
系統識別號 
U00022107200615343100 
中文論文名稱

開關式磁阻馬達之徑向力控制與應用 
英文論文名稱

Switched Reluctance Motor Radial Force Control and its Applications 
校院名稱 
淡江大學 
系所名稱(中) 
機械與機電工程學系博士班 
系所名稱(英) 
Department of Mechanical and ElectroMechanical Engineering 
學年度 
94 
學期 
2 
出版年 
95 
研究生中文姓名 
林逢傑 
研究生英文姓名 
FengChieh Lin 
學號 
890340028 
學位類別 
博士 
語文別 
英文 
口試日期 
20060714 
論文頁數 
100頁 
口試委員 
指導教授楊勝明 委員蔡明祺 委員廖聰明 委員劉添華 委員賴炎生 委員楊勝明

中文關鍵字 
磁阻馬達
徑向力控制

英文關鍵字 
switched reluctance motor
radial force control

學科別分類 

中文摘要 
本論文主要目的為建立12/8極磁阻馬達之徑向力控制法則，且將所提出之法則應用於降低馬達震動與建立自軸承控制系統。透過有限元素分析軟體分析並建立馬達之數學模式，其中馬達定子與轉子凸極間之吸引力模式為轉子角度與激磁電流之函數，並且在模式中考慮互感之影響。分析此吸引力可分解出馬達之轉矩與徑向力，最後得到轉矩與徑向力模式。
本論文提出三種徑向力控制法則，研究最初首先提出利用具有相移之單相弦波激磁法則控制磁阻馬達之轉矩及徑向力，之後再提出兩相弦波激磁法則用以提昇單相弦波激磁法則徑向力之操作能力。另外，亦研究六極激磁之徑向力控制法則。此三種徑向力控制法則皆可以有效將馬達轉矩及徑向力解耦，並產生期望之徑向力。其中單相弦波激磁法則之驗證結果顯示可以應用於降低馬達振動。兩相弦波激磁法則則用以實現單軸自軸承控制系統。此自軸承馬達之轉子只需要一個軸承用以維持馬達轉動與軸向位置，而另一端則可以自由地徑向移動，但由馬達所產生的徑向力平衡轉子並維持在氣隙的中心。

英文摘要 
The main objective of this research investigates the control of radial force of 12/8pole SRM, and the applications of this scheme to motor vibration reduction and selfbearing control. The mathematical models of the motor were analyzed and developed through finiteelement analysis. The attraction force between the stator and rotor pole teeth and its orientation was modeled as a function of the rotor angle and the excitation current. Mutual inductance was included in the modeling. The attraction force is decomposed into motor torque and radial force, and consequently, the torque and radial force produced by the motor is analyzed.
Three radial force control schemes were investigated in this research. In the beginning, singlephase sinusoidal currents with phase shift was proposed to control the SRM. Then, a twophase sinusoidal excitation scheme was presented to extend the force producing capability of the singlephase scheme. In addition, a sixpole excitation scheme for radial fore control was also investigated. All of these schemes have been verified to be able to produce radial force and torque effectively, and independently. The singlephase sinusoidal current scheme has been applied to show that motor vibration can be reduced by appropriate radial force control. The twophase sinusoidal excitation scheme has been applied to realize selfbearing control of the SRM. In this oneaxis selfbearing motor, the rotor needs only one bearing for rotation and constrain of axial movement; the other end can move freely in radial direction and is balanced at the center of the air gap with the radial force produced by the motor.

