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Stability analysis and sliding mode control of a single spherical bubble dynamics

The goal of the present paper is to apply control techniques to determine the Blake cavitation threshold for adiabatic bubbles. Considering state space representation of Rayleigh-Plesset (RP) equation, a stability condition is derived to predict the threshold for cavitation which was determined beforehand by mechanical bias. Moreover, sliding mode control has been utilized to regulate the radius of a single spherical bubble to the desired value to prevent collapse occurrence which has a great importance in some industrial applications. Simulation results are presented to show the effectiveness of the proposed method.