Modern Control Engineering

502 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method

7–12 Lag Compensation

In this section we first discuss the Nyquist plot and Bode diagram of the lag compensator.

Then we present lag compensation techniques based on the frequency-response approach.

Characteristics of Lag Compensators. Consider a lag compensator having the

following transfer function:

Gc(s)=Kc b

Ts+ 1

bTs+ 1

=Kc

s+

1

T

s+

1

bT

(b 7 1)

Outputs

5

2

0

3.5

4.5

1.5

0.5

3

4

2.5

1

t Sec

01 0.5 1.5 2 2.5 3 3.5 4 4.5 5

Unit-Ramp Responses of Compensated and Uncompensated Systems

Compensated system

Figure 7–100 Uncompensated system

Unit-ramp response

curves of the

compensated and

uncompensated

systems.

Outputs

1.4

0.6

0

1

1.2

0.4

0.2

0.8

t Sec

012 3 4 5 6

Unit-Step Responses of Compensated and Uncompensated Systems

Compensated system

Uncompensated system

Figure 7–99

Unit-step response

curves of the

compensated and

uncompensated

systems.

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