H.G. Visser

Optimal airport surface traffic planning using mixed-integer linear programming

We describe an ongoing research effort pertaining to the development of a surface traffic automation system that will help controllers to better coordinate surface traffic movements related to arrival and departure traffic. More specifically, we describe the concept for a taxi-planning support tool that aims to optimize the routing and scheduling of airport surface traffic in such a way as to deconflict the taxi plans while optimizing delay, total taxi-time, or some other airport efficiency metric. Certain input parameters related to resource demand, such as the expected landing times and the expected pushback times, are rather difficult to predict accurately. Due to uncertainty in the input data driving the taxi-planning process, the taxi-planning tool is designed such that it produces solutions that are robust to uncertainty. The taxi-planning concept presented herein, which is based on mixed-integer linear programming, is designed such that it is able to adapt to perturbations in these input conditions, as well as to account for failure in the actual execution of surface trajectories. The capabilities of the tool are illustrated in a simple hypothetical airport.

Optimization of Noise Abatement Departure Trajectories

This paper describes the development of a new tool that offers significant capabilities for the analysis and design of noise abatement procedures at any given airport. The proposed tool combines a noise model, a geographic information system and a dynamic trajectory optimization algorithm. The optimization algorithm essentially modifies routings and flightpaths such as to minimize the noise impact in the residential communities surrounding the airport, while satisfying all imposed operational and safety constraints. Numerical examples, involving departure trajectories from Amsterdam Airport Schiphol, are included to demonstrate the effectiveness and flexibility of the developed tool. Although the results obtained to date are for departure flights only, the employed methodology tool holds out equal promise for application to approach trajectories. In the numerical examples the characteristics of a Boeing 737-300 aircraft are used.

Energy management of three-dimensional minimum-time intercept

A real-time computer algorithm to control and optimize aircraft flight profiles is described and applied to a three-dimensional minimum-time intercept mission. The proposed scheme has roots in two well known techniques: singular perturbations and neighboring-optimal guidance. Use of singular-perturbation ideas is made in terms of the assumed trajectory-family structure. A heading/energy family of prestored point-mass-model state-Euler solutions is used as the baseline in this scheme. The next step is to generate a near-optimal guidance law that will transfer the aircraft to the vicinity of this reference family. The control commands fed to the autopilot (bank angle and load factor) consist of the reference controls plus correction terms which are linear combinations of the altitude and path-angle deviations from reference values, weighted by a set of precalculated gains. In this respect the proposed scheme resembles neighboring-optimal guidance. However, in contrast to the neighboring-optimal guidance scheme, the reference control and state variables as well as the feedback gains are stored as functions of energy and heading in the present approach. Some numerical results comparing open-loop optimal and approximate feedback solutions are presented.

Advanced Noise Abatement Departure Procedures: Custom Optimized Departure Profiles

This paper presents the concept of custom optimized departure profiles, as an advanced form of noise abatement departure procedures. This concept relies on fixed routes in combination with individually optimized vertical de parture profiles. Although some environmental performance is lost by fixing the gro und track, an increase in complexity associated with free routing is eliminated as well, leading to a concept that does not seem to be incompatible with today’s Air Traffic Control pr inciples. By using a primitive form of trajectory negotiation between airline and ATC, sel ected flights can be allowed to perform an optimized departure without interfering with non-participating traffic. Apart from the concept itself, this paper also describes the depar ture profile optimization tool, which is based on a previously developed trajectory optimiza tion tool called NOISHHH. Finally -in a numerical example- a current standard ICAO-A procedure is compared with two optimized profiles for a Boeing 737 departure from Amsterdam Airport. Fuel burn, noise impact and the required time to a specified point are compared for the three departure profiles.

Optimisation of RNAV noise and emission abatement standard instrument departures

In an effort to reduce the negative impact of civil aviation on the human environment, trajectory optimisation techniques have been used to minimise the single event impact of noise and gaseous emissions of departures on communities in the vicinity of airports. For this purpose, the earlier developed trajectory optimisation tool NOISHHH has been adapted to design departure trajectories optimised for environmental criteria, based on area navigation. The new version of NOISHHH combines a noise model, an emissions inventory model, a geographic information system and a dynamic trajectory optimisation algorithm to generate flight paths with minimised environmental impact. Operational constraints have been introduced to ensure that the resulting flight paths are fully compliant with the guidelines and regulations that apply to the design of standard instrument departures and the use of area navigation. To illustrate the capabilities of the new version of NOISHHH, two numerical examples are presented, which are both redesigns of standard instrument departures currently in use at Amsterdam Airport Schiphol.

