eurocontrol...the validation of these advanced atm concepts may require large scale atc simulations...

EUROPEAN ORGANISATIONFOR THE SAFETY OF AIR NAVIGATION

EUROCONTROL

EUROCONTROL EXPERIMENTAL CENTRE

FLIGHT MANAGEMENT AND GUIDANCE

CONTROL SYSTEM MODEL FOR AN

ATC SIMULATION TRAFFIC GENERATOR

EXECUTIVE SUMMARY OF

EEC REPORT NO. 303

EEC TASK AT71 (R02/APO)EATCHIP TASK ASE.ET2.ST04

ISSUED: NOVEMBER 1996

THE INFORMATION CONTAINED IN THIS DOCUMENT IS THE PROPERTY OF THE EUROCONTROL AGENCY AND NO PART SHOULD BEREPRODUCED IN ANY FORM WITHOUT THE AGENCY’S PERMISSION.

THE VIEWS EXPRESSED HEREIN DO NOT NECESSARILY REFLECT THE OFFICIAL VIEWS OR POLICY OF THE AGENCY.

Report Documentation Page

Reference: Security Classification:Executive Summary of UnclassifiedEEC Report No. 303Originator: Originator (Corporate Author) Name/Location:EEC — APO EUROCONTROL Experimental Centre(Aircraft Performance B.P. 15and Operations) F91222 BRETIGNY SUR ORGE Cedex

Telephone: +33 1 69 88 7500Sponsor: Sponsor (Contract Authority) Name/Location:EEC — APO EUROCONTROL Experimental Centre(Aircraft Performance B.P. 15and Operations) F91222 BRETIGNY SUR ORGE Cedex

Telephone: +33 1 69 88 7500TITLE:

Flight Management and Guidance Control System Model for an ATC SimulationTraffic Generator

Authors Date Pages Figures Tables Appendix ReferencesE. Hoffman 11/96 iv + 17 11 4 0 4J.M. LevrezEATCHIP Task EEC Task No. Task No. Sponsor Period

SpecificationASE.ET2.ST04 AT71 (R02/APO) Jan. 1994–Dec. 1995

Distribution Statement:(a) Controlled by : Head of APO(b) Special limitations : None(c) Copy to NTIS : NoDescriptors (keywords):

Aircraft Trajectory, 4D Guidance, Air Traffic Control Simulation, Flight Simulation, Trajec-tory Prediction

Abstract:

The evaluation of future Air Traffic Management (ATM) concepts require the simulation ofadvanced airborne Flight Management and Guidance Control Systems (FMGCS). Thisreport details algorithms suitable to be used in large scale ATM simulations to model thebehaviour of the airborne FMGCS. These algorithms have been prototyped and testedin the Matlab environment.

This report has been collated by mechanical means. Should there be missing pages, please report to:

EUROCONTROL Experimental CentrePublications Office

B.P. 1591222 BRETIGNY-SUR-ORGE CEDEX

France

Executive Summary of EEC Report No. 303

Summary

Future Air Traffic Management (ATM) concepts rely on a very tight coupling between theground systems and the airborne systems. In such scenarios, the key airborne element is theFlight Management and Guidance Control System (FMGCS). Its role is twofold. The “Guidanceand Control” aspect is the first one. The FMGCS has to steer the aircraft along a given refer-ence trajectory. It encompasses the traditional autopilot auto-throttle functionalities that equipmost modern aircraft. The second aspect is to create the reference trajectory. The challenge isto devise a trajectory, that goes from the departure point to the destination airport while alwaysremaining in the safe part of the aircraft flight domain, that satisfies all the constraints imposedby ATC or by the airspace structure and finally that is optimal from an airline economy pointof view. This process is referred to as “Trajectory Generation”. The constraints deal with nav-igation way-points that have to be over-flown, altitude, speed and time restrictions. All theseconstraints may be modified during a flight, hence requiring new trajectory generations duringflight. The exchange of trajectories and of constraints between the ground systems and theFMGCS involves complex communication and negotiation processes which are outside of thescope of the report. The validation of these advanced ATM concepts may require large scaleATC simulations involving many aircraft (in the order of 500).

