modeling of system electromechanical, Armature Controlled D.C Motor -Reduced Order Field Controlled D.C Motor

Armature Controlled D.C Motor
-Reduced Order
Field Controlled D.C Motor

1. Modeling of Electromechanical System Electrical and Mechanical System Basics Armature Controlled D.C Motor -Reduced Order Field Controlled D.C Motor 1

2. Electrical System 2 Component Laplace V-I Relation I-V Relation Resistor R Capacitor Inductor

3. Basic motion concepts v   adt ; x   vdt ; dt f  d  mv   ma N dt T  d  J    J  Nm J , Moment of inertia For rotational systems     dt ;     dt For translational systems 3 ..

4. Mechanical Translational 4

5. 5 Mechanical - Rotational

6. Mechanical Subsystem Input : voltage u Output : Angular velocity  Electrical Subsystem (loop method): Armature Controlled D.C Motor u i a T R a L a J  B e b V f =constant 6

7. Torque-Current: Voltage-Speed: Combing previous equations results in the following mathematical model: Power Transformation : Armature Controlled D.C Motor u i a T R a L a J  B e b V f =constant 7

8. Taking Laplace transform of the system’s differential equations with zero initial conditions gives: Eliminating I a yields the input-output transfer function Armature Controlled D.C Motor 8

9. Reduced Order Model Assuming small inductance, L a 0 Armature Controlled D.C Motor 9

10. If output of the D.C motor is angular position θ then we know Which yields following transfer function Armature Controlled D.C Motor u i a T R a L a J θ B e b V f =constant 10

11. Applying KVL at field circuit Field Controlled D.C Motor i f T m R f L f J ω B R a L a e a e f Mechanical Subsystem 11

12. Torque-Current : Combing previous equations and taking Laplace transform (considering initial conditions to zero) results in the following mathematical model: Power Transformation : where K f : torque constant Field Controlled D.C Motor 12

13. If angular position θ is output of the motor Eliminating I f (S) yields Field Controlled D.C Motor i f T m R f L f J θ B R a L a e a e f 13