Minimum State Unsteady Aerodynamic Shape Sensitivities Using Sensitivity of Optimal Solutions to Problem Parameters

Abstract

parameters involved, including the aerodynamic lag roots. Its solution is unique, and convergence of the solution process, based on standard mathematical programming techniques, allows accurate determination of all unknown variables. An improvement of the math-programming minimum-state fitting is presented here, and it is developed further to include sensitivity analysis for the resulting minimum-state series, free of the nonuniqueness and convergence issues that plagued previous attempts to obtain sensitivities of minimum-state fits. A variable planform double-swept forward wing case is used to demonstrate performance of the fitting technique itself, shape sensitivity calculations, and Taylor-series-based approximations that can be used to replace detailed full-order analysis in the course of multidisciplinary design optimization of flight vehicles. Nomenclature [A0], [A1], [A2] = minimum-state approximation matrices corresponding to aerodynamic stiffness, damping, and inertia, respectively a � 0� , a � 1� , a � 2� = elements of the matrices [A0], [A1], [A2] b = reference semichord length of wing [C] = structural viscous damping matrix c = reference chord length of wing [D], [E] = minimum-state approximation matrices