Feedback Systems

Input-Output Properties

Author: Charles A. Desoer,M. Vidyasagar

Publisher: SIAM

ISBN: 0898716705

Category: Mathematics

Page: 264

View: 524

A comprehensive treatment of the behavior of linear or nonlinear systems when they are connected in a closed-loop fashion.
Posted in Mathematics

Symmetries and Semi-invariants in the Analysis of Nonlinear Systems

Author: Laura Menini,Antonio Tornambè

Publisher: Springer Science & Business Media

ISBN: 9780857296122

Category: Technology & Engineering

Page: 340

View: 7487

This book details the analysis of continuous- and discrete-time dynamical systems described by differential and difference equations respectively. Differential geometry provides the tools for this, such as first-integrals or orbital symmetries, together with normal forms of vector fields and of maps. A crucial point of the analysis is linearization by state immersion. The theory is developed for general nonlinear systems and specialized for the class of Hamiltonian systems. By using the strong geometric structure of Hamiltonian systems, the results proposed are stated in a different, less complex and more easily comprehensible manner. They are applied to physically motivated systems, to demonstrate how much insight into known properties is gained using these techniques. Various control systems applications of the techniques are characterized including: computation of the flow of nonlinear systems; computation of semi-invariants; computation of Lyapunov functions for stability analysis and observer design.
Posted in Technology & Engineering

Plug-and-Play Monitoring and Performance Optimization for Industrial Automation Processes

Author: Hao Luo

Publisher: Springer

ISBN: 3658159286

Category: Technology & Engineering

Page: 149

View: 3930

Dr.-Ing. Hao Luo demonstrates the developments of advanced plug-and-play (PnP) process monitoring and control systems for industrial automation processes. With aid of the so-called Youla parameterization, a novel PnP process monitoring and control architecture (PnP-PMCA) with modularized components is proposed. To validate the developments, a case study on an industrial rolling mill benchmark is performed, and the real-time implementation on a laboratory brushless DC motor is presented.
Posted in Technology & Engineering

Non-identifier Based Adaptive Control in Mechatronics

Theory and Application

Author: Christoph M. Hackl

Publisher: Springer

ISBN: 3319550365

Category: Technology & Engineering

Page: 652

View: 9342

This book introduces non-identifier-based adaptive control (with and without internal model) and its application to the current, speed and position control of mechatronic systems such as electrical synchronous machines, wind turbine systems, industrial servo systems, and rigid-link, revolute-joint robots. In mechatronics, there is often only rough knowledge of the system. Due to parameter uncertainties, nonlinearities and unknown disturbances, model-based control strategies can reach their performance or stability limits without iterative controller design and performance evaluation, or system identification and parameter estimation. The non-identifier-based adaptive control presented is an alternative that neither identifies the system nor estimates its parameters but ensures stability. The adaptive controllers are easy to implement, compensate for disturbances and are inherently robust to parameter uncertainties and nonlinearities. For controller implementation only structural system knowledge (like relative degree, input-to-state stable zero dynamics and known sign of the high-frequency gain) is required. Moreover, the presented controllers guarantee reference tracking with prescribed asymptotic or transient accuracy, i.e. the tracking error eventually tends to or for all time evolves within an a priori specified region. The book presents the theory, modeling and application in a general but detailed and self-contained manner, making it easy to read and understand, particularly for newcomers to the topics covered
Posted in Technology & Engineering

Feedback Systems

An Introduction for Scientists and Engineers

Author: Karl Johan Aström,Richard M. Murray

Publisher: Princeton University Press

ISBN: 9781400828739

Category: Mathematics

Page: 408

View: 7402

This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available. Feedback Systems is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences. Covers the mathematics needed to model, analyze, and design feedback systems Serves as an introductory textbook for students and a self-contained resource for researchers Includes exercises at the end of every chapter Features an electronic solutions manual Offers techniques applicable across a range of disciplines
Posted in Mathematics

Feedback Control Theory

Author: John C. Doyle,Bruce A. Francis,Allen R. Tannenbaum

Publisher: Courier Corporation

ISBN: 0486318338

Category: Technology & Engineering

Page: 224

View: 9742

An excellent introduction to feedback control system design, this book offers a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems. Its explorations of recent developments in the field emphasize the relationship of new procedures to classical control theory, with a focus on single input and output systems that keeps concepts accessible to students with limited backgrounds. The text is geared toward a single-semester senior course or a graduate-level class for students of electrical engineering. The opening chapters constitute a basic treatment of feedback design. Topics include a detailed formulation of the control design program, the fundamental issue of performance/stability robustness tradeoff, and the graphical design technique of loopshaping. Subsequent chapters extend the discussion of the loopshaping technique and connect it with notions of optimality. Concluding chapters examine controller design via optimization, offering a mathematical approach that is useful for multivariable systems.
Posted in Technology & Engineering

