Sliding mode control of supersonic aeroelastic flutter via LMI

摘要

This paper presents a sliding mode control method via LMI (linear matrix inequality), which is used for the flutter suppression problem in supersonic airflow. For the purpose of control, a single trailing-edge control surface is used. The prototypical aeroelastic model describes the plunge and pitch motion, including cubic nonlinear structural stiffness and the nonlinear aerodynamic load. The modified third order Piston theory is employed to derive the aerodynamic force and moment in the supersonic airflow. Based on the Hopf bifurcation theory, the flutter speed is computed. The sliding surface is designed by the auxiliary state feedback matrix, which is obtained from solving a linear matrix inequality. To solve the chattering problem produced in traditional sliding mode control, the reaching law in robust global terminal sliding mode control is introduced. By Lyapunov theory, the states of the aeroelastic system asymptotically converge to equilibrium 0 under the designed control law. Results of simulation show that the proposed method is effective.