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INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, prim bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted Also, if unauthorized copyright material had to be removed, a note wiD indicate the deletion. Oversize materials (e.g^ maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the bade of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy; Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. A Bell & Howell Information Company 300 North Zeeb Road. Ann Arbor. Ml 48106-1346 USA 313/761-4700 800/521-0600 H ° ° Optimal Repetitive Control: Continuous-time and Sampled-data Formulations dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Thaddeus Eldon Peery, B.S., M.S. The Ohio State University 1995 Dissertation Committee: Approved by Professor Hitay Ozbay Professor Umit Ozguner Adviser Professor Krishnaswami Srinivasan Electrical Engineering Department UMI Number: 9534048 UMI Microform 9534048 Copyright 1995, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 © Copyright by Thaddeus Eldon Peery 1995 To all those who seak truth and honesty in all things. ii A cknowledgements First and foremost, I would like to thank my father, Mark E. Peery, for his un wavering support and friendship. Next, I would like to thank my advisor, Professor Hitay Ozbay, for his gentle and insightful leadership. A special thanks goes to my first mentor, Dean Daryle Riegle, of Vincennes University. I would also like to thank my other committee members, Professors Ozguner and Srinivasan, for their time, pa tience, and helpful suggestions. Finally, I thank my minor area Professors, Lee Potter and Anthony Bloch, for their excellence in both teaching and advising. In addition, I would like to thank all of the members of the “controls group” consisting of Professors Cruz, Ozguner, Ozbay, Passino, Utkin, and Yurkovich, along with all of their graduate students. It was the dynamic and energetic nature of this group that convinced me to come to The Ohio State University and remains my fa vorite thing about the graduate program. The group members who have been with me my entire time (or almost my entire time) here deserve special mention for their kind and generous help and comradery. They are (in alphabetical order): Kevin Burgess, Stewart DeVilbiss, Julie Hurtig, Layne Lenning, Keith Redmill, Wu-Chung Su, Onur Toker, and John Watkins. Some other group members whose time here overlapped with mine to a lessor extent, but whose help and support were especially significant, include: Tony Bailey, Dan Clancy, Sergey Drakunov, Lew Fulcher, Jim Gassman, Eric Laukonen, LaMoyne Porter, and Dave Schoenwald. Other group mem bers who contributed to the group dynamic sufficiently to make a lasting impression include: Scott Brown, Cem Hatipoglu, Hubert Chan, Murat Dogruel, Mindy Ever hart, Francisco Green, Franz Kautz, Andrew Kwong, Jeff Layne, Will Lennon, Sheila Longshore, Alfonsus Lunardhi, Amit Magan, Sashonda Morris, Vivek Moudgal, Tim Murphy, Jim Nivens, Shyamala Raghunathan, Martin Sikora, Martin Sommerville, Jeff Spooner, Cemil Ulus, Moeljono Widjaja, Jin Yang, Murat Zeren, and Mike Zim merman. Finally, there are some other students who, while not officially part of our group, contributed significantly to the group dynamic. They include: Scott Gray, Mark Hanes, Chris Masgras, Scott McMillan, Wendy Morrow, Bill Pearson, Jim Schrock, Aneil Shah, Kevin Smith, Steve Stitt, and Konur Unyelioglu. I would also like to thank several people from my professional past. First, I would like to thank my advisors from my M.S. at Purdue University, Professors John Chiasson and Stanislaw Zak. I would like to thank several people from my internship at the Honeywell Technology Center: Jim Krause (supervisor), Mary Jo Hoffman (internship mentor), Blaise Morton (friend/mentor), and Jen Sly (friend/office mate). I would also like to thank several people from Electrospace Systems, Incorporated: Mike Wolfe (supervisor), Les Allen (friend/program manager), the late Jeff Boughton (friend/office mate), Dorothy Metcalf (friend/secretary), Terry Beamer (department head), Bob Landis (friend/reliability engineer), and George Weber (office mate). I wish to thank several people for specific technical assistance. I thank Onur Toker for providing the software used in Chapter IV. I thank Professor Bamieh (of the University of Illinois) and his student Dan Stanek for providing additional details on the proofs in [5] and for valuable feedback on early drafts of [74], respectively. Finally, I would like to thank LaMoyne Porter for helpful discussions on genetic algorithms. Last, but not least, I would like to thank my Ohio State office mates, Behrouz Khayatian and Murat Zeren, for their pleasant companionship and fellowship, and “Professor Doug” the friendly Maintenance Engineer for relentlessly providing good cheer and lively banter. V ita May 28, 1963 .................................................... Born - Chester County, PA January 84 - June 85 ........................................Pre-Electrical Engineering Vincennes University Vincennes, Indiana Summer 86 ........................................................ Summer Intern Research and Engineering Lab General Dynamics Fort Worth Division August 1987 ...................................................... B.S. in Electrical Engineering Purdue University, West Lafayette, IN August 87 - January 89 .................................. Graduate Instructor Fellow Purdue University, West Lafayette, IN December 1988 ...................................................M.S. (Electrical) Engineering Purdue University, West Lafayette, IN January 89 - September 91 .............................Member Technical Staff Electrospace Systems Incorporated Richardson, Texas September 91 - August 92 ..............................University Fellow The Ohio State University Electrical Engineering Department September 92 - June 94 ...................................Research Associate The Ohio State University Control Research Laboratory Summer 93 ........................................................Doctoral Intern (researcher) Honeywell Technology Center Minneapolis, MN July 94 - June 95 ............................................. University Fellow The Ohio State University Electrical Engineering Department Publications Research Publications T. E. Peery and H. Ozbay “On H°° Optimal Repetitive Controllers”, Proceedings of the 32nd IEEE Conference on Decision and Control , San Antonio, Texas, pp. 1146- 1151, December 1993. H. Ozbay and T. E. Peery “On fixed order controllers for delay systems: Discrete- Time case”. Proceedings of the American Control Conference , San Francisco, CA, pp. 1030-1031, June 1993. Fields of Study Major Field: Electrical Engineering Major Area of Specialization: System and Control Theory Minor Areas of Specialization: Signal Processing/Communications Applied Mathematics T a b l e o f C o n t e n t s DEDICATION ............................................................................................................... ii ACKNOWLEDGEMENTS ........................................................................................ iii VITA ............................................................................................................................... vi LIST OF TABLES ......................................................................................................... xi LIST OF FIGURES ..................................................................................................... xii CHAPTER PAGE I Introduction ............................................................................................................. 1 1.1 Feedback control system s ......................................................................... 2 1.2 Repetitive control ...................................................................................... 4 1.3 H°° optimal control . ............................................................................ 6 1.4 Sampled-data system s ............................................................................... 8 1.5 Organization of the Dissertation ............................................................ 10 II Mathematical Definitions and Problem Statement ........................................ 12 2.1 Repetitive Control Theory .......................................................................

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