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srm

Badal Patnaik
Badal Patnaik

This document summarizes a research paper on implementing smooth transitions between optimal control modes in a switched reluctance motor (SRM). It begins with introductions to SRM technology and an overview of the paper contents. It then covers the operating principles, characteristics, control strategies, and modes of operation of SRMs. The document describes the development of a Simulink model for a proposed optimal controller, including subsystems for pulse width modulation and single pulse control. Simulation results are presented and analyzed for no-load operation, with load, and under speed and torque dynamics. The analysis shows the controller varies turn-on and turn-off angles optimally under different operating conditions to reduce ripple and enable smooth transitions between control modes. The conclusion

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Smooth transition between optimal control modes in SWITCH RELUCTANCE MOTOR By- Badal Patnaik - 1001227260 Sanjit Debta - 1001227317 D. Gouri Sankar - 1001227269 Debendra Kido - 1001227267 Ananya Subhadarsinee - 1001227255
Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
Introduction Concept of SRM-1938 Practical realization-mid 1960s,after the evolution of power electronics & computer aided EM design Also known as : -Variable Reluctance Motor -Brushless Reluctance Motor -Commutated Reluctance Motor
Construction Its a doubly-salient, singly- excited, independent stator exited motor The stator is same as PM motor but the rotor is simpler having no permanent magnet Stator windings on diametrically opposite poles are connected in series or parallel to form one phase
Construction 6/4,8/4,10/6,12/6,4/2,2/2 etc configurations are possible, but 6/4 & 8/4 are most common Higher the no. of stator/rotor pole combination, higher the no. of phase which aide to torque ripple reduction
Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
Principle of Operation
Principle of Operation Inductance of stator phase winding varies with rotor position Torque is produced only during variation of inductance Current is made available only during this variation, hence the need for rotor position feed back sensor
Periodic change of inductance with Rotor position Rotor Unaligned Position Lu La Inductance Profile Stator Aligned PositionRotor 慮1 慮3慮2 慮4 慮 L
Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
Characteristics of SRM All these characteristics cannot be obtained at a single operating point. HENCE THE NEED OF OPTIMAL CONTROL STRATEGY
Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
General Control Strategies Voltage Source control Hysteresis current control
Voltage Source control Both transistors are switched on at 慮0and both are switched off at 慮cConducts through D2 and D1 when negative voltage is applied between 慮c and 慮q
Voltage control waveforms
V Voltage source Control Converter 6/4 SRM V SRM with voltage source controller
Hysteresis current control Power switches are switched off or on according to the current is greater than or less than a reference current. The instantaneous phase current is measured and fed back to summing junction. The error is used directly to control the states of power transistors.
Hysteresis current control
SRM with hysteresis current controller iref Hysteresis Current Controller Converter 6/4 SRM V i i
Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
Modes of operation Single pulse mode PWM mode
Optimum Performance in Single Pulse mode L, 率 La L Lu 率c 率 慮 慮u慮a慮q慮c慮1 慮u 慮0 慮01 慮 硫s 硫r 留p 慮q慮c慮1 慮u 慮0 慮e1 慮e2 -Vdc Vdc
