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

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

Model reduction for linear and nonlinear gust loads analysis

Time domain gust response analysis based on large-order nonlinear aeroelastic models is computationally expensive. An approach to the reduction of nonlinear models for gust loads prediction is presented in this paper. The method uses information on the eigenspectrum of the coupled system Jacobian matrix and projects the full order model through a series expansion onto a small basis of eigenvectors which is capable of representing the full order model dynamics. Linear and nonlinear reduced models derived from computational fluid dynamics and linear/nonlinear structural models are generated in this way. The novelty in the paper concerns the representation of the gust term in the reduced model in a manner consistent with standard synthetic gust definitions, allowing a systematic investigation of the influence of a large number of gusts without regenerating the reduced model. The methodology is illustrated by results for an aerofoil, with a combination of linear and nonlinear structural and aerodynamic models used, and a wing model with modal structural model