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This work results from a Master's Dissertation on Aeronautical Engineering, and consists on the development of a Longitudinal Flight Controller algorithm based on LQR and Batz-Kleinman Controller Methods for an Experimental UAV equipped with a Telescopic Morphing Wing Prototype. The purpose of the algorithm is to allow for the automatic adjustment of the wingspan in accordance with the longitudinal airspeed and attitude of the aircraft in order to increase flight efficiency, while providing longitudinal control authority for stable flight under small atmospheric disturbances.