Robust linear and nonlinear modelling and analysis approaches for uncertain aeroelastic systems

Abstract

The goal to mitigate the increasing environmental impact of aviation has prompted research into advanced solutions which enable noxious and harmful emissions to be reduced. One of these is represented by aircraft design layouts able to achieve a decrease in aerodynamic drag and aircraft weight, with a tremendous benefit in terms of fuel saving.
An important drawback of these configurations (e.g. high aspect ratio and lightweight wings) is their increased flexibility and resulting large deformations, which in turn can drive the aircraft into dangerous instabilities featuring coupling among aerodynamics, structural dynamics and flight dynamics. The discipline addressing the interplay among these different physical mechanisms is called aeroelasticity. Flutter is a dynamic instability in which the aeroelastic coupling is able to produce self-sustained oscillatory motion, and is recognised as a very dangerous and safety-critical phenomenon.
The main issues with the established approaches for predicting flutter are the sensitivity to model uncertainties and the difficulty to reliably interpret the effect of nonlinearities on the response of the system. In order to address these challenging aspects, in this thesis techniques from robust control have been explored since this represents a natural setting for providing stability guarantees in the face of uncertainties and nonlinearities, and for constructing models featuring a good trade-off between complexity and reliability. In addition, dynamical systems approaches are investigated because they offer a powerful framework to understand the complex dynamics arising in aeroelastic systems and also observed experimentally.
The high-level objective of the thesis is therefore to explore novel approaches to model and analyse aeroelastic systems subject to generic uncertainty and nonlinearities by leveraging the advantages of the above frameworks. Linear methods are first investigated, and original contributions are provided for: construction of Linear Fractional Transformation models; efficient application of μ analysis to the flutter problem; and worst-case performance analysis of Linear Time-Varying systems. In the second part of the thesis, the nonlinear response known as Limit Cycle Oscillation and the closely related problem of determining Region of Attraction have been addressed by proposing novel analysis methodologies which contribute to the state-of-the-art by allowing the effect of uncertainties to be studied. The pursued reconciliation between robust control and dynamic system approaches finally culminates in the proposal of the concept of robust bifurcation margins, which has the potential to extend the use of μ analysis technique to the nonlinear context.

Date of Award	25 Jun 2019
Original language	English
Awarding Institution	University of Bristol
Supervisor	Andres Marcos (Supervisor) & Mark H Lowenberg (Supervisor)