## Introduction:

We usually want to know about the Speed Control of DC Motor. Today I’ m going to list all the methods that are used to control the speed of DC motors. There are three common and effective methods of controlling the speed of DC motors. We can simply control the speed of the motor by adjusting the magnitude of current in the Armature and Field Winding. We can change the current by various methods, the commonly used and effective methods for the Speed Control of DC Motor are,

- Field Flux Control (By changing the Field Resistance)
- Armature Voltage Control (By changing the Terminal Voltage)
- Armature Current Control (By changing the Armature Resistance)

Before we jump into Speed Control of DC Motor please read about different types of motors on the basis of the arrangement of Field and Armature Winding (Click here to read). All of them have different circuits and behaviors as well. Therefore, all the above mentioned three methods do not apply to all the types. The type may be affected by one or two of the three methods. We will discuss this in detail but before that let’s understand the three methods on a simple DC motor.

I have discussed the equivalent circuit of a DC Motor in my last article (Click here to read).

Where,

E_{A} = Internally generated EMF

L_{F} = Field Inductance

R_{F} = Field Resistance

R_{A} = Armature Resistance

The equation of Armature loop can be written as,

Where V_{T} is the terminal voltage.

### Field Flux Control (By changing the Field Resistance):

Speed Control of DC Motor can be controlled by this method. In this method, we will control the speed of the motor by controlling the magnetic flux produced by Field Winding. The Flux in the Field winding is directly proportional to the Field Current and the Field Current is inversely proportional to the Field Resistance (R_{F}). i.e,

Hence, we can decrease the Flux by increasing the Field Resistance and vice versa. We have seen how we can control the flux. Let’s see the effect of Flux on the speed on Motor. For instance, consider we have increased the Field Resistance (R_{F}) which will decrease the Field Current and Flux.

As we know,

Where,

E_{A} = Internally generated EMF

ω = Speed of Armature (Rotor)

ф = Magnetic Flux

K = Motor Constant

#### Working:

By decreasing the magnetic flux, the internally generated emf (E_{A}) is decreased.

Now by rearranging the eq(1), we get,

We have decreased the internally generated emf (E_{A}), which will increase the Armature Current. The Armature Current will affect the induced torque (T_{ind}) which can be given as,

Therefore, the increase in the Armature Current will increase the induced torque (T_{ind}). The motor is connected with the load. The load torque (T_{load}) is constant, therefore, the increase in the induced torque (T_{ind}) will increase the speed (ω) of the motor. This increase in speed will increase the internally generated emf (E_{A}) which can be seen from eq(2). The increase in the internally generated emf (E_{A}) will decrease the Armature Current (eq 3). This results in the reduction of torque to such extent that the induced torque becomes equal to the load torque. Now both the torques are equal. The motor is now in steady-state and the motor has greater speed than before.

#### Effect of Flux and Armature Current on Induced Torque:

One important thing to notice here is that we have decreased flux which increases the Armature Current. As we know that the torque induced is directly proportional to both Flux and Armature Current. Since we have decreased the Flux, which increases Armature Current, both the quantities are changed. Now the question is, what will be the effect on Torque induced? either it should increase or decrease. The answer is, Torque induced will increase because the change in current will dominate the change in flux.

From the whole discussion, we can conclude that the Flux is inversely proportional to speed(ω). We can change the flux by varying the Field current through variable Field Resistance(R_{F}).

This method is used when we want to run a motor above the base speed. The reason is that we can increase the resistance easily. The second reason is that if we try to run a motor at speed lower than the base speed we need to decrease the resistance. By decreasing the Field Resistance, the Field current will increase which can damage the winding. Therefore, this method is used to drive motor at a speed higher than the base speed. To make the speed higher we just need to increase the resistance and due to an increase in resistance, the current is lowered which will not damage the winding.

### Armature Voltage Control (By changing the Terminal Voltage):

This is the most common method of Speed Control of DC Motor. The armature voltage can be changed by increasing the terminal voltage, the effect of changing the terminal voltage can be seen from this equation,

This means by increasing the terminal voltage, the Armature current will increase and by decreasing it the Armature current will decrease.

Let’s consider the case that the Voltage is increased which will increase the Armature current. This increase in Armature current will increase the Torque induced as,

The load is constant and the torque induced is increased due to an increase in the current. The speed (ω) of the motor will increase. This increase in the speed of the motor will increase the internally generated emf (E_{A}) given by eq (2). i.e

Now by seeing eq (3), we can say that due to the increase in E_{A} the armature current will decrease which will further decrease the torque induced. The induced torque is reduced until it becomes equal to the load torque. At this stage, the motor will come in steady-state and working at a higher speed.

In short, we can say that the speed (ω) is directly proportional to the terminal voltage (V_{T}).

