Nonlinear model order reduction and control of very flexible aircraft

In the presence of aerodynamic turbulence, very flexible aircraft exhibit large deformations and as a result their behaviour is characterised as intrinsically nonlinear. These nonlinear effects become significant when the coupling of rigid–body motion with nonlinear structural dynamics occurs and needs to be taken into account for flight control system design. However, control design of large–order nonlinear systems is challenging and normally, is limited by the size of the system. Herein, nonlinear model order reduction techniques are used to make feasible a variety of linear and nonlinear control designs for large–order nonlinear coupled systems. A series of two–dimensional and three–dimensional test cases coupled with strip aerodynamics and Computational– Fluid–Dynamics is presented. A systematic approach to the model order reduction of coupled fluid–structure–flight dynamics models of arbitrary fidelity is developed. It uses information on the eigenspectrum of the coupled-system Jacobian matrix and projects the system through a Taylor series expansion, retaining terms up to third order, onto a small basis of eigenvectors representative of the full–model dynamics. The nonlinear reduced–order model representative of the dynamics of the nonlinear full–order model is then exploited for parametric worst–case gust studies and a variety of control design for gust load alleviation and flutter suppression. The control approaches were based on the robust H∞ controller and a nonlinear adaptive controller based on the model reference adaptive control scheme via a Lyapunov stability approach. A two degree–of–freedom aerofoil model coupled with strip theory and with Computational–Fluid–Dynamics is used to evaluate the model order reduction technique. The nonlinear effects are efficiently captured by the nonlinear model order reduction method. The derived reduced models are then used for control synthesis by the H∞ and the model reference adaptive control. Furthermore, the numerical models developed in this thesis are used for the description of the physics of a wind–tunnel model at the University of Liverpool and become the benchmark to design linear and nonlinear controllers. The need for nonlinear control design was demonstrated for the wind–tunnel model in simulation. It was found that for a wind–tunnel model with a cubic structural nonlinearity in the plunge degree–of–freedom, conventional linear control designs were inadequate for flutter suppression. However, a nonlinear controller was found suitable to increase the flight envelope and suppress the flutter. A large body of work dealt with the development of a numerical framework for the simulation of the flight dynamics of very flexible aircraft. Geometrically–exact nonlinear beam structural models were coupled with the rigid–body, the flight dynamics degrees–of–freedom and the strip theory aerodynamics, for the description of the nonlinear physics of free–flying aircraft. The flexibility effects of these vehicles on the flight dynamic response is quantified. It is found that different angle of attack and control input rotation is needed to trim a flexible aircraft and that a rigid analysis is not appropriate. Furthermore, it is shown that the aircraft flexibility has an impact on the flight dynamic response and needs to be included. The fully coupled models are consequently reduced in size by the nonlinear model reduction technique for a cheaper and a simpler computation of a variety of linear and nonlinear automatic control designs that are applied on the full–order nonlinear models inside the developed framework for gust load alleviation. The approach is tested on a Global Hawk type unmanned aerial vehicle developed by DSTL, on a HALE full aircraft configuration, and on a very large flexible free–flying wing. A comparison of the developed control algorithms is carefully addressed with the adaptive controller achieving better gust loads alleviation in some cases. Finally, future possible implementations and ideas related to the nonlinear model order reduction and the control design of flexible aircraft are discussed