High performance control for trajectory tracking of symmetric VTOL vehicles with significant aerodynamic effects

In this paper, we propose a high performance, Lyapunov based control design for symmetric VTOL vehicles to track trajectories at which aerodynamic effects are significant. We consider the case where an accurate model of aerodynamic forces may be obtained either analytically or empirically. A Lyapunov based control strategy is proposed. To avoid lengthy and noisy control expressions resulting from twice differentiating this aerodynamic model (as required by the standard backstepping algorithm), we propose a backstepping technique designed alongside two coupled filters. The first filter enables a cascade approach to be used, while the second provides a smoothed version of the higher order derivatives of the aerodynamic term for use in the dynamic inversion of the model. The resulting controller is described by equations significantly less complex and lengthy than if a standard linearization technique were used. Simulation results are presented for the specific case of a simple cylindrical VTOL vehicle. These results demonstrate the controller's ability to reject an initial condition mismatch, and invert the system dynamics sufficiently despite the approximations made to the backstepping technique used.