Modern Control Engineering

Section 10–7 / Design of Control Systems with Observers 789

Figure 10–28 shows the block diagram of the regulator system just designed. Figure

10–29 shows the block diagram of a possible configuration of the control system based

on the regulator system shown in Figure 10–28. The unit-step response curve for this

control system is shown in Figure 10–30. The maximum overshoot is about 28%and the

settling time is about 4.5 sec. Thus, the designed system satisfies the design requirements.

MATLAB Program 10–17

% Determination of transfer function of observer controller

A = [0 1 0;0 0 1;0 -1 0];

B = [0;0;1];

Aaa = 0; Aab = [1 0]; Aba = [0;0]; Abb = [0 1;-1 0];

Ba = 0; Bb = [0;1];

Ka = 16; Kb=[17 10];

Ke = [8;15];

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 =

302.0000 303.0000 256.0000

den =

1 18 113

• yu y


• 
  

302 s^2 + 303 s+ 256

s^2 + 18 s+ 113

Observer controller

1

s(s^2 + 1)

Plant

rur–y y

+–

302 s^2 + 303 s+ 256

s^2 + 18 s+ 113

1

s(s^2 + 1)

Observer controller Plant

Figure 10–29
Control system with
observer controller
in the feedforward
path.

Figure 10–28
Regulator system
with observer
controller.