Prediction of tiltrotor height-velocity diagrams using optimal control theory

Height-velocity (H-V) diagrams represent combinations of rotorcraft heights and speeds from which safe landings cannot be made in case of an engine failure. Boundary points of H-V diagrams for a tiltrotor aircraft are determined systematically using optimal control theories. A two-dimensional rigid-body model representative of the XV-15 tiltrotor aircraft is developed. The tabular aerodynamic data are interpolated with smooth functions to facilitate use in numerical optimizations. An optimal control problem is formulated that minimizes a linear combination of the height and speed at an engine failure, such that subsequent control actions can still land the tiltrotor aircraft with acceptable touchdown speeds and pitch attitudes. Path constraints are imposed on the control variables, their rates, and on state variables to reflect realistic flight limitations. This optimal control problem is converted into a parameter optimization via a collocation approach, and is numerically solved with the software NPSOL. Height-velocity diagrams are calculated by solving this optimal control problem repeatedly. The cases one-engine inoperative and all-engines failed are both considered. Effects of the gross weight variations on H-V diagrams are studied. Optimal landing flights for engine failures occurring on the boundaries of H-V diagrams are discussed. Sensitivity analyses are conducted to examine effects of various modeling errors on optimization results.