The Analysis of Vehicle’s In-Flight Behaviour Using Quasi-LPV and Nonlinear Models

Abstract

A vehicle's in-flight behaviour can be represented by the Newton-Euler equations of motion: usually, such a model has a nonlinear and continuous description based on ordinary differential equations. The model structure can be altered using analytic transformations and, when the model is implemented, its numerical precision may depend on the selection of a numerical solver. hence, the selection of a model's structure and an appropriate numerical solver can become the key development issues, if the model's numerical stability, convergence, and computational complexity are to be improved. This paper assesses the influence of a model's reference frame and a numerical solver on the accuracy of calculating a projectile's trajectory, for a case study of free-flight long-range ballistic experiments. The analysis is based on two model structures: the first is a six-degree-of-freedom nonlinear description of a spin-stabilized projectile, expressed in a rolling reference frame; the second is a quasi-LPV reformulation of the same projectile model, but expressed in a non-rolling reference frame. It is shown that inappropriate selection of a numerical solver can hinder the accuracy of the nonlinear model. At the same time, the model represented in a non-rolling reference frame offers a solution with higher accuracy, better convergence properties, and significantly reduced computation time.