A LATERAL DIRECTOR AUTOPILOT DESIGN FOR CONFLICT

RESOLUTION ALGORITHMS

Mustafa Suphi Erden, Kemal Leblebicioğlu

Department of Electrical & Electronics Engineering, Computer Vision and Intelligent Systems Research Laboratory,

Middle East Technical University, 06531 Ankara, Turkey

Keywords: Aircraft autopilot, aircraft lateral dynamics, air traffic management, conflict resolution.

Abstract: Conflict resolution, namely avoidance of aircraft crushes, is one of the main problems to be solved in a free

flight based air traffic system. The researches on conflict resolution are mainly performed in simulative

environments. In the work presented here, a simple lateral director autopilot is designed for conflict

resolution studies. Using such a simple autopilot, real aircraft dynamics can be incorporated to conflict

resolution techniques and the simulation results can be made closer to real situations.

1 INTRODUCTION

In studies on the problem of conflict resolution, the

airplanes are considered to be single points able to

go in any direction pointed by the conflict resolution

algorithm (Alliot et al., 1992; Bicchi and Pallottino,

2000; Clements, 1990; Erden, 2001; Erden, 2002;

Petrick and Felix, 1998; Pappas, 1997; Tomlin,

2000). These applications are based on the

assumption that the aircrafts can be piloted in any

commanded direction, which is not the case in

reality. It is possible that the results of conflict

resolution studies might be made closer to reality by

using some simplified aircraft dynamics and

autopilots. In this study a simple lateral autopilot

(Rauw, 1998; Sachs, 1999) is designed for conflict

resolution studies in order to serve as an interface

between the dynamics and the guiding mechanisms.

2 LINEARIZED LATERAL

DYNAMICS OF AIRCRAFT

The linearized lateral dynamics equations are given

as follows (McLean, 1990):

rarp

secr

tanrp

NNrNpNNr

LLrLpLLp

Ycos

γψ

γφ

δδβ

δφγββ

δδβ

′

++−=

∗

(1)

In these equations U

denotes the speed of the

aircraft in the x axis direction of the aircraft body

frame, pointing forward out of the nose of the

aircraft. The subscript 0 shows that this speed is

used as the trim (linearization) condition.

denotes

the sideslip angle, namely it is an indication of the

angle between the x axis of the body frame and

direction of flight in the lateral plane. It is given by

(

=v/U

) for small

values, where v stands for the

velocity component of the aircrfat in the y direction

of the body frame, pointing out through the right

wing. If

is not zero, then the aircraft nose direction

is not pointing to the direction of flight in the lateral

plane. p and r denote the angular velocities (roll and

yaw rates) of the aircraft with respect to the x and z

axis of the body frame; and

and

are the

corresponding roll and yaw angles.

and

stand

for the aileron and rudder deflections, respectively.

These two are used as the control parameters of the

lateral dynamics.

is the angle between the relative

wind (the direction of flight) and the horizontal

plane (McLean, 1990, p.36). The subscript 0 denotes

the value used for trimming. The primed stability

derivatives appearing in the equations are dependent

on some parameters of the aircraft (surface area of

the wing, mean aerodynamic chord, wing span),

density of air, and aerodynamic coefficients of the

aircraft that are obtained from wind tunnel tests.

(McLean, 1990, pp.51-55; Stevens and Lewis, 1992,

pp.65-80)

In the simulations of this research a very large,

four-engined, passenger jet aircraft, named Charlie,

is used. The stability derivatives for lateral motion

are given in Eq 2. These values are given for a flight

condition of U

=158m/s,

, in a height level of

6100m. These data are taken from (McLean, 1990,

pp.559-561).

330

Suphi Erden M. and Leblebicio

glu K. (2004).

A LATERAL DIRECTOR AUTOPILOT DESIGN FOR CONFLICT RESOLUTION ALGORITHMS.

