Stability And Stabilization Of Infinite Dimensional Systems With Applications
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Stability And Stabilization Of Infinite Dimensional Systems With Applications
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Author : Zheng-Hua Luo
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-01-22
Stability And Stabilization Of Infinite Dimensional Systems With Applications written by Zheng-Hua Luo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-22 with Computers categories.
The time evol11tion of many physical phenomena in nat11re can be de scribed by partial differential eq11ations. To analyze and control the dynamic behavior of s11ch systems. infinite dimensional system theory was developed and has been refined over the past several decades. In recent years. stim11lated by the applications arising from space exploration. a11tomated manufact11ring, and other areas of technological advancement, major progress has been made in both theory and control technology associated with infinite dimensional systems. For example, new conditions in the time domain and frequency domain have been derived which guarantee that a Co-semigroup is exponen tially stable; new feedback control laws helVe been proposed to exponentially ;;tabilize beam. wave, and thermoelastic equations; and new methods have been developed which allow us to show that the spectrum-determined growth condition holds for a wide class of systems. Therefore, there is a need for a reference book which presents these restllts in an integrated fashion. Complementing the existing books, e. g . . [1]. [41]. and [128]. this book reports some recent achievements in stability and feedback stabilization of infinite dimensional systems. In particular, emphasis will be placed on the second order partial differential equations. such as Euler-Bernoulli beam equations. which arise from control of numerous mechanical systems stich as flexible robot arms and large space structures. We will be focusing on new results. most of which are our own recently obtained research results.
Stability And Stabilization Of Infinite Dimensional Systems With Applications
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Author : Zheng-Hua Luo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stability And Stabilization Of Infinite Dimensional Systems With Applications written by Zheng-Hua Luo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
This book reports on recent achievements in stability and feedback stabilization of infinite systems. In particular emphasis is placed on second order partial differential equations, such as Euler-Bernoulli beam equations, which arise from vibration control of flexible robots arms and large space structures. Various control methods such as sensor feedback control and dynamic boundary control are applied to stabilize the equations. Many new theorems and methods are included in the book. Proof procedures of existing theorems are simplified, and detailed proofs have been given to most theorems. New results on semigroups and their stability are presented, and readers can learn several useful techniques for solving practical engineering problems. Until now, the recently obtained research results included in this book were unavailable in one volume. This self-contained book is an invaluable source of information for all those who are familiar with some basic theorems of functional analysis.
Stabilization Of Infinite Dimensional Systems
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Author : El Hassan Zerrik
language : en
Publisher:
Release Date : 2021
Stabilization Of Infinite Dimensional Systems written by El Hassan Zerrik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This book deals with the stabilization issue of infinite dimensional dynamical systems both at the theoretical and applications levels. Systems theory is a branch of applied mathematics, which is interdisciplinary and develops activities in fundamental research which are at the frontier of mathematics, automation and engineering sciences. It is everywhere, innumerable and daily, and moreover is there something which is not system: it is present in medicine, commerce, economy, psychology, biological sciences, finance, architecture (construction of towers, bridges, etc.), weather forecast, robotics, automobile, aeronautics, localization systems and so on. These are the few fields of application that are useful and even essential to our society. It is a question of studying the behavior of systems and acting on their evolution. Among the most important notions in system theory, which has attracted the most attention, is stability. The existing literature on systems stability is quite important, but disparate, and the purpose of this book is to bring together in one document the essential results on the stability of infinite dimensional dynamical systems. In addition, as such systems evolve in time and space, explorations and research on their stability have been mainly focused on the whole domain in which the system evolved. The authors have strongly felt that, in this sense, important considerations are missing: those which consist in considering that the system of interest may be unstable on the whole domain, but stable in a certain region of the whole domain. This is the case in many applications ranging from engineering sciences to living science. For this reason, the authors have dedicated this book to extension of classical results on stability to the regional case. This book considers a very important issue, which is that it should be accessible to mathematicians and to graduate engineering with a minimal background in functional analysis. Moreover, for the majority of the students, this would be their only acquaintance with infinite dimensional system. Accordingly, it is organized by following increasing difficulty order. The two first chapters deal with stability and stabilization of infinite dimensional linear systems described by partial differential equations. The following chapters concern original and innovative aspects of stability and stabilization of certain classes of systems motivated by real applications, that is to say bilinear and semi-linear systems. The stability of these systems has been considered from a global and regional point of view. A particular aspect concerning the stability of the gradient has also been considered for various classes of systems. This book is aimed at students of doctoral and master's degrees, engineering students and researchers interested in the stability of infinite dimensional dynamical systems, in various aspects.
