| In recent years, much research has been motivated by the idea of biologically-inspired flight. It is a conjecture of the United States Air Force that incorporating characteristics of biological flight into air vehicles will significantly improve the maneuverability and performance of modern aircraft. Although there are studies which involve the aerodynamics, structural dynamics, modeling, and control of flexible wing micro aerial vehicles (MAVs), issues of control and vehicular modeling as a whole are largely unexplored. Modeling with such dynamics lends itself to systems of partial differential equations (PDEs) with nonlinearities, and limited control theory is available for such systems.;In this work, a multiple component structure consisting of two Euler-Bernoulli beams connected to a rigid mass is used to model the heave dynamics of an aeroelastic wing MAV, which is acted upon by a nonlinear aerodynamic lift force. We seek to employ tools from distributed parameter modeling and linear control theory in an effort to achieve agile flight potential of flexible, morphable wing MAV airframes. Theoretical analysis of the model is conducted, which includes generating solutions to the eigenvalue problem for the system and determining well-posedness and the attainment of a C 0-semigroup for the linearly approximated model. In order to test the model's ability to track to a desired state and to gain insight into optimal morphing trajectories, two control objectives are employed on the model: target state tracking and morphing trajectory over time. |
