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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**DC Machine - State-Space Modeling**

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

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**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

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**DC Machine - State-Space Modeling**

Comparing (7) and (8): Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**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

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**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

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**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

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**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

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**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

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**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

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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

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