A Practical Investigation of H∞ Loop Shaping Controllers Using the Lmi Framework for a Hover System

Abstract. The design of a static parametric H∞ loop shaping controller using a linear matrix inequality (LMI) approach for a hover system is presented. The main steps to obtain such controller are explained. The parametric H∞ loop shaping technique explores more design flexibility by introducing a free parameter into the design process that ensures robust stabilization with regard to normalized coprime factor uncertainty of the shaped plant. The shaped plant is designed based on the closed-loop design specification by appropriately choosing the weighting transfer function matrices. Several controllers were designed using this methodology and were then evaluated with sets of specifications for robust stability and performance. This hover system is a laboratory system produced by Quanser Consulting and simulates typical behaviors of a VTOL ("vertical taking-off landing") aircraft, also known as X4-flyer. The dynamics of the hover can be described by a 6th order model taking as state variables the angles of roll, pitch, yaw and associated rates. Candidate controllers must solve the problem of tracking reference trajectories, ensure performance specifications and guarantee robust stability of the hover. Finally, we present experimental results obtained with the implementation of the designed controllers in the context of tracking problems of this hover system.