Control, simulation and stability analysis of nonlinear regular proper DAEs

At - Automatisierungstechnik

2014

Self Cite

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.

“…B. [10][11][12]). Die Grundiddee liegt darin, ein Zustandssystem mithilfe der Verkopplung zu berechnen, welches dieselbe Lösung wie das Deskriptorsystem besitzt.…”

Section: Einführungunclassified

Verkopplungsbasierte Methode zur Entkopplung nichtlinearer Deskriptorsysteme

At - Automatisierungstechnik

2014

Self Cite

“…The second important property is properness which means that the solution of the descriptor system does not depend on derivatives of the input function and is sometimes also called causality. The definitions can also be found in [12] or [15].…”

Section: System Descriptionmentioning

confidence: 99%

Coupling‐based methods to design feedback controllers and observers for nonlinear descriptor systems

Proc Appl Math and Mech

2014

Self Cite

This paper presents a new approach for analysis and controller design for nonlinear descriptor systems. Thereby, we assume that the descriptor system is given in semi-explicit form and has a continuously differentiable solution, which are very mild assumptions and are fulfilled for most practical applications. Based on the known coupling controller design we transfer the analysis and synthesis from the descriptor system to an equivalent system in state-space form. Methods like dynamic and static input-output decoupling, input-output linearization, model-based feedforward-controller design, zero dynamics, exact descriptor linearization, linear time variant Riccati control, and causal observer design have been introduced based on the coupling procedure [9]. In the following, we summarize the new approach and an algorithm to compute the required statespace system. Additionally, a short introduction how to use it for decoupling control, Riccati control, and causal observer design is given.

Design of Causal Observers for Nonlinear Descriptor Systems

Differential-Algebraic Equations Forum

2014

Self Cite

This contribution not only provides a new necessary and sufficient condition for causal observability of nonlinear descriptor systems but also a method to design the causal observer. The approach is based on the transformation of the descriptor system into a state-space form, the so called coupled state-space system. This description exists for all regular descriptor systems no matter if they are proper or not. If the new condition is satisfied, the coupled state-space system can be modified and can be used to design a state-space observer. It is shown, that this observer is also a causal observer for the original descriptor system. Two examples illustrate the capability of the new approach.