On-board near-optimal climb-dash energy management

Abstract

Reduced order modelling has been extensively used in the solution of problems in flight mechanics. In particular the lowest-order attractive due to its simplicity, energy model is but because of the assumptions made (γ = 0.0) is of little use for realtime guidance. The method of matched asymptotic expansions can be used to generate corrections by the use of boundary layer fairings, but this technique is too complex for an onboard-setting. A method suitable for an onboard guidance system is presented which makes use of some of the same ideas, i.e. that the energy determines the optimal altitude and pathangle, and trajectories which do not initially lie on the optimal schedule rapidly fair into it. (The optimal schedule is an Euler solution to the twopoint- -boundary-value-problem, found by a multiple shooting technique) . This transition which occurs instantaneously in the energy model, is approximated by the use of a feedback control law. The gains are determined by numerical differentiation about the nominal optimal path. Once the nominal path and the feedback gains have been found as functions of energy, they are represented using cubic splines for real-time implementation, requiring minimal onboard computaional and storage capabilities. The problem which was studied was to maximise range in symmetric flight with fuel open. Some computational results are presented comparing the paths generated by the feedback law to Euler solutions from the same point.