Modern Control Engineering

368 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method

or

Hence,

The value of can be determined from the magnitude condition

as follows:

Thus

Since the open-loop transfer function becomes

a root-locus plot of the compensated system can be obtained easily with MATLAB by entering

numanddenand using rlocuscommand. The result is shown in Figure 6–78.

=

11.2(s+1)

0.1s^4 +1.6s^3 +6s^2

Gc(s)G(s)H(s)=11.2

s+ 1

(s+6)s^2 (0.1s+1)

Gc(s)=11.2

s+ 1

s+ 6

Kc=^2

(s+6)s^2 (0.1s+1)

s+ 1

2

s=- 1 +j 13

=11.2000

Kc^2

s+ 1

s+ 6

1

s^2

1

0.1s+ 1

2

s=- 1 +j 13

= 1

Kc

Gc(s)=Kc

s+ 1

s+ 6

x= 1 +

1.73205

0.34641

= 6

Real Axis

• 10 – 5 0 5 10

Imag Axis

0

10

• 5

5

• 10

Root-Locus Plot of Compensated System

Figure 6–78

Root-locus plot of

the compensated

system.

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