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CHAPTER 1 INTRODUCTION/1 1.1Background/1 1.2The State of the Art/3 1.21 Marnetic Modeling and Analysis/6 1.22 Orientation Sensing/8 1.23 Control Methods/10 1.3 Book Outline/12 PART I MODELLING METHODS FOR PMSMS/21 CHAPTER 2 General Formulation OF PMSMs/21 2.1 PMSM Electromagnetic System Modeling/21 2.1.1 Governing Equations of Electromagnetic Field/21 2.1.2 Boundary Condition/24 2.1.3 Magnetic Flux Linkage and Energy/25 2.1.4 Magnetic Force/Torque/26 2.2 PMSM Rotor Dynamic /27 References/30 CHAPTER 3 Distributed Multi-Pole Models/31 3.1 Distributed Multi-Pole Model for PMs/31 3.1.1 PM Field with DMP Model/32 3.1.2 Numerical Illustrative Examples/35 3.2 Distributed Multi-Pole Model for EMs/43 3.2.1 Equivalent Magnetization of the ePM/45 3.2.2 Illustrations of Magnetic Field Computation/47 3.3 Dipole Force/Torque Model/47 3.3.1 Force and Torque on a Magnetic Dipole/47 3.3.2 Illustration of Magnetic Force Computation/49 3.4 Image Method with DMP Models/52 3.4.1 Image Method with Spherical Grounded Boundary/53 3.4.2 Illustrative Examples/56 3.4.3 Effects of Iron Boundary on the Torque/58 3.5 Illustrative Numerical Simulations for PMSM Design/62 3.5.1 Pole Pair Design/65 3.5.2 Static Loading Investigation/70 3.5.3 Weight-Compensating Regulator/71 References/79 CHAPTER 4 PMSM Force/Torque Model for Real-Time Control/81 4.1 Force/Torque Formulation/81 4.1.1 Magnetic Force/Torque Based on The Kernel Functions/82 4.1.2 Simplified Model: Axis-Symmetric EMs/PMs/85 4.1.3 Inverse Torque Model/86 4.2 Numerical Illustrations/86 4.2.1 Axis-Asymmetric EM/PMs/86 4.2.2 Axis-Symmetric EM/PM/90 4.3 Illustrative PMSM Torque Modelling /93 PART II SENSING Methods CHAPTER 5 Field-Based Orientation Sensing/99 5.1 Coordinate Systems and Sensor Placement/99 5.2 Field Mapping and Segmentation/100 5.3 Artificial Neural Network Inverse Map/102 5.4 Experimental Investigation/103 5.4.1 2-DOF Concurrent Characterization/104 References/107 CHAPTER 6 A Back-EMF Method for Multi-DOF Motion Detection/109 6.1 Back-EMF for Multi-DOF Motion Sensing/109 6.1.1 EMF Model in a Single EM-PM pair/111 6.1.2 Back-EMF with Multiple EM-PM pairs/112 6.2 Implementation of Back-EMF Method on a PMSM/114 6.2.1 Mechanical and Magnetic Structure of the PMSM/115 6.2.2 Numerical Solutions for the MFL Model/116 6.2.3 Experiment and Discussion/118 6.2.4 Parameter Estimation of the PMSM with back-EMF Method/120 References/122 PART III CONTROL METHODS CHAPTER 7 Direct Field-Feedback Ccontrol/125 7.1 Traditional Orientation Control Method for Spherical Motors/125 7.1.1 PD Control Law and Stability Analysis/126 7.1.2 Comments on Implementation of Traditional Control Methods/127 7.2 Direct Field-Feedback Control/128 7.2.1 Determination of Bijective Domain/129 7.2.2 DFC Control Law and Control Parameter Determination/129 7.2.3 DFC with Multi-sensors/130 7.3 Numerical 1-DOF Illustrative Example/131 7.3.1 Sensor Design and Bijective Domain Identification/131 7.3.2 Field-based Control Law/133 7.3.3 Numerical Illustrations of Multiple Bijective Domains/135 7.4 Experimental Investigation of DFC for 3-DOF PMSM/135 7.4.1 System Description/135 7.4.2 Sensor Design and Bijective Domains/138 7.4.3 Bijective domain/139 7.4.4 TCV Computation Using Artificial Neural Network (ANN)/142 7.4.5 Experimental Investigation/142 References/150 CHAPTER 8 A Two-mode PMSM for Haptic Applications/151 8.1 Description of the PMSM Haptic Device/151 8.1.1 Two-mode configuration Design for 6-DOF Manipulation/153 8.1.2 Numerical Model for Magnetic Field/Torque Computation/154 8.1.3 Field-based TCV Estimation/155 8.2 Snap-Fit Simulation/156 8.2.1 Snap-Fit Performance Analyses/158 8.2.2 Snap-Fit Haptic Application/159 References/164