In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, pages 330-334

DOI: 10.5220/0001133903300334

 SciTePress

39.0:N 0.13:L

018.0:N 0.38:L

14.0:N 0.65:L

07.0:N 2.05:L

42.0:N 0.014:Y

15.0:L 0.082:Y

pβ

−

′′

−

′

−

′

−

′

−

′

−

(2)

When these stability derivatives are substituted

in Eq.1, the A and B matrices of the linear system,

(3)

are as follows:

⎥

⎦

⎤

⎢

⎣

⎡

−−

00100

00010

0014.007.042.0

0038.065.005.2

0062.010082.0

⎥

⎦

⎤

⎢

⎣

⎡

−

39.0018.0

15.013.0

014.00

(4)

3 STRUCTURE OF THE LATERAL

DIRECTOR AUTOPILOT

Control of the lateral motion of aircraft is managed

by manipulating the roll angle with the aileron

deflections. Therefore, Roll Attitude Hold mode

(RAH) is the basic autopilot mode for lateral

autopilots. The deviation of the actual roll angle

from the desired roll angle is fed to the ailerons.

Heading Hold mode (HH) is the lateral autopilot

mode that functions to maintain a certain heading of

the aircraft. It uses the difference between the actual

yaw angle and desired yaw angle as the feedback.

This feedback is used to determine the magnitude of

the roll angle necessary to manage the desired

heading of the aircraft. Then it uses the RAH as the

inner loop to sustain that roll angle. Besides these

two modes, turn-coordinator is another important

part of the lateral autopilot. During turnings of

aircraft an undesired sideslip angle may occur if the

flight is not coordinated. The function of turn-

coordinator is to suppress the sideslip angle with

appropriate deflections of rudder. Fig. 1 shows the

block diagram of the described lateral autopilot

model.

Figure 1: Basic lateral autopilot block diagram

4 TURNING AND COORDINATED

TURN

The basic maneuver in lateral motion is the turning

maneuver in constant level. In this maneuver the

aircraft maintains a bank angle (roll angle). Since the

body frame is banked with respect to the Earth fixed

frame the lift force in the direction of (–z) axes of

the body frame (opposite to the gravity direction if it

is not banked) is also banked. The horizontal

component of the lift force maintains the centrifugal

force (f

) necessary for turning, and the vertical

component balances the weight. The situation is

shown in Fig. 2.

Figure 2: The centrifugal force due to banking of the lift

force

An analysis of Fig.2 with the physical laws

relating the centrifugal force to the turning radius

will reveal that, for a constant speed flight with

velocity U

, the bank angle required for a turning of

w radians per second is given with the formula in

Eq. 5. This formula shows that a larger banking is

required for a sharper turn.

⎟

⎠

⎞

⎜

⎝

⎛

−

tan

(5)

Due to the banking of the lift force, its vertical

component decreases and is no more sufficient to

balance the weight. More deflection of the elevator

is needed for compensating the decrease in the

vertical component; otherwise the aircraft will loose

height. This is achieved by the turn-compensator in

lateral autopilots. In the analysis above and in the

simulations of this research it is assumed that the

compensation for the loss of lift is achieved by a

hypothetical turn-compensator. Therefore, the

vertical component of the lift force is always equal

to the weight, sustaining the aircraft stay in the same

level in any maneuver.

A turn is said to be ‘coordinated’ when the

lateral acceleration and the sideslip velocity (v),

hence the sideslip angle (

), are zero. The condition

for a coordinated turn is that the rate of change of

the sideslip angle (

) is zero. The necessary

condition for that is given by, (McLean, 1990,

p.335).

)(sin

r =

(6)

A LATERAL DIRECTOR AUTOPILOT DESIGN FOR CONFLICT RESOLUTION ALGORITHMS

331

In any turn sideslip angle occurs if the rate of

yawing (r) is different from the value given by Eq.6.

The turn will not be coordinated in that case. If a

turning is not coordinated the derivations made on

Fig. 2 will not be valid, because the velocity vector

and the heading of the aircraft will not be pointing to

the same direction. The autopilot designed in this

work has the sideslip suppressor component as

shown in Fig. 1. This suppressor maintains the

sideslip angle close to zero during any maneuver

with proper rudder deflections. Therefore, in any

turn in simulations, Eq.6 is sustained very closely,

hence the turns may be considered to be coordinated.

