Linear PID and nonlinear sliding mode controllers are developed and applied to a spherical model of a contrast agent microbubble that describes its radial response to ultrasound input. The plant model is a compressible form of the Rayleigh-Plesset equation combined with a thin-shell model. A nonlinear control law for the second-order plant model is developed and used to design and simulate the sliding mode controller and is compared to the performance of a fixed-gain PID controller. The performance of the nonlinear controller on the contrast agent response is evaluated for various control scenarios. This work shows the feasibility of using a nonlinear control system to modulate the dynamic response of ultrasound contrast agents, and highlights the need for improved feedback mechanisms and control input methods. Applications of the nonlinear control system in this work include bubble radius stabilization in the presence of an acoustic wave, radial bubble growth and subsequent collapse, and periodic radial oscillation response while a bubble is within an acoustic forcing regime known to cause a chaotic response.

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