Sampled-Data Control for Periodic Objects

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 H 2 -optimization problem of a single-loop synchronous sampled-data system with control delay;

· description of the general H 2 -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.

Helps scientists and engineers working in relevant scientific and industrial fields Allows students in the relevant profile areas to broaden their scope of competence Assists mathematicians working in the field of control theory to expand the spectrum of problems considered

Auteur
Efim N. Rosenwasser is the head of the chair for automated ship complexes at the Marine Technical University Saint Petersburg, Russia. Professor Rosenwasser is one of the leading Russian control scientists. He is the author of more than 310 publications including 18 monographs. In cooperation with the late Professor Bernhard P. Lampe, he wrote the monographs Computer-Controlled Systems, Springer 2000, Multivariable Computer-Controlled Systems, Springer 2006, and Computer-Controlled Systems with Delay, Springer 2019.

Torsten Jeinsch holds the chair for Control Engineering at the Institute of Automation, Faculty of Computer Science and Electrical Engineering at the University of Rostock, Germany. Professor Jeinsch has been the initiator and leader of numerous research projects in theory and application of advanced control methods. He is author and co-author of more than 100 publications, including nine patents and two monographs.

Wolfgang Drewelow is a senior scientist at the Institute of Automation, Faculty of Computer Science and Electrical Engineering at the University of Rostock, Germany. Dr Drewelow has been involved with numerous national and international research grants and industrial projects in the development of advanced control methods and their application in different sectors of industry. He is the author of more than 100 publications, including four patents.

Contenu
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.- FloquetLyapunov 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 S.- 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), 0(s), 0(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 (s,t).- Construction of Matrix C T (s,t).- Transformation of Quality Functional.- H2-Optimization of the System S.