1. EEEB443 Control & Drives Modeling of DC Machines By
Dr. Ungku Anisa Ungku Amirulddin
Department of Electrical Power Engineering
College of Engineering
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
Dr. Ungku Anisa, July 2008

2. Outline Introduction Theory of Operation Field Excitation
Separately Excited DC Motor
State-Space Modeling
Block Diagrams and Transfer Functions
Measurement of Motor Constants
References
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

3. Introduction DC motor in service for more than a century
Dominated variable speed applications before Power Electronics were introduced
Advantage:
Precise torque and speed control without sophisticated electronics
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

4. Introduction Some limitations: Commonly used DC motors
High maintenance (commutators & brushes)
Expensive
Speed limitations
Sparking
Commonly used DC motors
Separately excited
Series (mostly for traction applications)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

5. DC Machine – Theory of Operation
Field winding - on stator pole
if produces f
Armature winding –on rotor
ia produces a
f and a mutually perpendicular
maximum torque
Rotor rotates clockwise
For unidirectional torque and rotation
ia must be same polarity under each field pole
achieved using commutators and brushes
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

6. DC Machine – Field Excitation
Depends on connections of field winding relative to armature winding
Types of DC machines:
Separately Excited
Shunt Excited
Series Excited
Compounded
Permanent Magnet
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

7. DC Machine – Field Excitation
Separately Excited
Field winding separated from armature winding
Independent control of if (f ) and ia (T)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

8. DC Machine – Field Excitation
Shunt Excited
Field winding parallel to armature winding
Variable-voltage operation complex
Coupling of f (if ) and T (ia) production
T vs  characteristic almost constant
AR = armature reaction
(as T , ia , armature flux weakens main flux  f , )
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

9. DC Machine – Field Excitation
Series Excited
Field winding in series with armature winding
Variable-voltage operation complex
Coupling of f (if ) and T (ia) production
T ia 2 since if = ia
High starting torque
No load operation must be avoided (T = 0,  )
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

10. DC Machine – Field Excitation
Compounded
Combines best feature of series and shunt
Series – high starting torque
Shunt – no load operation
Cumulative compounding
shunt and series field strengthens each other.
 Differential compounding
shunt and series field opposes each other.
Long-shunt connection
Short-shunt connection
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

11. DC Machine – Field Excitation
Permanent Magnet
Field provided by magnets
Less heat
No field winding resistive losses
Compact
Armature similar to separately excited machine
Disadvantages:
Can’t increase flux
Risk of demagnetisation due to armature reaction
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

12. Separately Excited DC Machine+ ea _ La Ra ia vt Lf Rf if + vf _
Field circuit
Armature circuit
Electromagnetic torque
Armature back e.m.f.
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

13. Separately Excited DC Motor
Motor is connected to a load.
Therefore,
where
TL= load torque
J = load inertia (kg/m2)
B = viscous friction coefficient (Nm/rad/s)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

14. DC Machine - State-Space Modeling
DC motor dynamic equations:
Therefore,
(1)
(2)
(3)
(4)
(5)
(6)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

15. DC Machine - State-Space Modeling
From (5) and (6), the dynamic equations in state-space form:
where s = differential operator with respect to time
This can be written compactly as:
(7)
(8)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

16. DC Machine - State-Space Modeling
Comparing (7) and (8):
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

17. DC Machine - State-Space Modeling
The roots of the system are the eigenvalues of matrix A
1 and 2 always have negative real part, i.e. motor is stable on open-loop operation.
(9)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

18. DC Machine – Block Diagrams and Transfer Functions
Taking Laplace transform of (1) and (3) and neglecting initial conditions:
These relationships can be represented in the following block diagram
(10)
(11)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

19. DC Machine – Block Diagrams and Transfer Functions
From the block diagram, the following transfer functions can be derived:
Since the motor is a linear system, the speed response due to simultaneous Va input and TL disturbance is:
The Laplace inverse of (14) gives the speed time response (t).
(12)
(13)
(14)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

20. DC Machine – Measurement of Motor Constants
To analyse DC motors we need values for Ra, La and Kb
Armature Resistance Ra
DC voltage applied at armature terminals such that rated ia flows
This gives the dc value for Ra
Need to also correct for temperature at which motor is expected to operate at steady state
Similar procedure can be applied to find Rf of field circuit
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

21. DC Machine – Measurement of Motor Constants
Armature Inductance La
Apply low AC voltage through variac at armature terminals
Measure ia
Motor must be at standstill (i.e.  = 0 and e = 0)
f = supply frequency in Hz
Ra = ac armature resistance
Similar procedure can be applied to find Lf of field circuit
(variac)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

22. DC Machine – Measurement of Motor Constants
EMF Constant Kb = K
Rated field voltage applied and kept constant
Shaft rotated by another dc motor up to rated speed
Voltmeter connected to armature terminals  gives value of Ea
Get values of ea at different speeds
Plot Ea vs. 
Slope of curve = Kb
Units of Kb = [V/rads-1]
Ea (V)
 (rad/s)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

23. References
Krishnan, R., Electric Motor Drives: Modeling, Analysis and Control, Prentice-Hall, New Jersey, 2001.
Chapman, S. J., Electric Machinery Fundamentals, McGraw Hill, New York, 2005.
Nik Idris, N. R., Short Course Notes on Electrical Drives, UNITEN/UTM, 2008.
Ahmad Azli, N., Short Course Notes on Electrical Drives, UNITEN/UTM, 2008.
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives