Mathematical Control Design For Linear Systems Practice Book

Mathematical Control Design for Linear Systems - Practice book is a concise exercise book for students of applied mathematics and engineering who are interested in testing their basic abilities in the design of linear control algorithms, as well as in the analysis of dynamical systems described by linear ordinary differential equations. It can be used as a useful tool to recap the basic concepts of systems theory and automatic control before tackling more advanced control courses. Just a fine selection of exercises that own a physical flavor are reported. Matlab codes and figures are included.

This is an introductory and self-contained book for eager students of applied mathematics and engineering, who want to have a tasting of the beautiful mathematics lying at the root of the design of control algorithms and strategies for linear dynamical systems. All it takes is the interest and fondness for the logical reasoning, together with the mastery of a few concepts from real and complex mathematical analysis and linear algebra. The control design is presented before the reader’s eyes in order to involve him intellectually and emotionally. The purpose is to really and exclusively reveal the logical steps underlying the control design and, at the same time, to educate in the most charming intellectual independence. Applications in Matlab-Simulink and Maple provide substance to the theoretical concepts, while graphics render the reader more pleasant.

One of the main problems in control theory is the stabilization problem consisting of finding a feedback control law ensuring stability; when the linear approximation is considered, the nat ural problem is stabilization of a linear system by linear state feedback or by using a linear dynamic controller. This prob lem was intensively studied during the last decades and many important results have been obtained. The present monograph is based mainly on results obtained by the authors. It focuses on stabilization of systems with slow and fast motions, on stabilization procedures that use only poor information about the system (high-gain stabilization and adaptive stabilization), and also on discrete time implementa tion of the stabilizing procedures. These topics are important in many applications of stabilization theory. We hope that this monograph may illustrate the way in which mathematical theories do influence advanced technol ogy. This book is not intended to be a text book nor a guide for control-designers. In engineering practice, control-design is a very complex task in which stability is only one of the re quirements and many aspects and facets of the problem have to be taken into consideration. Even if we restrict ourselves to stabilization, the book does not provide just recipes, but it fo cuses more on the ideas lying behind the recipes. In short, this is not a book on control, but on some mathematics of control.

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.

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

This book discusses analysis and design techniques for linear feedback control systems using MATLAB® software. By reducing the mathematics, increasing MATLAB working examples, and inserting short scripts and plots within the text, the authors have created a resource suitable for almost any type of user. The book begins with a summary of the properties of linear systems and addresses modeling and model reduction issues. In the subsequent chapters on analysis, the authors introduce time domain, complex plane, and frequency domain techniques. Their coverage of design includes discussions on model-based controller designs, PID controllers, and robust control designs. A unique aspect of the book is its inclusion of a chapter on fractional-order controllers, which are useful in control engineering practice.

Unifying two decades of research, this book is the first to establish a comprehensive foundation for a systematic analysis and design of linear systems with general state and input constraints. For such systems, which can be used as models for most nonlinear systems, the issues of stability, controller design, additonal constraints, and satisfactory performance are addressed. The book is an excellent reference for practicing engineers, graduate students, and researchers in control systems theory and design. It may also serve as an advanced graduate text for a course or a seminar in nonlinear control systems theory and design in applied mathematics or engineering departments. Minimal prerequisites include a first graduate course in state-space methods as well as a first course in control systems design.