Optimum turn-on & turn-off angle in single Pulse mode 11 e opt o c 縁縁 11 1 e opt c c 縁縁
Optimum Performance in PWM mode La Lu L 慮 慮 慮1慮u 慮01 i 慮0 慮c 慮q 慮e 慮a Vdc iref 率c -Vdc 慮u 硫s 硫r 留p
Optimum turn-on & turn-off angle in PWM mode dc refu V iL 縁 10 e esk opt c 縁縁縁 01 1 12
Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
Simulation block diagram with basic controller
Simulation block diagram with developed controller Turn-off angle (deg) Turn-on angle (deg) powergui Discrete , Ts = 1e-006 s. peak value max peak flux max Vdc 240 Unaligned ind -C- To Workspace2 offangle To Workspace1 onangle To Workspace t Theta e 1 Theta e Theta 1 52.5 Theta 01 Switched Reluctance Motor TL m A1 A2 B1 B2 C1 C2 A1 A2 B1 B2 C1 C2 TL m Switch 2 Switch1 Subsystem-4 Theta 1 Theta e1 sp-off Subsystem-3 Theta 1 Theta e1 sp-on Subsystem-2 Theta 1 Theta 01 Theta e pwm-off Subsystem-1 Theta 1 Theta 01 pwm-on Scope 1 Ref speed Signal4 Ref flux |u| Position _Sensor w alfa beta sig Load torque Signal 2 -K- Flux Control PID Eqn -3 1/u Current control PI Clock CONVERTER G V+ V- A1 A2 B1 B2 C1 C2 Base speed 325 Abstract |u| 240 V <Flux (V*s)><Flux (V*s)><Flux (V*s)><Flux (V*s)><Flux (V*s)><Flux (V*s)> <w (rad/s)> <w (rad/s)> <I (A)><I (A)> <Te (N*m)>
Block diagram of subsystems subsystem-1 subsystem-1 1 pwm-on sum 2 Theta 01 1 Theta 1 pwm -off 1 stroke angle 60 constant 1 Subtract 2Subtract 1 Product 2 Product 1 Inv theta e 2 1/u Theta e 3 Theta 01 2 Theta 1 1
Block diagram of subsystems subsystem-3 subsystem-4 1 sp-on 0.25 c-lambda Pre-eqn Eqn-sp-on 2 Theta e1 1 Theta 1 1 sp-off Product0.75 1-c lambda 2 Theta e1 1 Theta 1
Parameters of the 6/4 SRM Voltage = 240V dc, Current = 450A max, Rating of the SRM = 60 kw No. of phases = 3 No. of stator poles =6 No. of stator poles =4 Rotor pole pitch = 90 deg Stator pole arc = 36.00 deg Rotor pole arc = 38.50 deg Rotor position at which stator and rotor pole corners starts overlap =52.50 deg Aligned inductance =23.6x10- 03 H Unaligned inductance=0.67x10-03 H Max flux linkage=0.486 V.s Stator resistance=0.05 ohm Inertia=0.05 Kg.m.m Friction=0.02 N.m.s Base speed = 3100 rpm
Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
Simulation Results and Analysis
At No-Load with basic controller
At No-Load with developed controller
At No-Load with developed controller while crossing base speed
At No-Load : turn-on angle Tu rn on an gle (d eg ) Time (sec)
At No-Load : turn-off angle
Analysis of simulation results on No-load Type of controller at steady state rpm 0f 6560 PWM mode Single pulse mode Turn-on (degree) Turn-off (degree) Current ripple (Amps) Torque ripple (Nm) Turn-on (degree) Turn-off (degree) Current ripple (steady state) (Amps) Torque ripple (steady state) (Nm) Basic 45 75 0 to 200 (200) 36 to 148 (112) 45 75 0 to 30.5 (30.5) 10 to 18 (8) Developed 52.5 to 52.3 104 to 81 0 to 230 (230) 30 to 100 (70) 45.2 72 to 75 0 to 30 (30) 10 to 17.5 (7.5)
Analysis on No-load The developed controller operates with varied turn-on and turn-of angles. The torque ripple is reduced in both PWM and single pulse mode when the SRM is used with the developed controller. This is one aspect of the optimal performance of the SRM with the developed controller. While operating at steady state in single pulse mode, the maximum current/current ripple is less when the SRM is used with the developed controller. The transition is smooth in terms of flux, current, torque or speed when the motor shifts its operation from PWM mode to single pulse mode. SRM delivers better performance when used with a controller having varied turn-on and turn-off angles The turn-on and turn-off angles are varied at every instant in synchronization with the formulae for optimal condition.
