1. DC Machine

2. Content Introduction Elementary DC machine
Voltage and Torque Equations
Basic Type DC Machines
Dynamics characteristics of Magnet Permanent and Shunt DC Motor

3. Introduction DC machines application not widely used
DC generator is replaced by rectifier
DC Motor is still used in lower power :
Shunt DC Motor
Permanent Magnet DC Motor
Brushless DC motor becomes popular and widely used in electric vehicle.

4. Elementary of DC Machine
Stator coil as field winding  source of flux
Rotor coil as armature

5. Voltage Equation Voltage equation for field winding and rotor coil
Flux linkage :
Mutual inductance winding between field winding and armature as a function of Θr :
Θr = 0, π, 2 π,
L= Constant

6. Open circuit voltage

7. DC Machine with paralel winding
out
A and a rotor coil

8. Comutation of DC Machine with permanent magnet
Constant flux is established by magnet permanent
Small dc motor with low power control application

9. Voltage Equation Voltage field and coil winding is rotor speed
is referred as back emf

10. Torque Equation Electromagnetic torque
Torque and rotor speed equation :
J = inertia of the rotor (kg m2 or Js2 )
TL = mechanical load
Bm = mechanical damping ratio (Nms)
Te is positive in direction of θr and direction of TL opposes of Te

11. Basic Type of DC Machine (1)
Separate Winding
Shunt DC Machine

12. Shunt Characteristic

13. Basic Type of DC Machine (2)
Series Winding
Application : traction motor for train or bus, hoists and crane
High starting torque with mechanical load at normal operation

14. Series Characteristic
Torque and speed characteristics

15. Dynamic characteristics of permanent magnet and Shunt DC Machine
Two modes of dynamic operation are of interesting :
Starting from stall
Changing in mechanical load
Constant voltage source

16. Starting characteristics of permanent magnet DC motor
Direct on line starting for small power,
Current starting limitation in large hp motor

17. Dynamic performance during sudden changes in load torque.
DC motor 5 hp , 240 V, 127,7 rpm load 1 kg m2
DC motor 200 hp, 250 V, 600 rpm

18. Time Block Diagram and State Equation
Shunt DC motor
Solving field voltage equation and armature voltage equation:

19. Solving for dωr /dt :
State equation in matrix (vector matrix) :

20. Permanent Magnet DC Motor

21. System Equation :
x = state vector
u = input vector

22. Example For control Design  to express transfer functions between state and input variables.
To derive transfer function between state variables (ia and ωr) and input variables (ia and TL).
Inertia time constant
Second order differential equation in term of ωr:
Coefficient of dumping ratio

23. Finally ,

24. DC shunt Motor Constant Torque
Parameter :
Vt (rated)= 120 V ; Ia (rated) = 10 A ; n = 1200 rpm ; If = 1,6 A
Ra = 0.5 Ω La = 0.01H
Rf = 75 Ω Lf = 0.02 H
Mechanical Load = 50 N
Typical loads include belt conveyors with a fixed loading, extruders, hoists, and mine lifts.

26. Laplace Transform
Parameter dc permanent magnet : 6 V, ra = 7 Ω, LAA = 120 mH
kT = 2 oz.in/A, J = 150 µoz.in.s2 . No load rpm = 3350 rpm
I no load = 0,15 A

28. For step voltage
Inverse Laplace

29. Using euler equation :
Substituting parameter :

30. PR 1-5 ( Urut 1 - 20 ) 6-10 ( Urut 21 – 40) 11-15 ( Urut 41 – 60)

31. Electrical Motor Development
Basic Priciples of Electrical Machine Analysis
DC Machine
Reference Frame Theory
Induction Machine
Synchronous Machine
BLDC Machine