Modern Control Engineering

620 Chapter 8 / PID Controllers and Modified PID Controllers

A–8–6. Consider the system shown in Figure 8–49. It is desired to design a PID controller such that

the dominant closed-loop poles are located at For the PID controller,

choosea=1and then determine the values of Kandb.Sketch the root-locus diagram for the

designed system.

Solution.Since

Gc(s)G(s)=K

(s+1)(s+b)

s

1

s^2 + 1

s=- 1 ;j 13.

Gc(s)

Output to Disturbance Input

14

6

2

• 4

8

12

4

10

0

• 2

10 –^3 Response to Unit-Step Disturbance Input

t Sec

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

(a)

Output to Reference Input

1.2

0.6

0

0.8

1.0

0.4

0.2

Response to Unit-Step Reference Input

t Sec

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

(b)

Figure 8–48

(a) Response to

unit-step disturbance

input; (b) response to

unit-step reference

input.

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