We use this method to run the motor below the base speed. This method can also increase the speed by increasing terminal voltage but over-voltage can damage the insulation of winding. Therefore, we can only increase the voltage to some extent. Voltage can be lowered easily and it will not damage the winding as well. Therefore, this method is usually used to run the motor at a speed lower than the base speed. It can also be used to increase the voltage but we have to take care of insulation.

### Armature Current Control (By changing the Armature Resistance):

In this method, we need to change the Armature Resistance (R_{A}). The change in resistance will change the current in the armature. We have seen how a change in armature current changes the speed. By increasing resistance, the Armature current is decreased. Due to a decrement in armature current, the speed will also decrease. This method can be used to decrease the speed of the motor below the base speed. The problem with this method is that the increase in resistance will increase power losses. This can be used if the motor runs at the base speed most of its time and only for a short time slow speed is required. Further, this method is inexpensive while slowing down the speed with Armature Voltage control will much expensive.

## Speed Control of DC Motors:

We will discuss all the methods of Speed Control of DC Motor, which are,

- Shunt and Separately Excited DC Motors
- Series Motor
- Cumulatively Compounded DC Motors

### 1) Shunt and Separately Excited DC Motors:

We are again discussing these two types of motor together. I have mentioned the reason behind this in my previous post (Click here to read). The reason was that both motors possess the same characteristics. These motors can be controlled by the three methods. We use Armature Voltage and Field Control Method in common to control these motors. As describe above Armature resistance method increases losses, therefore, it is not commonly used. Let’s discuss the methods one by one.

##### i) By Field Control Method:

We can easily insert a variable resistance in the Field Winding of Separately Excited Motors. The equivalent circuit will be as,

In Shunt DC Motors the Variable Resistance inserted as,

We use this method to increase the speed of these motors above the base speed. The problem with this method is that when we increase the resistance, the slope becomes steeper. Due to this, after a particular value of induced torque, the speed will decrease rather than increasing. We need to keep track of that value of induced torque and speed will not increase after that value of induced torque. This can be better explained by seeing the graph below,

We can see from the above graph, by increasing the resistance the line becomes steeper. R2 > R1, by increasing the resistance to R2, the speed increases. There is an increase in speed increases until a specific point which is the intersection point in the graph. After this point, the speed will decrease.

It is clear that no-load speed is increased and near to stall condition, the speed decreases. This method is not suitable for small motors because they operate at speed near to stall conditions. This method can decrease the speed of such motors.

##### ii) By Armature Voltage Control Method:

We can apply a variable DC supply to change the voltage level. Here Armature Voltage (V_{A}) is equal to V_{T}. In Separately Excited Motor it will be as,

In Shunt Motors it can be applied as,

Here a separated variable DC source is given which can alter the Armature Voltage while the Field Voltage is not affected.

As we have discussed that this method is usually used to run a motor lower than the base speed. In this method, the slope of the curve remains constant. It can be seen from the following diagram,

##### iii) By Armature Current Control:

The armature current control is obtained by varying the Armature Resistance. In Separately excited motors the equivalent circuit can be given as,

The equivalent circuit of shunt motors will be,

As stated above this method will increase the losses. The curve becomes steeper and the speed decreases rapidly as the resistance is increased.

### 2) Series DC Motor:

DC series motor is controlled by the Armature Voltage method only. The problem with Armature Current and Flux method is that both of them need a change in resistance. In the Flux control method speed is inversely proportional to resistance. While in Armature current control the speed is inversely proportional to the resistance. We insert a variable resistor in series with the armature and field circuit. The problem with the Series motor is that both filed and armature are in series. If we insert resistance for armature current then this resistance will affect the Field flux as well. As we know both the methods show different behavior of speed on changing resistance, this method is not feasible. Further, inserting a variable resistance will increase losses. We can simply control the speed by the Armature Control method. The armature voltage is controlled by changing the Terminal Voltage. The circuit will be as,

### 3) Cumulatively Compounded Motor:

We know that these motors have both series and shunt fields. These can be controlled through all three methods.

##### i) By Field Control Method:

We can control it by Field Resistance method as,

Here we have made the parallel field resistor as a variable. Because it will not affect the current in the other branch is connected in parallel. I have discussed the benefit of a shunt connection in my previous article (Click here to read). We cannot change the series field resistor as it will change the armature current as well. We have discussed this problem in Series Motors.

##### ii) By Armature Voltage Control Method:

We can also change the speed by this method as,

The variable supply will change the Armature voltage and Field Voltage as well. But the effect of Armature voltage will be dominant.

##### iii) By Armature Current Control Method:

The current can be controlled by inserting a resistor in the series with the Armature Winding. As discussed above this resistor will increase losses.

## Conclusion:

We have studied the different types of Speed Control of DC Motor. These methods are applied on the basis of motor and the required speed control. Every method has its advantages and disadvantages.