An adaptive backstepping sliding mode control method for aeroelastic system

Abstract

This study proposes an efficient active control method to suppress the flutter occurred in a nonlinear airfoil with a softening spring structure. Firstly, an adaptive backstepping sliding mode control (ABSMC) method is introduced to improve the system stability and eliminate the limit cycle response. The control scheme is developed by combining the sliding mode control with the backstepping technique to ensure the sliding motion and the trajectory of motion error converge to zero in finite-time. In addition, a sliding mode surface is constructed to attain a free chattering and a fast convergence rate. Secondly, analytical methods based on the Lyapunov theory are utilized to derive the adaptive law to enhance robustness of the control system in order to guarantee the convergence of the trajectory error. Meanwhile, an adaptive law is employed to compensate uncertainty and disturbance to obtain a better disturbance rejection property. As a result, a finite-time stability of the airfoil control system can be achieved. Finally, a comparison between ABSMC and a backstepping second-order sliding mode control is carried out, which demonstrates the superiority of the proposed control method. Simulation results indicate that ABSMC can ensure the robustness of the system with uncertainty when the controller input was limited.