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Gain-scheduled H∞ controller with minimum Frobenius norm

H∞ Regler minimaler Frobenius-Norm bei vorbestimmter maximaler Regelkreisverstärkung

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Abstract

For microcontroller implementations, H∞ controllers with small numbers in their state-space realization are intended. Hence, minimum Frobenius norm is a design target. As an alternative, and useful for predetermining H∞ gain schedules, the infinity norm is included with the help of ramifications points of the eigenvalue contour of the Hamiltonian matrix.

Zusammenfassung

Für Mikrocontroller-Implementierung werden Regler mit kleinen Parameterwerten in ihrer Zustandsraumdarstellung vorgesehen. Eine kleine Regler-Matrixnorm erfüllt diese Anforderungen. Die H∞ Norm des Regelkreises wird über die Verzweigungspunkte der Eigenwertkontur der Hamilton-Matrix einbezogen.

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References

  • Gahinet, P., Apkarian, P., Chilali, M. (1996): Affine parameter-dependent Lyapunov functions and real parametric uncertainty. IEEE Trans. AC-41: 436–442.

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  • Weinmann, A. (2004): Optimal assignment of multiple control system eigenvalues with minimum controller norm. e & i 121 (2): 37–42.

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  • Weinmann, A. (2004a): H∞ controller under H∞ constraints. Intern. J. Automation Austria 12 (forthcoming).

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Authors and Affiliations

  1. Vienna University of Technology, Institute of Automation and Control, Gußhausstraße 27-29/376, A-1040, Vienna

    A. Weinmann Univ.-Prof. Dipl.-Ing. Dr. techn. (Senior Member IEEE)

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  1. A. Weinmann Univ.-Prof. Dipl.-Ing. Dr. techn.
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Correspondence to A. Weinmann Univ.-Prof. Dipl.-Ing. Dr. techn..

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Weinmann, A. Gain-scheduled H∞ controller with minimum Frobenius norm. Elektrotech. Inftech. 121, 72–76 (2004). https://doi.org/10.1007/BF03054970

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  • DOI: https://doi.org/10.1007/BF03054970

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