Topic 1 DC motor dynamics

Topic 1 DC motor dynamics - 2011 Edition BinWuProfessor...

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Topic 1 DC Motor Dynamics and Speed Control ELE847 Advanced Electromechanical Systems 2011 Edition Bin Wu Professor Dept of Electrical & Computer Engineering Office: ENG328 Tel: (416) 979 5000 ext: 6484 Email: [email protected] Advanced Electromechanical Systems ELE847 2 Introduction Main Topics 1. Introduction 2. Separately excited DC motors 3. Series DC motors 4. Motor starting 5. Diode rectifiers 6. Thyristor rectifiers 7. Motor speed control (open loop control) 8. Closed loop control with current feedback 9. Control with current and speed feedbacks Objectives 1. To develop DC motor dynamic models 2. To develop dynamic models for power converters 3. To investigate DC motor dynamic performance 4. To analyze and design DC motor speed control system

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Advanced Electromechanical Systems ELE847 3 DC motor classifications DC motor power ratings: a few Watts to a few megawatts (MW) Small size Medium size Large size Introduction Advanced Electromechanical Systems ELE847 4 DC motor steady state model (review) f V f I a V a I f R a R r ω f L r a a K E φω = V f , I f - field voltage and current (dc) V a , I a - armature voltage and current (dc) R f , R a - field and armature winding resistances L f field winding inductance E a induced voltage in armature (back emf) ω r - rotor electric speed K a - Armature constant Φ - Field flux Introduction
Advanced Electromechanical Systems ELE847 5 f V f I a V a I f R a R r ω f L r a a K E φω = Rotor speed: Q: How to adjust the rotor speed? A: By adjusting V a , and I f . φ ω a a r K E = Introduction DC motor steady state model (review) Advanced Electromechanical Systems ELE847 6 DC Motor dynamic model f v f i = a e a v a i f r a r r ω ff L aa L f r af i L ω dt i dL i r v f ff f f f + = Equation for the field circuit (RL circuit) v f , i f field voltage and current r f - field winding resistance L ff - field self inductance Fig 2.3 1 Page77, Textbook Separately Excited DC Motors

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Advanced Electromechanical Systems ELE847 7 DC Motor dynamic model f v f i = a e a v a i f r a r r ω ff L aa L f r af i L ω Equation for the armature circuit (RLE circuit) 43 42 1 f af r a aa a a a i L dt i dL i r v ω + + = v a , i a armature voltage and current r a - armature winding resistance L aa - armature self inductance L af - mutual inductance e a - back emf a e Separately Excited DC Motors Advanced Electromechanical Systems ELE847 8 Separately Excited DC Motors + + = a f aa a af r ff f a f i i sL r L sL r v v ω 0 DC Motor dynamic model f v f i = a e a v a i f r a r r ω ff L aa L f r af i L ω Define field flux linkage: Define field flux linkage: r v a f af v K e i L K ω = = Matrix form Simplified back emf e a Note: d/dt is replaced by Laplace operator s
Advanced Electromechanical Systems ELE847 9 DC motor dynamic model Electromagnetic torque Motor equation a f af e i i L T = a v i K = dt d J D T T r r L e ω ω = T L load torque in [Nm] D damping factor in [Nms] J

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