Nonlinear Model Reduction for Flexible Aircraft Control Design

Abstract

The paper describes a systematic approach to the model reduction of large dimension fluid-structure-flight models, and the subsequent flight control design of very flexible aircraft. System nonlinearities may be due to the large wing deformations, the coupling between flexible and rigid body dynamics and/or flow separation at large angles of incidence. A nonlinear reduced order model is used to reduce the computational cost and dimension of the large-order nonlinear system for a practical control law design. The approach uses information on the eigenspectrum of the coupled system Jacobian matrix and projects the system through a series expansion onto a small basis of eigenvectors representative of the full-order dynamics. For a pitch-plunge aerofoil with structural nonlinearities, a controller based on reduced models was designed to alleviate gust loads. The approach to model reduction was also demonstrated for a two-dimensional problem with aerodynamics modelled using the computational fluid dynamics equations, and a flexible wing modelled using the geometrically-exact nonlinear beam equations. In all cases, the model reduction was found adequate to predict the large order system dynamics at a neglegible cost compared to that incurred by solving the nonlinear full-order system.

Model Reduction of High-Fidelity Models for Gust Load Alleviation

“…The paper expands on previous work, 13 where the model reduction was applied to different test cases with a range of nonlinearities in both fluid and structural models and it was shown that control problem is possible on the reduced models generated. This paper demonstrates the use of the model reduction for a full-scale flexible unmanned aerial vehicle (UAV) interacting with gust and using control surfaces for loads alleviation.…”

An Adaptive Aeroelastic Control Approach using Non Linear Reduced Order Models

“…In the following results, the Schur complement form of the eigenvalue problem presented by Badcock and Woodgate 26 is used to track the migration of the three structural eigenvalues with the reduced velocity. The first comparison is made with a two degree-of-freedom (DoF) aerofoil model presented by Alighanbari and Price 27 as well as the original two degree-of-freedom model by Da Ronch et al 28 Since this specific comparison is made between a three degree-of-freedom and a two degree-of-freedom model, it is necessary to enforce a very high stiffness in the flap degree of freedom by setting a high value of ω 2 . This effectively limits the dynamics of the three degree-of-freedom model to a two degree-of-freedom system.…”

“…The coupled full order model follows the formulation presented in. 1 Results are obtained using two-noded displacement-based elements. In a displacement-based formulation, dominant nonlinearities arising from large deformations are cubic terms, as opposed to an intrinsic description where they appear up to second order.…”

“…[1][2][3][4] In this paper, the focus is on the exploitation of model order reduction for gust load alleviation by an adaptive control implementation. Previous work by the authors has focused on gust load prediction and alleviation using standard robust optimal control techniques based on H ∞ and H 2 .…”

Model Order Reduction for Control Design of Flexible Free-Flying Aircraft

“…Right and left eigenvectors are scaled to satisfy the biorthonormality condition,see . 10 The projection of the full order model is done using a transformation of coordinates ∆w = Φ z +Φz…”