Permanent Magnet Spherical Motors - Model and Field Based Approaches for Design, Sensing and Control

Preface

Contents

Nomenclature

1 Introduction

1.1 Background

1.2 The State of the Art

1.2.1 Magnetic Modeling and Analysis

1.2.2 Orientation Sensing

1.2.3 Control Methods

1.3 Book Outline

References

Modeling Methods

2 General Formulation of PMSMs

2.1 PMSM Electromagnetic System Modeling

2.1.1 Governing Equations of Electromagnetic Field

2.1.2 Boundary Conditions

2.1.3 Magnetic Flux Linkage and Energy

2.1.4 Magnetic Force/Torque

2.2 PMSM Rotor Dynamics

References

3 Distributed Multi-pole Models

3.1 Distributed Multi-pole Model for PMs

3.1.1 PM Field with DMP Model

3.1.2 Numerical Illustrative Examples

3.2 Distributed Multi-pole Model for EMs

3.2.1 Equivalent Magnetization of the ePM

3.2.2 Illustrations of Magnetic Field Computation

3.3 Dipole Force/Torque Model

3.3.1 Force and Torque on a Magnetic Dipole

3.3.2 Illustration of Magnetic Force Computation

3.4 Image Method with DMP Models

3.4.1 Image Method with Spherical Grounded Boundary

3.4.2 Illustrative Examples

3.4.3 Effects of Iron Boundary on the Torque

3.5 Illustrative Numerical Simulations for PMSM Design

3.5.1 Pole Pair Design

3.5.2 Static Loading Investigation

3.5.3 Weight-Compensating Regulator

Appendix

References

4 PMSM Force/Torque Model for Real-Time Control

4.1 Force/Torque Formulation

4.1.1 Magnetic Force/Torque Based on the Kernel Functions

4.1.2 Simplified Model: Axis-Symmetric EMs/PMs

4.1.3 Inverse Torque Model

4.2 Numerical Illustrations

4.2.1 Axis-Asymmetric EM/PMs

4.2.2 Axis-Symmetric EM/PM

4.3 Illustrative PMSM Torque Modelling

Sensing Methods

5 Field-Based Orientation Sensing

5.1 Coordinate Systems and Sensor Placement

5.2 Field Mapping and Segmentation

5.3 Artificial Neural Network Inverse Map

5.4 Experimental Investigation

5.4.1 2-DOF Concurrent Characterization

References

6 A Back-EMF Method for Multi-DOF Motion Detection

6.1 Back-EMF for Multi-DOF Motion Sensing

6.1.1 EMF Model in a Single EM-PM Pair

6.1.2 Back-EMF with Multiple EM-PM Pairs

6.2 Implementation of Back-EMF Method on a PMSM

6.2.1 Mechanical and Magnetic Structure of the PMSM

6.2.2 Numerical Solutions for the MFL Model

6.2.3 Experiment and Discussion

6.2.4 Parameter Estimation of the PMSM with Back-EMF Method

Appendix

References

Control Methods

7 Direct Field-Feedback Control

7.1 Traditional Orientation Control Method for Spherical Motors

7.1.1 PD Control Law and Stability Analysis

7.1.2 Comments on Implementation of Traditional Control Methods

7.2 Direct Field-Feedback Control

7.2.1 Determination of Bijective Domain

7.2.2 DFC Control Law and Control Parameter Determination

7.2.3 DFC with Multi-sensors

7.3 Numerical 1-DOF Illustrative Example

7.3.1 Sensor Design and Bijective Domain Identification

7.3.2 Field-Based Control Law

7.3.3 Numerical Illustrations of Multiple Bijective Domains

7.4 Experimental Investigation of DFC for 3-DOF PMSM

7.4.1 System Description

7.4.2 Sensor Design and Bijective Domains

7.4.3 Bijective Domain

7.4.4 TCV Computation Using Artificial Neural Network (ANN)

7.4.5 Experimental Investigation

Appendix

References

8 A Two-Mode PMSM for Haptic Applications

8.1 Description of the PMSM Haptic Device

8.1.1 Two-Mode Configuration Design for 6-DOF Manipulation

8.1.2 Numerical Model for Magnetic Field/Torque Computation

8.1.3 Field-Based TCV Estimation

8.2 Snap-Fit Simulation

8.2.1 Snap-Fit Performance Analyses

8.2.2 Snap-Fit Haptic Application

Appendix: PM/EM/Sensor Position Coordinates

References