Chebyshev Polynomials for Unsteady Aerodynamic Calculations in Aeroservoelasticity

The aerodynamic forces in the reduced frequency domain have to be approximated in the Laplace domain, in order to study the effects of the control laws on the flexible aircraft structure. This type of approximation of unsteady generalized aerodynamic forces from the frequency domain into the Laplace domain, acting on a Fly-By-Wire aircraft, presents an important challenge in the aeroservoelasticity area. In this paper we present a new method for approximation of the generalized aerodynamic forces, using Chebyshev polynomials and their orthogonality properties. A comparison of results expressed in terms of flutter speeds and frequencies obtained by this new method and by the Pad´e method is presented here. This new approximation method gives excellent results with respect to Pad´e method and is validated on the aircraft test model from NASA Dryden Flight Research Center.