Modern Control Engineering

Section 6–8 / Lag-Lead Compensation 341

The dominant closed-loop poles are located at

The other closed-loop poles are located at

Since the closed-loop pole at is very close to a zero at they almost cancel

each other. Thus, the effect of this closed-loop pole is very small. The remaining closed-loop pole

does not quite cancel the zero at The effect of this zero is to cause a

larger overshoot in the step response than a similar system without such a zero. The unit-step

response curves of the compensated and uncompensated systems are shown in Figure 6–59(a). The

unit-ramp response curves for both systems are depicted in Figure 6–59(b).

(s=-3.8604) s=-2.4.

s=-0.1003 s=-0.1,

s=-0.1003; s=-3.8604

s=-2.4539;j4.3099

t Sec

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

(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

t Sec

03 0.5 1 1.5 2 2.5 3.5 4

(b)

Outputs

1.5

2.5

4

0.5

0

3.5

2

3

1

Unit-Ramp Responses of Compensated and Uncompensated Systems

Compensated Uncompensated system

system

Figure 6–59
(a) Unit-step
response curves for
the compensated and
uncompensated
systems;
(b) unit-ramp
response curves for
both systems.