Modern Control Engineering

Section 10–4 / Design of Servo Systems 743

Unit-Step Response

Output

y

0

0.6

1.2

0.8

0.4

0.2

1

t Sec

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Figure 10–5
Unit-step response
curvey(t)versust
for the system
designed in
Example 10–4.

Note that since

we have

At steady state the control signal ubecomes zero.

Design of Type 1 Servo System when the Plant Has No Integrator. If the plant

has no integrator (type 0 plant), the basic principle of the design of a type 1 servo sys-

tem is to insert an integrator in the feedforward path between the error comparator

and the plant, as shown in Figure 10–6. (The block diagram of Figure 10–6 is a basic

form of the type 1 servo system where the plant has no integrator.) From the diagram,

we obtain

(10–31)

(10–32)

(10–33)

(10–34)

where x =state vector of the plant (n-vector)

j

=r-y=r-Cx

u =-Kx+kI j

y =Cx

x# =Ax+Bu

=-[160 54 11]C

r

0

0

S +160r= 0

u(q)=-[160 54 11]C

x 1 (q)

x 2 (q)

x 3 (q)

S +160r

u(q)=-Kx(q)+k 1 r(q)=-Kx(q)+k 1 r