 - j5.1962)Next, we obtain the observer gain matrix Kefor the minimum-order observer. MATLAB
Program 10–31 produces Ke.The result isKe= 6The response of the system with minimum-order observer to the initial condition can be ob-
tained as follows: By substituting u=-Kxinto the plant equation given by Equation (10–79)Openmirrors.com