Nonlinear order reduction of structural dynamic aircraft models

Abstract

New methods for nonlinear order reduction of structural dynamic aircraft models described by nonlinear differential equations have been developed. The methods are based on singular perturbations, weak coupling and cost functionals for selecting the physical states of the reduced order model, computing and analyzing the reduced order model. By introducing a formally affine nonlinear model structure, the cost functional vector optimization yields closed expressions for the reduced order system. Via Lagrange multipliers, even constraints with regard to the reduced order system can be considered, only extending these closed expressions. This leads to the notion of smaller and control-oriented realizations. Moreover, a unified approach to structural dynamic aircraft modeling for loads analysis and for structural dynamic control is developed, which allows us to apply the new reduction methods directly to both problems. Here, the methods are applied to a structural dynamic aircraft model in order to achieve a very low order model, suited for structural dynamic controller design.