The aim of this study is to provide a simple model of FMGCS functionalities suitable to beimplemented in a traffic generator used by such ATC simulations. Because of the large num-ber of aircraft that have to be simulated simultaneously and because of the complexity of theflight worthy FMGCS, directly using such a system in a simulation environment would be im-practical. The first part of the full report describes a trajectory generation algorithm. It relies onrelatively simple optimisation techniques. A trade off between robustness and computationalefficiency on one side and optimality of the trajectory on the other side has been performedwhile maintaining an adequate level of realism or accuracy. A similar approach has been usedin the second part of the full report. A guidance and control system is described using simplestandard feedback control techniques. All algorithms have been prototyped and tested in theMatlab environment. Some examples are given in the last part of the full report.

Trajectory Generation

Overview

The purpose of Part I of the full report is to describe a trajectory computation algorithm tobe used in a simulation of a simplified Flight Management System.

The objective is to compute a trajectory that satisfies a list of constraints. The expressionlist of constraints means that the aircraft is expected to fly along a sequence of navigation way-points, to be in specified ranges of altitude or of speed over some of these points and evento reach some of them in certain time windows. The term trajectory is used to describe thesequence of 4 dimensional aircraft positions. The trajectory is the result of the application ofa sequence of general control inputs to the aircraft. The aim of the algorithm is to find such aseries of control inputs that will cause the aircraft to move along a trajectory without violatingany of the constraints.

Outline

Part I of the full report is divided into five Chapters. Chapter 1 is a brief introduction. It alsocontains a description of the major assumptions made. Chapter 2 defines the key elements orobjects that are handled by the algorithms. The next three chapters contain the description ofthe algorithms, starting with Chapter 3 and the computation of the Top of Descent points. InChapter 4, altitude and speed constraints handling is added. Finally in Chapter 5, time con-straints are considered.

Revision 1.2 November 1996 Page 1 of 17


General Assumptions

First and foremost, generating a single trajectory that satisfies the constraint list is the maingoal. The optimality of the computed trajectories is only secondary. This might not seem real-istic since current generations of FMS already rely on the input of cost index values to generateoptimal (or simply extremal) trajectories. Such a simplification has been made in order to sim-plify and expedite calculations. In the full report, the trajectory generation process relies on theinput of a nominal trajectory profile. It is assumed that the cost index aspects are taken intoaccount when choosing the nominal profiles. Hence, either the trajectory is only loosely con-strained and because the nominal profile has been optimally chosen the resulting trajectory willbe near optimal, or the trajectory is highly constrained and since there are so few degrees offreedom available optimality is not a real issue. This approach is similar in nature to the onetaken in the EUROCONTROL PHARE EFMS project [1].

In general, the speed, altitude and time constraints are always collocated with a way-point (2dimensional point, (x,y) or (lat,lon). Hence, the definition of a constraint over a zone or volumeof airspace, or at a distance from a point is not allowed for. It is assumed that such constraintscan always be converted to way-point based constraints.

The constraints, and the trajectories in general, are tackled sequentially. The constraints atway-point (n+1) are only considered when a solution tackling constraints 1 ton has been found.Similarly the type of constraints (altitude, speed) are considered one after the other. Time con-straints are handled last. The algorithm first tries to produce a trajectory which satisfies all thealtitude and speed constraints before considering time constraints.

A combination of homotopy type techniques gradually altering a single parameter until asatisfactory solution is found and on partial tree search like methods [2, 3, 4] is relied on. Hence,solutions may be missed. An alternative would have been to consider the constraints (of all thetypes) at the same time and apply a global non linear optimisation algorithm to obtain a solutiontrajectory. This option has been dismissed because it was deemed too computer intensive andbecause the convergence of the algorithm to something usable is impossible to guarantee.

Should the trajectory be over constrained, i.e. a solution satisfying all the constraints cannotbe found, an approaching solution will be provided in any case. “Approaching” means if a con-straint on way-point n cannot be met, the distance between the constrained variable and theconstraint bounds is minimised before considering the next way-point (the distance between allthe constrained variables and all the constraint bounds is not minimised in a global manner).

