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

Reduction of nonlinear models for control applications

A systematic approach to the model reduction of high-fidelity fluid-structure-flight models and the subsequent flight control design for very flexible aircraft is considered. The test case is for an unmanned aerial vehicle. The full order model involves the geometrically-exact nonlinear beam equations coupled with a linear aerodynamic model. A nonlinear reduced order model is derived to reduce the computational cost and dimension of the full order nonlinear system while retaining the ability to predict nonlinear effects. 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. The small dimension model is then used to design control laws for applications sush as load alleviation. Results are presented for an aerofoil section and an unmanned aerial vehicle model to illustrate the approach

A nonlinear controller for flutter suppression: from simulation to wind tunnel testing

Active control for flutter suppression and limit cycle oscillation of a wind tunnel wing section is presented. Unsteady aerodynamics is modelled with strip theory and the incompressible two-dimensional classical theory of Theodorsen. A good correlation of the stability behaviour between simulation and experimental data is achieved. The paper focuses on the introduction of a nonlinearity in the plunge degree of freedom of an experimental wind tunnel test rig and the design of a nonlinear controller based on partial feedback linearization. To demonstrate the advantages of the nonlinear synthesis on linear conventional methods, a linear controller is implemented for the nonlinear system that exhibits limit cycle oscillations above the linear flutter speed. The controller based on partial feedback linearization outperforms the linear control strategy based on pole placement. Whereas feedback linearization allows to suppress fully the limit cycle oscillations, the pole placement fails to achieve any significant reduction in amplitude

An adaptive aeroelastic control approach using non linear reduced order models

A systematic approach to the model order reduction of high fidelity coupled fluid/structure/flight dynamics models and the subsequent control design is described. It 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-model dynamics. A nonlinear reduced order model is derived and is exploited for a worst case gust and adaptive control design. The investigation focuses on a flight control design based on the model reference adaptive control scheme via the Lyapunov stability approach. The novelty of this paper is two-fold. Firstly, it uses a single nonlinear reduced model for parametric worst case gust search. Secondly, it is shown that it makes feasible an implementation of a complex control methodology for a large nonlinear system. The adaptive controller is able to alleviate gust loads for a three degrees-of-freedom aerofoil and for an unmanned aerial vehicle. An investigation for the adaptation parameters is performed and their effect on control input actuation and aeroelastic closed-loop response is discussed

Assessing the impact of aerodynamic modelling on manoeuvring aircraft

This paper investigates the impact of aerodynamic models on the dynamic response of a free-flying aircraft wing. Several options for the aerodynamics are evaluated, from two-dimensional thin aerofoil aerodynamics and unsteady vortex-lattice method up to computational fluid dynamics. A nonlinear formulation of the rigid body dynamics is used in all cases. Results are generated using a numerical framework that will allow in the near future multi-disciplinary fluid/structure/flight analysis. In this paper, flexibility effects are neglected. A validation for fluid/flight models is presented. The well-established approach based on stability derivatives is also used, and is found in good agreement with solutions obtained from linear aerodynamic models. The uncertainties in predicted trajectories of the free-flying wing are, in general, large and attributed to the aerodynamics only. This suggests that a careful control law synthesis should be done to account for uncertainties from modelling technique

Experimental and numerical study of nonlinear dynamic behaviour of an aerofoil

The paper describes the experimental and numerical investigations on a plunge-pitch aeroelastic system with a hardening nonlinearity. The goals of this work are to achieve a better understanding of the behaviour of the model while it undergoes Limit Cycle Oscillations and to tune the numerical model to reproduce both linear and nonlinear aeroelastic response observed in the aeroelastic system. Moreover, this work is part of an overall project, which final aims are to test various control strategies for flutter suppression on the nonlinear aeroealstic system. The experimental model consists of a rigid wing supported by adjustable vertical and torsional leaf springs provided with a trailing edge control surface. In the present work the rig is extended to include a nonlinearity introduced by connecting the plunge degree of freedom to a perpendicular pretensioned cable. The numerical model is a 2 dof reduced order model representing the dynamics properties of the real system, the nonlinearity is incorporated in the state space equations by adding the cubic and fifth order terms in the stiffness matrix; the unsteady aerodynamic is modelled with strip theory and the incompressible two-dimensional classical theory of Theodorsen. In addition to provide a comparison with the experimental results, the numerical model has been used during the course of the project as an interactive tool to guide the choice of the stiffness stetting of the system. A comparison between experimental and numerical results is provided as well; for the linear model, they show a good agreement in the linear case, albeit not so much with the damping ratios. Once the nonlinearity is added, good agreement is achieved with the plunge LCO, but there still is room for improvement with pitch LCO. An in-depth investigation will be carried out to improve model tuning with respect to all parameters of the model

Active control for flutter suppression: an experimental investigation

This paper describes an experimental study involving the implementation of the method of receptances to control binary flutter in a wind-tunnel aerofoil rig. The aerofoil and its suspension were designed as part of the project. The advantage of the receptance method over conventional state-space approaches is that it is based entirely on frequency response function measurements, so that there is no need to know or to evaluate the system matrices describing structural mass, aeroelastic and structural damping and aeroelastic and structural stiffness. There is no need for model reduction or the estimation of unmeasured states, for example by the use of an observer. It is demonstrated experimentally that a significant increase in the flutter margin can be achieved by separating the frequencies of the heave and pitch modes. Preliminary results from a complementary numerical programme using a reduced-order model, based on linear unsteady aerodynamics, are also presente