dc motor speed control

The term ‘speed control’ here stands for intentional speed variation, carried out manually or automatically.

Dc motor speed control circuit

For the dc motor shown

V_t - I_aR_a=E_b                           .....(1)

and

E_b=P ΦZN/60A                 .....(2)

where, P=number of field poles

Φ=field flux per pole

Z=total number of armature conductors

N=motor speed in rpm

A=number of parallel path

From (1) and (2)

N=(V_t - I_aR_a)/KΦ

where,  K= PZ/60A      ... a constant for a given motor

So, speed depends on armature resistance, field flux and armeture terminal voltage and therefore these factors are varied to control speed of a dc motor.

Before going into the details of speed control methods it necessary to understand some commonly used terms.

Base speed :- is defined as the speed at which motor runs at rated armature voltage and rated field current. It is the nameplate speed of the motor.

Speed Regulation :- is defined as the ratio of speed change from no load to full load to the base speed.

i.e % speed regulation=(No load speed – Full load speed) / Base               speed

The various methods of speed control are explained below one by one.

DC motor speed control by varying armature circuit resistance

 In this method, an external resistance is inserted in series with the armature circuit to obtain speeds below the base speed only.

1.For DC Shunt Motor :-

DC shunt motor speed control   

When there is no armature series resistance then let the armature current be I_a1  and speed N₁

Therefore,  I_a1=(V_t - KΦ N₁)/ R_a

When R_g is inserted in the armature circuit, there will be no instant  change in speed due to inertia of motor and the equation becomes

I_a2=(V_t - KΦ N₁)/ (R_a+ R_g)

    = I_a1 (R_a/(R_a+ R_g))

In a shunt motor, field flux remains unchanged therefore, reduction of armature current from  I_a1 to I_a2  reduces the electromagnetic torque produced by the armature from  KΦ I_a1   to  KΦ I_a2.

Let the load torque be assumed constant during speed control. Therefore, since electromagnetic torque produced by the armature becomes less than load torque and the motor decelerates and consequently, back emf

E_b=P ΦZN/60A  also  decreases. As a result, armature current           

I_a1=(V_t – back emf )/ R_a

Increases till it becomes equal to initial value  I_a1 so that initial electromagnetic torque KΦ I_a1 is developed again.

Initially, N₁=(V_t - I_a1R_a)/KΦ

                 = E_b1/ KΦ                                   ...(1)

After R_g insertion steady state, N₂=(V_t -I_a1(R_a+R_g))/KΦ

                                                      = E_b2/ KΦ    ...(2)

Dividing (1) and (2)

(N₂/ N₁)=( E_b2/E_b1)= (V_t -I_a1(R_a+R_g))/ (V_t - I_a1R_a)

Shows  N₂ is less than N₁

To summarise (for constant load torque) :-

·       Armature current remains same.

·       Power supplied from mains to motor i.e V_t(I_a1+I_f) remains same.

·       Power delivered to armature i.e  E_b1 I_a1   decreases in proportion to the decrease in speed.

·       If R_g is increased to obtain lower speeds, motor efficiency is lowered.

η=power delivered to armature / power supplied by   mains

= 1-[(R_a+ R_g)I_a1/V_t]

Though, with this method creeping speeds of only a few rpm are easily obtainable but because of considerable wastage of energy at reduced speeds this method is used only where short time slow downs are required.

2. DC Series Motor speed control by varying armature resistance:-

Dc series motor speed control by armature resistance variation

From above figure, before adding R_g :-

V_t = KΦ N₁+I_a1(R_a+R_s)               ...K is a constant, K= PZ/60A

If  saturation is neglected, reluctance of field flux path is assumed constant and armature reaction is neglected then field flux is proportional to armature current.

So, above equation becomes

          V_t = KCI_a1N₁+I_a1(R_a+R_s)     ...C is a proportionality constant

∴               N₁= [V_t - I_a1(Ra+R_s)]/K₁I_{a1                                     ...} K₁=KC      ...(1)

After R_g is inserted in series with armature circuit

          V_t = [KCN₂+ (R_a+R_s+R_g)] I_a2

For constant load torque,

        KΦ₁I_a1= KΦ₂I_a2

or    KC I_a1²= KC I_a2²

or           I_a1= I_a2

∴            V_t = K₁I_a1N₂+I_a1(R_a+R_s+R_g)                

or     N₂= [V_t - I_a1(Ra+R_s+R_g)]/K₁I_a1              ...(2) 

dividing  (1) and(2)

N₂/N₁= [V_t - I_a1(Ra+R_s+R_g)]/ [V_t - I_a1(Ra+R_s)]

          =E_b2/ E_b1

The  armature circuit resistance control method suffers from  poor speed regulation. This drawback is overcome by using shunted armature method where instead of inserting resistance is series with armature, it is put in parallel with armature.

DC Motor Speed control by varying field flux :-

This method is also called field weakening method. It gives speeds above the base speed only.

1.DC Shunt Motor Speed control by varying flux :-

DC shunt motor speed control by field weakening method

The arrangement of connections is shown above. If field circuit resistance is increased, the field current and the flux per pole decrease. The motor speed cannot change suddenly due to inertia, therefore back emf reduces.

As,    I_a=(V_t – back emf )/ R_a

So, armature current increases. The percentage increase in I_a  is much more than percentage ddecrease in field flux. In view of this, the electromagnetic torque is increased and becomes greater than load torque, the motor get accelerated. Now, the back emf rises and I_a starts decreasing till torque reduce to again become equal to load torque.

Let armature current be I_a1 for flux Φ₁ and I_a2 for flux Φ₂ , then for constant load torque

        I_a1 = T_e/KΦ₁

     N₁=(V_t - I_a1R_a)/KΦ₁      ....(1)

and   

            I_a2 = T_e/KΦ₂ 

     N₂=(V_t - I_a2R_a)/KΦ₂      ....(2)

Also,   I_a1 Φ₁ = I_a2 Φ₂ =T_e=T_L

So, the new speed N₂ will be higher.

DC motor speed control by varying armature terminal voltage

(1)This method of speed control needs a variable source of voltage separated from the source supplying the field current. This method avoids disadvantages of poor speed regulation and low efficiency of armature-resistance control methods. 
(2)It is used to get speeds below base speed.

    Ward-leonard method is widely used.


Closely related :-
  (1) DC Motor Torque equation