All the computations are performed using Cartesian coordinates (x; y). The move to lati-tude/longitude is considered to be of minor complexity (and interest at this stage).

No information is kept on past constraints: the constraint list is gradually shortened as theflight progresses. Every time the trajectory generation algorithm is run, it is fed with an initialposition (which may be on the ground or in flight) plus a list of constraints to be satisfied.

Finally, the availability of an aircraft model with the proper high level interfaces is assumed.Such a model which accepts generic guidance targets as inputs is described in Part II of thefull report. The weather forecast information is directly handled by the aircraft model.

Aircraft Guidance and Control

Overview

The aim of Part II of the full report is to describe a candidate autopilot/auto-throttle for anAircraft Model using the Total Energy Model as its Aircraft Performance Model.

In general, an Aircraft Model can be decomposed as follows:

� an Aircraft Performance Model: the basic aerodynamics, engine dynamics and equationsof motion.

� a FCS: a Flight Control System comprises autopilot and auto-throttle.



� a Pilot Model: trajectory management, navigation and outer control loop of the aircraftperformance model.

� possibly a FMS: a Flight Management System.

� necessary data.

This part of the full report focuses on the relationships between the first two items of theabove list. The FCS is further decomposed in 2 parts, as shown on Figure 1. Whenever theterm Aircraft Model is used in the report, it only refers to:

� The Aircraft Performance Model: the Total Energy Model Equations of Motion.

� The FCS:

– A Lateral Autopilot that controls heading.

– A Longitudinal Autopilot/Auto-throttle that handles altitude and speed of the aircraft.

The independent modelling of the two autopilot channels (lateral and longitudinal) is possi-ble because of the complete decoupling of the lateral and longitudinal modes in the TEM equa-tions of motion.

Note that the operational flight envelope limitations of the airline procedures belong to thePilot Model.

Wind

Lateral Autopilotpsidot=f(States,psiref)TEM

States=f(psidot,pi,vdot)

Vdot,Thottle=f(States,CASref,Mref,href,hdotref,altmode))

psiref

altmode

hdotref (1) or href(−1)

hdotref

href

Mref

CASref

Figure 1: Aircraft Performance Model and Flight Control System

The resulting Aircraft Model has the following autopilot/auto-throttle functionalities:

� heading select and hold (psiref)



� speed select and hold (CASref/Mref whichever is smaller at a given time)

� altitude select and hold (href) or altitude rate hold (hdotref).

Outline

Part II of the full report is divided in 4 Chapters. Chapter 6 is a brief introduction. Chapter 7reviews the Aircraft Performance Model, ie the dynamical equations, used to compute the tra-jectory of the aircraft. The following 2 chapters contain the description of the autopilot functions.In Chapter 8, the focus is on the lateral channel of the autopilot. The longitudinal channels aredetailed in Chapter 9.

Examples

The aim of Part III of the full report is to provide examples of trajectories obtained using thealgorithms described previously.

There is no attempt at illustrating all the possible cases. The goal is to help understand thefunctionalities of the algorithms rather than demonstrate their correctness. Such a proof wouldhave required a much bigger and less readable document.

On the various figures, continuous lines depict the aircraft state histories, while dashed linesare reference values and dotted lines indicate windows.

Part III of the full report is divided into 6 Chapters. Chapter 10 is a brief introduction. Chapter11 is the description of the trajectory used as reference in this Part of the document. No partic-ular constraint has been imposed. In Chapter 12, various altitude constraints are introduced onthe nominal trajectory. In Chapter 13, various speed constraints are introduced on the nominaltrajectory. In Chapter 14, we switch to time constraints. Finally, in Chapter 15, constraints ofall types are imposed at the same time.

Nominal Trajectory (Example 1)

We describe here the baseline case. No constraint is imposed on the trajectory. The solecomputation that has to be performed is the finding of the TOD point.

The constraint list is given by Table 1. The default bounds are used. Hence, there is noconstraint.

Table 2 gives a short summary of the trajectory flown. Time of overflight, altitude and speedcan be found for each waypoint. When constraints are imposed, whether they were met canbe checked on this table.

