Four-dimensional fuel-optimal guidance in the presence of winds

We present a semi-analytic framework for the generation of initial guesses for the numerical solution of the landing trajectory optimization problem of an aircraft. Our approach consists of the following tasks: First, we introduce a geometric framework for the generation of length-suboptimal, curvature-constrained, threedimensional curves, which satisfy the following requirements: 1) the projection of the curves on the horizontal plane correspond to Dubins-like paths, and 2) an aircraft traveling along these curves is descending continuously until it reaches its final destination. Subsequently, we generate a time-parametrization of the geometric path such that the control inputs required to traverse the geometric path do not exceed the control limits of the aircraft. The resulting time-parameterized path along with the control input time histories is subsequently fed as an initial guess into a numerical optimal control solver, such as the one introduced in Ref. [1]. Simulation results demonstrate the advantages of employing the proposed initial guess generation scheme in terms of convergence of the numerical landing trajectory generation.

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“…See, for example, Refs. [2][3][4][5][6][7][8][9][10][11][12][13]. However, not much prior research accounts for the optimal landing problem.…”

Section: Introductionmentioning

confidence: 97%

Initial Guess Generation for Aircraft Landing Trajectory Optimization

Bakolas¹,

Zhao

Tsiotras

2011

AIAA Guidance, Navigation, and Control Conference

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“…BUITOWS [7] studies fuel-optimal descents with fixed arrival time, from fixed cruise conditions, considering the energy-state approximation and a constant along-track wind. Chakravarty [8] analyzes fuel-optimal cruise-descent trajectories with fixed terminal time and fixed range, considering the energy-state approximation along with matched asymptotic expansions and a horizontal altitude-dependent wind but, as in [6], neglecting the acceleration term in the dynamic equation.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Unpowered Descents of Commercial Aircraft in Altitude-Dependent Winds

Franco

Rivas

Valenzuela

2012

Journal of Aircraft

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Unpowered descents of commercial transport aircraft are optimized in tbe presence of altitude-dependent winds witb tbe objective of maximizing range. Tbe optimal problem and an optimized constant calibrated-airspeed procedure are analyzed. Tbe optimal problem is studied using tbe tbeory of singular optimal control. Tbe optimal control is of tbe bang-singular-bang type, and tbe optimal trajectories are formed by a singular arc and two minimum/maximum-patb-angle arcs joining tbe singular arc witb tbe given initial and final points. Tbe constant calibrated-airspeed procedure is optimized using parametric optimization tbeory. Results are presented for a model of a Boeing 767-300ER and for linear wind profiles. Tbe effects of botb tbe average wind and tbe wind sbear on tbe optimal results, as well as tbe effects of the aircraft weigbt, are analyzed. Tbe wind sbear is sbown to have a clear effect on tbe maximum range. Tbe comparison between tbe two sets of results sbows tbat tbe optimized constant calibratedairspeed descent is very close to optimal. From the operational point of view, the optimum descent calibrated airspeed is defined in terms of tbe wind profile and tbe aircraft weigbt. a CASJ Co Ci. D 8 H h, h L M m P S Sw t,tf V W w, w X max Aw 0 k p Nomenclature = speed of sound = optimum descent calibrated airspeed = drag coefficient = lift coefficient = drag = gravity acceleration = Hamiltonian = altitude, average altitude = lift = Mach number = aircraft mass = pressure = switching function = reference wing surface = time, flight time = aerodynamic speed = aircraft weight = wind speed, average wind speed = horizontal distance = maximum range = aerodynamic path angle, ground path angle = wind-shear parameter = temperature = adjoint variable = density

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“…To address this concern, the framework for analyzing performance bound of each aircraft using optimal control scheme is proposed in this paper. Optimal control scheme is widely used for obtaining the best trajectory with respect to the specific performance index as well as a feasible trajectory [5][6][7]. Descent weight of aircraft affects performance of descent trajectory significantly [8].…”

Section: Introductionmentioning

confidence: 99%

Fixed RTA fuel optimal profile descent based on analysis of trajectory performance bound

Park

Clarke

2012

2012 IEEE/AIAA 31st Digital Avionics Systems Conference (DASC)

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In this paper, the framework, so called Trajectory Performance Analyzer (TPA), for analyzing performance bound of descent trajectory using optimal control problem formulation is proposed. Minimum time trajectory and minimum fuel trajectory are obtained by trajectory optimizer of TPA and performance bound is determined between two optimal trajectory results. To consider effect of uncertainties from aircraft descent weight as well as effect of initial condition such as cruise speed, sensitivity analysis is performed. The feasible time of arrival to the meter fix is determined based on performance bound of the descent trajectory. To meet the scheduled time of arrival to the meter fix, fixed time RTA minimum fuel descent profile generation method is proposed. The proposed method is suboptimal minimum fuel trajectory generation method constructed with known FMS Vertical Navigation (VNAV) descent algorithms. The VNAV segments used in this method is determined by analyzing minimum fuel trajectories with fixed RTA. The numerical simulations with B737-800 and B767-400 are given to illustrate the proposed TPA framework and fixed RTA suboptimal trajectory generation method for FMS.

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Four-dimensional fuel-optimal guidance in the presence of winds

Cited by 50 publications

References 7 publications

Initial Guess Generation for Aircraft Landing Trajectory Optimization

Initial Guess Generation for Aircraft Landing Trajectory Optimization

Optimization of Unpowered Descents of Commercial Aircraft in Altitude-Dependent Winds

Fixed RTA fuel optimal profile descent based on analysis of trajectory performance bound

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