A Balanced Mode Decomposition Approach for Equation-Free Reduced-Order Modeling of LPV Aeroservoelastic Systems

Abstract

The paper proposes a novel approach to data-driven reduced-order modeling which combines the Dynamic Mode Decomposition technique with the concept of balanced realization. The information on the system comes from input, state, and output trajectories, and the goal is to derive a linear low-dimensional input-output model approximation. % of the system around a given trim point. Since the dynamics of aerospace systems markedly changes when some parameters are varied, it is desirable to capture this feature in the system's description. Therefore, a Linear Parameter-Varying representation made of a collection of state-consistent linear time-invariant reduced-order models is sought. The main technical novelty of the proposed algorithm consists of replacing the orthogonal projection onto the POD modes, typical of Dynamic Mode Decomposition techniques, with a balancing oblique projection. The advantages are that the input-output information in the lower-dimensional representation is maximized, and that a parameter-varying projection is possible while also achieving state-consistency. The validity of the proposed approach is demonstrated on a morphing wing for airborne wind energy applications by comparing its prediction capabilities with those of a recent algorithm from the literature.