A backstepping-based procedure with saturation functions to control the PVTOL system

In this study, we present a control strategy to solve the regulation problem for a simplified version of a PVTOL system strongly coupled. The strategy is split into two control actions that act simultaneously: one stabilizes asymptotically the vertical position; the other stabilizes both the horizontal and the angle positions. The first controller uses a simple feedback linearization procedure in conjunction with a saturation function. This controller assigns a quasilinear behavior to the vertical displacement. The second controller is based on a suitable backstepping procedure, and its task is to force the remaining variables converge asymptotically to the origin. In short, the resulting control is a nonlinear state feedback, whose performance is demonstrated by numerical simulations. The convergence analysis, based on the Lyapunov method, turned out to be quite simple if compared to other control methods found in the literature.