Figure 2 is a detailed plot of altitude versus time. Figure 3 gives an overview of the be-haviour of altitude, heading, speed and mass as a function of time. On Figure 4, CAS, Machand specific energy time histories are displayed as well as a plan view of the trajectory. Fi-nally, on Figure 5, vertical speed, acceleration time history can be found. An altitude and a xcoordinate time history plot have also been added.



xsectionref ysection

ref hsectionmin hsection

max CASsectionmin CASsection

max Machsectionmin Machsection

max tsectionmin tsection

max

0. 50000. hdefaultmin hdefault

max CASdefaultmin CASdefault

max Machdefaultmin Machdefault

max tdefaultmin tdefault

max





max





max





max





max





max





max





max





max





max

Table 1: Example 1: Route Constraints

point altitude (m) time (s) CAS (knots) Mach1 2999.96 328.00 298.30 0.542 6702.91 589.00 300.27 0.683 9128.44 812.00 296.65 0.784 9998.94 1026.00 278.22 0.785 10000.00 1241.00 278.20 0.786 10000.00 1457.00 278.20 0.787 10000.00 1672.00 278.20 0.788 8962.78 1887.00 299.76 0.789 3570.84 2370.00 300.25 0.5610 1005.08 3032.00 250.21 0.40

Table 2: Example 1: Resulting Trajectory



0 500 1000 1500 2000 2500 3000 35001000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Time (s)

Alti

tude

Figure 2: Example 1: Altitude Profile

0 1000 2000 3000 40000

2000

4000

6000

8000

10000

Time (s)

Alti

tude

0 1000 2000 3000 4000120

140

160

180

200

220

240

Time (s)

Spe

ed (

m/s

)

0 1000 2000 3000 4000−10

−5

0

5

10

Time (s)

Hea

ding

(de

g)

0 1000 2000 3000 40002.4

2.42

2.44

2.46

2.48

2.5x 10

5

Time (s)

Mas

s (k

g)

Figure 3: Example 1: Overview I



0 1 2 3

x 104

0

1

2

3

4

5

6x 10

5

x (m)

y (m

)

0 1000 2000 3000 4000240

260

280

300

320

Time (s)

CA

S (

Kt)

0 1000 2000 3000 40000.2

0.4

0.6

0.8

1

Time (s)

Mac

h

0 1000 2000 3000 40000

5

10

15x 10

4

Time (s)E

nerg

y

Figure 4: Example 1: Overview II

0 1000 2000 3000 40000

0.5

1

1.5

2

2.5x 10

4

Time (s)

x (m

)

0 1000 2000 3000 4000−20

−10

0

10

20

Time (s)

Ver

tical

Spe

ed (

m/s

)

0 1000 2000 3000 40000

2000

4000

6000

8000

10000

Time (s)

Alti

tude

0 1000 2000 3000 4000−1

−0.5

0

0.5

1

Time (s)

Acc

eler

atio

n (m

/s/s

)

Figure 5: Example 1: Overview III



Compounded Constraints (Example 11)

� Time, speed and altitude constraints are imposed over various way-points as indicatedin Table 3.

The results, summarizsed in Table 4 and detailed in Figures 6 to 11, show a typical exampleof the algorithm handling all the constraints in sequence and finding the best that can it achievein order to meet them.

xsectionref ysection

ref hsectionmin hsection

max CASsectionmin CASsection

max Machsectionmin Machsection

max tsectionmin tsection

max





max

10. 100000. 5000 5000 280 280 0.75 0.75 700 7000. 150000. 10000 10000 250 350 0.92 0.92 900 9000. 200000. 10800 10800 290 350 0.92 0.92 1100 11300. 250000. hdefault

min hdefaultmax CASdefault

min CASdefaultmax Machdefault

min Machdefaultmax tdefault

min tdefaultmax

0. 300000. 10500 11500 240 270 0.92 0.92 1600 16500. 350000. 9500 9800 266 320 0.92 0.92 1820 1850

