Robust Nonsingular Terminal Sliding Mode Control of Radius for a Bubble Between Two Elastic Walls

In many industrial and medical systems, there is a bubble between two elastic walls. On the other hand, the collapse of bubbles is considered a constant source of energy lost and causes system damage. This research is the first attempt to prevent from bubble collapse between two elastic boundaries by using control algorithms. In this paper, first, the nonlinear dynamic model of the bubble between two elastic walls is introduced and then rewritten into a state-space form. The second part of this paper is devoted to the design of the sliding mode controller, where the ultrasonic pressure plays the role of control input and the output is bubble radius. At first, terminal sliding mode control is proposed. Although this method ensures finite-time convergence, its main drawback is singularity in the control input signal. The nonsingular terminal sliding mode control is proposed to solve the problem of singularity in the control input signal. A rigorous stability analysis is also presented using the Lyapunov theory to demonstrate the stability of nonsingular sliding manifold. The effect of controller parameters on the performance of the closed-loop system is investigated. Finally, some simulation results including the case of parametric uncertainty are also presented to demonstrate the efficiency of the proposed scheme. The results of this study are of immediate interest for industrial applications such as designing pumps and valves and medical applications such as targeted ultrasound imaging and cancer treatment.