Extremum-Seeking Control for Enhanced Fuel Efficiency of Coaxial-Compound Rotorcraft

This study integrates extremum-seeking control (ESC) into the primary flight controller of an over-actuated coaxial-compound rotorcraft to reduce fuel consumption during trim and quasi-steady maneuvers. The control architecture includes an inner-loop attitude controller and an outer-loop controller for velocity and altitude. ESC exploits control redundancy by operating in the null space of the control effectiveness matrix along the longitudinal and vertical axes to optimize fuel flow without compromising primary flight objectives. In calm-air simulations, ESC achieved up to 11.6% fuel flow reduction in straight-and-level flight at 100 kt (representative of best endurance airspeed) and up to 4.5% reduction at 180 kt (higher speed trim condition). The controller reached the reduced fuel flow condition within 50 s after activation. Fuel flow reductions were largest for higher gross weights or under increased load factor, as in banked turn maneuvers. Under light-to-moderate turbulence, ESC continued to reduce fuel consumption, with a regularization function ensuring robust convergence and preventing instability due to rapid state fluctuations.