Speed Control in DC Motors
Speed Control in DC Motors
Shunt motor:
Electromagnetic torque is Te=Ka fd Ia, and the conductor emf is Ea=Vt - RaIa.
 Te
K a f d  m  V t  
 K afd
m 
Vt
K afd


 R a

Te R a
K afd 
1 
2
For armature voltage control: Ra and If are constant
2 
 m  K 1V t  K 2Te
For field control: Ra and Vt are constant
m 
Vt
K
f
I

f
Ra
K f I f 
2
Te
3 
For armature resistance control: Vt and If are constant
m 
Vt
K afd

R a  R adj
K afd 
2
Te
4 
Speed Control in Shunt DC Motors
Armature Voltage Control:
Ra and If are kept constant and the armature
terminal voltage is varied to change the motor
speed.
 m  K 1V t  K 2 T e
K1 
1
K afd
;
K2 
1
K afd 
2
; f d is const .
For constant load torque, such as applied by an
elevator or hoist crane load, the speed will
change linearly with Vt. In an actual
application, when the speed is changed by
varying the terminal voltage, the armature
current is kept constant. This method can also
be applied to series motor.
Speed Control in Shunt DC Motors
Field Control:
Ra and Vt are kept constant, field rheostat is varied to
change the field current.
m 
Vt
K
f
I

f
Ra
 K f I f 2
Te
For no-load condition, Te=0. So, no-load speed varies
inversely with the field current.
Speed control from zero to base speed is usually
obtained by armature voltage control. Speed control
beyond the base speed is obtained by decreasing the field
current. If armature current is not to exceed its rated
value (heating limit), speed control beyond the base
speed is restricted to constant power, known as constant
power application.
P  V t I a  const  E a I a  T e  m
Te 
Ea Ia
m

const .
m
Speed Control in Shunt DC Motors
Armature Resistance Control:
Vt and If are kept constant at their rated value,
armature resistance is varied.
m 
Vt
K afd

R a  R adj
K afd 
2
Te  K 5  K 6Te
The value of Radj can be adjusted to obtain
various speed such that the armature current Ia
(hence torque, Te=KafdIa) remains constant.
Armature resistance control is simple to
implement. However, this method is less
efficient because of loss in Radj. This resistance
should also been designed to carry armature
current. It is therefore more expensive than the
rheostat used in the field control method.
Speed Control in Series DC Motors
Armature Voltage Control:
A variable dc voltage can be applied to a series motor to
control its speed. A variable dc voltage can be obtained
from a power electronic converter.
fd  K s Ia
V t  E a  I a  Ra  R s 
 K a f d  m  I a  Ra  R s 
 K a  K s I a  m  I a  R a  R s 
Ia 
Vt
K a K s  m  Ra  R s
Torque in a series motor can be expressed as
2
Te  K a f d I a  K a K s I a

K
K a K sV t
a K s m
or ,  m 
2
  Ra  R s 
Vt
Te K a K s

2

Ra  R s
KaKs

Vt
Te K a K s
Speed Control in Series DC Motors
Field Control:
Control of field flux in a sries motor is achieved by
using a diverter resistance.
The developed torque can be expressed as.

Rd
T e  K a f d I a  K a K s 
 R s  Rd
where , K  K a K s and  
Vt  E a
 R s Rd
 
 R s  Rd
 2
 I a  K  I a2

Rd
R s  Rd

 I a  I a R a

 K a f d  m  I a R s  I a Ra
 K a  K s  I a  m    R s  R a  I a
  K  m   R s  R a  I a
or , I a 
Vt
K  m   R s  R a
Speed Control in Series DC Motors


Vt

T e  K  
K



R

R

m
s
a 
2
Speed Control in Series DC Motors
Armature Resistance Control:
Torque in this case can be expressed as
Te 
 R a  R adj
KV t
2
 Rs  K m
2
Rae is an external resistance connected in series with
the armature.
For a given supply voltage and a constant developed
torque, the term (Ra+Rae+Rs+Km) should remain
constant. Therefore, an increase in Rae must be
accompanied by a corresponding decrease in m.
 R a  R adj
 Rs  K m

2

KV t
Te
or , R a  R adj  R s  K  m 
or ,  m 
Vt
KT e

2
K
Te
Vt
R a  R adj  R s
K
Power Division in DC Machines
DC Generator
Input from
Arm. copper loss
Ia2Ra+brush contact
loss
Arm. terminal
Elec-
prime-
magnetic
power = Vta Ia
Output power
= V t IL
mover
Power =EaIa
No-load rotational loss
Series field loss IL2Rs
(friction
+shunt field loss If2Rf
+windage+core)+stray load
loss
Arm. copper loss
Ia2Ra+brush contact
loss
Input power
Arm. terminal
ElecOutput
DC Motor
from mains =Vt
power = Vta Ia
IL
Series field loss IL2Rs
+shunt field loss If2Rf
magnetic
available at the
Power =EaIa
shaft
No-load rotational loss
(friction
+windage+core)+stray load
loss
Efficiency

Power Output
Power

Power
Input
Input  Losses
Power
 1
Input
Losses
Power
Input
The losses are made up of rotational losses (3-15%), armature
circuit copper losses (3-6%), and shunt field copper loss (1-5%).
The voltage drop between the brush and commutator is 2V and
the brush contact loss is therefore calculated as 2Ia.
DC Machines Formulas
Problem 9-1 to 9-7 (Page 621)
Solution to Problem 9-1 (Page 621)
Solution to Problem 9-2 (Page 621)
Solution to Problem 9-5 (Page 621)
Problem 9-13 (Page 623)
Solution to Problem 9-13 (Page 623)
Solution to Problem 9-13 (Page 623)
The End