Design and application of gain-scheduling control for a Hover: Parametric H<inf>∞</inf> loop shaping approach

Abstract

This paper presents synthesis conditions for the design and application of Linear Parameter-Varying (LPV) controllers for a 3DOF (Degrees of Freedom) Hover. This laboratory plant simulates typical behaviors of an VTOL ("vertical taking-off landing") aircraft, also known as X4-flyer. The dynamics of the Hover are described by a 6 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> order model taking as state variables the angles of roll, pitch, yaw and associated rates. The design problem has been formulated via parametric H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> loop shaping control by describing the uncertainly as perturbations to normalized coprime factors of the shaped plant. The design strategy is characterized by the insertion of a free parameter that aims to increase the flexibility of the design ensuring robust stabilization of the linear parameter-varying system. For the existence of a gain-scheduled parametric H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> loop shaping controller, a set of sufficient conditions has been derived in an LMI framework. Finally, we present experimental results obtained with the application of the parametric H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> loop shaping controller for the tracking of reference trajectories of the Hover.