Filling a gap in the literature, this book is a presentation of recent results in the field of PID controllers, including their design, analysis, and synthesis. Emphasis is placed on the efficient computation of the entire set of PID controllers achieving stability and various performance specifications, which is important for the development of future software design packages, as well as further capabilities such as adaptive PID design and online implementation. The results presented here are timely given the resurgence of interest in PID controllers and will find widespread application, specifically in the development of computationally efficient tools for PID controller design and analysis. Serving as a catalyst to bridge the theory--practice gap in the control field as well as the classical--modern gap, this monograph is an excellent resource for control, electrical, chemical, and mechanical engineers, as well as researchers in the field of PID controllers.

Filling a gap in the literature, this book is a presentation of recent results in the field of PID controllers, including their design, analysis, and synthesis. Emphasis is placed on the efficient computation of the entire set of PID controllers achieving stability and various performance specifications, which is important for the development of future software design packages, as well as further capabilities such as adaptive PID design and online implementation. The results presented here are timely given the resurgence of interest in PID controllers and will find widespread application, specifically in the development of computationally efficient tools for PID controller design and analysis. Serving as a catalyst to bridge the theory--practice gap in the control field as well as the classical--modern gap, this monograph is an excellent resource for control, electrical, chemical, and mechanical engineers, as well as researchers in the field of PID controllers.

Time delays are important components of many systems in, for instance, engineering, physics, economics, and the life sciences, because the transfer of material, energy, and information is usually not instantaneous. Time delays may appear as computation and communication lags, they model transport phenomena and heredity, and they arise as feedback delays in control loops. This monograph addresses the problem of stability analysis, stabilization, and robust fixed-order control of dynamical systems subject to delays, including both retarded- and neutral-type systems. Within the eigenvalue-based framework, an overall solution is given to the stability analysis, stabilization, and robust control design problem, using both analytical methods and numerical algorithms and applicable to a broad class of linear time-delay systems.? In this revised edition, the authors make the leap from stabilization to the design of robust and optimal controllers and from retarded-type to neutral-type delay systems, thus enlarging the scope of the book within control; include new, state-of-the-art material on numerical methods and algorithms to broaden the book?s focus and to reach additional research communities, in particular numerical linear algebra and numerical optimization; and increase the number and range of applications to better illustrate the effectiveness and generality of their approach.?

This work is concerned with the design of PID controllers, calculation of set point weighting parameter and identification of transfer function models for unstable systems with time delay and without or with a zero.

This book provides an introduction to the analysis and control of Linear Parameter-Varying Systems and Time-Delay Systems and their interactions. The purpose is to give the readers some fundamental theoretical background on these topics and to give more insights on the possible applications of these theories. This self-contained monograph is written in an accessible way for readers ranging from undergraduate/PhD students to engineers and researchers willing to know more about the fields of time-delay systems, parameter-varying systems, robust analysis, robust control, gain-scheduling techniques in the LPV fashion and LMI based approaches. The only prerequisites are basic knowledge in linear algebra, ordinary differential equations and (linear) dynamical systems. Most of the results are proved unless the proof is too complex or not necessary for a good understanding of the results. In the latter cases, suitable references are systematically provided. The first part pertains on the representation, analysis and control of LPV systems along with a reminder on robust analysis and control techniques. The second part is concerned with the representation and analysis of time-delay systems using various time-domain techniques. The third and last part is devoted to the representation, analysis, observation, filtering and control of LPV time-delay systems. The book also presents many important basic and advanced results on the manipulation of LMIs.

In many industrial applications, the existing constraints mandate the use of controllers of low and fixed order while typically, modern methods of optimal control produce high-order controllers. The authors seek to start to bridge the resultant gap and present a novel methodology for the design of low-order controllers such as those of the P, PI and PID types. Written in a self-contained and tutorial fashion, this book first develops a fundamental result, generalizing a classical stability theorem – the Hermite–Biehler Theorem – and then applies it to designing controllers that are widely used in industry. It contains material on: • current techniques for PID controller design; • stabilization of linear time-invariant plants using PID controllers; • optimal design with PID controllers; • robust and non-fragile PID controller design; • stabilization of first-order systems with time delay; • constant-gain stabilization with desired damping • constant-gain stabilization of discrete-time plants.

Recently, there have been significant developments in robust control of time-delay systems. This volume presents a systematic treatment of robust control for such systems in the frequency domain. The emphasis is on systems with a single input or output delay, although the delay-free part of the plant can be multi-input-multi-output, in which case the delays in different channels should be the same. The author covers the whole range of H-infinity control of time-delay systems: from controller parameterization implementation; from the Nehari problem to the four-block problem; from theoretical developments to practical issues. The major tools used are similarity transformation, the chain-scattering approach and J-spectral factorization. Self-contained, "Robust Control of Time-delay Systems" will interest control theorists and mathematicians working with time-delay systems. Its methodical approach will be of value to graduates studying general robust control theory or its applications in time-delay systems.

The early 21st century has seen a renewed interest in research in the widely-adopted proportional-integral-differential (PID) form of control. PID Control in the Third Millennium provides an overview of the advances made as a result. Featuring: new approaches for controller tuning; control structures and configurations for more efficient control; practical issues in PID implementation; and non-standard approaches to PID including fractional-order, event-based, nonlinear, data-driven and predictive control; the nearly twenty chapters provide a state-of-the-art resumé of PID controller theory, design and realization. Each chapter has specialist authorship and ideas clearly characterized from both academic and industrial viewpoints. PID Control in the Third Millennium is of interest to academics requiring a reference for the current state of PID-related research and a stimulus for further inquiry. Industrial practitioners and manufacturers of control systems with application problems relating to PID will find this to be a practical source of appropriate and advanced solutions.

This monograph presents a new analytical approach to the design of proportional-integral-derivative (PID) controllers for linear time-invariant plants. The authors develop a computer-aided procedure, to synthesize PID controllers that satisfy multiple design specifications. A geometric approach, which can be used to determine such designs methodically using 2- and 3-D computer graphics is the result. The text expands on the computation of the complete stabilizing set previously developed by the authors and presented here. This set is then systematically exploited to achieve multiple design specifications simultaneously. These specifications include classical gain and phase margins, time-delay tolerance, settling time and H-infinity norm bounds. The results are developed for continuous- and discrete-time systems. An extension to multivariable systems is also included. Analytical Design of PID Controllers provides a novel method of designing PID controllers, which makes it ideal for both researchers and professionals working in traditional industries as well as those connected with unmanned aerial vehicles, driverless cars and autonomous robots.