1. Dr. Syed Saad Azhar Ali saadali@mail.au.edu.pk Control Systems Dr. Syed Saad Azhar Ali

2. saadali@mail.au.edu.pk 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.

3. Dr. Syed Saad Azhar Ali saadali@mail.au.edu.pk DC motor

4. Dr. Syed Saad Azhar Ali saadali@mail.au.edu.pk Continued… The air-gap flux of the motor is proportional to the field current,provided the field is not saturated, so that

5. Dr. Syed Saad Azhar Ali saadali@mail.au.edu.pk Continued… The torque developed by the motor is assumed to be related linearly to Φ and the armature current

6. Dr. Syed Saad Azhar Ali saadali@mail.au.edu.pk Continued… Field Controlled DC motor

7. Dr. Syed Saad Azhar Ali saadali@mail.au.edu.pk Continued… Field Controlled DC motor Now considering… And finding the Laplace Transform

8. Dr. Syed Saad Azhar Ali saadali@mail.au.edu.pk The back electromotive-force voltage which is induced to oppose the input voltage to the armature is (for a constant field)

9. Dr. Syed Saad Azhar Ali saadali@mail.au.edu.pk Continued… Field Controlled DC motor The field current is related to the field voltage as

10. Dr. Syed Saad Azhar Ali saadali@mail.au.edu.pk Continued… Field Controlled DC motor The motor torque T m (s) is equal to the torque delivered to the load. This relation may be expressed as

11. Dr. Syed Saad Azhar Ali saadali@mail.au.edu.pk 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

12. Dr. Syed Saad Azhar Ali saadali@mail.au.edu.pk Block Diagram

13. Dr. Syed Saad Azhar Ali saadali@mail.au.edu.pk Assignment 1 Part II Obtain the TF for the Armature Controlled DC motor along with its block Diagram