Reston: American Institute of Aeronautics and Astronautics, Inc.
This paper studies the optimal level turn of a solar-powered unmanned aerial vehicle flying in the atmosphere. The objective is to maximize the heading changes in level turn. Since the solar-powered unmanned aerial vehicle will not expel fuel during theflight, its mass remains constant. The standard procedures offinding an optimal trajectory by incorporation of the necessary conditions for optimality and the constraint of the constant mass are applied. Analytical results are presented with detailed derivations of the optimal level turn properties and trajectories. A closed-form optimal bank-angle control law expressed in terms of the states of the unmanned aerial vehicle is obtained. A maximum power setting limit for an optimum level turn is also established. The study shows that the optimal level turn can be obtained only when the power is set below the power required for steady level flight at the initial speed; to have optimal level turn trajectories, the power must be kept below that limit, rather than increasing to make the turn. The relation between the normalized power required for a level turn and the normalized velocity, which is independent of the flying altitude, is constructed in a closed-form representation. Numerical examples using an in-house-designed solar-powered unmanned aerial vehicle are used to demonstrate the properties, controls, and trajectories of optimal level turns using the proposed method. The proposed optimal control is further investigated with the effects of wind and aerodynamic coefficient variations. The study shows that the head wind drags the trajectory and increases the turning angle, while the tail wind loosens the trajectory and decreases the turning angle. The study also shows that the heading change due to the aerodynamic coefficients variation is insignificant.
Journal of Guidance, Control, and Dynamics 33(5), pp.1347-1356