Statistical gain-scheduling method for aircraft flight simulation

A global polynomial variable scheduling method for aircraft controller is proposed to achieve runtime benefits with no degradation of controller stability. The method is benchmarked against two conventional methods: nearest neighbor and bilinear interpolation. An examination of conventional method constructs reveals recursive local approximation generation as the most expensive step, whereas discontinuities and lack of first derivative smoothness lead to poor approximations. The proposed method features a multivariate polynomial as the variable scheduling mechanism that addresses both drawbacks concurrently and achieves significant runtime improvements by virtue of its very simple functional form. The mathematical formulation of the proposed approach is discussed along with practical considerations for implementation. Numerical flight dynamics simulations are conducted with the three methods for four flight maneuvers and using four scheduling variable sets of increasing resolution. Results show the proposed method significantly reduces runtime relative to nearest neighbor, and even more so relative to bilinear interpolation. Results also indicate comparable controller stability in terms of deviation from margins of optimum solutions.