PID Controllers for Time-Delay Systems: (Control Engineering)

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.

Table of Contents:
The Hermite-Biehler Theorem and its Generalization.- PI Stabilization of Delay-Free Linear Time-Invariant Systems.- PID Stabilization of Delay-Free Linear Time-Invariant Systems.- Preliminary Results for Analyzing Systems with Time Delay.- Stabilization of Time-Delay Systems using a Constant Gain Feedback Controller.- PI Stabilization of First-Order Systems with Time Delay.- PID Stabilization of First-Order Systems with Time Delay.- Control System Design Using the PID Controller.- Analysis of Some PID Tuning Techniques.- PID Stabilization of Arbitrary Linear Time-Invariant Systems with Time Delay.- Algorithms for Real and Complex PID Stabilization.

Review :
"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