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What are the speed control methods of dc motor?
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There are three types for controlling the speed of DC motor.

1. By field control

2. By armature control

3. By voltage control

1.Field control of DC motor :-  

In field control of DC motor terminal voltage is kept constant.
The field flux (_) is directly proportional to the field current (_) { _∝_ }. 
Speed (N) is inversely proportional to field flux (_) { N ∝/_  }.
So as the field flux (_) will be less speed (N) will be more.
If the current is less field flux (_)  is less hence the speed (N) will be more.
We can control speed by field diverter method or by using tapped field control.

2.Armature control of DC motor :- 
For controlling speed through armature external resistance is used in armature.
 By adding variable resistance to armature the armature current is reduced hence the speed is reduced.
More the resistance more the decrease in speed.

_=" " /60

_ is the back emf.
is the flux.
Z is the Number of armature conductors.
N is the speed.
P is the Number of poles.
A is the number of parallel paths.

_=V-_" "  _
V is the voltage.
_" " is the armature current.
_ is the armature resistance.

_=" " /
So the _ is directly proportional to and N.
N∝ _/
N∝("V−" _" "  _)/
From the equation it is seen that rotor speed is depend on voltage and field current.
So by varying field current by variable armature resistance we can control the speed of the DC motor.
We can also control speed by varying terminal voltage but it is rarely used because of high cost.

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