A nonlinear stability analysis of elastic flight vehicle

Abstract

Purpose

The purpose of this paper is to present a nonlinear model along with stability analysis of a flexible supersonic flight vehicle system.

Design/methodology/approach

The mathematical state space nonlinear model of the system is derived using Lagrangian approach such that the applied force, moment, and generalized force are all assumed to be nonlinear functions of the system states. The condition under which the system would be unstable is derived and when the system is stable, the region of attraction of the system equilibrium state is determined using the Lyapunov theory and sum of squares optimization method. The method is applied to a slender flexible body vehicle, which is referenced by the other researchers in the literature.

Findings

It is demonstrated that neglecting the nonlinearity in external force, moment and generalized force, as it was assumed by other researchers, can cause significant variations in stability conditions. Moreover, when the system is stable, it is shown analytically here that a reduction in dynamic pressure can make a larger region of attraction, and thus instability will occur in a larger angle of attack, greater angular velocity and elastic displacement.

Practical implications

In order to carefully study the behavior of aeroelastic flight vehicle, a nonlinear model and analysis is definitely necessary. Moreover, for the design of the airframe and/or control purposes, it is essential to investigate region of attraction of equilibrium state of the stable flight vehicle.

Originality/value

Current stability analysis methods for nonlinear elastic flight vehicles are unable to determine the state space region where the system is stable. Nonlinear modeling affects the determination of the stability region and instability condition. This paper presents a new approach to stability analysis of the nonlinear flexible flight vehicle. By determining the region of attraction when the system is stable, it is demonstrated analytically, in this research, that decreasing the dynamic pressure can produce larger region of attraction.

Citation

Shamaghdari, S. and Nikravesh, S.K.Y. (2012), "A nonlinear stability analysis of elastic flight vehicle", Aircraft Engineering and Aerospace Technology, Vol. 84 No. 6, pp. 404-412. https://doi.org/10.1108/00022661211272954