This study presents an approach to develop a controller for stabilization of a flapping wing micro-air vehicle (MAV) operating in gusty environments. The rigid-wing MAV is modeled as a nonlinear periodic system and the periodic-shooting method is used to find a trimmed periodic orbit. A linearized discrete-time representation of the system is created about this trimmed periodic orbit. This linearized representation is used for control synthesis based on linear quadratic regulator (LQR) theory. The kinematic variables controlling the wing motion are used as control inputs. The controller is implemented on the nonlinear system model to stabilize the system in the presence of external disturbances, both longitudinal and lateral, modeled as discrete gusts in this study. The performance of the controller, in terms of the gust speed tolerance, is studied on the nonlinear system for various controller designs. The studies show that the LQR based controller is able to stabilize the system under both longitudinal and lateral gust disturbances, although the maximum gust speed tolerated by each controller is influenced by a variety of parameters discussed in this paper. The numerical simulations show that the gust tolerance under the longitudinal gust is far superior to the lateral gust tolerance. The study also shows that lateral control of the MAV can be achieved using only the wing-stroke magnitude and wing-stroke offset as the control inputs for each wing.
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