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Krasovskii Passivity and μ -Synthesis Controller Design for Quasi-Linear Affine Systems

Author

Listed:
  • Vlad Mihaly

    (Department of Automation, Technical University of Cluj-Napoca, Str. G. Bariţiu nr. 26-28, 400027 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

  • Mircea Şuşcă

    (Department of Automation, Technical University of Cluj-Napoca, Str. G. Bariţiu nr. 26-28, 400027 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

  • Petru Dobra

    (Department of Automation, Technical University of Cluj-Napoca, Str. G. Bariţiu nr. 26-28, 400027 Cluj-Napoca, Romania)

Abstract

This paper presents an end-to-end method to design passivity-based controllers (PBC) for a class of input-affine nonlinear systems, named quasi-linear affine. The approach is developed using Krasovskii’s method to design a Lyapunov function for studying the asymptotic stability, and a sufficient condition to construct a storage function is given, along with a supply-rate function. The linear fractional transformation interconnection between the nonlinear system and the Krasovskii PBC (K-PBC) results in a system which manages to follow the provided input trajectory. However, given that the input and output of the closed-loop system do not have the same physical significance, a path planning is mandatory. For the path planning component, we propose a robust controller designed using the μ -synthesis mixed-sensitivity loop-shaping for the linearized system around a desired equilibrium point. As a case study, we present the proposed methodology for DC-DC converters in a unified manner, giving sufficient conditions for such systems to be Krasovskii passive in terms of Linear Matrix Inequalities (LMIs), along with the possibility to compute both the K-PBC and robust controller alike.

Suggested Citation

  • Vlad Mihaly & Mircea Şuşcă & Petru Dobra, 2021. "Krasovskii Passivity and μ -Synthesis Controller Design for Quasi-Linear Affine Systems," Energies, MDPI, vol. 14(17), pages 1-24, September.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:17:p:5571-:d:629921
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    References listed on IDEAS

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    1. Mian Wang & Fen Tang & Xuezhi Wu & Jingkai Niu & Yajing Zhang & Jiuhe Wang, 2021. "A Nonlinear Control Strategy for DC-DC Converter with Unknown Constant Power Load Using Damping and Interconnection Injecting," Energies, MDPI, vol. 14(11), pages 1-24, May.
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