Trajectory tuning for the tracking problem of the underactuated mechanical systems: application to the PVTOL aircraft

Abstract

The Planer vertical take-off and landing (PVTOL) aircraft is a typical example of an underactuated mechanical system and has a nonminimum-phase nature. When considering output tracking control, the Input/Output (I/O) linearization method is not appropriate since the stability of the internal dynamics is not guaranteed. Hauser et al. regarded this system as a slightly nonminimum-phase system which approximates to a minimum-phase one. Their control scheme yielded good results when the coupling factor was small, but the results were not acceptable when the coupling factor increased. In this article, we propose two approaches to improve the control performance. First, we consider the approximation error of Hauser's scheme as uncertainty, and apply the Linear Quadratic Regulator (LQR) method, which possesses robustness against uncertainty, to determine the stabilizing feedback coefficients. Second, from the fact that the tracking error is unavoidable, we use the “virtual reference trajectory” to design the tracking control law, and optimize this trajectory to reduce the tracking error between the “actual reference trajectory” and the “resulting trajectory”. This optimization also improves the control performance by choosing a suitable performance index. By using our approach, we achieve better performance even if the coupling factor is increased. We show these results by numerical simulation.