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Normal forms, high gain and funnel control for linear differential-algebraic systems

Please always quote using this URN:urn:nbn:de:0296-matheon-8716
  • We consider linear differential-algebraic m-input m-output systems with positive strict relative degree or proper inverse transfer function; in the single-input single-output case these two disjoint classes make the whole of all linear DAEs without feedthrough term. Structural properties - such as normal forms (i.e. the counterpart to the Byrnes-Isidori form for ODE systems), zero dynamics, and high-gain stabilizability - are analyzed for two purposes: first, to gain insight into the system classes and secondly, to solve the output regulation problem by funnel control. The funnel controller achieves tracking of a class of reference signals within a pre-specified funnel; this means in particular, the transient behaviour of the output error can be specified and the funnel controller does neither incorporate any internal model for the reference signals nor any identification mechanism, it is simple in its design. The results are illuminated by position and velocity control of a mechanical system encompassing springs, masses, and dampers.

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Metadaten
Author:Timo Reis, Thomas Berger, Achim Ilchmann
URN:urn:nbn:de:0296-matheon-8716
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/07/16
Release Date:2011/07/16
Tag:differential-algebraic equations; funnel control; high-gain output feedback; minimum phase; stabilization; strict relative degree; zero dynamics
Institute:Research Center Matheon
Technische Universität Berlin
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Axx General theory / 34A09 Implicit equations, differential-algebraic equations [See also 65L80]
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Hxx Control problems [See also 49J15, 49K15, 93C15] / 34H15 Stabilization
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Bxx Controllability, observability, and system structure / 93B52 Feedback control
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Dxx Stability / 93D15 Stabilization of systems by feedback
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Dxx Stability / 93D21 Adaptive or robust stabilization
Preprint Number:809
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