The Control Systems Handbook
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Author : William S. Levine
language : en
Publisher: CRC Press
Release Date : 2018-10-03
The Control Systems Handbook written by William S. Levine and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Technology & Engineering categories.
At publication, The Control Handbook immediately became the definitive resource that engineers working with modern control systems required. Among its many accolades, that first edition was cited by the AAP as the Best Engineering Handbook of 1996. Now, 15 years later, William Levine has once again compiled the most comprehensive and authoritative resource on control engineering. He has fully reorganized the text to reflect the technical advances achieved since the last edition and has expanded its contents to include the multidisciplinary perspective that is making control engineering a critical component in so many fields. Now expanded from one to three volumes, The Control Handbook, Second Edition organizes cutting-edge contributions from more than 200 leading experts. The third volume, Control System Advanced Methods, includes design and analysis methods for MIMO linear and LTI systems, Kalman filters and observers, hybrid systems, and nonlinear systems. It also covers advanced considerations regarding — Stability Adaptive controls System identification Stochastic control Control of distributed parameter systems Networks and networked controls As with the first edition, the new edition not only stands as a record of accomplishment in control engineering but provides researchers with the means to make further advances. Progressively organized, the first two volumes in the set include: Control System Fundamentals Control System Applications
The Control Handbook Three Volume Set
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Author : William S. Levine
language : en
Publisher: CRC Press
Release Date : 2018-10-08
The Control Handbook Three Volume Set written by William S. Levine and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-08 with Technology & Engineering categories.
At publication, The Control Handbook immediately became the definitive resource that engineers working with modern control systems required. Among its many accolades, that first edition was cited by the AAP as the Best Engineering Handbook of 1996. Now, 15 years later, William Levine has once again compiled the most comprehensive and authoritative resource on control engineering. He has fully reorganized the text to reflect the technical advances achieved since the last edition and has expanded its contents to include the multidisciplinary perspective that is making control engineering a critical component in so many fields. Now expanded from one to three volumes, The Control Handbook, Second Edition brilliantly organizes cutting-edge contributions from more than 200 leading experts representing every corner of the globe. They cover everything from basic closed-loop systems to multi-agent adaptive systems and from the control of electric motors to the control of complex networks. Progressively organized, the three volume set includes: Control System Fundamentals Control System Applications Control System Advanced Methods Any practicing engineer, student, or researcher working in fields as diverse as electronics, aeronautics, or biomedicine will find this handbook to be a time-saving resource filled with invaluable formulas, models, methods, and innovative thinking. In fact, any physicist, biologist, mathematician, or researcher in any number of fields developing or improving products and systems will find the answers and ideas they need. As with the first edition, the new edition not only stands as a record of accomplishment in control engineering but provides researchers with the means to make further advances.
Nonsmooth Lyapunov Analysis In Finite And Infinite Dimensions
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Author : Yury Orlov
language : en
Publisher: Springer Nature
Release Date : 2020-02-08
Nonsmooth Lyapunov Analysis In Finite And Infinite Dimensions written by Yury Orlov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-08 with Technology & Engineering categories.
Nonsmooth Lyapunov Analysis in Finite and Infinite Dimensions provides helpful tools for the treatment of a broad class of dynamical systems that are governed, not only by ordinary differential equations but also by partial and functional differential equations. Existing Lyapunov constructions are extended to discontinuous systems—those with variable structure and impact—by the involvement of nonsmooth Lyapunov functions. The general theoretical presentation is illustrated by control-related applications; the nonsmooth Lyapunov construction is particularly applied to the tuning of sliding-mode controllers in the presence of mismatched disturbances and to orbital stabilization of the bipedal gate. The nonsmooth construction is readily extendible to the control and identification of distributed-parameter and time-delay systems. The first part of the book outlines the relevant fundamentals of benchmark models and mathematical basics. The second concentrates on the construction of nonsmooth Lyapunov functions. Part III covers design and applications material. This book will benefit the academic research and graduate student interested in the mathematics of Lyapunov equations and variable-structure control, stability analysis and robust feedback design for discontinuous systems. It will also serve the practitioner working with applications of such systems. The reader should have some knowledge of dynamical systems theory, but no background in discontinuous systems is required—they are thoroughly introduced in both finite- and infinite-dimensional settings.
Dynamics And Control Of Mechanical Systems In Offshore Engineering
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Author : Wei He
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-02
Dynamics And Control Of Mechanical Systems In Offshore Engineering written by Wei He and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-02 with Technology & Engineering categories.
