Modern Control Engineering

and from Equation (8–17)

we obtain

(8–19)

Equations (8–17) and (8–19) give the transfer functions of the controllers re-

spectively. The block diagram of the designed system is shown in Figure 8–69.

Note that if the maximum overshoot were much higher than 25%and/or the settling time

were much larger than 1.2 sec, then we might assume a search region (such as 3 a6,

3 b6,and 6 c 12 ) and use the computational method presented in Example 8–4 to

find a set or sets of variables that would give the desired response to the unit-step reference input.

Problems

Gc1(s) and Gc2(s),

=0.01s

• a0.7403+

1.20148

s

+0.11403sb

Gc2(s)= a0.7403+

1.20148

s

+0.12403sb

Gc1(s)=0.7403+

1.20148

s

+0.11403s

Problems 641

100

s(s+1)

0.01s

Y(s)

D(s)

R(s)

+– 1.20148 ++ ++

s

0.7403++ 0.11403s

Figure 8–69
Block diagram of the
designed system.

B–8–1.Consider the electronic PID controller shown in
Figure 8–70. Determine the values ofR 1 ,R 2 ,R 3 ,R 4 ,C 1 ,
andC 2 of the controller such that the transfer function
Gc(s)=Eo(s)Ei(s)is =30.3215 (s+0.65)

2

s

Gc(s)=39.42a 1 +

1

3.077s

+0.7692sb

+

+

Ei(s) E(s)

Eo(s)

C 1 C 2

R 1

R 2

R 3

R 4

Figure 8–70

Electronic PID controller.