Optimisation of unsteady aerodynamic forces for aircraft aeroservoelastic studies

One main aspect of the aeroservoelasticity is the optimization of the unsteady generalized aerodynamic forces

Q(k, M)

from the frequency domain into the Laplace domain

Q(s)

, where

k

represents the reduced frequency,

M

is the Mach number and

s

is the Laplace variable. These forces were calculated at NASA DFRC by use of the finite element software STARS and by use of Doublet Lattice Method DLM and Constant Pressure Method [

1

]. The optimization yielding until now in the literature the smallest order time-domain state-space model is the MS method. In this paper, we present a new optimization method of the generalized aerodynamic forces for aeroservoelastic studies by use of Chebyshev polynomials and their orthogonality properties. A comparison of results obtained by use of this new method with the flutter results obtained experimentally at NASA DFRC (Dryden Flight Research Laboratory) is presented on the F/A-18 SRA (System Research Aircraft). The Chebyshev optimization method provides the smallest error by comparison with the other method’s given errors. Due to the fact that the Chebyshev polynomials had to be generated using the data provided on the F/A-18 SRA, which involve large differences between the values of the elements contained in the unsteady generalized aerodynamic forces matrices (1e+10), certain restraints regarding the threshold of the error had to be imposed, i.e. for smaller elements we have imposed an error value of 1e-4 and for larger elements an error value of 1e-2. Without these restraints, the Chebyshev polynomials cannot be generated. In case when the approximation order for Chebyshev method is increased, then the overall error will decrease even faster than by use of the LS method.