Control Systems

Dr. Syed Saad Azhar Ali

Mathematical model and Transfer Function of DC motor

The dc motor is a component that converts direct current (dc) electrical energy into rotational mechanical energy, which is available to drive an external load.

DC motor

Continued…

• The air-gap flux of the motor is proportional to the field current,provided the field is not saturated, so that

Continued…

• The torque developed by the motor is assumed to be related linearly to Φ and the armature current

Continued… Field Controlled DC motor

Continued… Field Controlled DC motor

Now considering…

And finding the Laplace Transform

• The back electromotive-force voltage which is induced to oppose the input voltage to the armature is (for a constant field)

Continued… Field Controlled DC motor

• The field current is related to the field voltage as

Continued… Field Controlled DC motor

• The motor torque Tm(s) is equal to the torque delivered to the load. This relation may be expressed as

Continued… Field Controlled DC motor

• The load torque for rotating inertia is

• Equating Tm(s) to TL(s) and making use of the above equations result in the transfer function

Block Diagram

Assignment 1 Part II

• Obtain the TF for the Armature Controlled DC motor along with its block Diagram