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Control system design based on holistic eigenvalue allocation

Regelsystementwurf auf der Basis holistischer Eigenwertvorgabe

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An Erratum to this article was published on 01 June 2001

Abstract

A trade-off between optimum allocation of the entire set of eigenvalues and the size of controller norm or a general actuator effort is carried out for continuous-time and discrete-time systems. Controllers achieving appropriate results are termed holistic. The design is based on the trace and determinant of the closed-loop state-space matrix. To solve the problem within the scope of actuating effort, the norm of the state controller matrixor the actuator effort transfer matrix are taken into consideration. The method is also extended for designing holistic observers. For preserving stability, a Lyapunov condition is included.

Zusammenfassung

Die Vorgabe der Eigenwerte einer linearen Mehrgrößenregelung wird in ihrer Gesamtheit besorgt. Regler, die diese Vorgabe erfüllen, werden als holistisch bezeichnet. Der Entwurf benutzt nur die Spur der inversen Koeffizientenmatrix der geschlossenen Regelung bzw. die Determinante der Koeffizientenmatrix direkt bei kontinuierlichen bzw. zeitdiskreten Systemen. Obwohl diese Methode von einer nur notwendigen Stabilitätsbedingung ausgeht, ist sie auch auf instabile Regelstrecken anwendbar. Als Rahmen für die holistische Eigenwertvorgabe ist nur ein Richtwert des Steueraufwands erforderlich, mit dem sie optimal in Abstimmung gebracht wird. Die Methode ist auch auf holistische Beobachter ausgedehnt und um eine Lyapunov-Bedingung für Stabilität erweitert.

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  1. Institute of Automatic Control, Vienna University of Technology, Gusshausstrasse 27-29/375, A-1040, Vienna

    A. Weinmann ÖVE (Senior Member IEEE)

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  1. A. Weinmann ÖVE
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Correspondence to A. Weinmann ÖVE.

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An erratum to this article is available at http://dx.doi.org/10.1007/BF03158919.

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Weinmann, A. Control system design based on holistic eigenvalue allocation. Elektrotech. Inftech. 118, 167–173 (2001). https://doi.org/10.1007/BF03159524

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