LINEARIZATION AND CONTROL OF DUAL-AXIS MICROMIRROR ZHAO YI NATIONAL UNIVERSITY OF SINGAPORE 2006 LINEARIZATION AND CONTROL OF DUAL-AXIS MICROMIRROR ZHAO YI (M. Eng.) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2006 Acknowledgements I would like to express my sincere gratitude to many people who have lent their assistance throughout these years of research. This thesis would not have been completed successfully without them. First and foremost, I am deeply indebted to my advisors, Associate Professor Tay Eng Hock and Associate Professor Chau Fook Siong, for their constant guidance and valuable suggestions they gave me during the last three years. Associate Professor Tay have helped me to gain insights into the world of MEMS. He provides an environment, which allows creativity and free ideas, and instills in me the confidence to carry out independent research. His undying enthusiasm propelled me to explore new realms of research and be constantly in search of novel ideas. I would also like to express my deep gratitude to Associate Professor Chau. I will always remember his patience in imparting many tips and suggestions that are crucial in overcoming the obstacles faced in this research. His constant encouragement and ii Acknowledgements iii critical reviews prove vital to the success of this research. Special thanks go out to Assistant Professor Zhou Guangya, for his timely and helpful suggestions, especially at the beginning of this research. I will like to show my sincere gratefulness to Professor Ben M. Chen for his valuable suggestion for some of my papers and this thesis, particularly in the control part. Sincere thanks also goes to Associate Professor Quan Chenggen for his important comments during the qualification exam. I would also like to thank the numerous anonymous referees who have reviewed parts of this work prior to publication in journals and conference proceedings and whose valuable comments have contributed to the clarification of many of the ideas presented in this thesis. I sincerely thank my parents for their support in my earlier years of study, my wife for her love and encouragement and my one year old baby for the happiness she brings to me. My final thanks go to the National University of Singapore for awarding me the research scholarship for my Ph.D. study here, and to the other staff in the Department of Mechanical Engineering from whom I have learned much through modules and seminars during these years. Zhao Yi Feb 2006 Summary The electrostatically actuated dual-axis micromirror based on MEMS technology has attracted much attention due to its promising applications. However, the inherent nonlinearity of the electrostatic torques results in two problems. One is the scanning distortion within the stable range. Another is the scanning instability, known as the ”pull-in” problem, when the driving voltages go beyond certain thresholds. The objectives of this study are (1) to investigate the scanning nonlinearity of a dual-axis micromirror and subsequently to propose methods to linearize the distorted scanning field, and (2) to stabilize the device beyond the pull-in point thereby extending its useful scanning range. Two linearization methods, i.e. Radial basis function (RBF) neural network (NN) and Delaunay triangulation (DT) are proposed to reduce or eliminate scanning nonlinearity, thus correcting the distorted scanning field. A position feedback integral sliding mode control (ISMC) algorithm iv Summary v is applied to stabilize the micromirror beyond its pull-in point. Both static and dynamic performances are investigated experimentally. The static tests show that the static scanning field of dual-axis micromirror is distorted. And the distortion rates increase with the increment of tilt angles. For the moderate 50 V bias voltage, the distortion rates observed are about 30%. On the other hand, the dynamic testing shows that the system is severely under-damped, which results in large percentage of overshoot (53% for x -axis and 90% for y-axis) and long settling times (15 ms for x -axis and 24 ms for y-axis). The dynamic testing also reveals that there exists quite significant cross-axis coupling. RBF NN and DT methods are designed to linearize the distorted scanning field. The nonlinearity mapping is firstly captured. Then an inverse mapping based on RBF NN or DT is designed to counteract the nonlinearity. The results show that both of the methods can capture the scanning nonlinearity very well and produce linearized scanning field. The distortion rates are dramatically reduced. The linearized scanning field demonstrates distortion rates of less than 5%. In terms of closed-loop control, the PID method demonstrates the ability to improve transient response, leading to short settling time (less than ms for both axes), and no overshoot. At the same time cross-axis coupling is eliminated. As a nonlinear control method, the integral sliding mode control shows its ability to stabilize the system beyond pull-in point. The system exhibits an extended stable range, which is more than 30% larger than the system without applying the method. Summary It is concluded that the proposed linearization and control techniques have demonstrated their abilities to overcome the stated problems in dual-axis micromirrors. vi Contents Acknowledgements ii Summary iv Table of Content x Nomenclature xi List of Tables xv List of Figures xvi Introduction 1.1 Overview of Dual-Axis Micromirror . . . . . . . . . . . . . . . . . . 