Analysis, monitoring and control of morphing wing structures based on the inverse Finite Element Method

Morphing capabilities allow for the design of a wing structure able to drastically change its external shape. The adaptive and flexible morphing wing is thus able to achieve high efficiency throughout the entire flight envelope reducing, for instance, consumption and pollution and improving aerodynamic performance. In order to achieve its potential, a morphing wing necessitates the development of an effective controller and, in particular, of an accurate feedback system able to provide a real-time reconstruction of the multitude of possible shapes achievable by the morphing wing. In developing a feedback system, successful results have been collected by recreating the displacement field of the wing structure from the actual measurements of the strains of the structure itself. This approach is an inverse problem called shape sensing. Notably, the shape sensing methodology known as iFEM (inverse Finite Element Method) has already shown promising applications in both open and closed loop control strategies for morphing wing structures. However, closed loop control architectures have not been tested thoroughly yet. Therefore, this master thesis focuses on the development of a closed loop control system for the actuation of a morphing wing structure using the iFEM reconstructed shape as feedback. The objective is to observe the behavior of the iFEM results in a closed loop environment as well as to evaluate the effectiveness of the iFEM code in providing feedback for the control scheme. To simulate the actuation of the structure and the strain measurements, a FEM of model of the structure is created. The closed loop architecture is implemented in a MATLAB environment. At each iteration the MATLAB code calculates the difference between the target and iFEM reconstructed displacements. Following a least-squares approach this difference is used to compute the actuation loads. The least square problem is ill-posed thus, as the complexity of the structure (and, as a consequence, of its model) increases, regularization is needed. Therefore, the Tikhonov regularization method is introduced. The results are presented for both a simple plate and a more realistic trailing edge model. In both structures the morphing potential is exploited by modifying the camber of the structure so that it follows an arbitrary shape. The response of the control scheme and the structure to different operational conditions and external disturbances is tested. For the trailing edge model, the external disturbance is simulated by the pressure distribution over the morphed structure, which is extracted at each iteration using the software Xfoil.