Modern Control Engineering

Section 10–7 / Design of Control Systems with Observers 787

ry

Plant

r+ u

Observer

controller

+

• 
  


• u

r yu

Plant

r–y Observer

+– controller

(a)

(b)

r yObserver u

+– controller

1

s(s^2 + 1)

Plant

Figure 10–27
Control system with
observer controller
in the feedforward
path.

Configuration 1: Consider the system shown in Figure 10–27. In this system the refer-

ence input is simply added at the summing point. We would like to design the observer

controller such that in the unit-step response the maximum overshoot is less than 30%

and the settling time is about 5 sec.

In what follows we first design a regulator system. Then, using the observer controller

designed, we simply add the reference input rat the summing point.

Before we design the observer controller, we need to obtain a state-space represen-

tation of the plant. Since

we obtain

By choosing the state variables as

we get

y =Cx

x

=Ax+Bu

x 3 =y$

x 2 =y

x 1 =y

y

%

+y

=u

Y(s)

U(s)

=

1

sAs^2 + 1 B

Figure 10–26
(a) Control system
with observer
controller in the
feedforward path;
(b) Control system
with observer
controller in the
feedback path.