Modern Control Engineering

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

The maximum overshoot in the step response of the compensated system is approximately

38 %. (This is much larger than the maximum overshoot of 21%in the design presented in Exam-

ple 6–8.) It is possible to decrease the maximum overshoot by a small amount from 38%, but not

to 20%ifg=bis required, as in this example. Note that by not requiring g=b, we have an ad-

ditional parameter to play with and thus can reduce the maximum overshoot.

6–9 Parallel Compensation

Thus far we have presented series compensation techniques using lead, lag, or lag–lead

compensators. In this section we discuss parallel compensation technique. Because in the

parallel compensation design the controller (or compensator) is in a minor loop, the de-

sign may seem to be more complicated than in the series compensation case. It is, how-

ever, not complicated if we rewrite the characteristic equation to be of the same form

as the characteristic equation for the series compensated system. In this section we pres-

ent a simple design problem involving parallel compensation.

Basic Principle for Designing Parallel Compensated System. Referring to

Figure 6–60(a), the closed-loop transfer function for the system with series compensa-

tion is

The characteristic equation is

GivenGandH, the design problem becomes that of determining the compensator Gc

that satisfies the given specification.

1 +Gc GH= 0

C

R

=

Gc G

1 +Gc GH

G 1 (s) G 2 (s)

H(s)

Gc(s)

Gc(s) G(s)

H(s)

(a)

(b)

+–

+

+

R C

RC

Figure 6–60

(a) Series

compensation;

(b) parallel or

feedback

compensation.

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