Linearisierung und Entkopplung von Deskriptorsystemen

Müller, P. C.

doi:10.1007/bf01236232

Cited by 3 publications

(4 citation statements)

References 8 publications

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“…Neutral boron-containing systems with a π-electron doublet (heterocyclic counterparts of the cyclopropenyl cation 55 are called borirenes (64-66, Scheme 32) and azadiboriridines (67, Scheme 33) 80,81 and were synthesized by Berndt and co-workers (64), 82,83 Habben and Meller (65), 84 and Paetzold, Schleyer, and their co-workers (66) (Scheme 33). 81,[85][86][87][88] In azadiboriridines 67, the B-B bond distances range from 156 to 162 pm, indicating considerable double bond character. Amino groups attached to boron somewhat decrease the delocalization energy.…”

Section: Known and Potential Monocyclic Three-membered Heterocyclic R...mentioning

confidence: 99%

Aromaticity as a Cornerstone of Heterocyclic Chemistry

2004

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Section: Known and Potential Monocyclic Three-membered Heterocyclic R...mentioning

confidence: 99%

Aromaticity as a Cornerstone of Heterocyclic Chemistry

2004

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“…Darüber hinaus existieren Verfahren, die nur für propere Deskriptorsysteme geeignet sind und bei denen Fallunterscheidungen den Entwurf erschweren [14]. Problematisch ist vor allem, dass bei diesem Entwurf sogar bei properen Deskriptorsystemen Eingangsableitungen auftreten können.…”

Section: Einführungunclassified

Verkopplungsbasierte Methode zur Entkopplung nichtlinearer Deskriptorsysteme

Labisch

Konigorski

2014

At - Automatisierungstechnik

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Zusammenfassung: Dieser Beitrag beschreibt ein neues Verfahren zur Entkopplung nichtlinearer Deskriptorsysteme. Dabei werden keine Einschränkungen bezüglich des Index, der Properheit oder spezielle Steuerbarkeitseigenschaften angenommen, da das neue Verfahren auf der Interpretation eines Deskriptorsystems als spezielles Verkopplungsproblem basiert. Zu Beginn werden neue invariante Gröẞen des Deskriptorsystems, die maximalen Differenzordnungen, eingeführt, auf deren Basis erstmals notwendige und hinreichende Bedingungen für die Entkoppelbarkeit nichtlinearer Deskriptorsysteme hergeleitet werden. Das Verfahren wird am Ende an einem akademischen Beispielsystem demonstriert und am realen Prüf-stand eines Parallelroboters angewandt. Schlüsselwörter: Deskriptorsystem, Entkopplung, Verkopplungsregelung.Abstract: This paper presents a new approach for the design of decoupling controllers for nonlinear descriptor systems. No assumption on the index, the properness, or special controllability conditions are needed as the design is based on the interpretation of a descriptor system as a special coupling problem. At the beginning, new invariants for descriptor systems, the maximal differential orders, are introduced. They are used to state necessary and sufficient conditions to solve the decoupling problem for nonlinear descriptor systems for the first time. The new approach is exemplified with an academic example and the test bed of a parallel robot.

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“…Some steps have been taken for the optimal control design [24], but especially for non-proper systems many problems still have to be solved. First results on the method of nonlinear decoupling and exact linearization by state feedback have been presented is [9,30]. But both papers are restricted by some assumptions on the nonlinear descriptor systems: it is assumed either that the algebraic variables only appear in linear form [9] or that the descriptor system is proper [30].…”

Section: Nonlinear Systemsmentioning

confidence: 99%

“…First results on the method of nonlinear decoupling and exact linearization by state feedback have been presented is [9,30]. But both papers are restricted by some assumptions on the nonlinear descriptor systems: it is assumed either that the algebraic variables only appear in linear form [9] or that the descriptor system is proper [30]. Still some aspects are open and the problem is under consideration.…”

Section: Nonlinear Systemsmentioning

confidence: 99%

Aspects of Modeling Dynamical Systems by Differential-Algebraic Equations

Müller¹

2001

Mathematical and Computer Modelling of Dynamical Systems

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In recent years the analysis and synthesis of control systems in descriptor form has been established. The general description of dynamical systems by differential-algebraic equations (DAE) is important for many applications in mechanics and mechatronics, in electrical and electronic engineering, and in chemical engineering as well. In this contribution the pros and cons of system modelling by differential-algebraic equations are discussed and an actual state of the art of descriptor systems is presented. Firstly, the advantages of modelling are touched in general and illustrated in detail by Lagranges equations of ®rst kind, by subsystem modeling and by the statement of the tracking control problem. Secondly, the development of tools for numerical integration is discussed resulting in the comment that today stable and ef®cient DAE solvers exist and that the simulation of descriptor systems is not a problem any longer. Thirdly, the methods of analyzing and designing descriptor systems are considered. Here, linear and nonlinear systems have to be distinguished. For linear descriptor systems more or less the required methods to solve usual control tasks are available in principal. But actually a related program package for fast and reliable application of these methods is still missed. However, in the near future such a toolbox is expected. Main dif®culties arise for nonlinear problems. A few results on stability and optimal control are known only and still a lot of research work has to be effected. In spite of these de®ciencies, all over the descriptor system approach is very attractive for modeling and simulation, and will become attractive more and more for analysis and design.

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Linearisierung und Entkopplung von Deskriptorsystemen

Cited by 3 publications

References 8 publications

Aromaticity as a Cornerstone of Heterocyclic Chemistry

Aromaticity as a Cornerstone of Heterocyclic Chemistry

Verkopplungsbasierte Methode zur Entkopplung nichtlinearer Deskriptorsysteme

Aspects of Modeling Dynamical Systems by Differential-Algebraic Equations

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