5 DIRECTION CONTROL AND

LOCALIZER

In case of coordinated turns, the heading of the

aircraft can be taken as the yaw angle. This is

equivalent with the sideslip angle,

, being zero. For

small bank angles we can drop the ‘sin’ in Eq.5, and

write,

φψ

⎟

⎠

⎞

⎜

⎝

⎛

(6)

As Eq.6 reveals, the rate of turn of aircraft is

approximately proportional to the bank angle. A

simple direction controller for the aircraft can be in

the form,

)(

act

ref

comm

ψψ

−=

(7)

For this control law, the ‘controller-yaw angle’

block in Fig. 1 should be filled with K

Localizing the aircraft in a desired direction is

the main concern for lateral motion control systems.

When an aircraft approaches to the airport for

landing, it should have been aligned to the direction

of runway. VHF-omni range (VOR) navigation is

the most commonly used system for this purpose.

Fig. 3 shows a graphical representation of the

system.

Figure 3: Graphical representation of VOR system

VOR navigation system makes use of the radio

navigation systems to generate the steering

commands to put the aircraft in the runway’s bearing

direction. (Nelson, 1998, pp.314-318; McLean,

1990, p.381). The information of (

ref

) and R are

used to generate the angle Γ. The output signal of

the VOR transmitter is proportional to the angle Γ,

and this signal is used to generate the

com

command

for the director autopilot to make the Γ angle zero.

6 DESIGN OF LATERAL

DIRECTOR AUTOPILOT

The aim in this section is not to design a

sophisticated lateral autopilot, rather, to design a

suitable one sufficient to incorporate the linearized

lateral dynamics of an aircraft with any conflict

resolution algorithm. The RAH and HH modes of

the lateral autopilot will be incorporated in PID

controllers. There will be a sideslip suppressor to

strengthen the coordinated turn assumption, and the

principles of the VOR navigation system will be

utilized in a modified form.

In more concrete terms, the aim can be stated as

‘to design an autopilot to put the aircraft in any

direction in its flight level’. It is assumed that the

position and heading of the aircraft, and the direction

it should go are input to the control system, as

shown in Fig. 4.

Figure 4: Position of the aircraft and the direction it should

go in

What differs the situation in Fig. 4 from the

situation in Fig. 3 is that there is no runway, no VOR

transmitter, and no radio signal communication. The

data for the reference direction is already available

in the aircraft from the conflict resolution algorithm

without a communication process. Since there is no

VOR transmitter it is meaningless to use an angle of

Γ as in Fig. 3. It is more practical to use the

information of d and v

. Any ordered two points in

space determines a directed line. Let us denote this

direction with the vector v

and name it as the

‘direction of the line’. v

gives the information of

reference yaw angle. The difference between the

reference yaw and actual yaw of the aircraft will be

one of the control signals of the director. When the

heading of the aircraft is in the direction of v

, the

line aircraft follows will be parallel to the reference

directed line. However, these two lines are desired to

be coincident, not to be in parallel. Therefore the

information of d should be utilized to coincide the

ICINCO 2004 - ROBOTICS AND AUTOMATION

332

path of the aircraft with the reference line. The

second control signal of the director will be d. The

controller should manage to make

and d zero

simultaneously. In the director, the two control

signals produce two aileron deflection (

)

commands and these are fed to the dynamics of the

aircraft with a weighted sum. The block diagram is

given in Fig. 5.

Figure 5: Block diagram of the lateral director

The three main parts of the lateral director

autopilot are seen in Fig. 5: Heading controller,

distance controller, and sideslip suppressor. The

aileron deflection command of the heading

controller is multiplied by a weight factor and added

to the command of distance controller, which is also

multiplied with a negative weight (these weights are

arranged to be 1 for the aircraft used in simulations).

These weighting factors may be obtained by ad-hoc

methods for different aircrafts. The rudder deflection

should be negative in order to suppress a positive

sideslip angle. PID controllers are used for all

control blocks. The sideslip suppressor is simply a

PID controller. The heading controller and distance

controller blocks are shown in Fig. 6.

Figure 6: Block diagrams of the heading and distance

controllers

The PID parameters of the heading controller are

determined by ad-hoc methods. The distance

controller takes the error yaw angle (psie) with the

distance (d) and generates an aileron command. The

parameters of the PID controller and the gains in

distance controller are obtained again by ad-hoc

methods. In fact the controller is not a PID but a PI

controller since the D parameter is zero. The

function block labeled as ‘Fcn’ determines the

distance command according to the heading of the

aircraft with respect to the reference direction.

