DC Motor speed control means
to have full control on the speed of DC Motor. The variation in speed of DC
Motor because of variation in load is not the speed control. Therefore
intentional variation in speed of DC Motor is called Speed Control.

As we know that for a DC
Motor having armature resistance Ra, rotating at some speed Wm,

Vt = Ea + IaRa where Ea = Back EMF, Ia = Armature current
and Vt = Supply Voltage

But Ea = KaØWm where Ka =
constant = PZ/2πa so,

KaØWm = Vt - IaRa

Therefore, Wm = Speed = (Vt
- IaRa) /KaØ ………………………………(1)

From equation (1), it is
clear that speed of a DC Motor can be controlled by the following methods:

- By varying the Armature circuit resistance

- By changing the field flux

- By varying the armature terminal voltage i.e. supply voltage.

We will discuss the first
method of speed control i.e. by changing the Armature circuit resistance for DC
Shunt Motor in this post. I will post on other methods, so be there.

**Speed Control by Varying the Armature Circuit Resistance:**

This method is called
Armature Circuit Resistance Control method. In this method intentionally an
external resistance is inserted in the Armature circuit of DC Motor. As an
external resistance is added, hence there will be power loss in this resistance
due to which the speed of DC motor will be less than its Name Plate speed or
base speed.

Power input = Loss in External
Resistance + Power Output of Motor, neglecting Motor losses.

So output power of DC Motor
will reduce.

**Therefore, by Armature Circuit Resistance Control method only speed below base speed can be obtained.**

**Speed Control of DC Shunt Motor by Armature Circuit Resistance Control Method:**

The connection diagram for
speed control of DC Shunt Motor using Armature Circuit Resistance Control
method is shown in figure below. As shown in figure an External variable
Resistance Rg is connected in series with the Armature circuit, called
Controller.

Assuming
a constant Torque drive, the torque requirement of the drive will be constant.
But Te = KaØIa so DC Shunt Motor will take constant armature current Ia to meet
the constant torque requirement from the supply main as field flux Ø remain
constant.

Therefore Power delivered by the supply main to the DC Shunt
Motor = VtIa

But,

Power Delivered by Supply = I

^{2}(Rg+Ra) Loss + Output Power of DC Shunt Motor
VtIa = I

^{2}(Rg+Ra) +Pmo where Pmo = Motor Output
So, Pmo = VtIa - I

^{2}(Rg+Ra)
But Pmo = TeWm

So, Wm = [VtIa - I

^{2}(Rg+Ra)] / Te ……………………..(2)
If
we assume that no external series resistance has been connected to armature
circuit and operating speed of DC Motor is W

_{m0}then Rg = 0 and speed = W_{m0}_{}

Therefore from equation (2),

W

_{m0}= (VtIa - I^{2}Ra) / Te ……………………………………(3)
From equation (2) and (3),

Wm/ W

_{m0}= [VtIa - I^{2}(Rg+Ra)] / (VtIa - I^{2}Ra) <1
So, Wm < W

_{m0}_{}

Thus
it is clear that speed of DC Shunt Motor reduces. As Rg is variable Resistor
hence by changing this Resistance Rg we can have full control of speed of DC
Shunt Motor. It is also clear that as we increase the value of External Series
Resistor Rg, ohmic loss in this Rg will increase and hence the output of DC
Motor will reduce which in turn will result in decreased speed.

It
shall also be noted that as we increase the value of Rg, the efficiency of DC
Shunt Motor will reduce as the output power of DC Motor is reducing.

**Speed Torque Characteristics of DC Shunt Motor for Different Value of Rg:**

Assuming
the no load speed of DC Shunt Motor = W

_{0}and operating speed at a given Torque Te = Wm1 then
Te =
KaØIa

So from
equation (2) it is clear that we increase the value of External Series Resistance
Rg, operating speed of DC Shunt Motor will decrease proportionally as shown in
figure below.

**Speed Control of DC Series Motor by Armature Circuit Resistance Control Method:**

I will discuss this method
for DC Series Motor by conventional way as you will find in most of the books
but you can proceed in the same way as discussed for DC Shunt Motor.

The connection diagram for speed
control of DC Series Motor by Armature Circuit Resistance Control Method is
shown below.

Before the introduction of External
Series Resistor Rg,

Vt = KaØW

_{m0}+ I_{a1}(Ra+Rs) where Rs = Field Resistance
If we assume no saturation
then filed flux Ø will be proportional to the Armature current Ia. Therefore we
can write,

Ø = CIa where C is some
constant.

In our case, Ø1 = CI

_{a1}_{}

Therefore,

Vt = KaCI

_{a1}W_{m0}+ I_{a1}(Ra+Rs)
Let KaC = K = Constant

So,

Vt = KI

_{a1}W_{m0}+ I_{a1}(Ra+Rs)
Hence, W

_{m0}= [Vt - I_{a1}(Ra+Rs)] / KI_{a1}…………………………..(1)
After the insertion of
External Series Resistance Rg,

Vt = KaCWmI

_{a2}+(Ra+Rs+Rg)I_{a2}………………………………..(2)
For constant Torque Load, Torque
= Constant

KaØ1I

_{a1}= KaØ2 I_{a2}_{}

KaC(I

_{a1})^{2}= KaC(I_{a2})^{2}^{}

Hence, I

_{a1}= I_{a2}_{}

Therefore for constant
Torque Load DC Series Motor will take same Armature Current from the supply
main as in case of DC Shunt Motor.

From equation (2),

Vt = KWmI

_{a2}+ (Ra+Rs+Rg)I_{a2}assuming KaC = K =Constant
So,

Wm = [Vt - (Ra+Rs+Rg)I

_{a2}] / KI_{a2}………………………………..(3)
From equation (1) and (3),

Wm/ W

_{m0}= [Vt - (Ra+Rs+Rg)I_{a2}] / [Vt - I_{a1}(Ra+Rs)] <1
Therefore, Wm < W

_{m0}_{}

Thus the speed of DC Series
Motor reduces by adding a Series External resistance Rg.

**Speed Torque Characteristics of DC Series Motor for Different Value of Rg:**

As
we know that,

Te =
KaØIa

But Ø
= CIa

Hence,
Te = KaCIa

^{2}^{}

So from
equation (3) it is clear that we increase the value of External Series Resistance
Rg, operating speed of DC Series Motor will decrease as shown in figure below.

**Hope you enjoyed this post. Your suggestion and feedback is very important to me. Thank you!**

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