# Speed Control of DC Motor

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 ω_{m},

V_{t} = E_{a} + I_{a}R_{a} where E_{a} = Back EMF, I_{a} = Armature current and V_{t} = Supply Voltage

But E_{a} = K_{a}Øω_{m} where K_{a} = constant = PZ/2πa so,

K_{a}Øω_{m} = V_{t} – I_{a}R_{a }

Therefore, ω_{m} = Speed = (V_{t} – I_{a}R_{a}) /K_{a}Ø ………………………………(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.

**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 T_{e} = K_{a}ØI_{a} 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 = V_{t}I_{a}

But,

Power Delivered by Supply = I^{2}(R_{g}+R_{a}) Loss + Output Power of DC Shunt Motor

V_{t}I_{a} = I^{2}(R_{g}+R_{a}) +P_{mo} where P_{mo} = Motor Output

So, P_{mo} = V_{t}I_{a} – I^{2}(R_{g}+R_{a})

But P_{mo} = T_{e}ω_{m}

So, ω_{m} = [V_{t}I_{a} – I^{2}(R_{g}+R_{a})] / T_{e} ……………………..(2)

If we assume that no external series resistance has been connected to armature circuit and operating speed of DC Motor is ω_{m}_{0} then R_{g} = 0 and speed = ω_{m}_{0}

Therefore from equation (2),

ω_{m0} = (V_{t}I_{a} – I^{2}R_{a}) / T_{e} ……………………………………(3)

From equation (2) and (3),

ω_{m}/ ω_{m}_{0} = [V_{t}I_{a} – I^{2}(R_{g}+R_{a})] / (V_{t}I_{a} – I^{2}R_{a}) <1

So, ω_{m} < ω_{m}_{0}

Thus it is clear that speed of DC Shunt Motor reduces. As R_{g} is variable Resistor hence by changing this Resistance R_{g} 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 R_{g}, ohmic loss in this R_{g} 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 R_{g}, 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 R**_{g}:

_{g}:

Assuming the no load speed of DC Shunt Motor = ω_{0} and operating speed at a given Torque Te = ω_{m1} then

_{e}= K

_{a}ØI

_{a}

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.

_{g},

_{t}= K

_{a}Øω

_{m0}+ I

_{a1}(R

_{a}+R

_{s}) where R

_{s}= Field Resistance

_{a}where C is some constant.

_{1}= CI

_{a1}

_{ }

_{t}= K

_{a}CI

_{a1}ω

_{m0}+ I

_{a1}(R

_{a}+R

_{s})

_{a}C = K = Constant

_{t}= KI

_{a1}ω

_{m0}+ I

_{a1}(R

_{a}+R

_{s})

_{m0}= [V

_{t}– I

_{a1}(R

_{a}+R

_{s})] / KI

_{a1}…………………………..(1)

_{t}= K

_{a}Cω

_{m}I

_{a2}+(R

_{a}+R

_{s}+R

_{g})I

_{a2}………………………………..(2)

_{a}Ø

_{1}I

_{a1}= K

_{a}Ø

_{2}I

_{a2}

_{ }

_{a}C(I

_{a1})

^{2}= K

_{a}C(I

_{a2})

^{2}

^{ }

_{a1}= I

_{a2}

_{ }

_{t}= Kω

_{m}I

_{a2}+ (R

_{a}+R

_{s}+R

_{g})I

_{a2}assuming K

_{a}C = K =Constant

_{m}= [V

_{t}– (R

_{a}+R

_{s}+R

_{g})I

_{a2}] / KI

_{a2}………………………………..(3)

_{m}/ ω

_{m0}= [V

_{t}– (R

_{a}+R

_{s}+R

_{g})I

_{a2}] / [Vt – I

_{a1}(R

_{a}+R

_{s})] <1

_{m}< ω

_{m0}

_{ }

Thus the speed of DC Series Motor reduces by adding a Series External resistance R_{g}.

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

As we know that,

T_{e} = K_{a}ØI_{a}

But Ø = CI_{a}

Hence, T_{e} = K_{a}CI_{a}^{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!**

Awesome post.