Intelligent controlling microbubble radial oscillations by using Slave–Master Feedback control

•Dynamic of radial oscillations of encapsulated microbubble have been studied.•A method based on Slave–Master Feedback to suppress unstable radial oscillations is introduced.•Mean Lyapunov exponent theory is applied in stability analysis.•Based on the obtained outcome acoustic pressure amplitude is one of most important factors in stability of the microbubble.

Dynamics of acoustically driven microbubbles in ultrasonic fields are known to be complex and uncontrollable phenomena indicative of a highly active nonlinear as well as chaotic behavior. In this paper, a method based on Slave–Master Feedback (SMF) to suppress unstable radial oscillations of contrast agents is presented. In the proposed control process, the encapsulated microbubbles as the slave system is coupled with a dynamical system as the master, so that the output of the coupled system is able to produce a stable oscillation. A great virtue of this control technique is its flexibility. In comparison with existing techniques, the present dynamical chaos control method does not need to know more than one variable. The numerical results show its strong impact on reducing the chaotic oscillations to regular ones.