With heavy Load of 80 Nm
At 80 Nm Load: turn-on angle Tu rn on an gle (de g) Time (sec) 0 1 2 3 4 5 6 7 8 30 35 40 45 50 55
At 80 Nm Load: turn-off angle Tu rn off an gle (de g) Time (sec) 0 1 2 3 4 5 6 7 8 20 40 60 80 100 120 140 160
With speed dynamics (6560 to 8000 rpm)
With speed dynamics : Turn-on angle Tu rn on an gle (de g) Time (sec) 0 1 2 3 4 5 6 34 36 38 40 42 44 46 48 50 52 54
Tu rn off an gle (de g) Time (sec) 1 2 3 4 5 6 60 70 80 90 100 110 With speed dynamics : Turn-off angle
With torque dynamics : 5 to 20 Nm
With torque dynamics : 5 to 20 Nm
Tu rn on an gle (de g) Time (sec) 0 1 2 3 4 5 6 7 8 34 36 38 40 42 44 46 48 50 52 54 With torque dynamics : turn-on angle
With torque dynamics : turn-off angle Tu rn off an gle (de g) Time (sec) 1 2 3 4 5 6 7 60 70 80 90 100 110
Analysis of Simulation results on Load Application PWM mode Single-pulse mode Turn-on angle (degree) Turn-off angle(degree) Turn-on angle (degree) Turn-off angle(degree) 80 Nm of load at 6560 rpm ref speed 52.5 to 52 128 to 72 43 to 32.2 64 to 78 Steep increase of load from 5 to 20 Nm at 6560 rpm ref speed 52.5 to 52.2 104 to74 41.2 to 40 to 40.2 to 35.8 66 to 68 to73 Steep increase of speed from 6560 to 8000 rpm at 5 Nm of load 52.5 to 52.2 104 to74 41.2 to 40 to 40.2 to 34.4 to 36 67 to 68 to 75 to 73
Analysis on Load The controller operates by varying the turn-on and turn-off angles at every instant as per the requirement of that operating point. When the operation of the motor shifts from PWM mode to single pulse mode, the turn-on angle is advanced to cater to the torque demand as the overlapping of the phases is reduced. When there is a sudden increase of load from 5 Nm to 20 Nm or sudden increase of speed from 5650 rpm to 8000 rpm the turn-on angle is advanced and the turn-off angle is retarded to balance the new torque demand. The emphasis is made to show that to maintain optimal operating condition the turn-on and turn-off angles vary to make the transition smooth between the two optimal control modes It is proved now that the developed controller is able to control the SRM over its entire speed and torque range.
Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
CONCLUSION This project studies optimal control modes of the SRM by striking a balance between maximum efficiency and minimum torque ripple and thus calculates the optimum switch on angles and switch off angles. The turn on and turn off angles are calculated through simple formulas and implemented through Simulink building blocks. The optimum controller determines the turn-on and turn-off angles at every instant and accordingly the converter switches are fired to cater to the torque and speed demand of that instant. To validate the effectiveness of the controller, simulation is carried out on a variety of load and speed combination and the effectiveness is verified.
