Peak-Seeking Control for Drag Reduction in Formation Flight

Formation flight is a known method of improving the overall aerodynamic efficiency of a pair of aircraft. In particular, one craft flying in the correct position in the vortex wake of another can realize substantial reductions in drag, with the amount of the reduction dependent on the relative positions of the two craft. This paper looks at such a pair, with one craft flying behind and to the side of the lead plane. The precise position of the second craft relative to the first to maximize the drag reduction is to be determined online, leading to a peak-seeking control problem. A new method of speak-seeking control, using a Kalman filter to estimate the characteristics of the drag reduction, is derived and discussed. A simple model of the two-plane formation using horseshoe vortices is defined, and the peakseeking controller is applied to this model. The method is demonstrated in simulation using this simplified model. S an airplane flies, it causes an upwash ahead of the wing and leaves a wake behind. This wake is characterized by the downwash behind the wing and by an accompanying upwash in the area on either side of the downwash region. By flying in the area of upwash, a second aircraft can gain a substantial efficiency boost because of the reduction in induced drag it will experience. This leads to the well-known fact that two aircraft flying in an appropriate formation can achieve overall efficiency much greater than were they flying separately. 1 This effect is analyzed using inviscid aerodynamic assumptions and lifting-line theory in Ref. 2, where it is noted that the effects were considered by Munk as early as 1919. The theory was put to test in actual aircraft by Hummel, 3 who established a fifteen per cent reduction on the second of a pair of civilian aircraft. Because of the gains in efficiency, formation flight has been investigated as a way of increasing the range and duration of autonomous aerial vehicles. In Refs. 4 and 5, formations of several aircraft are considered, with the object of creating a solar-powered formation that could cruise at high altitude for arbitrarily long times. In Ref. 4, decentralized controllers are derived for a formation of five highaspect-ratio craft and are shown to be capable of maintaining a prescribed formation despite the nonlinear, destabilizing moments induced on each plane by the aircraft ahead of it in the formation. The formation maintenance problem for a pair of F-16 class aircraft is considered in Ref. 6, though that paper relegates the rolling moments on the trailing craft to an inner-loop controller and considers only the lift and side force in designing an autopilot for the trailing plane. In this paper, only a pair of aircraft is considered. The two craft can be thought of as a leader and a follower. The leader flies straight