Introduction to Mathematical Systems Theory

Author: J.C. Willems
Publisher: Springer Science & Business Media
ISBN: 9781475729535
Release Date: 2013-11-11
Genre: Mathematics

Using the behavioural approach to mathematical modelling, this book views a system as a dynamical relation between manifest and latent variables. The emphasis is on dynamical systems that are represented by systems of linear constant coefficients. The first part analyses the structure of the set of trajectories generated by such dynamical systems, and derives the conditions for two systems of differential equations to be equivalent in the sense that they define the same behaviour. In addition the memory structure of the system is analysed through state space models. The second part of the book is devoted to a number of important system properties, notably controllability, observability, and stability. In the third part, control problems are considered, in particular stabilisation and pole placement questions. Suitable for advanced undergraduate or beginning graduate students in mathematics and engineering, this text contains numerous exercises, including simulation problems, and examples, notably of mechanical systems and electrical circuits.

Control of Surge in Centrifugal Compressors by Active Magnetic Bearings

Author: Se Young Yoon
Publisher: Springer Science & Business Media
ISBN: 9781447142409
Release Date: 2012-06-19
Genre: Technology & Engineering

Surge Control of Active-magnetic-bearing-suspended Centrifugal Compressors sets out the fundamentals of integrating active magnetic bearing (AMB) rotor suspension technology in compressor systems, and describes how this relatively new bearing technology can be employed in active control of compressor surge initiation. The authors provide a self-contained and comprehensive review of rotordynamics and the fundamentals of AMB technology. The active stabilization of compressor surge employing AMBs in a machine is fully explored, from modeling of instability and controller design, to the implementation and experimental testing of the control algorithm in a specially-constructed, industrial-size centrifugal compression system. The results of these tests demonstrate the great potential of the new surge control method suggested in this text. This book will be useful for engineers in industries that involve turbocompressors and magnetic bearings, as well as for researchers and graduate students in the field of applied control. Whatever their level of experience, engineers working in the fields of turbomachinery, magnetic bearings, rotordynamics and controls will find the material in this book absorbing as all these important aspects of engineering are integrated to create a multi-disciplinary solution to a real-life industrial problem and the book is a suitable introduction to the area for newcomers.

Modern Control Systems Global Edition

Author: Richard C. Dorf
ISBN: 1292152974
Release Date: 2016-12-14

For courses in Control Theory Developing Problem-Solving Skills Through Integrated Design and Analysis The purpose of Dorf's Modern Control Systems, Thirteenth Edition is to present the structure of feedback control theory and to provide a sequence of exciting discoveries. The book demonstrates various real-world, global engineering problems while touching on evolving design strategies like green technology. Some of the themes at-hand include climate change, clean water, sustainability, waste management, emissions reduction, and minimizing energy. Throughout the text, students apply theory to the design and analysis of control systems. The Thirteenth Edition continues to explore the role of and need for automated and precise control systems in green engineering. Key examples of green engineering, such as wind turbine control and the modeling of a photovoltaic generator to achieve maximum power delivery, are discussed in detail. The text is organized around the concept of control systems theory in the context of frequency and time domains. Written to be equally useful for all engineering disciplines, it covers topics such as classical control, employing root locus design, frequency and response design using Bode and Nyquist plots.

Linear Systems and Control

Author: Martin J. Corless
Publisher: CRC Press
ISBN: 0203911377
Release Date: 2003-03-27
Genre: Mathematics

Based largely on state space models, this text/reference utilizes fundamental linear algebra and operator techniques to develop classical and modern results in linear systems analysis and control design. It presents stability and performance results for linear systems, provides a geometric perspective on controllability and observability, and develops state space realizations of transfer functions. It also studies stabilizability and detectability, constructs state feedback controllers and asymptotic state estimators, covers the linear quadratic regulator problem in detail, introduces H-infinity control, and presents results on Hamiltonian matrices and Riccati equations.

Linear Continuous Time Systems

Author: Lyubomir T. Gruyitch
Publisher: CRC Press
ISBN: 9781351642897
Release Date: 2017-07-28
Genre: Technology & Engineering

This book aims to help the reader understand the linear continuous-time time-invariant dynamical systems theory and its importance for systems analysis and design of the systems operating in real conditions, i.e., in forced regimes under arbitrary initial conditions. The text completely covers IO, ISO and IIO systems. It introduces the concept of the system full matrix P(s) in the complex domain and establishes its link with the also newly introduced system full transfer function matrix F(s). The text establishes the full block diagram technique based on the use of F(s), which incorporates the Laplace transform of the input vector and the vector of all initial conditions. It explores the direct relationship between the system full transfer function matrix F(s) and the Lyapunov stability concept, definitions and conditions, as well as with the BI stability concept, definitions, and conditions. The goal of the book is to unify the study and applications of all three classes of the of the linear continuous-time time-invariant systems, for short systems.

Linear Discrete Time Systems

Author: Zoran M. Buchevats
Publisher: CRC Press
ISBN: 9781351707589
Release Date: 2017-11-22
Genre: Technology & Engineering

This book covers crucial lacunae of the linear discrete-time time-invariant dynamical systems and introduces the reader to their treatment, while functioning under real, natural conditions, in forced regimes with arbitrary initial conditions. It provides novel theoretical tools necessary for the analysis and design of the systems operating in stated conditions. The text completely covers two, well known systems, IO and ISO, along with a new system, IIO. It discovers the concept of the full transfer function matrix F(z) in the z-complex domain, which incorporates the Z-transform of the system, input and another variable, vectors, all with arbitrary initial conditions. Consequently, it addresses the full system matrix P(z) and the full block diagram technique based on the use of F(z), which incorporates the Z-transform of the system, input and another variable, vectors, all with arbitrary initial conditions. The book explores the direct relationship between the system full transfer function matrix F(z) and the Lyapunov stability concept, definitions, and conditions, as well as with the BI stability concept, definitions, and conditions. The goal of the book is to unify the study and applications of all three classes of the linear discrete-time time-invariant system, for short systems.

