A state-space model for loads analysis based on tangential interpolation

Abstract

In this work an approach for the generation of a generalized state-space aeroservoelastic model based tangential interpolation, also known as Loewner rational interpolation, is presented. The resulting differential algebraic system (DAE) system is reduced to a set of ordinary differential equations (ODE) by residualization of the non-proper part of the Transfer function matrix. The generalized state-space is of minimal order and allows for the application of the force summation method (FSM) for the aircraft loads recovery, which shows a superior convergence when compared to the mode displacement method (MDM) for an increasing number of generalized coordinates for the cut loads recovery. Compared to the classical rational function approximation (RFA) approach, the presented method provides a minimal order realization with exact interpolation of the unsteady aerodynamic forces in tangential directions, avoiding any selection of poles (lag states). After a demonstration of the tangential interpolation techniques on the transcendental Theodorsen and Sears functions, the new approach is applied to the generation of an aeroservoelastic model for loads evaluation of the NASA Common Research model under atmospheric disturbances, showing an excellent agreement with the reference model in the frequency domain. Applications include the aerodynamic transfer function matrices generated by either potential flow or linearized computational fluid dynamics (CFD) solvers. The resulting aeroservoelastic model of minimal order is used for the design of an H-infinity-optimal controller for gust loads alleviation (GLA).