Optimal energy-based 4D guidance and control for terminal descent operations

This paper presents an energy-optimal guidance and control strategy for 4-dimensional (4D) Trajectory-Based Operations (TBO) in the descent phase, supporting the development of 4D Human-Machine Interface (HMI) formats. The vertical guidance strategy uses multi-phase optimal control techniques based on point-mass aircraft dynamics to determine an energy-optimal descent profile fulfilling prescribed time constraints, additionally generating a set of control inputs which can be passed to the control module. The control strategy is decomposed into attitude and time-and-energy (T&E) components. The attitude control module corrects for cross-track deviations from the nominal profile previously calculated by the guidance algorithm, while the T&E control module corrects for the along-track distance and total energy deviations from the nominal profile. A virtual energy term is introduced which allows the control module to compensate for time deviations from the 4D trajectory. The proposed T&E guidance and control modules are verified through a number of representative case studies, showing that the proposed guidance and control modules allow the aircraft to follow a T&E-optimal 4D trajectory and to recover from deviations in the initial energy states. A prototype HMI is subsequently introduced to present the recommended control inputs to the pilot, also supporting assisted energy management in 4D descent operations.