REFERENCES [1] C.J. Van Duijn, Development of methods, algorithms and soft wares for optimal design of switched reluctance drives [2] F. Soares and P.J. Costa Branco, Simulation of a 6/4 switched reluctance motor based on Matlab/Simulink environment [3] R Krishnan, Switched Reluctance Motor Drives; Modeling, Simulation, Analysis, Design and Applications [4] Han-Kyung Bae, Control of Switched Reluctance Motors considering mutual inductance [5] Ardeshir Motomedi-Sedeh, Speed control of switched reluctance motors [6] M. T. DiRenzo, "Switched Reluctance Motor Control Basic Operation and Example Using the TMS320F240, Texas Instruments Application Note," 2000. [7] C. Mademlis and I. Kioskeridis, Performance optimization in switched reluctance motor drives with online commutation angle control, IEEE [8] C. Mademlis and I. Kioskeridis, Maximum efficiency in Single Pulse Controlled switched reluctance motor drives, IEEE [9] C. Mademlis and I. Kioskeridis, Smooth Transition between Optimal Control Modes in switched reluctance motoring, IEEE [10] Matlab R 2008a, Version 7.6
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  • 1. Smooth transition between optimal control modes in SWITCH RELUCTANCE MOTOR By- Badal Patnaik - 1001227260 Sanjit Debta - 1001227317 D. Gouri Sankar - 1001227269 Debendra Kido - 1001227267 Ananya Subhadarsinee - 1001227255
  • 2. Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
  • 3. Introduction Concept of SRM-1938 Practical realization-mid 1960s,after the evolution of power electronics & computer aided EM design Also known as : -Variable Reluctance Motor -Brushless Reluctance Motor -Commutated Reluctance Motor
  • 4. Construction Its a doubly-salient, singly- excited, independent stator exited motor The stator is same as PM motor but the rotor is simpler having no permanent magnet Stator windings on diametrically opposite poles are connected in series or parallel to form one phase
  • 5. Construction 6/4,8/4,10/6,12/6,4/2,2/2 etc configurations are possible, but 6/4 & 8/4 are most common Higher the no. of stator/rotor pole combination, higher the no. of phase which aide to torque ripple reduction
  • 6. Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
  • 8. Principle of Operation Inductance of stator phase winding varies with rotor position Torque is produced only during variation of inductance Current is made available only during this variation, hence the need for rotor position feed back sensor
  • 9. Periodic change of inductance with Rotor position Rotor Unaligned Position Lu La Inductance Profile Stator Aligned PositionRotor 慮1 慮3慮2 慮4 慮 L
  • 10. Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
  • 11. Characteristics of SRM All these characteristics cannot be obtained at a single operating point. HENCE THE NEED OF OPTIMAL CONTROL STRATEGY
  • 12. Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
  • 13. General Control Strategies Voltage Source control Hysteresis current control
  • 14. Voltage Source control Both transistors are switched on at 慮0and both are switched off at 慮cConducts through D2 and D1 when negative voltage is applied between 慮c and 慮q
  • 17. Hysteresis current control Power switches are switched off or on according to the current is greater than or less than a reference current. The instantaneous phase current is measured and fed back to summing junction. The error is used directly to control the states of power transistors.
  • 19. SRM with hysteresis current controller iref Hysteresis Current Controller Converter 6/4 SRM V i i
  • 20. Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
  • 21. Modes of operation Single pulse mode PWM mode
  • 22. Optimum Performance in Single Pulse mode L, 率 La L Lu 率c 率 慮 慮u慮a慮q慮c慮1 慮u 慮0 慮01 慮 硫s 硫r 留p 慮q慮c慮1 慮u 慮0 慮e1 慮e2 -Vdc Vdc
