Generation of a reduced-order LPV/LFT model from a set of large-scale MIMO LTI flexible aircraft models

Abstract

In the civilian aviation industry, the aeroelastic behavior of an aircraft is often modeled at frozen flight and mass configurations using high fidelity numerical tools. Unfortunately, the resulting large-scale models cannot be handled in such form by modern analysis and control techniques, which generally require the considered models to be written as low-order Linear Fractional Representations (LFR). In this context, a methodology is described to derive a reduced-order Linear Parameter Varying (LPV) model from a reference set of large-scale Multiple Input Multiple Output (MIMO) Linear Time Invariant (LTI) models describing a given system at frozen configurations. The proposed approach is in two steps. The reference models are first reduced using recent advances in Krylov methods, leading to a set of low-order state-space representations with consistent state vectors. An LPV model is then obtained by polynomial approximation and converted into an LFR of reasonable size. A special effort is made to avoid data overfitting by using as simple as possible approximation formulas. The method is applied to a long-range commercial aircraft model developed in an industrial context: a set of large-scale flexible models linearized at different mass configurations is converted into a single low-order LPV model. More generally, any kind of purely numerical models for which the analytical structure is unknown can be considered.