Adaptive control design for a supercavitating vehicle model based on fin force parameter estimation

In this paper, an adaptive control using the backstepping technique is applied for a supercavitating vehicle model to account for the unknown slope of the fin force with respect to fin angle of attack in the vehicle model. In the supercavitating-vehicle benchmark model, the fin force was modeled as a linear function with respect to the fin angle of attack, and the corresponding slope was considered to be a known constant for a fixed cavitation number. However, more realistic modeling for the fin force shows that the fin force slope is a function of the fin deflection angle, fin sweepback angle and fin immersion. In addition, noting that the cavity shape at the transom region determines immersion of the fins, the fin immersion and thus the slope of the fin force is also impacted by the so-called memory effect due to cavity–vehicle interaction. In this paper, we consider the fin effectiveness parameter relative to the cavitator, which is used to compute the slope of the fin force in the aforementioned benchmark model, to be an unknown parameter. Then a parameter estimation law is designed for this fin effectiveness parameter and an adaptive backstepping controller is designed for the supercavitating vehicle model. We prove the boundedness of all variables (and convergence of the vehicle state variables under certain conditions) via Lyapunov stability theory. In addition, if the bound of the fin effectiveness parameter is known, a projection of the parameter adaptive law can be used and the resulting modified controller will maintain the same properties. Evaluation results through simulation on both initial response and tracking performance of the closed-loop system show the effectiveness of the developed algorithm.