Nonnegative Matrices in the Mathematical Sciences

Author: Abraham Berman,Robert J. Plemmons

Publisher: Academic Press

ISBN: 1483260860

Category: Mathematics

Page: 334

View: 6589

Nonnegative Matrices in the Mathematical Sciences provides information pertinent to the fundamental aspects of the theory of nonnegative matrices. This book describes selected applications of the theory to numerical analysis, probability, economics, and operations research. Organized into 10 chapters, this book begins with an overview of the properties of nonnegative matrices. This text then examines the inverse-positive matrices. Other chapters consider the basic approaches to the study of nonnegative matrices, namely, geometrical and combinatorial. This book discusses as well some useful ideas from the algebraic theory of semigroups and considers a canonical form for nonnegative idempotent matrices and special types of idempotent matrices. The final chapter deals with the linear complementary problem (LCP). This book is a valuable resource for mathematical economists, mathematical programmers, statisticians, mathematicians, and computer scientists.
Posted in Mathematics

Stochastic Systems

Estimation, Identification, and Adaptive Control

Author: P. R. Kumar,Pravin Varaiya

Publisher: SIAM

ISBN: 1611974259

Category: Mathematics

Page: 358

View: 7464

Since its origins in the 1940s, the subject of decision making under uncertainty has grown into a diversified area with application in several branches of engineering and in those areas of the social sciences concerned with policy analysis and prescription. These approaches required a computing capacity too expensive for the time, until the ability to collect and process huge quantities of data engendered an explosion of work in the area. This book provides succinct and rigorous treatment of the foundations of stochastic control; a unified approach to filtering, estimation, prediction, and stochastic and adaptive control; and the conceptual framework necessary to understand current trends in stochastic control, data mining, machine learning, and robotics.
Posted in Mathematics

Modeling Life

The Mathematics of Biological Systems

Author: Alan Garfinkel,Jane Shevtsov,Yina Guo

Publisher: Springer

ISBN: 3319597310

Category: Mathematics

Page: 445

View: 2813

This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?
Posted in Mathematics

Nonlinear Systems Analysis

Second Edition

Author: M. Vidyasagar

Publisher: SIAM

ISBN: 9780898719185

Category: Differential equations, Nonlinear

Page: 498

View: 9618

When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems.
Posted in Differential equations, Nonlinear

Linear System Theory

Author: Frank M. Callier,Charles A. Desoer

Publisher: Springer Science & Business Media

ISBN: 1461209579

Category: Technology & Engineering

Page: 509

View: 4022

This book is the result of our teaching over the years an undergraduate course on Linear Optimal Systems to applied mathematicians and a first-year graduate course on Linear Systems to engineers. The contents of the book bear the strong influence of the great advances in the field and of its enormous literature. However, we made no attempt to have a complete coverage. Our motivation was to write a book on linear systems that covers finite dimensional linear systems, always keeping in mind the main purpose of engineering and applied science, which is to analyze, design, and improve the performance of phy sical systems. Hence we discuss the effect of small nonlinearities, and of perturbations of feedback. It is our on the data; we face robustness issues and discuss the properties hope that the book will be a useful reference for a first-year graduate student. We assume that a typical reader with an engineering background will have gone through the conventional undergraduate single-input single-output linear systems course; an elementary course in control is not indispensable but may be useful for motivation. For readers from a mathematical curriculum we require only familiarity with techniques of linear algebra and of ordinary differential equations.
Posted in Technology & Engineering

Mathematical Modelling in Science and Technology

The Fourth International Conference, Zurich, Switzerland, August 1983

Author: Xavier J.R. Avula,Rudolf E. Kalman,Anthanasios I. Liapis

Publisher: Elsevier

ISBN: 1483190595

Category: Mathematics

Page: 1022

View: 993

Mathematical Modelling in Science and Technology: The Fourth International Conference covers the proceedings of the Fourth International Conference by the same title, held at the Swiss Federal Institute of Technology, Zurich, Switzerland on August 15-17, 1983. Mathematical modeling is a powerful tool to solve many complex problems presented by scientific and technological developments. This book is organized into 20 parts encompassing 180 chapters. The first parts present the basic principles, methodology, systems theory, parameter estimation, system identification, and optimization of mathematical modeling. The succeeding parts discuss the features of stochastic and numerical modeling and simulation languages. Considerable parts deal with the application areas of mathematical modeling, such as in chemical engineering, solid and fluid mechanics, water resources, medicine, economics, transportation, and industry. The last parts tackle the application of mathematical modeling in student management and other academic cases. This book will prove useful to researchers in various science and technology fields.
Posted in Mathematics

