0195136047.pdf

800 BASIC CONTROL SYSTEMS

excited dc motor. A simplified schematic diagram of such a system is shown in Figure E16.2.3(a),

in which the tachometer, error detector, and amplifier are represented functionally rather than by

electric circuit connections. Assume the motor field current is held constant, the load torque is

ignored, and the generator speed is held constant under all conditions of operation.

Determine the transfer functionso/Egando/Ee, and develop a block diagram for the

system.

(a)

(b)

if

ia

ef

Rf Lf

Generator

field

Constant

field

Tachometer

ωg = constant

Rag + Ram

= Re

Lag + Lam

= Le

+

−

Speed

Reference

voltage er

efb = Kωω 0 Bm, Jm

Td

ee

eg em

Amplifier

Ka

−

Rf + sLf (Ra + sLa) (Bm + sJm) + K^2 m

K Ω

a

Kg Km

Kω

Ee Ef Eg

Efb

ER

ω 0

Figure E16.2.3(a)Schematic representation of a simplified Ward–Leonard dc motor control.(b)Block

diagram of (a).

Solution

For the dc generator with constant speed, we have

ef=ifRf+Lf

dif

dt

eg=Kgif

whereKgis a constant, and

Eg(s)

Ef(s)

=

Kg

Rf+sLf

The differential equation in the armature circuits is given by

eg=iaRe+Le

dia

dt

+em (1)

where

em=Kmωo (2)