Data-driven nonlinear aeroelastic models of morphing wings for control

Abstract

Accurate and efficient aeroelastic models are critically important for enabling the optimization and control of highly flexible aerospace structures, which are expected to become pervasive in future transportation and energy systems. Advanced materials and morphing wing technologies are resulting in next-generation aeroelastic systems that are characterized by highly coupled and nonlinear interactions between the aerodynamic and structural dynamics. In this work, we leverage emerging data-driven modelling techniques to develop highly accurate and tractable reduced-order aeroelastic models that are valid over a wide range of operating conditions and are suitable for control. In particular, we develop two extensions to the recent dynamic mode decomposition with control (DMDc) algorithm to make it suitable for flexible aeroelastic systems: (1) we introduce a formulation to handle algebraic equations, and (2) we develop an interpolation scheme to smoothly connect several linear DMDc models developed in different operating regimes. Thus, the innovation lies in accurately modelling the nonlinearities of the coupled aerostructural dynamics over multiple operating regimes, not restricting the validity of the model to a narrow region around a linearization point. We demonstrate this approach on a high-fidelity, three-dimensional numerical model of an airborne wind energy system, although the methods are generally applicable to any highly coupled aeroelastic system or dynamical system operating over multiple operating regimes. Our proposed modelling framework results in real-time prediction of nonlinear unsteady aeroelastic responses of flexible aerospace structures, and we demonstrate the enhanced model performance for model predictive control. Thus, the proposed architecture may help enable the widespread adoption of next-generation morphing wing technologies.

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations

“…The main idea of the method is to efficiently compute the regression of linear/nonlinear terms to a least-square linear dynamics approximation from experimental or numerical observable data. Despite its first appearance in the fluid dynamics context [ 55 , 56 ], DMD has been used in many other applications such as epidemiology [ 51 ], biomechanics [ 16 ], urban mobility [ 3 ], climate [ 44 ] and aeroelasticity [ 28 ], especially in structure extraction from data and control-oriented methods.…”

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

“…In Section II.A the general data-driven low-order modeling problem is presented. Section II.B reviews then the algebraic DMD with Control (aDMDc) [16], an equation-free ROM algorithm from the literature used for comparison in the result section.…”

“…The algebraic Dynamic Mode Decomposition with Control (aDMDc) algorithm was recently proposed in [16] to extend the DMDc algorithm to systems described by algebraic-differential equations. The DMDc algorithm from [5] is first briefly reviewed.…”

“…The aDMDc builds on the DMDc approach and addresses the presence of algebraic constraints in the dynamic equations which might arise when considering unsteady aerodynamics features. Specifically, the FSI model employed in [16] implements a 3D panel with wake's features inspired by the method in [17], which leads to a dependence of the states evolution on the inputs at the next time step. Therefore, a slightly different starting point from the general one presented in (1) has to be considered, namely:…”

“…After describing the steps of the Balanced Mode Decomposition (BMD) algorithm, its performance is compared with a recent extension of the DMD with control algorithm. Precisely, the algebraic DMDc (aDMDc) algorithm was proposed in [16] to extend DMDc to the case of parameters' variation and to systems described by algebraic, besides differential, equations. Including algebraic constraints is indeed very important when considering state trajectories generated by aerodynamic solvers capturing unsteady effects, such as in panel methods or unsteady vortex lattice methods [17].…”