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Design of robust fractional-order sliding mode with fuzzy supervisor to control the nonlinear oscillation of two interacting bubbles

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Abstract

In modern medical techniques, the medical bubbles are widely employed for ultrasonic imaging, targeted drug delivery, and cancer treatment. However, the nonlinear oscillations of medical bubbles restrict the applications of bubble technology in medicine. To prevent bubble oscillations, this problem is solved through control engineering point of view. For this purpose, the nonlinear dynamics of two interacting bubbles in the incompressible liquid is presented. In continuation, the fractional-order sliding mode controller is proposed to regulate the radius of bubbles. In this closed-loop system, the ultrasonic waves play the role of control input signals and the outputs are the radius of bubbles which are measured by the image processing. The stability of the closed-loop system is ensured by the Lyapunov theorems. The switching gains are scheduled adaptively according to the fuzzy logic system. The simulation results including the cases of parametric uncertainty, measurement noise, and analysis of the steady state error are presented to demonstrate the efficiency of the proposed method. The results of this research are of immediate interest for modern medical applications.

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Data will be available to the readers upon a formal request from the corresponding author.

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Funding

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran

    Ehsan Badfar

  2. Department of Control Engineering, Faculty of Electrical and Computer Engineering, Technical and Vocational University (TVU), Tehran, Iran

    Mahdi Ardestani

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

    Mahmoud Najafi

Authors
  1. Ehsan Badfar
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  2. Mahdi Ardestani
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  3. Mahmoud Najafi
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Contributions

EB contributed to writing, simulation, mathematical formulation; MA contributed to supervision, writing, simulation; MN contributed to supervision, mathematical formulation.

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Correspondence to Mahdi Ardestani.

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Badfar, E., Ardestani, M. & Najafi, M. Design of robust fractional-order sliding mode with fuzzy supervisor to control the nonlinear oscillation of two interacting bubbles. Int. J. Dynam. Control 11, 1914–1925 (2023). https://doi.org/10.1007/s40435-022-01096-z

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  • DOI: https://doi.org/10.1007/s40435-022-01096-z

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