Continuous Differentiation of Complex Systems Applied to a Hypersonic Vehicle

摘要

An implementation of a three-dimensional model for an air-breathing hypersonic vehicle using algorithmic differentiation is presented. Motivation for this work is given in terms of difficulties encountered while calculating the linearized flight dynamics of another hypersonic vehicle model. The new model automatically calculates derivatives with respect to flight condition variables, control variables, model parameters, and design variables. The differentiation approach used here is unique in that it calculates both left- and right-hand derivatives at first-order discontinuities. Other approaches including complex step and finite difference are compared with the present implementation. Difficulties encountered in the derivation include handling of if statements, iterative solution of systems, and sorting. Hypersonic flight for a simple climbing and accelerating trajectory is considered to demonstrate the use of the model, and the effect of ballast mass on the short-period and Dutch-roll modes is also shown.