Modern Control Engineering

844 Chapter 10 / Control Systems Design in State Space

e

02468

0

0.2

0.4

0.6

0.8

1

t (sec)

x^1 x^2

0.6

0.8

1

1.2

0.4

0.2

0

02468 02468

−0.2

0

0.5

−0.5

− 1

− 2

−1.5

−2.5

t (sec) t (sec)

Figure 10–53

Response curves to

initial condition.

The transfer function of the observer controller, when the system uses the minimum-order

observer, can be obtained by use of MATLAB Program 10–33. The result is

num

den

=

7 s+ 32

s+ 10

=

7 (s+4.5714)

s+ 10

MATLAB Program 10–33

% Determination of transfer function of observer controller ---- minimum-order observer

A = [0 1;0 -2];

B = [0;4];

Aaa = 0; Aab = 1; Aba = 0; Abb = -2;

Ba = 0; Bb = 4;

Ka = 4; Kb = 0.5;

Ke = 6;

Ahat = Abb - Ke*Aab;

Bhat = AhatKe + Aba - KeAaa;

Fhat = Bb - Ke*Ba;

Atilde = Ahat - Fhat*Kb;

Btilde = Bhat - Fhat(Ka + KbKe);

Ctilde = -Kb;

Dtilde = -(Ka + Kb*Ke);

[num,den] = ss2tf(Atilde, Btilde, -Ctilde, -Dtilde)

num =

7 32

den =

1 10

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