The book investigates fundamental issues in flexible manipulator systems, including distributed parameter modeling and boundary controller design. It presents theoretical explorations of several fundamental problems concerning the dynamics and control of these systems. By integrating fresh concepts and results to form a systematic approach to control, it also provides a basic theoretical framework. In turn, the book offers a comprehensive treatment of flexible manipulator systems, addressing topics ranging from related distributed parameter modeling and advanced boundary controller design for these systems with input constraint, to active control with output constraint. In brief, the book addresses dynamical analysis and control design for flexible manipulator systems. Though primarily intended for researchers and engineers in the control system and mechanical engineering community, it can also serve as supplemental reading on the modeling and control of flexible manipulator systems at the postgraduate level.

This book provides a comprehensive review of fundamental issues in the dynamical modeling and vibration control design for several flexible mechanical systems, such as flexible satellites, flexible aerial refueling hoses, and flexible three-dimensional manipulators. Offering an authoritative reference guide to the dynamics and control of flexible mechanical systems, it equips readers to solve a host of problems concerning these systems. It provides not only a complete overview of flexible systems, but also a better understanding of the technical levels involved. The book is divided into ten chapters: Chapters 1 and 2 lay the foundations, while the remaining chapters explore several independent yet related topics in detail. The book’s final chapter presents conclusions and recommendations for future research. Given its scope, the book is intended for researchers, graduate students, and engineers whose work involves control systems, flexible mechanical systems, and related areas.

The main objectives of the book are to introduce the design method of boundary control strategies for the axially moving structures to reduce their vibration. This book provides the reader with a thorough grounding in the boundary controller design. Our goal is to provide advanced boundary controller design methods and their stability analysis methods and offer simulation examples and MATLAB programs for each boundary control algorithm. For each chapter, several engineering application examples are given and the contents of each chapter in this book are independent, so that readers can just read their own needs. In this book, all the control algorithms and their programs are described separately and classified by the chapter name, which can be run successfully in MATLAB. The book can benefit researchers, engineers, and graduate students in the fields of PDE modeling and boundary vibration control of flexible structures.

This monograph provides a rigorous treatment of problems related to partial asymptotic stability and controllability for models of flexible structures described by coupled nonlinear ordinary and partial differential equations or equations in abstract spaces. The text is self-contained, beginning with some basic results from the theory of continuous semigroups of operators in Banach spaces. The problem of partial asymptotic stability with respect to a continuous functional is then considered for a class of abstract multivalued systems on a metric space. Next, the results of this study are applied to the study of a rotating body with elastic attachments. Professor Zuyev demonstrates that the equilibrium cannot be made strongly asymptotically stable in the general case, motivating consideration of the problem of partial stabilization with respect to the functional that represents “averaged” oscillations. The book’s focus moves on to spillover analysis for infinite-dimensional systems with finite-dimensional controls. It is shown that a family of L2-minimal controls, corresponding to low frequencies, can be used to obtain approximate solutions of the steering problem for the complete system. The book turns from the examination of an abstract class of systems to particular physical examples. Timoshenko beam theory is exploited in studying a mathematical model of a flexible-link manipulator. Finally, a mechanical system consisting of a rigid body with the Kirchhoff plate is considered. Having established that such a system is not controllable in general, sufficient controllability conditions are proposed for the dynamics on an invariant manifold. Academic researchers and graduate students interested in control theory and mechanical engineering will find Partial Stabilization and Control of Distributed-Parameter Systems with Elastic Elements a valuable and authoritative resource for investigations on the subject of partial stabilization.

Flexible robotic manipulators pose various challenges in research as compared to rigid robotic manipulators, ranging from system design, structural optimization, and construction to modeling, sensing, and control. Although significant progress has been made in many aspects over the last one-and-a-half decades, many issues are not resolved yet, and simple, effective, and reliable controls of flexible manipulators still remain an open quest. Clearly, further efforts and results in this area will contribute significantly to robotics (particularly automation) as well as its application and education in general control engineering. To accelerate this process, the leading experts in this important area present in this book the state of the art in advanced studies of the design, modeling, control and applications of flexible manipulators.

This book is a self-contained collection of recent research findings providing a comprehensive and systematic unified framework for both analysis and synthesis for singularly perturbed systems. It paves the way for the gap between frequency-domain-transfer-function-based results and time-domain-state-space-based results to be bridged. It is divided into three parts focusing on: fundamental background of singular perturbation; general singular perturbation methodologies and time-scale techniques and the theoretical foundation of finite-frequency control; the analysis and synthesis of singularly perturbed systems; and real-world engineering applications implementing the results developed in systems like wind turbines and autonomous-aerial-vehicle hovering. It also presents solutions to analysis and design problems in terms of linear matrix inequalities. Lastly, it provides valuable reference material for researchers who wish to explore the design of controllers for such systems.

The increasing requirements for active control of large aerospace, chemical and mechanical systems have focused attention on recent research into the control of distributed parameter systems. The increasing capabilities in computation, instrumentation and actuators have made possible implementation of sophisticated control schemes based on this research. This volume represents state of the art reports on the theory and current and future applications, and should be considered essential reading for all those involved in the production of such systems.