Modern Control Engineering

Example Problems and Solutions 379

Then

Noting that

the angle contribution of the lag portion is –1.697° and the magnitude contribution is 0.9837. This

means that the dominant closed-loop poles lie close to the desired location

Thus the compensator designed,

is acceptable. The feedforward transfer function of the compensated system becomes

A root-locus plot of the compensated system is shown in Figure 6–88(a). An enlarged root-locus

plot near the origin is shown in Figure 6–88(b).

Gc(s)G(s)=

1280(s+3.7)(s+0.1442)

s(s+53.35)(s+0.01)(s+2)(s+8)

Gc(s)= 128 a

s+3.70

s+53.35

ba

s+0.1442

s+0.01

b

s=- 2 ;j2 13.

n

s 1 +0.1442

s 1 +0.01

2

s 1 =- 2 +j 213

=-1.697°

2 s^1 +0.1442

s 1 +0.01

2

s 1 =- 2 +j 213

=0.9837

1

T 2

=0.1442

Real Axis

− 60 − 40 − 20 0 20 40 60

(a)

Imag Axis

60

− 60

− 40

40

0

20

− 20

Root-Locus Plot of Compensated System

Figure 6–88
(a) Root-locus plot of compensated system; (b) root-locus plot near the origin.

Real Axis

− 10 − 5 0 5 10

(b)

Imag Axis

10

− 10

8

− 6

− 8

6

0

4

− 2

2

− 4

Root-Locus Plot of Compensated System near the Origin

Desired closed-loop poles