Considering Fig. 4., when the

is near 90

there is

not much need for aileron deflection to decrease the

distance, because the aircraft is already heading in

the direction to decrease the distance. On the other

hand it needs a strong aileron deviation when the

angle

approaches to zero. The sign arrangement

block is necessary for arrangement of sign of

distance. When the aircraft passes to the other side

of the directed line (refer to Fig. 4) the sign of the

distance becomes negative. The initial sign of the

distance should be determined properly according to

the aircraft being above or below the line, and

consistency should be attained so that the system

works properly in any configuration.

The outputs of the lateral director are taken as

the yaw angle rate (r) and the sideslip angle (

These are the necessary information to determine the

path the aircraft follows in the two dimensional

lateral plane. Although the sideslip angle is very

close to zero as a result of the sideslip suppressor,

this small value is still used in simulations. The yaw

angle of the aircraft is simply the integral of the yaw

rate. The aircraft flies with constant speed in the

direction of

actual

. The subsection performing

these calculations is called the ‘position tracker’.

7 A SAMPLE RESULT

The integration of the autopilot, dynamics of the

aircraft and the position tracker is shown in Fig. 7,

with a plot of the route that the aircraft follows in an

example situation. In this example situation, the

commanded directed line is the y=0 line with the

direction of increasing x. Accordingly, the psiref

command is made

/2 taking the +y direction as the

north. The d command is equal to the y position of

the aircraft. All the ad-hoc parameter arrangements

are made considering the configuration in Fig. 7.

The path is arranged to be fast enough to catch the

directed direction with little overshoot.

Figure 7: Autopilot, lateral dynamics, and position tracker

system; the path followed by the aircraft for a 90

right

turn in 1500m ahead

REFERENCES

Alliot, JM., H. Gruber, G. Jolly, M. Schoenauer, 1992.

Genetic algorithms for solving air traffic control

A LATERAL DIRECTOR AUTOPILOT DESIGN FOR CONFLICT RESOLUTION ALGORITHMS

333

conflicts. In Proceedings 9

IEEE Conference of

Artificial Intelligence Application.

Bicchi, A., L. Pallottino, 2000. On optimal cooperative

conflict resolution for air traffic management systems.

In Proceedings IEEE Transactions on Intelligent

Transportation Systems.

Clements, J.C., 1999. The optimal control of collision

avoidance trajectories in air traffic management. In

Transportation Research Part B 33 (1999) 265-280.

Erden, M.S., K. Leblebicioğlu, U. Halıcı, 2001. Çok ajanlı

system yaklaşımıyla hava trafiği kontrolü, In 9.Sinyal

İşleme ve Uygulamaları Kurultayı, Gazimağosa –

KKTC.

Erden, M.S., K. Leblebicioğlu, U. Halıcı, 2002. Conflict

resolution by negotiation. Abstract In IFAC 15

World

Congress Book of Abstracts, 230, Barcelona, Spain;

full paper in the related CD.

McLean, D., 1990. Automatic Flight Control Systems,

Prentice Hall International (UK) Ltd.

Nelson, R.C., 1998. Flight Stability and Automatic

Control, McGraw-Hill Companies Inc.

Pappas, G.J., C.J. Tomlin, J. Lygeros, D.N. Godbole and

S.S. Sastry, 1997. A next generation architecture for

air traffic management systems. In IEEE Conference

on Decision and Control, pp 2405-2440, San Diego,

California, USA.

Petrick, H., M. C. Felix, 1998. A soft dynamic

programming approach for on-line aircraft 4-D

trajectory optimization. In European Journal of

Operational Research 107, 87-95.

Rauw, M.O., 1998. FDC 1.2-A SIMULINK Toolbox for

Flight Dynamics and Control Analysis, Chapter 11,

February 8.

Sachs, G., 1999. Flight path predictor for minimum pilot

compensation, Aerospace Science and Technology, 4,

247-257.

Stevens B.L. and F.L. Lewis, 1992. Aircraft Control and

Simulation, John Willey & Sons Inc.

Tomlin, C., R. Ghosh, 2000. Maneuver design for multiple

aircraft conflict resolution. In Proceedings of the

American Control Conference, Chicago, Illinos.

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