Section 10–4 / Design of Servo Systems 739
x.=Ax+Bu y=Cx
x 2
x 3
xn
k 2
k 1
k 3
kn
r
u
x
y=x 1
+– +–
Figure 10–4
Type 1 servo system
when the plant has
an integrator.
10–4 Design of Servo Systems
In this section we shall discuss the pole-placement approach to the design of type 1
servo systems. Here we shall limit our systems each to have a scalar control signal uand
a scalar output y.
In what follows we shall first discuss a problem of designing a type 1 servo system
when the plant involves an integrator. Then we shall discuss the design of a type 1 servo
system when the plant has no integrator.
Design of Type 1 Servo System when the Plant Has An Integrator. Assume
that the plant is defined by
(10–19)
(10–20)
where
As stated earlier, we assume that both the control signal uand the output signal yare
scalars. By a proper choice of a set of state variables, it is possible to choose the output
to be equal to one of the state variables.ASee the method presented in Chapter 2 for
obtaining a state-space representation of the transfer function system in which the output
ybecomes equal to x 1 .B
Figure 10–4 shows a general configuration of the type 1 servo system when the plant
has an integrator. Here we assumed that y=x 1 .In the present analysis we assume that
C= 1 *n constant matrix
B=n* 1 constant matrix
A=n*n constant matrix
y =output signal (scalar)
u =control signal (scalar)
x=state vector for the plant (n-vector)
y =Cx
x# =Ax+Bu
