Modern Control Engineering

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

t Sec

0 1 2 3 4 5 6 7 8

(a)

Outputs

0.4

0.8

1.8

0

1.2

0.6

1

0.2

1.4

1.6

Unit-Step Responses of Compensated and Uncompensated Systems

Uncompensated system

Compensated

system

Steady-state error of compensated system = 0.0125

Steady-state error of uncompensated

system= 0.125

Compensated

system Uncompensated system

t Sec

0 1 2 3 4 5 6 7 8 9 10

(b)

Outputs

10

4

0

6

9

2

1

8

5

7

3

Unit-Ramp Responses of Compensated and Uncompensated Systems

Figure 6–57

Transient-response

curves for the

compensated system

and uncompensated

system. (a) Unit-step

response curves;

(b) unit-ramp

response curves.

The unit-step response curves and unit-ramp response curves before and after compensation

are shown in Figure 6–57. (Notice a long tail of a small amplitude in the unit-step response of the

compensated system.)

EXAMPLE 6–9 Consider the control system of Example 6–8 again. Suppose that we use a lag–lead compensator

of the form given by Equation (6–24), or

Gc(s)=Kc

as+

1

T 1

bas+

1

T 2

b

as+

b

T 1

bas+

1

bT 2

b

(b 7 1)

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