-10. 400000. hdefaultmin hdefault




max





max





max

Table 3: Example 11: Route Constraints

point altitude (m) time (s) CAS (knots) Mach1 3491.062530 419.000000 272.829873 0.5056382 4998.322613 697.000000 280.244186 0.5691873 7238.001222 916.000000 350.324493 0.8075154 9812.201429 1125.000000 298.360833 0.8208345 10499.997744 1369.000000 225.709433 0.6660226 10500.000000 1599.000000 256.282497 0.7486687 9505.647426 1807.000000 300.255062 0.8091828 6930.229323 2026.000000 300.246166 0.6859749 3000.258874 2560.000000 257.640886 0.463986

10 1000.001510 3282.000000 250.216168 0.400278

Table 4: Example 11: Resulting Trajectory



0 500 1000 1500 2000 2500 3000 35000.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Mac

h

Figure 6: Example 11: Mach Profile

0 500 1000 1500 2000 2500 3000 3500100

150

200

250

300

350

400

Time (s)

CA

S (

Kt)

Figure 7: Example 11: CAS Profile



0 500 1000 1500 2000 2500 3000 35001000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

Time (s)

Alti

tude

Figure 8: Example 11: Altitude Profile

0 1000 2000 3000 40000

2000

4000

6000

8000

10000

12000

Time (s)

Alti

tude

0 1000 2000 3000 400050

100

150

200

250

300

Time (s)

Spe

ed (

m/s

)

0 1000 2000 3000 4000−0.015

−0.01

−0.005

0

0.005

0.01

0.015

Time (s)

Hea

ding

(de

g)

0 1000 2000 3000 40002.38

2.4

2.42

2.44

2.46

2.48

2.5x 10

5

Time (s)

Mas

s (k

g)

Figure 9: Example 11: Overview I



−20 −10 0 10 200

1

2

3

4

5

6x 10

5

x (m)

y (m

)

0 1000 2000 3000 4000100

150

200

250

300

350

400

Time (s)

CA

S (

Kt)

0 1000 2000 3000 40000.2

0.4

0.6

0.8

1

Time (s)

Mac

h

0 1000 2000 3000 40000

5

10

15x 10

4

Time (s)E

nerg

y

Figure 10: Example 11: Overview II

0 1000 2000 3000 4000−15

−10

−5

0

5

10

15

Time (s)

x (m

)

0 1000 2000 3000 4000−40

−20

0

20

40

Time (s)

Ver

tical

Spe

ed (

m/s

)

0 1000 2000 3000 40000

5000

10000

15000

Time (s)

Alti

tude

0 1000 2000 3000 4000−1.5

−1

−0.5

0

0.5

1

1.5

Time (s)

Acc

eler

atio

n (m

/s/s

)

Figure 11: Example 11: Overview III


BIBLIOGRAPHY Executive Summary of EEC Report No. 303

Bibliography

[1] EFMS Development Group. “EFMS Technical Reference Document”. EUROCONTROLDOC 91 20 18, Eurocontrol, June 1993.

[2] Philip E. Gill, Walter Murray, and Margaret H. Wright. Practical Optimization. AcademicPress, 1981.

[3] William K. Press, Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling. “ Numericalrecipes. The art of scientific computing.”. Cambridge University Press, 1986.

[4] J. Stoer and R. Bulirsch. Introduction to Numerical Analysis. Springer-Verlag, 1980.


