This book introduces and illustrates modeling, sensing, and control methods for analyzing, designing, and developing spherical motors. It systematically presents modelsfor establishing the relationships among the magnetic fields position/orientation and force/torque, while also providing time-efficient solutions to assist researchers and engineers in studying and developing these motors. In order to take full advantage of spherical motors’ compact structure in practical applications, sensing and control methods that utilize their magnetic fields and eliminate the need to install external sensors for feedback are proposed. Further, the book investigates for the first time spherical motors’force/torque manipulation capability, and proposes algorithms enabling the ball-joint-like end-effector for haptic use based on these motors’hybrid position/force actuation modes. While systematically presenting approaches to their design, sensing and control, the book also provides many examples illustrating the implementation issues readers may encounter.
Table of Contents
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
