Disturbance Observer-Based Backstepping Terminal Sliding Mode Aeroelastic Control of Airfoils

This paper studies aeroelastic control for a two-dimensional airfoil–flap system with unknown gust disturbances and model uncertainties. Open loop limit cycle oscillation (LCO) happens at the post-flutter speed. The structural stiffness and quasi-steady and unsteady aerodynamic loads of the aeroelastic system are represented by nonlinear models. To robustly suppress aeroelastic vibration within a finite time, a backstepping terminal sliding-mode control (BTSMC) is proposed. In addition, a learning rate (LR) is incorporated into the BTSMC to adjust how fast the aeroelastic response converges to zero. In order to overcome the fact that the BTSMC design is dependent on prior knowledge, a nonlinear disturbance observer (DO) is designed to estimate the variable observable disturbances. The closed-loop aeroelastic control system has proven to be globally asymptotically stable and converges within a finite time using Lyapunov theory. Simulation results of an aeroelastic two-dimensional airfoil with both trailing-edge (TE) and leading-edge (LE) control surfaces show that the proposed DO-BTSMC is effective for flutter suppression, even when subjected to gusts and parameter uncertainties.