Design of a Low Order Model for Flexible Aircraft

The changes on aircraft structures and the increased use of advanced and light materials have led to the design of more efficient and flexible aircraft. This implies that rigid body dynamics are no longer sufficient to describe the aircraft behaviour in atmospheric flight. Furthermore, the frequencies of the lower structural modes are close to the frequencies of the rigid aircraft dynamics and, thus, a possible coupling between structural dynamics and piloting task must be taken in consideration during aircraft modelling. In this thesis, an analytical method, based on a mixed Newtonian-Lagrangian approach, is used to derive a simplified model of the flexible aircraft which maintains a "strong" link with the rigid aircraft equations of motion. Moreover, flexible displacements and torsional variables, starting from the Lagrange’s equations, are discretized from the beginning by means of the Galërkin method, i.e. by means of a finite number of generalized coordinates. This approach allows to derive directly a finite-order system of ordinary differential equations, making it less complex and suitable for real time simulation and control law synthesis. Once the flexible model is defined, a proper gust model must be applied to evaluate the aircraft response. In this work both discrete and continuous gust models are presented, in order to both generate large rigid aircraft loads and excite the elastic modes of the structure. The models here considered are based on continuous random turbulence theory and, thus, a prior introduction to probability and Power Spectral Density (PSD) methods is given. Finally, the implementation of Dryden and von Kármán continuous turbulence models is addressed, since these models are the most used in aircraft design. So, the aircraft response to a gust can be evaluated, both in terms of deformation variables and dynamic loads, generated on the structure. Two methods of load determination are presented and compared. The first method is directly linked to the mixed Newtonian-Lagrangian model and it is more accurate, while the second proposed method is based on the strip theory and aims to reconstruct the loads with limited knowledge of the structural model. To conclude the study, a closed loop control system able to reduce the gust loads is designed. The objective is to decrease fatigue loads and improve passenger comfort by controlling the flexible structure deformations. The control strategy, here proposed, is a Linear Quadratic Regulator (LQR) for the rigid body dynamics, to indirectly reduce the flexible structure response, after a gust, by means of elevator and (symmetric) aileron deflections.