Modern Control Engineering

Section 10–9 / Robust Control Systems 813

K

(b)

w

u

z

y

P

G

w

u

y

K

WmI WsI

(a)

y

z 2

z 1

z

• ++

Figure 10–45
(a) Generalized
plant diagram;
(b) simplfied version
of the generalized
plant diagram
shown in (a).

Finding Transfer Functionz(s)/w(s)from a Generalized Plant Diagram. Consider

the generalized plant diagram shown in Figure 10–46.

In this diagram w(s)is the exogenous disturbance and u(s)is the manipulated vari-

able.z(s)is the controlled variable and y(s)is the observed variable.

Consider this control system consisting of the generalized plant P(s)and the con-

trollerK(s). The equation that relates the outputs z(s)andy(s)and the inputs w(s) and

u(s)of the generalized plant P(s)is

The equation that relates u(s)andy(s)is given by

u(s)=K(s)y(s)

Define the transfer function that relates the controlled variable z(s) to the exogenous

disturbancew(s)as (s). Then

z(s)=£(s)w(s)

£

B

z(s)

y(s)

R = B

P 11

P 21

P 12

P 22

RB

w(s)

u(s)

R