Wolfgang Drewelow

Dieses Buch widmet sich dem Problem der Sampled-Data-Regelung endlich-dimensionaler linearer kontinuierlicher periodischer Objekte (FDLCP). Es füllt eine Forschungslücke bei der Behandlung dieses wichtigen Themas. Die hier vorgestellten Methoden basieren auf der parametrischen Übertragungsmatrix, die sich bei der Untersuchung von Sampled-Data-Systemen mit linearen zeitinvarianten Objekten bewährt hat. Das Buch zeigt, dass dieses Konzept erfolgreich auf Sampled-Data-Systeme mit FDLCP-Objekten übertragen werden kann. Es ist in fünf Teile gegliedert: eine Einführung in den Frequenzansatz zur mathematischen Beschreibung von FDLCP-Objekten einschließlich der Bestimmung ihrer Struktur und ihrer Darstellung als Reihenschaltung von periodischen Modulatoren und einem linearen zeitinvarianten Objekt;die Konstruktion der parametrischen Übertragungsmatrix für verschiedene Arten von offenen und geschlossenen Abtastsystemen mit FDLCP-Objekten;die Lösung vonProblemen der kausalen modalen Steuerung von FDLCP-Objekten auf der Grundlage des mathematischen Apparats der determinierten Polynomgleichungen;die Betrachtung des Problems der Konstruktion eines quadratischen Qualitätsfunktionals für das H2-Optimierungsproblem eines einschleifigen synchronen Sampled-Data-Systems mit Totzeit in der Stellgröße;Beschreibung des allgemeinen H2-Optimierungsverfahrens. Das notwendige mathematische Referenzmaterial ist an den relevanten Stellen des Buches enthalten. Sampled-Data-Regelung für periodische Objekte richtet sich an Wissenschaftler und Ingenieure, die sich mit der Erforschung und dem Entwurf von Systemen mit FDLCP-Objekten befassen, an Doktoranden, die ihre Kompetenzen erweitern wollen, an ihre Dozenten und an Mathematiker, die auf dem Gebiet der Regelungstheorie arbeiten.

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.

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.