1.2 Operation Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Contents viii 1.3.1 Scanning Field Distortion . . . . . . . . . . . . . . . . . . . 1.3.2 Pull-In Instability . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Purpose and Scope of Thesis . . . . . . . . . . . . . . . . . . . . . . 10 1.6 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Literature Review 2.1 2.2 2.3 12 Linearization Approaches . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.1 Differential Driving Scheme . . . . . . . . . . . . . . . . . . 13 2.1.2 Voltage Compensation . . . . . . . . . . . . . . . . . . . . . 15 2.1.3 Radial Basis Function (RBF) NN . . . . . . . . . . . . . . . 16 2.1.4 Delaunay Triangulation (DT) . . . . . . . . . . . . . . . . . 17 Stable Range Extension Techniques . . . . . . . . . . . . . . . . . . 19 2.2.1 Geometry Modification . . . . . . . . . . . . . . . . . . . . . 19 2.2.2 Capacitor Feedback . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.3 Position Feedback Control . . . . . . . . . . . . . . . . . . . 24 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Theory 29 3.1 System Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 Open-Loop Linearization . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.1 RBF Neural Network Design . . . . . . . . . . . . . . . . . . 40 3.2.2 Delaunay Triangulation . . . . . . . . . . . . . . . . . . . . 43 Closed-Loop Control . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.3 Contents 3.4 ix 3.3.1 PID Control Design Within Stable Range . . . . . . . . . . 50 3.3.2 ISMC Design Beyond Stable Range . . . . . . . . . . . . . . 53 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Experimentation 56 4.1 Fabrication Process PolyMUMPs . . . . . . . . . . . . . . . . . . . 56 4.2 Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Results and Discussion 5.1 5.2 5.3 5.4 67 Micromirror System Characterization . . . . . . . . . . . . . . . . . 67 5.1.1 System Simulation . . . . . . . . . . . . . . . . . . . . . . . 67 5.1.2 Experimental Testing . . . . . . . . . . . . . . . . . . . . . . 70 5.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.2.1 Linearization Results of RBF Neural Networks . . . . . . . . 76 5.2.2 Linearization Results of Delaunay Triangulation . . . . . . . 82 5.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Closed-Loop Control . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.3.1 PID Control Results . . . . . . . . . . . . . . . . . . . . . . 91 5.3.2 Stabilization Beyond Pull-In Point by ISMC . . . . . . . . . 99 5.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Appendix A List of Publication Journal Papers 1. Yi Zhao, F E H Tay, F S Chau, and Guangya Zhou, Linearization of the scanning field for 2D torsional micromirror by RBF neural network, Sensors and Actuators: A. Physical, 2005, Vol 121 pp. 230-236. 2. Yi Zhao, F E H Tay, F S Chau, and Guangya Zhou, Control-Oriented Modeling of 2D Torsinal Micromirror, International Journal of Software Engineering and Knowledge Engineering, 2005, Vol 15, pp. 249-255. 3. Yi Zhao, F E H Tay, F S Chau, and Guangya Zhou, A nonlinearity compensation approach based on Delaunay triangulation to linearize the scanning field of dual-axis micromirror, Journal of Micromechanics and Microengineering, 2005, Vol 15, pp. 1972-1978. 4. Guangya Zhou, F E H Tay, Fook Siong Chau, Yi Zhao, VJ Logeeswaran, Micromechanical torsional digital-to-analog converter for open-loop angular positioning applications, J. Micromech. Microeng. 2004, Vol 14, pp. 737-745. 123 124 5. Yi Zhao, Francis E.H. Tay, Fook Siong Chau, Guangya Zhou, Fast and Precise Positioning of Electrostatically Actuated Dual-Axis Micromirror by Multi-Loop Digital Control, Sensors and Actuators: A. Physical (To be published at the end of 2006). 6. Yi Zhao, Francis E.H. Tay, Fook Siong Chau, Guangya Zhou, A study of electrostatic spring softening for dual-axis micromirror, Optik, 2006, Vol 117, pp. 367-372. 