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Pré-Publication, Document De Travail Année : 2018

The minimum time-to-climb and fuel consumption problems and CAS/Mach procedure for aircraft

Résumé

In this article, we are interested in optimal aircraft trajectories in climbing phase. We consider the cost index criterion which is a convex combination of the time-to-climb and the fuel consumption. We assume that the thrust is constant and we control the air slope of the aircraft. This optimization problem is modeled as a Mayer optimal control problem with a single-input affine dynamics in the control and with two pure state constraints, limiting the Calibrated AirSpeed (CAS) and the Mach speed. The candidates as minimizers are selected among a set of extremals given by the maximum principle. We first analyze the minimum time-to-climb problem with respect to the bounds of the state constraints, combining small time analysis, indirect multiple shooting and homotopy methods. This investigation emphasizes two strategies: the common CAS/Mach procedure in aeronautics and the classical Bang-Singular-Bang policy in control theory. We then compare these two procedures for the cost index criterion.
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hal-01936193 , version 1 (27-11-2018)

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  • HAL Id : hal-01936193 , version 1

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Olivier Cots, Joseph Gergaud, D Goubinat. The minimum time-to-climb and fuel consumption problems and CAS/Mach procedure for aircraft. 2018. ⟨hal-01936193⟩
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