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Analysis and Synthesis of Precision Resolver System

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Analysis and Synthesis of Precision Resolver System ANALYSIS AND SYNTHESIS OF PRECISION RESOLVER SYSTEM NAY LIN HTUN AUNG (B.Eng, YIT, M.Eng, NUS) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2015 DECLARATION I hereby declare that the thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. NAY LIN HTUN AUNG 01 DEC 2015 Acknowledgements First and foremost, I would like to express my gratitude to my co-supervisor, Adjunct Associate Prof. Bi Chao from Data Storage Institute, for his guidance, in-depth knowledge, support and encouragement during the course of this work. I would also like to thank my main supervisor, Associate Prof. A. Al. Mamun from department of Electrical Computer Engineering, National University Singapore, for his valuable suggestions and critical review of my work. I would like to thank for all the help I have received from my colleagues, Mr. Lim Choon Pio, Dr. Jiang Quan, Dr. Lin Song, Dr. Hla Nu Phyu and Dr. Yu Yinquan, from the motor team in Data Storage Institute, who helped me one way or another. Special thanks go to my wife, Ma Tin Lay Nwe, mother of my lovely daughter, Khaing Nay New, for her consistent support and encouragement till I complete this dissertation. I wish to acknowledge the opportunity of pursuing a PhD by providing tuition fee support and a yearly book allowance in the form of Scientific Staff Development Award (SSDA) offered by Agency for Science Technology and Research (A*STAR) . Table of Contents Summary ....................................................................................................................... v List of Tables .............................................................................................................. vii List of Figures ............................................................................................................ viii 1 Introduction ............................................................................................................... 1 1.1 Background ................................................................................................... 1 1.2 Rotary encoders ............................................................................................ 2 1.3 Synchros ........................................................................................................ 3 1.4 Resolvers ....................................................................................................... 6 1.4.1 Principle of resolver operation .............................................................. 7 1.4.2 Excitation for resolvers ......................................................................... 8 1.4.3 Brushless resolvers ................................................................................ 9 1.4.4 Variable reluctance resolvers .............................................................. 11 1.4.5 Retrieving the position angle from resolver ........................................ 12 1.4.6 Resolver specifications ....................................................................... 16 1.4.7 Linear resolvers ................................................................................... 20 1.5 Thesis structure ........................................................................................... 22 2 Literature review ...................................................................................................... 24 2.1 Introduction ................................................................................................. 24 2.2 Design and development of resolvers ......................................................... 24 2.3 Modelling and performance analysis of resolvers ...................................... 27 2.4 Resolver to digital conversion .................................................................... 29 2.4.1 Hardware-based conversion ................................................................ 29 2.4.2 Software-based conversion ................................................................. 31 2.4.3 Resolver accuracy improvement and errors compensation ................. 33 3 Analysis of a brushless resolver .............................................................................. 40 i 3.1 Introduction ................................................................................................. 40 3.2 Voltage equations ........................................................................................ 40 3.3 Simulation of a brushless resolver .............................................................. 44 3.4 Resolver errors ............................................................................................ 48 3.5 Estimation of position error ........................................................................ 50 3.5.1 General form of position error ............................................................ 51 3.5.2 Imbalance amplitude ........................................................................... 51 3.5.3 Quadrature error .................................................................................. 52 3.5.4 Inductance harmonics ......................................................................... 53 3.5.5 Phase shift ........................................................................................... 54 3.5.6 Summary of estimated errors .............................................................. 55 3.5.7 Accuracy and Allowable Errors’ Constraints ..................................... 56 3.6 Conclusion .................................................................................................. 58 4 Demodulation by synchronous integration .............................................................. 59 4.1 Introduction ................................................................................................. 59 4.2 Demodulation methods and effect of noise ................................................. 59 4.2.1 Demodulation by synchronous peak detection ................................... 60 4.2.2 Demodulation by product detection .................................................... 61 4.2.3 Demodulation by band pass filtering and decimation ......................... 63 4.2.4 Other demodulation methods .............................................................. 65 4.3 Demodulation by synchronous integration: A robust demodulation method …………………………………………………………………………….65 4.3.1 Demodulation when the rotor is at stand-still ..................................... 66 4.3.2 Demodulation when the rotor is in motion ......................................... 68 4.3.3 Implementation issues of DBSI .......................................................... 71 4.4 Simulation results of DBSI ......................................................................... 74 4.4.1 Demonstration of the DBSI................................................................. 75 4.4.2 Evaluation of DBSI ............................................................................. 76 ii 4.5 Experimental results .................................................................................... 82 4.6 Conclusion .................................................................................................. 85 5 Initial calibration and error compensation ............................................................... 87 5.1 Introduction ................................................................................................. 87 5.2 Systematic errors and their significance ..................................................... 87 5.3 Resolver error compensation ...................................................................... 88 5.4 Sinusoidal parameters estimation based initial calibration method ............ 90 5.4.1 Quantitative analysis on amplitude estimation with DFT ................... 94 5.4.2 Simulation results ................................................................................ 96 5.4.3 Experimental setup .............................................................................. 97 5.4.4 Experimental results ............................................................................ 97 5.5 Complex Fourier expression of demodulated non-ideal resolver outputs. 100 5.6 Online error compensation method developed in the research ................. 102 5.7 Simulation results...................................................................................... 106 5.8 Experiment results .................................................................................... 107 5.9 Conclusion ................................................................................................ 110 6 Synthesis of a new type of linear resolver ............................................................. 112 6.1 Introduction ............................................................................................... 112 6.2 Design approach of the new type of resolver ............................................ 114 6.3 Core structure and windings arrangement of the PCB resolver ................ 116 6.4 Equivalent circuit of PCB resolver ........................................................... 117 6.5 Core material ............................................................................................. 119 6.6 Excitation transformer
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