Aeroelastic Control and Estimation with a Minimal Nonlinear Modal Description

Abstract

Modal-based, nonlinear Moving Horizon Estimation (MHE) and Model Predictive Control (MPC) strategies for very flexible aeroelastic systems are presented. They are underpinned by an aeroelastic model built from a 1D intrinsic (based on strains and velocities) description of geometrically-nonlinear beams and an unsteady Vortex Lattice aerodynamic model. Construction of a nonlinear, modal-based, reduced order model of the aeroelastic system, employing a state-space realisation of the linearised aerodynamics around an arbitrary reference point, allows us to capture the main nonlinear geometrical couplings at a very low computational cost.

Adaptive Sampling for Interpolation of Reduced-Order Aeroelastic Systems

“…Projection of the aerodynamic input/output channels onto a lower dimensional subspace by means of other methods would be equally suited; however, as the objective is to couple them with structure, the vibration modes make for an ideal candidate. This approach has been used for the applications in [4,32,33] successfully and the Krylov reduction process for these MIMO systems is outlined in detail in this paper. The Krylov-reduced linear UVLM is then coupled to a linearised structural model reduced by modal truncation [34] resulting in a linear, parametric reduced order aeroelastic state-space.…”

“…This will be the lower end of the spectrum given the underlying assumptions of the UVLM method which make it valid for low reduced frequencies. The Krylov-based reduction of the linear UVLM subsystem of the aeroelastic model has been described in detail in [33], and has been hitherto applied as "black box" reduction method [4,32,33]. This section will therefore summarize the basics of the method, and will use the numerical example to showcase the performance of the Krylov method applied to the UVLM system, as well as supporting the UVLM-specific algorithmic choices made based on the system and reduction method properties.…”

“…In terms of the actual assembly of the reduced order bases, the projection matrices that span the Krylov subspaces are constructed using the Arnoldi iteration with a Modified Gram-Schmidt orthogonalization method [33]. In a nutshell, the 𝑽 and 𝒁 matrices are assembled by sequentially concatenating vectors of the form…”

“…If any new vector is linearly dependent to those already part of the projection matrix they are not added. For more details on the assembly of Krylov subspaces the reader is referred to [33,58,60].…”

Data-driven unsteady aeroelastic modeling for control

“…has limitations for wings with significant camber or viscous effects [30,31]. Other nonlinear modeling approaches include Volterra kernels [32,33] and modal models [34][35][36], although there are considerably fewer control techniques for nonlinear systems [37,38]. Moreover, linear models are often sufficient for even large amplitude motions [39] until leading edge separation and stall [40].…”