0195136047.pdf

16.2 FEEDBACK CONTROL SYSTEMS 799

and a common voltageea. An analog electric circuit can then be drawn as in Figure E16.2.1(d) for

a separately excited dc motor, in which the inertia is represented by a capacitance, the damping

by a shunt conductance, and the load–torque component of current is shown flowing through an

equivalent impedanceZL. The time constants,τiassociated with inertia andτmassociated with the

damping-type load torque that is proportional to speed (in terms of the analog-circuit notations),

are given by

τi=RaCeq and τm=Ceq/Geq (16)

Note in the preceding analysis thatKmis proportional to the constant motor field currentIf.

The self-inductance of the armature can often be neglected except for a motor driving a load

that has rapid torque pulsations of appreciable magnitude.

EXAMPLE 16.2.2

A voltage amplifier without feedback has a nominal gain of 500. The gain, however, varies in
the range of 475 to 525 due to parameter variations. In order to reduce the per-unit change to
0.02, while maintaining the original gain of 500, if the feedback is introduced, find the new direct
transfer gainGand the feedback factorH.

Solution

IfG′is the gain without feedback, it follows that

∂G′

G′

=

525 − 475

500

= 0. 1

From Equation (16.2.7),

∂M

M

=

∂G

G

(

1

1 +HG

)

= 0. 02 (1)

whereGstands for the new transmission gain with feedback. Also, from Equation (16.2.3),

M=

G

1 +HG

= 500 (2)

From Equation (1),

1 +HG=

0. 1

0. 02

= 5 (3)

Substituting Equation (3) into Equation (2), one obtains

G= 500 ( 1 +HG)= 500 ( 5 )= 2500

and from Equation (3),

H=

5 − 1

2500

= 0. 0016

EXAMPLE 16.2.3

The Ward–Leonard system, which is used in the control of large dc motors employed in rolling
mills, is a highly flexible arrangement for effecting position and speed control of a separately