論文目次 
CONTENTS
CHINESE ABSTRACT I
ABSTRACT II
ACKNOWLEDGEMENTS IV
CONTENTS V
LIST OF FIGURES VIII
LIST OF TABLES XIV
LIST OF SYMBOLS XV
CHAPTER 1 INTRODUCTION 1
1.1 Motivation 1
1.2 Review of Prior Work 3
1.3 Contributions of the Dissertation 5
1.4 Outline of the Contents 6
CHAPTER 2 MATHEMATICAL MODELS OF SWITCHED RELUCTANCE MOTOR 8
2.1 Introduction 8
2.2 Single Pole Model 9
2.3 MultiPole Model 12
2.4 Simulation Results 15
CHAPTER 3 RADIAL FORCE CONTROL WITH SINGLE PHASE SINUSOIDAL EXCITATIONS 20
3.1 Introduction 20
3.2 Radial Force Control with SinglePhase Sinusoidal Excitations 21
3.3 Radial force and torque limitations 27
3.4 Phase Commutation 31
3.5 Experimental Results 33
3.6 Discussions 42
CHAPTER 4 RADIAL FORCE CONTROL WITH SIXPOLE EXCITATIONS 44
4.1 Introduction 44
4.2 Radial Force Control with SixPole Excitations 44
4.3 Simulation Results 49
4.4 Control System 52
4.5 Experimental Results 54
4.6 Discussions 60
CHAPTER 5 RADIAL FORCE CONTROL WITH TWOPHASE SINUSOIDAL EXCITATIONS 61
5.1 Introduction 61
5.2 SinglePhase Sinusoidal Excitations with Consideration of Mutual Inductance 62
5.3 Radial Force Control with TwoPhase Sinusoidal Excitations 64
5.4 Simulation Results 66
5.5 Control System 68
5.6 Experimental Results 70
5.7 Discussions 75
CHAPTER 6 SELFBEARING CONTROL 77
6.1 Introduction 77
6.2 Control System 77
6.3 Experimental Results 79
6.4 Discussions 87
CHAPTER 7 CONCLUSIONS AND RECOMMENDATION FOR FUTURE WORK 88
7.1 CONCLUTIONS 88
7.2 FUTURE WORK 90
REFERENCE 91
APPENDIX 97
LIST OF FIGURES
Fig. 2.1. Schematic and coordinate systems of the 12/8 pole SRM. 10
Fig. 2.2. Attraction force produced by pole A1. 10
Fig. 2.3. The relationship between qp and qr. 12
Fig. 2.4. Comparison of qf vs. qr calculated by FEA and by Eq.(2.3). 15
Fig. 2.5. Comparison of torque and radial force calculated with FE software and by Eqs.(2.4)(2.6), (a) torque, (b) radial force. 16
Fig. 2.6. Comparison of torque and radial force calculated with FE software and by Eqs.(2.7)(2.9), (a) torque, (b) radial force. 16
Fig. 2.7. Comparison of torque and radial force calculated with FE software and by Eqs.(2.10)(2.14), when three poles of phase A are excited, (a) torque, (b) radial force. 17
Fig. 2.8. Comparison of torque and radial force calculated with FE software and by Eqs.(2.10)(2.14), when four poles of phase A are excited, (a) torque, (b) radial force. 17
Fig. 2.9. Comparison of torque and radial force calculated with FE software and by Eqs.(2.7)(2.8), Eqs.(2.10)(2.13), (a) iA1=1A, iA2=1A, 2A, and 3A, respectively, (b) iA1=1A, iA2=2A, iA3=1A, 2A, and 3A, respectively, (c) iA1=1A, iA2=2A, iA3=1A, iA4=1A, 2A, 3A, and 4A, respectively. 18
Fig. 3.1. Control block diagram for torque and radial force control with singlephase sinusoidal excitations. 25
Fig. 3.2. FEA calculated waveforms when iT = 2A, iF =2 A, qr = 5o, and qf varied from 0 to 360o,(a) phase A currents, (b) torque, (c) radial force. 26
Fig. 3.3. FE analysis calculated radial force waveforms when qr varied from 0 o to 15o and qf varied from 0 to 360o. 26
Fig. 3.4. Radial force and toque calculated with FE under singlephase excitations, iT=iT_rated, iF= imax, qf varied from 0 to 360o, qr=0o, 7o, and 14o, respectively, (a)iA1~iA4 , (b)torque, (c)radial force. 28
Fig. 3.5. Radial force calculated with FE under singlephase excitations, iT= 33%, 66%, and 100% iT_rated, respectively, qf varied from 0 to 360o, qr = 0o, (a)iA1, (b)radial force. 29
Fig. 3.6. Operating range of the SRM used in this paper, (a) iF vs. iT, (b) radial force vs. motor torque. 30