Optimal lateral-escape maneuvers for microburst encounters during final approach

This paper is concerned with the optimization of lateral-escape trajectories in a microburst wind field for an aircraft on final approach. The objective is to minimize the peak value of altitude drop. An extensive numerical effort has been undertaken to investigate the characteristics of open-loop extremal solutions for various locations of the microburst. When a sufficiently large aerodynamic roll-angle limit is specified and the center of the microburst is not too far offset from the centerline extension of the approach runway, typically three trajectories can be found that satisfy the first-order necessary conditions of optimality for a given set of boundary conditions, namely, a trajectory that passes the microburst center to the left, a trajectory passing the center to the right, and a trajectory passing right through the center. The results bear out that a lateral-escape maneuver, in which an aircraft is turned away from the microburst center, may significantly improve an aircrafts surv ivability, in comparison to an escape maneuver that is restricted to a vertical plane. One of the most striking observations in this study is that, in contrast to nonturning escape maneuvers, lateral-escape maneuvers often exhibit a climb, rather than a descent, in the initial phase. The insight obtained from the present study may help the development of near-optimal lateral-escape guidance strategies for onboard application.

Optimal Airport Surface Traffic Planning Using Mixed Integer Linear Programming

We describe an ongoing research effort pertaining to the development of a surface traffic automation system that will help controllers to better coordinate surface traffic movements related to arrival and departure traffic. More specifically, we describe the concept for a taxi-planning support tool that aims to optimize the routing and scheduling of airport surface traffic in such a way as to deconflict the taxi plans while optimizing delay, total taxi-time, or some other airport efficiency metric. Certain input parameters related to resource demand, such as the expected landing times and the expected pushback times, are rather difficult to predict accurately. Due to uncertainty in the input data driving the taxi-planning process, the taxi-planning tool is designed such that it produces solutions that are robust to uncertainty. The taxi-planning concept presented herein, which is based on mixed-integer linear programming, is designed such that it is able to adapt to perturbations in these input conditions, as well as to account for failure in the actual execution of surface trajectories. The capabilities of the tool are illustrated in a simple hypothetical airport.

First-order corrections in optimal feedback control of singularly perturbed nonlinear systems

In this paper first-order correction terms, developed by using the method of matched asymptotic expansions, are incorporated in the feedback solution of a class of singularly perturbed nonlinear optimal control problems frequently encountered in aerospace applications. This improvement is based on an explicit solution of the integrals arising from the first-order matching conditions and leads to correct the initial values of the slow costate variables in the boundary layer. Consequently, a uniformly valid feedback control law, corrected to the first-order, can be synthesized. The new method is applied to an example of a constant speed minimum-time interception problem. Comparison of the zeroth- and first-order feedback control laws to the exact optimal solution demonstrates that first-order corrections greatly extend the domain of validity of the approximation obtained by singular perturbation methods.

Optimal turn-back manoeuvre after engine failure in a single-engine aircraft during climb-out:

Abstract When a single-engine aircraft suffers an engine failure shortly after take-off, the pilot is forced to execute a power-off glide to a landing. If the engine failure occurs at a low altitude, there is no choice but to land straight ahead. However, when the engine failure occurs at a higher altitude, the possibility arises to turn the aircraft back to the runway. The latter option has the potential to improve survivability, in particular, when the surrounding terrain turns out to be inhospitable. The goal of the present study is to establish under what conditions returning to the runway is a feasible and safe option. To this end, the turn-back landing problem is formulated as an optimal control problem and solved numerically using the direct optimization technique of collocation and non-linear programming. The aircraft model employed in the numerical examples concerns an F-16 fighter aircraft, modelled as a point mass. The influence of wind on the optimal turn-back manoeuvre is also discussed.

Uniformly valid feedback expansions for optimal control of singularly perturbed dynamic systems

This paper shows how to construct a feedback control law for a class of singularly perturbed autonomous optimization problems. The control law is expressed as a single power series in the small parameter ∈ representing the ratio of the two effective time scales of the problem. The present approach avoids the need of expansion matching. The method is applied to a constant-speed interception problem. Comparison of numerical results with the exact solution shows an excellent agreement.