Controller Design for Distributed Parameter Systems

1. Front Matter

   Pages i-xii

   PDF

2. Introduction

   • Kirsten A. Morris

   Pages 1-11

3. Infinite-Dimensional Systems Theory

   • Kirsten A. Morris

   Pages 13-69

4. Dynamics and Stability

   • Kirsten A. Morris

   Pages 71-102

5. Optimal Linear-Quadratic Controller Design

   • Kirsten A. Morris

   Pages 103-153

6. Disturbances

   • Kirsten A. Morris

   Pages 155-190

7. Estimation

   • Kirsten A. Morris

   Pages 191-218

8. Output Feedback Controller Design

   • Kirsten A. Morris

   Pages 219-252

9. Back Matter

   Pages 253-287

   PDF

This book addresses controller and estimator design for systems that vary both spatially and in time: systems like fluid flow, acoustic noise and flexible structures. It includes coverage of the selection and placement of actuators and sensors for such distributed-parameter systems.

The models for distributed parameter systems are coupled ordinary/partial differential equations. Approximations to the governing equations, often of very high order, are required and this complicates both controller design and optimization of the hardware locations.

Control system and estimator performance depends not only on the controller/estimator design but also on the location of the hardware. In helping the reader choose the best location for actuators and sensors, the analysis provided in this book is crucial because neither intuition nor trial-and-error is foolproof, especially where multiple sensors and actuators are required, and moving hardware can be difficult and costly. Themechatronic approach advocated, in which controller design is integrated with actuator location, can lead to better performance without increased cost. Similarly, better estimation can be obtained with carefully placed sensors. The text shows how proper hardware placement varies depending on whether, disturbances are present, whether the response should be reduced to an initial condition or whether controllability and/or observability have to be optimized.

This book is aimed at non-specialists interested in learning controller design for distributed-parameter systems and the material presented has been used for student teaching. The relevant basic systems theory is presented and followed by a description of controller synthesis using lumped approximations. Numerical algorithms useful for efficient implementation in real engineering systems and practical computational challenges are also described and discussed.

• Distributed-parameter Systems
• Feedback Control
• Sensor Location
• Actuator Location
• Mathematical Models
• Infinite-dimensional Systems

“There are several features that make this text very timely and unique. … the author concludes each chapter with a self-contained section summarizing the primary contents for the chapter and related advanced topics, along with a comprehensive (yet concise) set of references. … Through its combination of theory, approximation techniques, and examples, the text provides a valuable resource for both instructors and readers seeking a self-contained introduction to control and estimation for distributed parameter systems.” (Ralph C. Smith, IEEE Control Systems Magazine, Vol. 43 (1), February, 2023)

• Department of Applied Mathematics, University of Waterloo, Waterloo, Canada

  Kirsten A. Morris

Prof. Kirsten Morris’ research interests are control and estimation of systems modelled by partial differential equations and also systems, such as smart materials, involving hysteresis. Her recent research has focused on improving performance through attention to actuator location as part of controller design, and sensor location as part of estimator design.  She has written an undergraduate textbook "Introduction to Feedback Control", and was editor of the book  “Control of Flexible Structures”. She is a professor in  the Applied Mathematics Department at the University of Waterloo. From 2005-2008 she was Associate Dean for Graduate Studies & Research in the Faculty of Mathematics. She has held visiting positions at ICASE (NASA Langley), the Fields Institute, the Institute for Mathematics & Applications in Minneapolis and the Institut de Mathematiques in Bordeaux. Prof. Morris served as a vice-president of the IEEE Control System Society from 2013-2016, vice-chair of the SIAM Control & Systems Theory group 2016-2017 and chair of that organization 2018-2019. She was an associate editor with the IEEE Transactions on Automatic Control and is currently an editor for the journals SIAM Journal on Control & Optimization, Mathematics of Control, Signals & Systems, and the Asian Journal of Control and she is a member of the editorial board of the  SIAM  book series Advances in Design & Control.

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