Sommaire du Rapport CEE No. 303

Traduction en Langue Francaise

Resume

Les concepts futurs de gestion du trafic aerien reposent sur une integration tres forte dessystemes sols et des systemes avioniques embarques. Dans de tels scenarios, l’element avion-ique embarque cle est le systeme de gestion et de commande du vol (“Flight Management andGuidance Control System (FMGCS)”). Son role est double. Tout d’abord, on trouve l’aspect “pi-lotage guidage”. Le FMGCS doit guider l’avion le long d’une trajectoire de reference donnee.Cela recouvre toutes les fonctions traditionnelles des auto-pilotes et des auto-manettes quiequipent la plupart des avions modernes. Le second aspect consiste a creer effectivementcette trajectoire. La gageure est de trouver une trajectoire qui relie le point de depart a l’aeroportde destination, tout en restant dans la partie sure du domaine de vol, tout en satisfaisant toutesles contraintes imposees par le controle aerien et tout en etant finalement optimale d’un pointde vue economique pour une compagnie aerienne. Nous nommons ce processus “generer”une trajectoire. Les contraintes traitent des limitations en altitude, vitesse ou temps ou ausurvol de points de navigation qui peuvent etre imposes. Toutes ces contraintes peuvent fortbien etre modifiees durant un vol, necessitant donc la regeneration de trajectoires durant levol. L’echange de trajectoires et de contraintes entre les systemes sols et les FMGCS est faitdans le cadre de processus de communication et negociation complexes qui sont en dehors duchamp du rapport. La validation de ces concepts de gestion du trafic aerien avances necessitedans certain cas la mise en oeuvre de simulations a grande echelle du controle du trafic aerienqui impliquent de nombreux aeronefs (de l’ordre de 500). Le but de cette etude est de fournirun modele simple des fonctions du FMGCS qui puisse etre implemente dans un generateurde trafic utilise par de telles simulations. Le grand nombre d’avions devant etre simules demaniere simultanee et la complexite des equipements embarques rendent difficile l’utilisationdirecte de ces equipements. La premiere partie du rapport decrit un algorithme de generationde trajectoire. Il repose sur des techniques relativement simples d’optimisation. Un compromisentre l’optimalite des resultats et entre la robustesse, ou l’efficacite numerique a ete rechercheetout en maintenant un niveau de precision et de realisme satisfaisant. La meme approche aete utilisee dans la seconde partie du rapport ou est decrit un systeme de pilotage guidage re-posant sur une technique d’automatique dite de retour de sortie. Tous les algorithmes ont eteprototypes et testes dans l’environnement Matlab. Des exemples d’application sont donnesdans la derniere partie du rapport.

Revision 1.2 Novembre 1996 Page 13 de 17


Generation de Trajectoires

Avant Propos

La Partie I du rapport vise a decrire un algorithme de calcul de trajectoire adapte a la sim-ulation d’un systeme de gestion de vol simplifie.

L’objectif est de calculer une trajectoire satisfaisant une liste de contraintes. Le terme “listede contraintes” signifie que l’avion doit suivre une route definie par une liste de points de navi-gation, tout en restant dans des domaines d’altitude ou de vitesse predefinis lors du survol decertains de ces points et doit atteindre certains d’entre eux dans une fenetre temporelle precise.Le terme de “trajectoire” est utilise pour decrire une suite de positions 4D. C’est le resultat del’application d’une suite de commandes sur l’avion. Le but de l’algorithme est donc de trouverune suite de commandes qui vont faire naviguer l’avion le long d’une trajectoire en ne violantaucune des contraintes.

Plan

La Partie I du rapport est divisee en cinq Chapitres. Le Chapitre 1 est une breve introduc-tion. Il contient aussi une description des principales hypotheses faites. Le Chapitre 2 definitles elements ou objets essentiels qui sont manipules par les algorithmes. Les trois chapitressuivants contiennent la description meme des algorithmes, en commencant avec le Chapitre3 et le calcul des points de descente. Le Chapitre 4 voit l’ajout du traitement des contraintesd’altitude et de vitesse. Finalement, les contraintes de temps sont traitees dans le Chapitre 5.

Hypotheses Generales

Tout d’abord, le principal objectif est de generer une trajectoire satisfaisant une liste de con-traintes. L’optimalite des trajectoires calculees n’est que secondaire. Cela pourrait semblerpeu realiste car les systemes actuels de gestion du vol utilisent deja des indices de cout pourgenerer des trajectoires optimales (ou extremes). Une telle hypothese a ete faite dans le butde simplifier et d’accelerer les calculs. Dans le rapport, la generation de trajectoires utilise unprofil nominal. Il est donc suppose que les aspects de cout sont pris en compte dans le choixdes profils nominaux. Ainsi, soit la trajectoire est tres peu contrainte et puisque le profil nominala ete choisi de maniere optimale, la trajectoire resultante sera quasi-optimale, soit la trajectoireest fortement contrainte et puisque qu’il n’y a que tres peu de degres de liberte, l’optimalite n’estpas un probleme. Cette approche est similaire a celle choisie par le projet EUROCONTROLPHARE EFMS [1].

