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)