Energy Management for Electric Aircraft via Optimal Control: Cruise Phase

The demand for energy savings and reducing environmental and noise impact has lead to an unprecedented interest and rapid development of electric aircraft technology. In order to improve the efficiency of an All-Electric Aircraft (AEA) during the cruise phase, this paper formulates the corresponding energy optimization as an optimal control problem (OCP). The OCP is formulated around minimizing the so-called Direct Operating Cost (DOC), a combination of time-related and battery charge costs. It is shown that this OCP leads to a singular control structure when the thrust is taken as the control input. We then proceed to derive the analytical solution on the singular arc using the Pontryagin’s Minimum Principle (PMP); moreover, the control structure and "junction" points are obtained through the numerical solver Tomlab. One of the main contributions of this work is considering the impact of the battery dynamics on the overall operating cost. In particular, by implementing the so-called Empirical Circuit Model (ECM) for the battery in our problem setup, we provide a comparative analysis on the effect of the battery modeling on the resulting optimal thrust profile.