Chaos control of nonlinear aeroelastic pitch plunge model

Abstract

This paper deals with the control of chaos in a nonlinear aeroelastic pitch-plunge model for aircraft wings. While design of nonlinear controllers to asymptotically stabilise the initial bifurcation exists in the current literature, the primary goal of this paper is to control the chaotic motion using feedback linearisation. For this purpose, a pitch-plunge model with two flaps is considered for the study. The approach proposed for the control of chaos is that of a tracking problem where the system is controlled to a defined limit cycle; thus the chaotic motion is replaced by orbital stability. Using Lie algebra, a feedback linearisation is performed by transforming the nonlinear space to a linear one. The error dynamics is established as the deviation of the chaotic trajectory from that of the desired path and tracking is achieved by reducing the error to zero. The ability of this approach to control chaos is demonstrated for a certain set of parameters of the pitch-plunge model, chosen from the literature. In order to validate the approach followed in this paper, the Rossler system undergoing chaotic motion is tracked to a LCO and results are compared with the literature.