  • 23. Optimum turn-on & turn-off angle in single Pulse mode 11 e opt o c 縁縁 11 1 e opt c c 縁縁
  • 24. Optimum Performance in PWM mode La Lu L 慮 慮 慮1慮u 慮01 i 慮0 慮c 慮q 慮e 慮a Vdc iref 率c -Vdc 慮u 硫s 硫r 留p
  • 25. Optimum turn-on & turn-off angle in PWM mode dc refu V iL 縁 10 e esk opt c 縁縁縁 01 1 12
  • 26. Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
  • 27. Simulation block diagram with basic controller
  • 28. Simulation block diagram with developed controller Turn-off angle (deg) Turn-on angle (deg) powergui Discrete , Ts = 1e-006 s. peak value max peak flux max Vdc 240 Unaligned ind -C- To Workspace2 offangle To Workspace1 onangle To Workspace t Theta e 1 Theta e Theta 1 52.5 Theta 01 Switched Reluctance Motor TL m A1 A2 B1 B2 C1 C2 A1 A2 B1 B2 C1 C2 TL m Switch 2 Switch1 Subsystem-4 Theta 1 Theta e1 sp-off Subsystem-3 Theta 1 Theta e1 sp-on Subsystem-2 Theta 1 Theta 01 Theta e pwm-off Subsystem-1 Theta 1 Theta 01 pwm-on Scope 1 Ref speed Signal4 Ref flux |u| Position _Sensor w alfa beta sig Load torque Signal 2 -K- Flux Control PID Eqn -3 1/u Current control PI Clock CONVERTER G V+ V- A1 A2 B1 B2 C1 C2 Base speed 325 Abstract |u| 240 V <Flux (V*s)><Flux (V*s)><Flux (V*s)><Flux (V*s)><Flux (V*s)><Flux (V*s)> <w (rad/s)> <w (rad/s)> <I (A)><I (A)> <Te (N*m)>
  • 29. Block diagram of subsystems subsystem-1 subsystem-1 1 pwm-on sum 2 Theta 01 1 Theta 1 pwm -off 1 stroke angle 60 constant 1 Subtract 2Subtract 1 Product 2 Product 1 Inv theta e 2 1/u Theta e 3 Theta 01 2 Theta 1 1
  • 30. Block diagram of subsystems subsystem-3 subsystem-4 1 sp-on 0.25 c-lambda Pre-eqn Eqn-sp-on 2 Theta e1 1 Theta 1 1 sp-off Product0.75 1-c lambda 2 Theta e1 1 Theta 1
  • 31. Parameters of the 6/4 SRM Voltage = 240V dc, Current = 450A max, Rating of the SRM = 60 kw No. of phases = 3 No. of stator poles =6 No. of stator poles =4 Rotor pole pitch = 90 deg Stator pole arc = 36.00 deg Rotor pole arc = 38.50 deg Rotor position at which stator and rotor pole corners starts overlap =52.50 deg Aligned inductance =23.6x10- 03 H Unaligned inductance=0.67x10-03 H Max flux linkage=0.486 V.s Stator resistance=0.05 ohm Inertia=0.05 Kg.m.m Friction=0.02 N.m.s Base speed = 3100 rpm
  • 32. Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
  • 34. At No-Load with basic controller
  • 35. At No-Load with developed controller
  • 36. At No-Load with developed controller while crossing base speed
  • 37. At No-Load : turn-on angle Tu rn on an gle (d eg ) Time (sec)
  • 38. At No-Load : turn-off angle
  • 39. Analysis of simulation results on No-load Type of controller at steady state rpm 0f 6560 PWM mode Single pulse mode Turn-on (degree) Turn-off (degree) Current ripple (Amps) Torque ripple (Nm) Turn-on (degree) Turn-off (degree) Current ripple (steady state) (Amps) Torque ripple (steady state) (Nm) Basic 45 75 0 to 200 (200) 36 to 148 (112) 45 75 0 to 30.5 (30.5) 10 to 18 (8) Developed 52.5 to 52.3 104 to 81 0 to 230 (230) 30 to 100 (70) 45.2 72 to 75 0 to 30 (30) 10 to 17.5 (7.5)
  • 40. Analysis on No-load The developed controller operates with varied turn-on and turn-of angles. The torque ripple is reduced in both PWM and single pulse mode when the SRM is used with the developed controller. This is one aspect of the optimal performance of the SRM with the developed controller. While operating at steady state in single pulse mode, the maximum current/current ripple is less when the SRM is used with the developed controller. The transition is smooth in terms of flux, current, torque or speed when the motor shifts its operation from PWM mode to single pulse mode. SRM delivers better performance when used with a controller having varied turn-on and turn-off angles The turn-on and turn-off angles are varied at every instant in synchronization with the formulae for optimal condition.