Practical Applied Mathematics

Modelling, Analysis, Approximation

Author: Sam Howison

Publisher: Cambridge University Press

ISBN: 9780521842747

Category: Mathematics

Page: 326

View: 5926

Drawing from a wide variety of mathematical subjects, this book aims to show how mathematics is realised in practice in the everyday world. Dozens of applications are used to show that applied mathematics is much more than a series of academic calculations. Mathematical topics covered include distributions, ordinary and partial differential equations, and asymptotic methods as well as basics of modelling. The range of applications is similarly varied, from the modelling of hair to piano tuning, egg incubation and traffic flow. The style is informal but not superficial. In addition, the text is supplemented by a large number of exercises and sideline discussions, assisting the reader's grasp of the material. Used either in the classroom by upper-undergraduate students, or as extra reading for any applied mathematician, this book illustrates how the reader's knowledge can be used to describe the world around them.
Posted in Mathematics

Unsolved Problems in Mathematical Systems and Control Theory

Author: Vincent D. Blondel,Alexandre Megretski

Publisher: Princeton University Press

ISBN: 1400826152

Category: Mathematics

Page: 352

View: 4184

This book provides clear presentations of more than sixty important unsolved problems in mathematical systems and control theory. Each of the problems included here is proposed by a leading expert and set forth in an accessible manner. Covering a wide range of areas, the book will be an ideal reference for anyone interested in the latest developments in the field, including specialists in applied mathematics, engineering, and computer science. The book consists of ten parts representing various problem areas, and each chapter sets forth a different problem presented by a researcher in the particular area and in the same way: description of the problem, motivation and history, available results, and bibliography. It aims not only to encourage work on the included problems but also to suggest new ones and generate fresh research. The reader will be able to submit solutions for possible inclusion on an online version of the book to be updated quarterly on the Princeton University Press website, and thus also be able to access solutions, updated information, and partial solutions as they are developed.
Posted in Mathematics

Control System Synthesis

A Factorization Approach

Author: Mathukumalli Vidyasagar

Publisher: Morgan & Claypool Publishers

ISBN: 1608456633

Category: Technology & Engineering

Page: 227

View: 3464

This book introduces the so-called "stable factorization approach" to the synthesis of feedback controllers for linear control systems. The key to this approach is to view the multi-input, multi-output (MIMO) plant for which one wishes to design a controller as a matrix over the fraction field F associated with a commutative ring with identity, denoted by R, which also has no divisors of zero. In this setting, the set of single-input, single-output (SISO) stable control systems is precisely the ring R, while the set of stable MIMO control systems is the set of matrices whose elements all belong to R. The set of unstable, meaning not necessarily stable, control systems is then taken to be the field of fractions F associated with R in the SISO case, and the set of matrices with elements in F in the MIMO case. The central notion introduced in the book is that, in most situations of practical interest, every matrix P whose elements belong to F can be "factored" as a "ratio" of two matrices N,D whose elements belong to R, in such a way that N,D are coprime. In the familiar case where the ring R corresponds to the set of bounded-input, bounded-output (BIBO)-stable rational transfer functions, coprimeness is equivalent to two functions not having any common zeros in the closed right half-plane including infinity. However, the notion of coprimeness extends readily to discrete-time systems, distributed-parameter systems in both the continuous- as well as discrete-time domains, and to multi-dimensional systems. Thus the stable factorization approach enables one to capture all these situations within a common framework. The key result in the stable factorization approach is the parametrization of all controllers that stabilize a given plant. It is shown that the set of all stabilizing controllers can be parametrized by a single parameter R, whose elements all belong to R. Moreover, every transfer matrix in the closed-loop system is an affine function of the design parameter R. Thus problems of reliable stabilization, disturbance rejection, robust stabilization etc. can all be formulated in terms of choosing an appropriate R. This is a reprint of the book Control System Synthesis: A Factorization Approach originally published by M.I.T. Press in 1985.
Posted in Technology & Engineering

Linear Matrix Inequalities in System and Control Theory

Author: Stephen Boyd,Laurent El Ghaoui,Eric Feron,Venkataramanan Balakrishnan

Publisher: SIAM

ISBN: 9781611970777

Category: Control theory

Page: 193

View: 8425

In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.
Posted in Control theory