Control Theory and Design

Author: Patrizio Colaneri
Publisher: Elsevier
ISBN: 0080503101
Release Date: 1997-05-20
Genre: Technology & Engineering

Control systems design methodologies have long suffered the traditional and myopic dichotomy between time and frequency domain approaches, each of them being specialized to cope with only scarcely overlapping performance requirements. This book is aimed at bridging the two approaches by presenting design methodologies based on the minimization of a norm (H2/H() of a suitable transfer function. A distinctive feature of these techniques is the fact that they do not create only one solution to the design problem, instead they provide a whole set of admissible solutions which satisfy a constraint on the maximum deterioration of the performance index. A systematic book on this topic is long overdue. Self-contained and practical in its approach, Control Theory and Design enables the reader to use the relevant techniques in various real-life applications. The text covers the basic facts of robustcontrol and theory as well as more recent achievements, such as robust stability and robust performance in presence of parameter uncertainties. It features a new perspective on classical LQC results and further sections on robust synthesis, nonclassicaloptimization problems, and analysis and synthesis of uncertain systems. Control Theory and Design is essential reading for graduates and those entering the research field. The required mathematical background is provided so that the book is also suitable for undergraduate students with some knowledge of basic systemsand control. Provides a self-contained manual for learning control systems and design Contains a clear and concise presentation of the technical background needed Includes a new perspective of classical LQG results Contains updated results and novel contributions to nonstandard RH2/RH infinity symbol problems Covers all the theory from the basic to the more advanced issues

Mathematical System Theory

Author: Ac Antoulas
Publisher: Springer Science & Business Media
ISBN: 9783662085462
Release Date: 2013-04-17
Genre: Technology & Engineering

Over the past three decades R.E. Kalman has been one of the most influential personalities in system and control theory. His ideas have been instrumental in a variety of areas. This is a Festschrift honoring his 60th birthday. It contains contributions from leading researchers in the field giving an account of the profound influence of his ideas in a number of areas of active research in system and control theory. For example, since their introduction by Kalman in the early 60's, the concepts of controllability and observability of dynamical systems with inputs, have been the corner stone of the great majority of investigations in the field.

A Mathematical Introduction to Control Theory

Author: Shlomo Engelberg
Publisher: World Scientific Publishing Company
ISBN: 9781783267811
Release Date: 2015-04-08
Genre: Technology & Engineering

Striking a nice balance between mathematical rigor and engineering-oriented applications, this second edition covers the bedrock parts of classical control theory — the Routh-Hurwitz theorem and applications, Nyquist diagrams, Bode plots, root locus plots, and the design of controllers (phase-lag, phase-lead, lag-lead, and PID). It also covers three more advanced topics — non-linear control, modern control, and discrete-time control. This invaluable book makes effective use of MATLAB® as a tool in design and analysis. Containing 75 solved problems and 200 figures, this edition will be useful for junior and senior level university students in engineering who have a good knowledge of complex variables and linear algebra.

An Introduction to Invariant Imbedding

Author: R. Bellman
Publisher: SIAM
ISBN: 1611971276
Release Date: 1992
Genre: Invariant imbedding

Here is a book that provides the classical foundations of invariant imbedding, a concept that provided the first indication of the connection between transport theory and the Riccati Equation. The reprinting of this classic volume was prompted by a revival of interest in the subject area because of its uses for inverse problems. The major part of the book consists of applications of the invariant imbedding method to specific areas that are of interest to engineers, physicists, applied mathematicians, and numerical analysts. A large set of problems can be found at the end of each chapter. Numerous problems on apparently disparate matters such as Riccati equations, continued fractions, functional equations, and Laplace transforms are included. The exercises present the reader with "real-life" situations. The material is accessible to a general audience, however, the authors do not hesitate to state, and even to prove, a rigorous theorem when one is available. To keep the original flavor of the book, very few changes were made to the manuscript; typographical errors were corrected and slight changes in word order were made to reduce ambiguities.

Control Theory Tutorial

Author: Steven A. Frank
Publisher: Springer
ISBN: 9783319917078
Release Date: 2018-05-29
Genre: Technology & Engineering

This open access brief introduces the basic principles of control theory in a concise self-study guide. It complements the classic texts by emphasizing the simple conceptual unity of the subject. A novice can quickly see how and why the different parts fit together. The concepts build slowly and naturally one after another, until the reader soon has a view of the whole. Each concept is illustrated by detailed examples and graphics. The full software code for each example is available, providing the basis for experimenting with various assumptions, learning how to write programs for control analysis, and setting the stage for future research projects. The topics focus on robustness, design trade-offs, and optimality. Most of the book develops classical linear theory. The last part of the book considers robustness with respect to nonlinearity and explicitly nonlinear extensions, as well as advanced topics such as adaptive control and model predictive control. New students, as well as scientists from other backgrounds who want a concise and easy-to-grasp coverage of control theory, will benefit from the emphasis on concepts and broad understanding of the various approaches.