Application of aeroservoelastic modeling using minimum-state unsteady aerodynamic approximations

Various control analysis, design, and simulation techniques for aeroservoelastic applications require the equations of motion to be cast in a linear time-invariant state-space form. Unsteady aerodynamic forces have to be approximated as transfer functions of the Laplace variable in order to put them in this framework. For the minimum-state method, the number of augmenting states representing the unsteady aerodynamics is a function only of the number of denominator roots in the approximation. Results are shown of applying various approximation enhancements (including optimization, mode, and frequency-dependent weighting of the tabular data, and constraint selection) of a minimum-state formulation of the equations of motion of an active flexible wing wind-tunnel model. The results demonstrate that good mathematical models can be developed which have a factor of 10 fewer augmenting aerodynamic equations than more traditional approaches. This reduction facilitates the design of lower-order control systems, analysis of control system performance, and near real-time simulation of aeroservoelastic phenomena.