Flight envelope estimation for helicopters under icing conditions via the zonotopic reachability analysis

Abstract

This paper presents a new approach to estimating a flight envelope for a helicopter flying under clean and icing conditions based on a zonotopic reachability analysis. The helicopter is stabilized with a statefeedback linear controller to maintain its attitude around a trim point. Given the sets of possible initial conditions and disturbance inputs, and control effectiveness indices, this analysis results in reachable sets of state variables of the helicopter for a finite time interval. The reachability analysis is thus useful for predicting whether or not the helicopter evolves into an unsafe flight condition when it undergoes degraded control effectiveness ensued from the icing condition. The merit of this approach is shown through a case study about the Raptor-90 unmanned helicopter stabilized with either the linear quadratic regulator (LQR) or the H-infinity controller in a hover-flight mode. This helicopter is considered to be affected by both symmetric and asymmetric icing conditions. The case study shows that the H-infinity controller outperforms the LQR controller as the former is able to cope with greater loss of control effectiveness caused by the icing conditions. Moreover, as compared to the longitudinal control input, the lateral and directional control inputs are more susceptible to adverse effects of the icing conditions. These results verify not only the effects of ice contamination upon the helicopter dynamics and control, but also the capability of the proposed approach for flight envelope estimation. (C) 2020 Elsevier Masson SAS. All rights reserved.