A methodology for using nonlinear aerodynamics in aeroservoelastic analysis and design

Abstract

A methodology is presented for using the VolterraWiener theory of nonlinear systems in aeroservoelastic (ASE) analyses and design. The theory is applied to the development of nonlinear aerodynamic response models that can be defined in state-space form and are, therefore, appropriate for use in modern control theory. The theory relies on the identification of nonlinear kernels that can be used to predict the response of a nonlinear system due to an arbitrary input. A numerical kernel identification technique, based on unit impulse responses, is presented and applied to a simple bilinear, single-input-singleoutput (SISO) system. The linear kernel (unit impulse response) and the nonlinear second-order kernel of the system are numerically-identified and compared with the exact, analytically-defined linear and second-order kernels. This kernel identification technique is then applied to the CAP-TSD (Computational Aeroelasticity ProgramTransonic Small Disturbance) code for identification of the linear and second-order kernels of a NACA64AOlO rectangular wing undergoing pitch at M=0.5, M=0.85 (transonic), and M=0.93 (transonic).Results presented demonstrate the feasibility of this approach for use with nonlinear, unsteady aerodynamic responses.

Volterra Kernels Assessment via Time-Delay Neural Networks for Nonlinear Unsteady Aerodynamic Loading Identification

“…In fact, the high-frequency noise covers up the kernel content if a comparison is performed directly and without any filtering in the time domain. It is also important to note that the kernels of first-order presented in all the analyses correspond to the first-order kernel of a second-order system, that is different from the first-order kernel of a first-order system [23]. The performance of the kernels of higher-order is evaluated in the following sections using convolved responses for the approximation of unsteady aerodynamic loads.…”

“…Classical kernel identification is based on applying impulse inputs of various orders. By assuming that the system is weakly nonlinear [23], a suitable representation can be obtained retaining only the first two kernels of the series. The discrete-de Paula et al…”