  • 41. With heavy Load of 80 Nm
  • 42. At 80 Nm Load: turn-on angle Tu rn on an gle (de g) Time (sec) 0 1 2 3 4 5 6 7 8 30 35 40 45 50 55
  • 43. At 80 Nm Load: turn-off angle Tu rn off an gle (de g) Time (sec) 0 1 2 3 4 5 6 7 8 20 40 60 80 100 120 140 160
  • 44. With speed dynamics (6560 to 8000 rpm)
  • 45. With speed dynamics : Turn-on angle Tu rn on an gle (de g) Time (sec) 0 1 2 3 4 5 6 34 36 38 40 42 44 46 48 50 52 54
  • 46. Tu rn off an gle (de g) Time (sec) 1 2 3 4 5 6 60 70 80 90 100 110 With speed dynamics : Turn-off angle
  • 47. With torque dynamics : 5 to 20 Nm
  • 48. With torque dynamics : 5 to 20 Nm
  • 49. Tu rn on an gle (de g) Time (sec) 0 1 2 3 4 5 6 7 8 34 36 38 40 42 44 46 48 50 52 54 With torque dynamics : turn-on angle
  • 50. With torque dynamics : turn-off angle Tu rn off an gle (de g) Time (sec) 1 2 3 4 5 6 7 60 70 80 90 100 110
  • 51. Analysis of Simulation results on Load Application PWM mode Single-pulse mode Turn-on angle (degree) Turn-off angle(degree) Turn-on angle (degree) Turn-off angle(degree) 80 Nm of load at 6560 rpm ref speed 52.5 to 52 128 to 72 43 to 32.2 64 to 78 Steep increase of load from 5 to 20 Nm at 6560 rpm ref speed 52.5 to 52.2 104 to74 41.2 to 40 to 40.2 to 35.8 66 to 68 to73 Steep increase of speed from 6560 to 8000 rpm at 5 Nm of load 52.5 to 52.2 104 to74 41.2 to 40 to 40.2 to 34.4 to 36 67 to 68 to 75 to 73
  • 52. Analysis on Load The controller operates by varying the turn-on and turn-off angles at every instant as per the requirement of that operating point. When the operation of the motor shifts from PWM mode to single pulse mode, the turn-on angle is advanced to cater to the torque demand as the overlapping of the phases is reduced. When there is a sudden increase of load from 5 Nm to 20 Nm or sudden increase of speed from 5650 rpm to 8000 rpm the turn-on angle is advanced and the turn-off angle is retarded to balance the new torque demand. The emphasis is made to show that to maintain optimal operating condition the turn-on and turn-off angles vary to make the transition smooth between the two optimal control modes It is proved now that the developed controller is able to control the SRM over its entire speed and torque range.
  • 53. Content Introduction Principle of operation Characteristics General control strategy Modes of operation Simulink model for proposed controller Simulation results and Analysis Conclusion References
  • 54. CONCLUSION This project studies optimal control modes of the SRM by striking a balance between maximum efficiency and minimum torque ripple and thus calculates the optimum switch on angles and switch off angles. The turn on and turn off angles are calculated through simple formulas and implemented through Simulink building blocks. The optimum controller determines the turn-on and turn-off angles at every instant and accordingly the converter switches are fired to cater to the torque and speed demand of that instant. To validate the effectiveness of the controller, simulation is carried out on a variety of load and speed combination and the effectiveness is verified.
  • 55. REFERENCES [1] C.J. Van Duijn, Development of methods, algorithms and soft wares for optimal design of switched reluctance drives [2] F. Soares and P.J. Costa Branco, Simulation of a 6/4 switched reluctance motor based on Matlab/Simulink environment [3] R Krishnan, Switched Reluctance Motor Drives; Modeling, Simulation, Analysis, Design and Applications [4] Han-Kyung Bae, Control of Switched Reluctance Motors considering mutual inductance [5] Ardeshir Motomedi-Sedeh, Speed control of switched reluctance motors [6] M. T. DiRenzo, "Switched Reluctance Motor Control Basic Operation and Example Using the TMS320F240, Texas Instruments Application Note," 2000. [7] C. Mademlis and I. Kioskeridis, Performance optimization in switched reluctance motor drives with online commutation angle control, IEEE [8] C. Mademlis and I. Kioskeridis, Maximum efficiency in Single Pulse Controlled switched reluctance motor drives, IEEE [9] C. Mademlis and I. Kioskeridis, Smooth Transition between Optimal Control Modes in switched reluctance motoring, IEEE [10] Matlab R 2008a, Version 7.6
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