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Control design for beam stabilization with self-sensing piezoelectric actuators: managing presence and absence of hysteresis

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Abstract

This paper deals with the modelling and stabilization of a flexible clamped beam controlled with a piezoelectric actuator in the self-sensing configuration. We derive the model starting from general principles, using the general laws of piezoelectricity. The obtained model is composed by a PDE, describing the flexible deformations dynamics, interconnected with an ODE describing the electric charge dynamics. Firstly, we show that the derived linear model is well-posed and the origin is globally asymptotically stable when a voltage control law, containing the terms estimated in the self-sensing configuration, is applied. Secondly, we make the more realistic assumption of the presence of hysteresis in the electrical domain. Applying a passive control law, we show the well-posedness and the origin’s global asymptotic stability of the nonlinear closed-loop system.

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Funding

This work has been received funding from MIAI@Grenoble Alpes project (Grant ANR-19-P3IA-0003) and by the ANR Labex CIMI (Grant ANR-11-LABX- 0040).

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Author notes

  1. Christophe Prieur and Sophie Tarbouriech have contributed equally to this work.

Authors and Affiliations

  1. Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab, Grenoble, 38000, France

    Andrea Mattioni & Christophe Prieur

  2. LAAS-CNRS, Université de Toulouse, 31031, Toulouse, France

    Sophie Tarbouriech

Authors
  1. Andrea Mattioni
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  2. Christophe Prieur
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  3. Sophie Tarbouriech
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Contributions

CP and ST had the main ideas regarding including electric dynamics in the model. CP and ST wrote the beginning of section 2. AM wrote the modelling and the linear case sections (sections 2 and 3). AM and CP wrote section 4. All authors reviewed the manuscript.

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Correspondence to Andrea Mattioni.

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Mattioni, A., Prieur, C. & Tarbouriech, S. Control design for beam stabilization with self-sensing piezoelectric actuators: managing presence and absence of hysteresis. Math. Control Signals Syst. (2024). https://doi.org/10.1007/s00498-024-00393-6

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  • DOI: https://doi.org/10.1007/s00498-024-00393-6

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