Les contraintes d’altitude, de vitesse et de temps sont toujours attachees a un point deroute (point (x,y) ou (lat,lon)). Ainsi, la definition de contraintes sur une zone ou un volumed’espace aerien, ou bien encore a une certaine distance d’un point n’est pas autorisee. Il estsuppose que de telles contraintes peuvent toujours etre transformees en contraintes attacheesa un point de route.

Les contraintes et les trajectoires, de maniere generale, sont traitees sequentiellement. Lescontraintes au point de route (n + 1) ne sont considerees que lorsqu’une solution satisfaisantles contraintes sur les points 1 a n a ete trouvee. De plus, les differents types de contraintes (al-titude, vitesse) sont traites l’un apres l’autre. Les contraintes de temps sont traitees en dernier.L’algorithme essaye d’abord de produire une trajectoire qui satisfait toutes les contraintes d’altitudeet de vitesse avant de prendre en compte les contraintes de temps.

Une combinaison de techniques de type homotopie, un seul parametre est progressive-ment modifie jusqu’a l’obtention d’une solution satisfaisante, et de parcours partiel d’arbre estutilisee [2, 3, 4]. Il est donc possible que des solutions soient oubliees. Une autre methode au-rait ete de prendre en compte toutes les contraintes (de tous types) en meme temps et d’appliquerun algorithme d’optimisation non lineaire pour obtenir une trajectoire. Cette option n’a pas ete



retenue car elle a ete jugee trop gourmande numeriquement. La convergence de l’algorithmeest egalement impossible a garantir.

Dans le cas ou la trajectoire est sur-contrainte, une solution satisfaisant toutes les con-traintes ne peut etre trouvee, une solution approchante sera alors proposee. “Approchante”signifie que si la contrainte sur le point n ne peut etre satisfaite, la distance entre la variablecontrainte et les bornes de la contrainte sera minimisee avant de considerer le point de routesuivant (la distance entre toutes les variables contraintes et les bornes des contraintes nonsatisfaites n’est pas minimisee de maniere globale).

Tous les calculs sont faits en coordonnees cartesiennes (x; y). La conversion en latitude/lon-gitude ne devrait pas poser de probleme.

Aucune information n’est conservee sur les contraintes passees: la liste de contraintes estgraduellement reduite lors de l’avancement du vol. L’algorithme de generation utilise en entreela position initiale de l’avion (au sol ou en en vol) plus une liste de contraintes a satisfaire.

Finalement, une telle approche repose sur l’utilisation sous-jacente d’un modele avion avecdes interfaces de haut niveau appropriees. Un tel modele acceptant comme commande desvaleurs cibles de guidage est decrit dans la Partie II du rapport. Les informations de previsionmeteorologique sont traitees directement par le modele avion.

Pilotage Guidage du Modele Avion

Avant Propos

La Partie II du rapport vise a decrire un eventuel systeme auto-pilote/ auto-manette pour unmodele avion utilisant le modele a energie totale comme son modele de performance avion.

Un modele avion peut se decomposer de la maniere suivante:

� un modele de performance avion: l’aerodynamique, la dynamique des moteurs et lesequations du mouvement.

� un systeme de commande du vol qui comprend l’auto-pilote et l’auto-manette.

� un modele de pilote: il assure la gestion des trajectoires, la navigation et la boucle decommande externe du modele de performance avion.

� eventuellement un systeme de gestion de vol.

� les donnees necessaires.

Le rapport se concentre sur les relations entre les deux premiers elements de la liste pre-cedente. Le systeme de commande du vol se decompose en 2 parties comme le montre laFigure 1. Chaque fois que le terme modele avion est utilise dans le rapport, il ne fait referencequ’au:

� modele de performance avion: les equations du mouvement utilisent la modelisation aenergie totale

� systeme de commande du vol qui comprend:

– un auto-pilote lateral qui commande le cap.– un systeme auto-pilote longitudinal/auto-manette qui controle l’altitude et la vitesse

de l’avion.

