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.

Linear Systems Theory

Author: João P. Hespanha
Publisher: Princeton University Press
ISBN: 9781400890088
Release Date: 2018-02-16
Genre: Mathematics

A fully updated textbook on linear systems theory Linear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. This updated second edition of Linear Systems Theory covers the subject's key topics in a unique lecture-style format, making the book easy to use for instructors and students. João Hespanha looks at system representation, stability, controllability and state feedback, observability and state estimation, and realization theory. He provides the background for advanced modern control design techniques and feedback linearization and examines advanced foundational topics, such as multivariable poles and zeros and LQG/LQR. The textbook presents only the most essential mathematical derivations and places comments, discussion, and terminology in sidebars so that readers can follow the core material easily and without distraction. Annotated proofs with sidebars explain the techniques of proof construction, including contradiction, contraposition, cycles of implications to prove equivalence, and the difference between necessity and sufficiency. Annotated theoretical developments also use sidebars to discuss relevant commands available in MATLAB, allowing students to understand these tools. This second edition contains a large number of new practice exercises with solutions. Based on typical problems, these exercises guide students to succinct and precise answers, helping to clarify issues and consolidate knowledge. The book's balanced chapters can each be covered in approximately two hours of lecture time, simplifying course planning and student review. Easy-to-use textbook in unique lecture-style format Sidebars explain topics in further detail Annotated proofs and discussions of MATLAB commands Balanced chapters can each be taught in two hours of course lecture New practice exercises with solutions included

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.

Feedback Control Theory

Author: John C. Doyle
Publisher: Courier Corporation
ISBN: 9780486318332
Release Date: 2013-04-09
Genre: Technology & Engineering

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.

Mathematical Control Theory

Author: Eduardo D. Sontag
Publisher: Springer Science & Business Media
ISBN: 9781461205777
Release Date: 2013-11-21
Genre: Mathematics

Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.

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.

Modern Control System Theory and Design

Author: Stanley M. Shinners
Publisher: John Wiley & Sons
ISBN: 0471249068
Release Date: 1998-05-06
Genre: Technology & Engineering

A comprehensive treatment of control systems, integrating classical and modern theories while promoting an interactive computer based approach to design solutions. Contains many practical examples.

A Course in Robust Control Theory

Author: Geir E. Dullerud
Publisher: Springer Science & Business Media
ISBN: 9781475732900
Release Date: 2013-03-14
Genre: Mathematics

During the 90s robust control theory has seen major advances and achieved a new maturity, centered around the notion of convexity. The goal of this book is to give a graduate-level course on this theory that emphasizes these new developments, but at the same time conveys the main principles and ubiquitous tools at the heart of the subject. Its pedagogical objectives are to introduce a coherent and unified framework for studying the theory, to provide students with the control-theoretic background required to read and contribute to the research literature, and to present the main ideas and demonstrations of the major results. The book will be of value to mathematical researchers and computer scientists, graduate students planning to do research in the area, and engineering practitioners requiring advanced control techniques.

Essentials of Robust Control

Author: Kemin Zhou
ISBN: 0135258332
Release Date: 1998
Genre: Science

Based upon the popular "Robust and Optimal Control" by Zhou, et al. (PH, 1996), this book offers a streamlined approach to robust control that reflects the most recent topics and developments in the field. FEATURES: Features coverage of state-of-the-art topics, including... Gap metric. V-gap metric. Model validation. Real mu. Offers the essentials of both robust and "Ha control" and is suitable for "self-study." Adopts a self-contained approach, including detailed proof and development of each topic. Incorporates MATLAB tools--accompanied by step-by-step illustrations--throughout the book to execute computations. Supports discussions with numerous diagrams and figures. Guides readers through a wealth of worked examples depicting step-by-step development. Provides highlights of key results at the beginning of the book. Constructs a strong pedagogical framework in each chapter, including... Guidelines for selecting topics. Chapter highlights. Lists of key terms and symbols. End-of-chapter notes. Exercises. Features more than 50 illustrative examples, 95 figures, and 150 exercises and problems.