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Stability analysis and sliding mode control of a single spherical bubble described by Keller–Miksis equation

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Abstract

This paper transforms the Keller–Miksis (KM) model, which is the main equation describing the bubble behavior, into a state space representation and presents a stability condition for the system using the linearized form of the KM equation. The dynamic of the cavitation bubble is analyzed for different gases, and its burst time is measured. Then, a sliding mode controller (SMC) is designed for the nonlinear system to regulate the radius of a single spherical bubble and prevent collapse occurrence, which has a great importance in some industrial applications. The system's robustness in the presence of uncertainties in bubble parameters is one of its most significant control objectives obtained in the controller designed in this paper. A comparison is also made between this controller and the controller previously designed for the simpler bubble model (Rayleigh–Plesset (RP) model). Also, the chattering created by SMC is eliminated by two methods. Simulation results are presented to show the effectiveness of the proposed method.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Tarbiat Modares University (TMU), Tehran, Iran

    Bahar Rahmatizadeh & Mohamad Taghi Hamidi Beheshti

  2. Department of Electrical and Computer Engineering, Ale Taha University of Technology, Tehran, Iran

    Masoumeh Azadegan

  3. Department of Mathematical Science, Kent State University, Kent, OH, USA

    Mahmoud Najafi

Authors
  1. Bahar Rahmatizadeh
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  2. Mohamad Taghi Hamidi Beheshti
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  3. Masoumeh Azadegan
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  4. Mahmoud Najafi
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Correspondence to Mohamad Taghi Hamidi Beheshti.

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Rahmatizadeh, B., Beheshti, M.T.H., Azadegan, M. et al. Stability analysis and sliding mode control of a single spherical bubble described by Keller–Miksis equation. Int. J. Dynam. Control 9, 1757–1764 (2021). https://doi.org/10.1007/s40435-021-00775-7

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  • DOI: https://doi.org/10.1007/s40435-021-00775-7

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