Relaxation Oscillations in Aircraft Cruise-Dash Optimization

Abstract : Periodic solutions in energy approximation are sought for aircraft optimal cruise-dash problems. The cost functional is the weighted sum of the time taken and the fuel used average over the cycle. It is known from previous work that in energy-state approximation, relaxed-steady-state control gives lower costs than the steady-state solution. However, this control is not implementable. Higher approximations to this are sought via averaging oscillations. The 'fast' dynamics (path-angle/altitude/throttle/lift- coefficient) is modeled in terms of periodic solutions in a boundary-layer-like motion which does not die out but moves along with the progression of the 'slow' state energy. This is shown not to help the situation. A better approximation in terms of relaxation oscillations is proposed. Unlike earlier models, the energy is allowed to vary. However, the net change in energy per cycle is zero. Fast, constant-energy climbs and descents and slow energy transitions are 'spliced' together in zeroth order approximation to obtain the periodic solutions. The energies in question are determined as part of the problem. This technique is shown to produce a more practical solution, but still needs improvement for practical application. Keywords: Flight path optimization; Cost effectiveness.