Dynamics and Control of Mechanical Systems in Offshore Engineering is a comprehensive treatment of marine mechanical systems (MMS) involved in processes of great importance such as oil drilling and mineral recovery. Ranging from nonlinear dynamic modeling and stability analysis of flexible riser systems, through advanced control design for an installation system with a single rigid payload attached by thrusters, to robust adaptive control for mooring systems, it is an authoritative reference on the dynamics and control of MMS. Readers will gain not only a complete picture of MMS at the system level, but also a better understanding of the technical considerations involved and solutions to problems that commonly arise from dealing with them. The text provides: · a complete framework of dynamical analysis and control design for marine mechanical systems; · new results on the dynamical analysis of riser, mooring and installation systems together with a general modeling method for a class of MMS; · a general method and strategy for realizing the control objectives of marine systems with guaranteed stability the effectiveness of which is illustrated by extensive numerical simulation; and · approximation-based control schemes using neural networks for installation of subsea structures with attached thrusters in the presence of time-varying environmental disturbances and parametric uncertainties. Most of the results presented are analytical with repeatable design algorithms with proven closed-loop stability and performance analysis of the proposed controllers is rigorous and detailed. Dynamics and Control of Mechanical Systems in Offshore Engineering is primarily intended for researchers and engineers in the system and control community, but graduate students studying control and marine engineering will also find it a useful resource as will practitioners working on the design, running or maintenance of offshore platforms.
Controller Design For Distributed Parameter Systems
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Author : Kirsten A. Morris
language : en
Publisher: Springer Nature
Release Date : 2020-06-01
Controller Design For Distributed Parameter Systems written by Kirsten A. Morris and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-01 with Technology & Engineering categories.
This book addresses controller and estimator design for systems that vary both spatially and in time: systems like fluid flow, acoustic noise and flexible structures. It includes coverage of the selection and placement of actuators and sensors for such distributed-parameter systems. The models for distributed parameter systems are coupled ordinary/partial differential equations. Approximations to the governing equations, often of very high order, are required and this complicates both controller design and optimization of the hardware locations. Control system and estimator performance depends not only on the controller/estimator design but also on the location of the hardware. In helping the reader choose the best location for actuators and sensors, the analysis provided in this book is crucial because neither intuition nor trial-and-error is foolproof, especially where multiple sensors and actuators are required, and moving hardware can be difficult and costly. The mechatronic approach advocated, in which controller design is integrated with actuator location, can lead to better performance without increased cost. Similarly, better estimation can be obtained with carefully placed sensors. The text shows how proper hardware placement varies depending on whether, disturbances are present, whether the response should be reduced to an initial condition or whether controllability and/or observability have to be optimized. This book is aimed at non-specialists interested in learning controller design for distributed-parameter systems and the material presented has been used for student teaching. The relevant basic systems theory is presented and followed by a description of controller synthesis using lumped approximations. Numerical algorithms useful for efficient implementation in real engineering systems and practical computational challenges are also described and discussed.
Modelling Dynamics In Processes And Systems
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Author : Wojciech Mitkowski
language : en
Publisher: Springer
Release Date : 2009-05-02
Modelling Dynamics In Processes And Systems written by Wojciech Mitkowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-02 with Mathematics categories.
Dynamics is what characterizes virtually all phenomenae we face in the real world, and processes that proceed in practically all kinds of inanimate and animate systems, notably social systems. For our purposes dynamics is viewed as time evolution of some characteristic features of the phenomenae or processes under consideration. It is obvious that in virtually all non-trivial problems dynamics can not be neglected, and should be taken into account in the analyses to, first, get insight into the problem consider, and second, to be able to obtain meaningful results. A convenient tool to deal with dynamics and its related evolution over time is to use the concept of a dynamic system which, for the purposes of this volume can be characterized by the input (control), state and output spaces, and a state transition equation. Then, starting from an initial state, we can find a sequence of consecutive states (outputs) under consecutive inputs (controls). That is, we obtain a trajectory. The state transition equation may be given in various forms, exemplified by differential and difference equations, linear or nonlinear, deterministic or stochastic, or even fuzzy (imprecisely specified), fully or partially known, etc. These features can give rise to various problems the analysts may encounter like numerical difficulties, instability, strange forms of behavior (e.g. chaotic), etc. This volume is concerned with some modern tools and techniques which can be useful for the modeling of dynamics. We focus our attention on two important areas which play a key role nowadays, namely automation and robotics, and biological systems. We also add some new applications which can greatly benefit from the availability of effective and efficient tools for modeling dynamics, exemplified by some applications in security systems.
Linear Port Hamiltonian Systems On Infinite Dimensional Spaces
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Author : Birgit Jacob
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-13
Linear Port Hamiltonian Systems On Infinite Dimensional Spaces written by Birgit Jacob and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-13 with Science categories.
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This combined approach leads to easily verifiable conditions for well-posedness and stability. The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.