An Application of Finite Hilbert Transforms in the Derivation of a State Space Model for an Aeroelastic System

Abstract

Dynamic modeling of various aeroelastic control systems requires, at some point in the derivation of the model, an application of Shngen's inversion formula for finite Hilbert transforms to obtain a desired representation for the solution of the airfoil equation. Conditions on initial data to guarantee well-posedness of the resulting model equations must be matched with those needed to justify the validity of the inversion formula. We show that this compatibility can be achieved by assuming that the circulation history belongs to a weighted L 2 space. The resulting state space formulation provides a suitable setting for control design for the aeroelastic system.