We know that the speed of shunt motor is given by:

where, Va is the voltage applied across
the armature and φ is the flux per pole and is proportional to the field
current If. As explained earlier, armature current Ia is decided by the
mechanical load present on the shaft. Therefore, by varying Va and If we can
vary n. For fixed supply voltage and the motor connected as shunt we can vary
Va by controlling an external resistance connected in series with the armature.
If of course can be varied by controlling external field resistance Rf
connected with the field circuit. Thus for .shunt motor we have essentially two
methods for controlling speed, namely by:

### 1. varying armature resistance.

### 2. varying field resistance.

###
__Speed
control by varying armature resistance __

__Speed control by varying armature resistance__

The
inherent armature resistance

*r*being small, speed_{a }*n*versus armature current*I*characteristic will be a straight line with a small negative slope In the discussion to follow we shall not disturb the field current from its rated value. At no load (i.e.,_{a }*I*= 0) speed is highest and Note that for shunt motor voltage applied to the field and armature circuit are same and equal to the supply voltage_{a }*V*. However, as the motor is loaded,*I*drop increases making speed a little less than the no load speed_{a}r_{a }*n*_{0}. For a well designed shunt motor this drop in speed is small and about 3 to 5% with respect to no load speed. This drop in speed from no load to full load condition expressed as a percentage of no load speed is called the*inherent speed regulation*of the motor.
It is for this reason, a
d.c shunt motor is said to be practically a constant speed motor (with no
external armature resistance connected) since speed drops by a small amount
from no load to full load condition.

Since eT=kI φ, for
constant φ operation, Te becomes simply proportional to Ia. Therefore, speed
vs. torque characteristic is also similar to speed vs. armature current
characteristic

The slope of the n vs Ia or n vs Te characteristic can be modified by
deliberately connecting external resistance rext in the armature circuit. One
can get a family of speed vs. armature curves for various values of rext. From
these characteristic it can be explained how speed control is achieved. Let us assume that the load torque TL is constant and field current is also kept
constant. Therefore, since steady state operation demands Te = TL, Te = akIφ
too will remain constant; which means Ia will not change. Suppose rext = 0,
then at rated load torque, operating point will be at C and motor speed will be
n. If additional resistance rext1 is introduced in the armature circuit, new
steady state operating speed will be n1 corresponding to the operating point D.
In this way one can get a speed of n2 corresponding to the operating point E,
when rext2 is introduced in the armature circuit. This same load torque is
supplied at various speed. Variation of the speed is smooth and speed will
decrease smoothly if rext is increased. Obviously, this method is suitable for
controlling speed below the base speed and for supplying constant rated load
torque which ensures rated armature current always. Although, this method provides
smooth wide range speed control (from base speed down to zero speed), has a
serious draw back since energy loss takes place in the external resistance rext
reducing the efficiency of the motor

__Speed control by varying field current__

In this method field circuit resistance is
varied to control the speed of a d.c shunt motor. Let us rewrite .the basic
equation to understand the method

If we vary

*I*, flux φ will change, hence speed will vary. To change_{f}*I*an external resistance is connected in series with the field windings. The field coil produces rated flux when no external resistance is connected and rated voltage is applied across field coil. It should be understood that we can only decrease flux from its rated value by adding external resistance. Thus the speed of the motor will rise as we decrease the field current and speed control above the_{f }*base*speed will be achieved. Speed versus armature current characteristic for two flux values φ and 1φ. Since 1<φφ, the no load speed*'on*for flux value 1φ is more than the no load speed*n*corresponding to φ. However, this method will not be suitable for constant load torque._{o }
To
make this point clear, let us assume that the load torque is constant at rated
value So
from the initial steady condition, we have 1=L ratedea ratedT=TkIφ. If load
torque remains
constant and flux is reduced to 1φ, new armature current in the steady state is obtained
from 11aL ratekI=T φ. Therefore new armature current is

But
the fraction,1 1>φφ; hence new armature current will be greater than the
rated armature current and the motor will be overloaded. This
method therefore, will be suitable
for a load whose torque demand decreases with the rise in speed keeping the output
power constant Obviously this method is
based on flux weakening of the main field. Therefore at higher speed
main flux may become so weakened, that armature reaction
effect will be more pronounced causing problem in commutation

###
__Speed
control by armature voltage variation__

In
this method of speed control, armature is supplied from a separate variable d.c voltage
source, while the field is separately excited with fixed rated voltage . Here
the armature
resistance and field current are not varied. Since the no load speed N 0=Va/knφ,
the speed versus Ia characteristic will
shift parallely for different values of Va. As flux remains constant, this
method is suitable for constant torque loads. In a way armature voltage control
method is similar to that of armature resistance control method except that the
former one is much superior as no extra power loss takes place in the armature
circuit. Armature voltage control method is adopted for controlling speed from
base speed down to very small speed as one should not apply across the armature
a voltage which is higher than the rated voltage.

__Ward Leonard method: combination of__*V*and_{a }*I*control_{f }
In
this scheme, both field and armature control are integrated Arrangement for
field control is rather simple. One has to simply connect an appropriate
rheostat in the field circuit for this purpose. However, in the pre power electronic
era, obtaining a

*variable*d.c supply was not easy and a separately excited d.c generator was used to supply the motor armature. Obviously to run this generator, a*prime mover*is required. A 3-phase induction motor is used as the prime mover which is supplied from a 3-phase supply. By controlling thefield current of the generator, the generated emf, hence Va can be varied. The potential divider connection uses two rheostats in parallel to facilitate reversal of generator field current
First the induction motor is started with generator field
current zero (by adjusting the jockey positions of the rheostats). Field supply
of the motor is switched on with motor field rheostat set to zero. The applied
voltage to the motor Va, can now be gradually increased to the rated value by
slowly increasing the generator field current. In this scheme, no starter is
required for the d.c motor as the applied voltage to the armature is gradually
increased. To control the speed of the d.c motor below base speed by armature
voltage, excitation of the d.c generator is varied, while to control the speed
above base speed field current of the d.c motor is varied maintaining constant
Va. Reversal of direction of rotation of the motor can be obtained by adjusting
jockeys of the generator field rheostats. Although, wide range smooth speed
control is achieved, the cost involved is rather high as we require one
additional d.c generator and a 3-phase induction motor of simialr rating as
that of the d.c motor whose speed is intended to be controlled.