La modelisation independante des deux canaux de l’auto-pilote (lateral et longitudinal) estpossible parce que les modes lateraux et longitudinaux sont completement decouples dans lesequations du mouvement utilisant l’energie totale.

Notez que les limitations operationnelles du domaine de vol decoulant des procedures descompagnies aeriennes relevent du modele pilote.

Le modele avion resultant a les fonctions auto-pilotes auto-manettes suivantes:



� selection et tenue de cap (psiref)

� selection et tenue de vitesse (le plus petit de CASref et Mref a un instant donne)

� selection et tenue d’altitude (href) ou selection et tenue d’une vitesse verticale (hdotref).

Plan

La Partie II du rapport est divisee en 6 Chapitres. Le Chapitre 6 est une breve introduction.Le Chapitre 7 passe en revue le modele de performance avion: les equations de la dynamiqueutilisees pour calculer la trajectoire de l’avion. Les 2 chapitres contiennent une description desfonctions de l’auto-pilote. Le Chapitre 8 se concentre sur le canal lateral de l’auto-pilote. Lescanaux longitudinaux sont detailles dans le Chapitre 9.

Exemples

La Partie III du rapport vise a fournir des exemples de trajectoires obtenues en utilisant lesalgorithmes decrits precedemment.

Il ne s’agit nullement d’illustrer tous les cas possibles. Le but est d’aider a la comprehen-sion des fonctions des algorithmes plutot que de prouver leur exactitude. Une telle preuvenecessiterait un document beaucoup plus volumineux et encore moins lisible.

Sur les diverses figures, les lignes continues representent le comportement temporel del’avion, les lignes discontinues les valeurs commandees et celles en pointilles les fenetres descontraintes.

La Partie III du rapport est divisee en 6 Chapitres. Le Chapitre 10 est une breve introduc-tion. Le Chapitre 11 est une description de la trajectoire qui sert de reference dans cette par-tie du rapport. Aucune contrainte particuliere n’a ete imposee. Dans le Chapitre 12, diversescontraintes d’altitude sont imposees sur la trajectoire nominale. Dans le Chapitre 13, diversescontraintes de vitesse sont imposees sur la trajectoire nominale. Dans le Chapitre 14, ce sontdes contraintes de temps. Finalement, dans le Chapitre 15, des contraintes de tous types sontappliquees simultanement.

Trajectoire Nominale (Exemple 1)

Il s’agit de la description du cas de reference. Aucune contrainte n’est imposee sur la tra-jectoire. Le seul calcul effectue est celui du point de debut de descente.

La liste de contrainte est contenue dans la Table 1. Les bornes par defaut sont utilisees.En consequence, il n’y a pas de contrainte.

La Table 2 propose un resume de la trajectoire obtenue. Pour chaque point de route estindique l’heure de survol, l’altitude et la vitesse. Il est donc possible de verifier facilement al’aide de cette table si les contraintes imposees sont satisfaites.

La Figure 2 contient le trace detaille de l’altitude en fonction du temps. La Figure 3 donnedes indications generales quant a l’evolution de l’altitude, du cap, de la vitesse et de la masseen fonction du temps. Sur la Figure 4, on trouve les representations graphiques des historiquestemporels de la CAS, du Mach et de l’energie specifique en plus d’une vue plane de la trajec-toire. Enfin sur la Figure 5, on trouve les evolutions de la vitesse verticale, de l’acceleration,l’altitude et de la coordonnee x.

Contraintes Multiples (Exemple 11)

Des contraintes de temps, de vitesse et d’altitude sont imposees sur divers points de routecomme indique dans la Table 3.



A l’examen des resultats dont le resume se trouve dans la Table 4 et les details dans lesFigures 6 a 11, il est effectivement possible de se rendre compte que l’algorithme traite lescontraintes en sequence et fait de son mieux pour les satisfaire l’une apres l’autre.


eurocontrol...the validation of these advanced atm concepts may require large scale atc simulations...

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