The Proportional-Integral-Derivative (PID) controller operates the majority of modern control systems and has applications in many industries; thus any improvement in its design methodology has the potential to have a significant engineering and economic impact. Despite the existence of numerous methods for setting the parameters of PID controllers, the stability analysis of time-delay systems that use PID controllers remains extremely difficult and unclear, and there are very few existing results on PID controller synthesis.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. The focus is on linear time-invariant plants that may contain a time-delay in the feedback loop-a setting that captures many real-world practical and industrial situations. 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.

Adaptive Internal Model Control is a methodology for the design and analysis of adaptive internal model control schemes with provable guarantees of stability and robustness. Written in a self-contained tutorial fashion, this research monograph successfully brings the latest theoretical advances in the design of robust adaptive systems to the realm of industrial applications. It provides a theoretical basis for analytically justifying some of the reported industrial successes of existing adaptive internal model control schemes, and enables the reader to synthesise adaptive versions of their own favourite robust internal model control scheme by combining it with a robust adaptive law. The net result is that earlier empirical IMC designs can now be systematically robustified or replaced altogether by new designs with assured guarantees of stability and robustness.

Successfully classroom-tested at the graduate level, Linear Control Theory: Structure, Robustness, and Optimization covers three major areas of control engineering (PID control, robust control, and optimal control). It provides balanced coverage of elegant mathematical theory and useful engineering-oriented results.

The first part of the book develops results relating to the design of PID and first-order controllers for continuous and discrete-time linear systems with possible delays. The second section deals with the robust stability and performance of systems under parametric and unstructured uncertainty. This section describes several elegant and sharp results, such as Kharitonov's theorem and its extensions, the edge theorem, and the mapping theorem. Focusing on the optimal control of linear systems, the third part discusses the standard theories of the linear quadratic regulator, Hinfinity and l1 optimal control, and associated results.

Written by recognized leaders in the field, this book explains how control theory can be applied to the design of real-world systems. It shows that the techniques of three term controllers, along with the results on robust and optimal control, are invaluable to developing and solving research problems in many areas of engineering.

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. Structure and Synthesis of PID Controllers seeks to start to bridge the resultant gap and presents 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 research monograph 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, generalization of the Hermite-Biehler theorem, 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. Practitioners, researchers and graduate students should find this book a valuable source of information on cutting-edge research in the field of control.

Written in a self-contained tutorial fashion, this monograph successfully brings the latest theoretical advances in the design of robust adaptive systems to the realm of industrial applications. It provides a theoretical basis for verifying some of the reported industrial successes of existing adaptive control schemes and enables readers to synthesize adaptive versions of their own robust internal model control schemes.

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.