Special issue on PID control in the information age: Theoretical advances and applications

Abstract

For well over a century, from the enabling of early governors to a standard tool in process control, PID (proportional–integral–derivative) control stood out as the most favored method for its unparalleled simplicity, ease of implementation, and cost-effectiveness, and indeed has been an enduring gift to feedback control. For a technique so mature and seemingly so ageless, what can be new and worthy of attention? Surprisingly, even in a post-modern and information-centric era of time, PID control continues to demonstrate its sustained power and inexplicable charm, with incredible vitality and widespread acceptance by industrial control and automation communities. In coping with the increased complexity and challenge of contemporary engineering systems, there has been renewed interest in PID control, on fundamental issues concerning robustness, performance, structure, and optimization, as well as on practical design, implementation, and tuning. Recent studies on PID control have led to new and improved design and tuning rules, and expansions into new, emerging problem areas and application domains. These call for a reexamination and further development of the fascinating subject of PID control theory and applications. This special issue responds to the recent surge of research activities and is aimed at bringing together the latest advances central to PID control. A total of 22 articles are featured in the issue, which attests to the richness and versatility of PID control, and its depth and breadth. We must marvel at the fact that even for such a century-old topic, there are still gems to be discovered. Exactly one hundred years ago, in the year of 1922, Nicolas Minorsky published his landmark paper—believed to be the first published theory—on PID control, “Directional Stability of Automatically Steered Bodies” (Journal of the American Society of Naval Engineers, vol. 34, no. 2, May 1922, pp. 280–309), thus heralding in the birth of the formal PID control theory, alongside the theories of Maxwell, Routh, and Hurwitz. This, we take as a pleasant coincidence, and it appears fitting for commemoration. Thus, at its centennial mark, we are pleased to present this special issue and hope that it will inspire new thoughts and ideas for the continuing development and prosperity of PID control in years to come. It should be said that although intended for the reader's convenience this classification is rather crude, and is by no means accurate nor necessary; in fact, each article may be intertwined with some others from a different group, and hence may well cross into several categories. We briefly introduce below the contributions. Traditionally, PID control presumes, except in rare instances, a linear plant model, while in physical implementation, the underlying system contains intrinsically nonlinear characteristics. As such, PID design and tuning techniques for nonlinear systems are of both theoretical interest and practical importance. Zhao and Guo1 considered a regulation problem for a class of non-affine nonlinear uncertain plants. They constructed an extended PD (EPD) controller and showed that by tuning the EPD parameters appropriately from a set defined by the nonlinear characteristics, it is possible to achieve global regulation. Lyu and Lin2 studied the PID control problem for planar uncertain nonlinear systems with a bounded time-varying input delay. The system uncertainty is characterized by bounds on the growth rates of the nonlinear function and by a bound on the range of time delay in the system model. The authors obtained linear matrix inequality (LMI) conditions for the uncertain nonlinear system to be stabilized globally uniformly asymptotically under PID feedback, and a bound on the delay range. Similarly, Xiong and Hou3 investigated uncertain nonlinear non-affine discrete-time systems. By employing a dynamic linearization scheme, they showed that a PID controller based on the linearized model, when appropriately co