Fig. 3.7. Phase A and phase C currents when commutating from Phase A to C. 32
Fig. 3.8. Comparison of FE calculated force and torque waveforms for (a) conventional commutation, (b) proposed commutation scheme. 33
Fig. 3.9. Experimental setup. 34
Fig. 3.10. Radial force and phase A currents when the SRM was at standstill, Fr* =15N, load torque = 0.7Nm, qr = 0 o, 7 o, 14o, respectively, and rotating at 1Hz, singlephase excitation, (a) radial force, (b) iA1~iA4, (c)(d) radial force. 35
Fig. 3.11. Radial force and phase A currents when the SRM was at standstill, qr = 14o, load torque = 1Nm, Fr* = 30N and rotating at 1Hz, singlephase excitation, (a) radial force, (b) pole A1~A4 currents. 36
Fig. 3.12. Block diagram of the experimental system. 37
Fig. 3.13. Motor currents and vibration spectrum with the square current control, motor speed=1000 rpm(17Hz), (a) iA1, iB1, and iC1, (b) vibration spectrum. 39
Fig. 3.14. Currents and vibration spectrum with the sinusoidal currents, motor speed=1000 rpm, and Fr* =35N, 25 Hz: (a) iA1, iB1, and iC1; (b) vibration spectrum. 40
Fig. 3.15. Same conditions as in Fig. 3.14, (a) frequency of Fr*=17 Hz, and (b) frequency of Fr*=34 Hz. 40
Fig. 3.16. Comparison of motor vibration spectrum when an eccentric inertia was attached at the rotor, motor speed=1000 rpm, (a) Fr* = 0, (b) Fr* =35N, 17 Hz. 41
Fig. 3.17. Currents and vibration spectrum with the conventional commutation, motor speed=1000 rpm, (a) iA1, iB1, and iC1, (b) vibration spectrum. 41
Fig. 3.18. Currents and vibration spectrum with the proposed commutation, motor speed=1000 rpm, (a) iA1, iB1, and iC1, (b) vibration spectrum. 42
Fig. 4.1. Idealized inductance of 12/8pole SRM. 46
Fig. 4.2. Schematic of the SRM, conduction phase: phase A, and radial force producing poles: B1, B2. 46
Fig. 4.3. Motor radial force calculated with FE, qr = 0 o, Fr*=10N, 20N, 30N, respectively, no load, Fr* varied from 0 to 360o, (a) radial force vector, (b) iA1~iA4 , when Fr* = 10N, (c) iA3 for various Fr*. 50
Fig. 4.4. Motor radial force calculated with FE, qr = 0 o, 7 o, 14 o, respectively, no load, Fr* varied from 0 to 360o, (a) radial force vector, (b) iA3 for various qr. 51
Fig. 4.5. (a) Compensation torque calculated with the same conditions as shown in Fig.4.4, (b) motor torque after compensation. 51
Fig. 4.6. Radial force calculated with FE, Fr*=15N, Fr* varied from 0 to 360o, qr = 7o, and iT* =1A, 2A and 3A, respectively. 52
Fig. 4.7. Calculate iF1*, iF2* and dT from FX*, FY* and qr. 53
Fig. 4.8. Block diagram of the control system. 53
Fig. 4.9. Radial force and pole A1~A4 currents, standstill, qr = 0 oM, Fr* = 10N, no load, and Fr* varied from 0 to 360o, (a) radial force vector, (b) pole A1~A4 currents. 56
Fig. 4.10. Radial force, standstill, qr = 0 oM, Fr* = 15N, no load, and Fr* varied from 0 to 360o, (a) included, and (b) not included the mutual inductance. 57
Fig. 4.11. Radial force and iA3 current, standstill, Fr* = 15N, Fr* varied from 0 to 360o, (a) radial force when qr = 7oM, (b) radial force when qr = 14oM, (c) iA3 for various qr. 57
Fig. 4.12. Radial force vector and pole A1~A4 currents, 100 rpm under 0.5 Nm load torque and Fr* set to: (a) 0N, (b)10N and rotating synchronously with the rotor, (c)10N and rotating at 1 Hz. 58
Fig. 4.13. Radial force vector, 600 rpm under 0.5Nm load torque and Fr* set to: (a) 0N, (b)10N and rotating synchronously with the rotor, (c)10N and rotating at 1 Hz. 59
