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PID Controllers for Time-Delay Systems

  • Book
  • © 2005

Overview

Authors:
  1. Guillermo J. Silva

    1. IBM, Austin, USA

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  2. Aniruddha Datta

    1. Department of Electrical Engineering, Texas A&M University, College Station, USA

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  3. S. P. Bhattachaiyya

    1. Department of Electrical Engineering, Texas A&M University, College Station, USA

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  • The PID controller operates the majority of modern control systems and has applications in many industries
  • Improvement in PID design methodology – one focus of this book – has the potential to have a significant engineering and economic impact
  • There are very few existing results on PID controller synthesis; this book fills a gap in the literature by presenting recent and original results in design and analysis, as well as synthesis

Part of the book series: Control Engineering (CONTRENGIN)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    Pages 1-19

  3. The Hermite-Biehler Theorem and its Generalization

    Pages 21-37

  4. PI Stabilization of Delay-Free Linear Time-Invariant Systems

    Pages 39-56

  5. PID Stabilization of Delay-Free Linear Time-Invariant Systems

    Pages 57-75

  6. Preliminary Results for Analyzing Systems with Time Delay

    Pages 77-107

  7. Stabilization of Time-Delay Systems using a Constant Gain Feedback Controller

    Pages 109-134

  8. PI Stabilization of First-Order Systems with Time Delay

    Pages 135-159

  9. PID Stabilization of First-Order Systems with Time Delay

    Pages 161-190

  10. Control System Design Using the PID Controller

    Pages 191-222

  11. Analysis of Some PID Tuning Techniques

    Pages 223-241

  12. PID Stabilization of Arbitrary Linear Time-Invariant Systems with Time Delay

    Pages 243-263

  13. Algorithms for Real and Complex PID Stabilization

    Pages 265-295

  14. Back Matter

    Pages 297-330
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Keywords

About this book

This monograph presents our recent results on the proportional-integr- derivative (PID) controller and its design, analysis, and synthesis. The fo­ cus is on linear time-invariant plants that may contain a time delay in the feedback loop. This setting captures many real-world practical and in­ dustrial situations. The results given here include and complement those published in Structure and Synthesis of PID Controllers by Datta, Ho, and Bhattacharyya [10]. In [10] we mainly dealt with the delay-free case. The main contribution described here is the efficient computation of the entire set of PID controllers achieving stability and various performance specifications. The performance specifications that can be handled within our machinery are classical ones such as gain and phase margin as well as modern ones such as Hoo norms of closed-loop transfer functions. Finding the entire set is the key enabling step to realistic design with several design criteria. The computation is efficient because it reduces most often to lin­ ear programming with a sweeping parameter, which is typically the propor­ tional gain. This is achieved by developing some preliminary results on root counting, which generalize the classical Hermite-Biehler Theorem, and also by exploiting some fundamental results of Pontryagin on quasi-polynomials to extract useful information for controller synthesis. The efficiency is im­ portant for developing software design packages, which we are sure will be forthcoming in the near future, as well as the development of further capabilities such as adaptive PID design and online implementation.

Reviews

"Those who have followed the area closely will notice that the authors of PID Controllers for Time-Delay Systems have taken a path quite different from other researchers. In particular, the authors have concentrated on characterizing the complete set of PID controls that stabilize a system. This approach gives the old topic a rather modern flavor. The significance of this line of research is obvious….

This book is a systematic presentation of many important aspects of the authors’ work on PID control with emphasis on time-delay systems. The book describes the set of PID controllers that stabilize the system and explains how to use this set to design PID controllers that achieve robustness, nonfragility, and improved performance….

The book is of interest to practicing engineers, graduate students, and researchers working in the systems and control area. The authors do an excellent job presenting the materials systematically, striking a balance between mathematical rigor and accessibility to average readers. The book contains numerous diagrams and many illustrative examples to enhance its readability...[and] is very well written and can be used for self-study and as a reference."   —IEEE Control Systems Magazine

"This monograph presents some recent results on the proportional-integral-derivative (PID) controller and its design, analysis and synthesis.... It seems that these results are timely and in line with the resurgence of interest in the PID controller and the general rekindling of interest in fixed- and low-order controller design. As is known, there are hardly any results in modern and postmodern control theory in this regard, while such controllers are the ones of choice in applications.... It is hoped that the monograph will act as a catalyst to bridge the gap between theory and practice and also the gap between classical and modern control theory."  —Mathematical Reviews

Authors and Affiliations

  • IBM, Austin, USA

    Guillermo J. Silva

  • Department of Electrical Engineering, Texas A&M University, College Station, USA

    Aniruddha Datta, S. P. Bhattachaiyya

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