Sampled-Data Control for Periodic Objects

Rosenwasser, Efim N./ Jeinsch, Torsten/ Drewelow, Wolfgang

Springer International Publishing AG（2024/02発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 263 p.
• 商品コード 9783031019586

Full Description

This book is devoted to the problem of sampled-data control of finite-dimensional linear continuous periodic (FDLCP) objects. It fills a deficit in coverage of this important subject. The methods presented here are based on the parametric transfer matrix, which has proven successful in the study of sampled-data systems with linear time-invariant objects. The book shows that this concept can be successfully transferred to sampled-data systems with FDLCP objects. It is set out in five parts:

·  ·         an introduction to the frequency approach for the mathematical description of FDLCP objects including the determination of their structure and their representation as a serial connection of periodic modulators and a linear time-invariant object;

·         construction of parametric transfer matrix for different types of open and closed sampled-data systems with FDLCP objects;

·         the solution of problems of causal modal control of FDLCP objects based on the mathematical apparatus of determinant polynomial equations;

·         consideration of the problem of constructing a quadratic quality functional for the H2-optimization problem of a single-loop synchronous sampled-data system with control delay;

·         description of the general H2-optimization procedure.



Necessary mathematical reference material is included at relevant points in the book.

Sampled-Data Control for Periodic Objects is of use to: scientists and engineers involved in research and design of systems of systems with FDLCP objects; graduate students wishing to broaden their scope of competence; their instructors; and mathematicians working in thefield of control theory.

Contents

Part I: The Frequency Approach to the Mathematical Description of Linear Periodic Objects.-  Discrete Operational Transformations of Functions of Continuous Argument and Operator Description of LTI Systems.- State-Space Analysis of Finite-Dimensional Linear Continuous Periodic (FDLCP) Objects.- Frequency Method in the Theory of FDLCP Objects.- Floquet-Lyapunov Decomposition and its Application.- Part II: PTM approach to SD systems with FDLCP Objects.- Open-Loop SD System with FDLCP Object.- Open-Loop SD System with FDLCP Object and Delay.- Closed-Loop SD System with FDLCP Object and Delay.- Part III: Determinant Polynomial Equations, SD Modal Control and Stabilization of FDLCP Objects.- Polynomial Matrices.- Rational Matrices.- Determinant Polynomial Equations, Causal Modal Control and Stabilization of Discrete Systems.- 11 Synchronous SD Stabilization of FDLCP Objects.- Asynchronous SD Stabilization of FDLCP Objects.- Part IV Building the Quality Functional for the H2-Optimization Task of the System Sτ.- General PTM Properties of Synchronous Open-Loop SD System with Delay.- 14 PTM of the Closed-Loop SD System with Delay as Function of Argument s.- Calculation of Matrices v0(s), ξ0(s), ψ0(s).- System Function.- Representing the PTM of a Closed-Loop Synchronous SD System by the System Function.- H2-Norm of the Closed-Loop SD System.- Construction of the Quality Functional.- Part V H2-Optimization of the Closed-Loop SD System.- Scalar and Matrix Quasi-polynomials.- Minimization of a Quadratic Functional on the Unit Circle.- Construction of Matrix η(s,t).- Construction of Matrix C ̃T (s,t).- Transformation of Quality Functional.- H2-Optimization of the System Sτ.