Data-driven acoustic control of a spherical bubble using a Koopman linear quadratic regulator

Area of Science:

• Nonlinear Dynamics and Control
• Acoustic Manipulation
• Fluid Dynamics

Background:

• Koopman operator theory linearizes nonlinear systems in function spaces.
• Data-driven methods approximate these function spaces for control.
• Acoustic control of bubbles is challenging due to nonlinear dynamics.

Purpose of the Study:

• To apply Koopman linear quadratic regulator (KLQR) for acoustic control of a single spherical bubble.
• To achieve objectives including large-amplitude oscillations, stabilization, and complex periodic motions.
• To demonstrate the efficacy of linear control strategies on nonlinear bubble dynamics.

Main Methods:

• Utilized Koopman operator theory to transform nonlinear bubble dynamics (Rayleigh-Plesset equation) into a linear representation.
• Implemented a Koopman linear quadratic regulator (KLQR) for feedback control.
• Employed acoustic driving (broadband and single-frequency) to manipulate bubble oscillations.

Main Results:

• KLQR effectively controlled the nonlinear radial oscillations of a spherical bubble.
• Achieved prescribed oscillation trajectories, including simple harmonic, stabilized, periodic, and quasiperiodic motions.
• Demonstrated robustness and the ability to track arbitrary trajectories without initial guesses.

Conclusions:

• Koopman operator theory provides a powerful framework for controlling nonlinear systems like acoustic bubbles.
• KLQR offers a robust and versatile method for precise acoustic bubble manipulation.
• This data-driven linear control approach overcomes limitations of previous methods.