7. Yi Zhao, Francis E.H. Tay, Fook Siong Chau, Guangya Zhou, Stabilization of Dual-Axis Micromirror Beyond the Pull-In Point by Integral Sliding Mode Control, Journal of Micromechanics and Microengineering, 2006, Vol 16, pp. 1242-1250. Conference Papers 1. Yi Zhao, Francis E.H. Tay, Fook Siong Chau, Guangya Zhou, A Neual Compensator for Mis-Alignment of Double-Gimballed Mirror, The 1st International Symposium on Micro and Nano Technology, 14-17 March, 2004, Honolulu, Hawaii, USA. 2. Yi Zhao, F E H Tay, F S Chau, and Guangya Zhou, Effect of Bias voltage On Resonant Frequency For Dual-Axis Micromirror, 3rd International Conference on Materials for Advanced Technologies, 3-8 July 2005, Singapore, pp. 185-188. Appendix B RBF NN Code in C Language 125 126 127 Appendix C Micromorror Modelling in Matlab 128 129 130 131 132 Appendix D PID Control in Matlab 133 134 135 136 Appendix E Graphic Programme in LabVIEW 137 138 [...]... Overview of Dual- Axis Micromirror The dual- axis micromirror has attracted much attention because of its promising applications, such as free-space fiber optic switch [11]-[13], miniaturized projection display [14]-[16] and endoscopic optical coherence tomography [17] This device is generally a double-gimballed structure and has 3-DOF (degrees of freedom), two rotation motions (around x -axis and y -axis) and. .. Portrait of SMC 53 3.13 Schematic of ISMC 55 4.1 Cross-Sectional View of PolyMUMPs [105] 56 4.2 Top view of the dual- axis micromirror 59 4.3 Cross-section view of the dual- axis micromirror 60 4.4 Mask design of mirror 61 4.5 Support layout 61 4.6 Wire-bonded dual- axis. .. control parameters 94 xv List of Figures 1.1 3D model of MEMS dual- axis micromirror with electrostatic actuation 3 1.2 Schematic of one-DOF electrostatic actuation model 5 1.3 Normalized displacement and driving voltage 6 1.4 Typical distorted scanning field of dual- axis micromirror 6 1.5 Pull-in problem of parallel plate model 9 2.1 Differential... 1.1: 3D model of MEMS dual- axis micromirror with electrostatic actuation piezoelectric [23]-[27], electromagnetic [28]-[32], magnetostrictive [33]-[35] and electrostatic have been reported Among them, electrostatic actuation is a popular actuation scheme for the dual- axis micromirror, since it has the merits of low power consumption, simple driving electronics and ease of fabrication and integration... Wire-bonded dual- axis micromirror ready for testing 62 4.7 SEM view of the dual- axis micromirror 62 4.8 Schematic of system testing set-up 63 4.9 Schematic for differential voltage operation 64 4.10 Picture of the experimental set-up 66 4.11 A close view of the optical detecting system 66 List of Figures 5.1 Schematic of simulation... calibration methods and closed-loop control 10 1.6 Thesis Outline 11 methods of a dual- axis micromirror The fabrication techniques and design methodologies, although mentioned, are not the highlights of this thesis Moreover, this thesis will not discuss the optical performances, such as insertion loss and scanning resolution 1.6 Thesis Outline In Chapter 1, a general introduction of MEMS micromirror, including... with it and the purpose of this thesis are given Techniques associated with the linearization and the stable range extension are reviewed in Chapter 2 Chapter 3 presents the theoretical analysis micromirror is modelled Firstly, the MEMS dual- axis After that, the design methodologies of the two linearization methods, RBF NN and DT, are presented Finally, the design procedures for the two close-loop control. .. early of 1990s, microelectromechanical systems (MEMS) emerged with the aid of the development of integrated circuit (IC) fabrication process, and numerous novel devices have been reported in diverse areas of engineering and science The term MEMS refers to a collection of microsensors and actuators which can sense its environment and have the ability to react to changes in that environment with the use of. .. distorted scanning field of dual- axis micromirror 1.3 Problem Statement 7 dV = dx Ê k d0 − 3x √ 2A x (1.4) The above equation indicates that for a unit increment of displacement, the increment of voltage is smaller and smaller When x = d0 /3, the increment of voltage reaches zero The incremental displacement with respect to voltage is shown in Fig 1.3 In one degree -of- freedom (DOF), the operation nonlinearity... projection, etc, the concepts and feasibility of more complex MEMS devices have been proposed and demonstrated for a wide range of applications, such as microfluids, aerospace, biomedicine, chemical analysis, wireless communication, data storage, display and optics During the last two decades, all kinds of MEMS have been reported, such as optical MEMS [1][2], 1 1.1 Overview of Dual- Axis Micromirror 2 bioMEMS . LINEARIZATION AND CONTROL OF DUAL- AXIS MICROMIRROR ZHAO YI NATIONAL UNIVERSITY OF SINGAPORE 2006 LINEARIZATION AND CONTROL OF DUAL- AXIS MICROMIRROR ZHAO YI (M. Eng.) A. Cross-Sectional View of PolyMUMPs [105]. . . . . . . . . . . . . . . 56 4.2 Top view of the dual- axis micromirror. . . . . . . . . . . . . . . . . 59 4.3 Cross-section view of the dual- axis micromirror. . PID control parameters. . . . . . . . . . . . . . . . . . . . . . . . . 94 xv List of Figures 1.1 3D model of MEMS dual- axis micromirror with electrostatic actuation. 3 1.2 Schematic of one-DOF