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Robust Linear and Non-Linear Control of Magnetically Levitated Systems Robust linear and non-linear control of magnetically levitated systems Thesis Submitted to The University of Wales for The Degree of Doctor of Philosophy Alexandre Nikolov Pechev Institute of Magnetics, Electronics and Electrical Systems School of Engineering Cardiff University September, 2004 UMI Number: U584675 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI U584675 Published by ProQuest LLC 2013. Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 Declaration This work has not previously been accepted in substance for any degree and is not being concurrently submitted in candidature for any degree. Signed (c;12 '' ’ate) D ate........ This thesis is the result of my own investigations, except where otherwise stated. Other sources are acknowledged bv footnotes giving explicit references. A bibliography is appended. Signei Date I hereby give consent for my thesis, if accepted, to be available for photocopying and for inter-library loan, and for the title and summary to be made available to outside organisa­ tions. Signed Date Acknowledgements I would like* to express my gratitude to Professor P.K. Sinha, Emeritus Professor at the University of Heading, for his financial and academic support during the course of this work. No doubt that without his support this project would not have been possible. I would like also to thank Professor H. Bolton for giving me the opportunity to be a part of Cardiff University and to both him and Dr. A. Haddad for their constructive’ comments and suggestions on the thesis. I am greatly indebted to Elena for her love, patience and understanding. Last but not least I would like to express my gratitude to my parents in Bulgaria for their love. To my son Dennis , my family and my parents A bstract The two most advanced applications of contactless magnetic levitation are high-speed mag­ netic hearings and magnetically levitated vehicles (Maglev) for ground transportation using superconducting magnets and controlled d.c. electromagnets. The repulsion force from su­ perconducting magnets provide stable levitation with low damping, while the suspension force generated by electromagnets is inherently unstable. This instability, due to the in­ verse force-distance relationship, requires the addition of feedback controllers to sustain stable suspension. The problem of controlling magnetically levitated systems using d.c. electromagnets under different operating conditions has been studied in this thesis with a design process primarily driven by experimental results from a representative single-magnet test rig and a multi-magnet vehicle. The controller-design stages are presented in detail and close rela­ tionships have been constructed between selection of performance criteria for the derivation process and desired suspension characteristics. Both linear and nonlinear stabilising com­ pensators have been developed. Simulation and experimental results have been studied in parallel to assess operational stability and the main emphasis has been given to assessing performance under different operational conditions. For the experimental work, a new dig­ ital signal processor-based hardware platform has been designed, built with interface to Matlab/Simulink. The controller design methods and algorithmic work presented in this thesis can be divided into: non-adaptive, adaptive, optimal linear and nonlinear. Adaptive algorithms based on model reference control have been developed to improve the performance of the suspension system in the presence of considerable variations in external payload and force disturbances. New design methods for Maglev suspension have been developed using ro­ bust control theory ('Hoc, and fi—synthesis). Single- and multi-magnet control problems have been treated using the same framework. A solution to the /H00 controller-optimisation prob­ lem has been derived and applied to Maglev control. The sensitivity to robustness has been discussed and tools for assessing the robustness of the closed-loop system in terms of sus­ taining stability and performance in the presence of uncertainties in the suspension model have been presented. Multivariable controllers based on 'H00 and /i—synthesis have been developed for a laboratory scale experimental vehicle weighing 88 kg with four suspension magnets, and experimental results have been derived to show superiority of the proposed design methods in terms of ability to deal with external disturbances. The concept of Hoo control has been extended to the nonlinear setting using the concepts of energy and dissipa- tivity, and nonlinear state-feedback and output-feed back controllers for Maglev have been developed and reported. Simulation and experimental results have been presented to show the improved performance of these controllers to attenuate guideway-induced disturbances while maintaining acceptable suspension qualities and larger operational bandwidth. Contents 1 Introduction 1 1.1 Background ...................................................................................................................... 1 1.2 Control work m o tiv a tio n .............................................................................................. 2 1.3 Control work background .............................................................................................. 4 1.4 Scope of this t h e s i s ........................................................................................................ 9 1.5 Overview of the t h e s i s ................................................................................................. 10 2 Electromagnetic Suspension System: modelling, simulation and transputer- based control 16 2.1 Electromagnetic suspension model ............................................................................. 16 2.2 Experimental system ..................................................................................................... 18 2.3 State-feedback control for M aglev ............................................................................. 20 2.4 Transputer-based platform for control ...................................................................... 23 2.5 Software environment for transputers-based co ntrol .......................................... 26 2.6 Host interface ................................................................................................................... 28 2.7 Transputer implementation of the state feedback controller ............................... 29 3 Adaptive pole placement and model reference control of Maglev systems 31 3.1 On-line identification of Maglev m o d el .................................................................. 31 3.1.1 Problem formulation and background information ................................ 31 3.1.2 Implementation and results .......................................................................... 34 3.2 Adaptive pole-placement control ................................................................................ 36 3.2.1 Outline of implementation issues ................................................................ 39 3.3 Model reference adaptive control of a Maglev system ....................................... 41 3.3.1 Implementation of the adaptive algorithm .............................................. 43 3.3.2 Results.................................................................................................................... 44 4 DSP environment for Maglev control 48 4.1 Digital signal processors .............................................................................................. 48 4.2 DSP based hardware ..................................................................................................... 49 4.3 DSP software for Maglev control ................................................................................ 53 4.4 Control algorithms ported to DSP-based control framework .............................. 53 4.4.1 State-feedback control .................................................................................... 54 4.4.2 Adaptive pole-placement control ............................. 55 4.4.3 Model reference control ....................................................................................... 56 4.5 Fuzzy logic control .......................................................................................................... 59 4.6 Fuzzy logic control for M aglev ..................................................................................... 63 4.6.1 Fuzzy control with constant acceleration ................... 63 4.6.2 Fuzzy controller for Maglev with fuzzy acceleration ............................. 69 4.6.3 Fuzzy controller using three state* variable's ............................................... 70 5 Design of DSP hardware for Maglev control 7 4 5.1 Design preliminaries .......................................... 74 5.2 Commercial DSP hardware* .......................................................................................... 75 5.3 Hardware* d
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