Fig. 4.14. Radial force vector, 1000 rpm under 0.5Nm load torque and Fr* set to: (a) 0N, (b)10N and rotating synchronously with the rotor, (c)10N and rotating at 1 Hz. 59
Fig. 5.1. Force and torque for twophase excitation. 66
Fig. 5.2. Radial force and toque calculated with FE under twophase excitations, qr = 14o in phase A, T* = 0.1Nm, Fr*=15N, 30N, and 45N, respectively, (a) iA3 , (b) iB3 , (c) torque, (d) radial force. 67
Fig. 5.3. Operating range (Fr vs. T) of the SRM used twophase sinusoidal excitations for various qr. 68
Fig. 5.4. Radial force control system. 69
Fig. 5.5. Selection of excitation strategy. 69
Fig. 5.6. Calculate current commands for twophase excitations. 69
Fig. 5.7. Radial force and phase A, B currents, standstill, qr = 14o, load torque = 0.1Nm, Fr* =15N, 30N, 45N, respectively, and rotating at 1Hz, twophase excitation, (a) radial force, (b) iA1, (c) iB1. 71
Fig. 5.8. Radial force and phase A currents, 100 rpm under 1.0Nm load torque and Fr* set to (a) 0N, (b)15N, (c)45N, and rotating synchronously with the rotor. 72
Fig. 5.9. The same operating conditions as Fig.5.8 except motor speed = 500rpm, Fr* set to (a) 0N, (b)15N, (c)45N. 73
Fig. 5.10. The same operating conditions as Fig.5.8 except motor speed = 1000rpm, Fr* set to (a) 0N, (b)15N, (c)45N. 73
Fig. 5.11. Fr* rotating synchronously with the rotor and stepped from 15N to 45N at time=0.5sec, 500rpm under 0.3Nm load torque, (a)Fx vs. Fy, (b) Fx, Fy vs. time (c) iA1, (d) motor speed. 74
Fig. 5.12. Radial force vector, 500 rpm under 0.3Nm load torque, and Fr* =45N and the frequency is (a)0Hz at 45o, (b)4Hz, (c)8Hz, (d)16Hz. 75
Fig. 6.1. Schematic of the selfbearing SRM. 78
Fig. 6.2. Block diagram of the selfbearing control system. 79
Fig. 6.3. Radial position responses, standstill and subjected to 0.03Nm load torque, qr = 0o, x* = y* = 0.1mm, 10Hz, (a) position responses vs. time, (b) x vs. y. 80
Fig. 6.4. Radial position responses, same running conditions as Fig.6.3, (a) iT = 1A, (b)iT = 2A, (c)iT = 3A. 80
Fig. 6.5. Control responses, standstill and subjected to 0.1Nm load torque, qr = 0o, x* = y* = 0, (a) X, Yaxis radial position feedback, X, Yaxis radial force commands, and motor speed, (b) phase A currents. 81
Fig. 6.6. Control responses, 100rpm and subjected to 0.1Nm load torque, x* = y* = 0, (a) X, Yaxis radial position feedback, X, Yaxis radial force commands, motor speed, and torque command, (b) position feedback in XY form, (c) A1, B1, C1 currents. 82
Fig. 6.7. Control responses, 100 rpm and subjected to 0.7Nm load torque, x* = y* = 0, (a) X, Yaxis radial position feedback, X, Yaxis radial force commands, motor speed, and torque command, (b) position feedback in XY form, (c) A1, B1, C1 currents. 84
Fig. 6.8. Control responses, 1500rpm and subjected to 0.25Nm load torque, x* = y* = 0, (a) X, Yaxis radial position feedback, X, Yaxis radial force commands, motor speed, and torque command, (b) position feedback in XY form, (c) A1, B1, C1 currents. 85
Fig. 6.9. Control responses, 1500rpm and subjected to 0.7Nm load torque, x* = y* = 0, (a) X, Yaxis radial position feedback, X, Yaxis radial force commands, motor speed, and torque command, (b) position feedback in XY form, (c) A1, B1, C1 currents. 86
Fig. 6.10. Comparisons of radial position errors at various motor speed and load, (a)500rpm, load torque = 0.1Nm, (b) 500rpm, load torque = 0.7Nm, (c)1000rpm, load torque = 0.1Nm, (d) 1000rpm, load torque = 0.7Nm. 87
LIST OF TABLES
Table 4.1 Selection of force control poles. 47

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