AN EXPERIENCE WITH THE NEURAL NETWORK FOR

AUTO-LANDING SYSTEM OF AN AIRCRAFT

Dr. Sreenatha G. Anavatti

School of Aerospace, Civil and Mechanical Engineering, University of New South Wales at ADFA, Canberra, Australia

Dr. Choi J. Young

School of Electrical Engineering and Computer Science, Seoul National University, Seoul, Korea

Mr. Francois Pischery

Laboratoire d’Automatique, Industrielle Institut National des Sciences Appliquees, de Lyon, Villeurbanne, France

Keywords: Auto-landing, Robust Control, Neural Network, Aircraft Dynamics

Abstract: Generalization by the Neural Networks is an added advantage that can provide very good robustness and

disturbance rejection properties. By providing a sufficient number of training samples (inputs and their

corresponding outputs), a network can deal with some inputs it has never seen before. This ability makes

them very interesting for control applications because not only they can learn complicated control functions

but they are able to respond to changing or unexpected environments. Aircraft landing system provides one

such scenario wherein the flight conditions change quite dramatically over the path of descent. The present

work discusses the training of a neural network to imitate a robust controller for auto-landing of an

aircraft. The comparisons with the robust controller indicate the additional advantages of the neural

network

1 INTRODUCTION

Auto-landing is a requirement in the modern aircraft

due to the necessity for operations under all weather

conditions, whether it is civilian aircraft or military

aircraft. Considerable efforts have gone in designing

suitable control systems for enhancing the auto-

landing capability[1,5]. The auto-landing consists of

the two phases, the descent phase and the flare.

During the descent phase, the glide slope control

system guides the aircraft down a pre-determined

glide-slope. When the aircraft reaches a pre-selected

altitude, the flare control system reduces the rate of

descent and causes the aircraft to flare out and touch

down with an acceptably low rate of descent. The

control system achieves this by the control of the

flight path angle γ. It is shown in reference (John H.

Blakelock, 1991) that the automatic control of the

flight path angle without simultaneous control of the

airspeed (either manual or automatic) is practically

not possible. The combination of these three

systems provides the full longitudinal control of the

aircraft.

The dynamics of the aircraft is governed by

stability derivatives which are functions of flight

regime (speed, altitude, density, temperature, etc.).

Due to the variations in the flight regime during

landing, the dynamics of the aircraft change

considerably over the entire flight regime. Hence, a

time varying mathematical model is required. Due

to the difficulty in handling time-varying differential

equations, mathematical models at a number of

points in the descent are considered simultaneously.

This adds a large amount of uncertainty in modelling

employed in the design of flight control systems. In

addition, disturbances in terms of gusts and sensor

and actuator noise can alter the performance of

control system considerably. Hence, there is a

necessity for having robust control systems that can

handle parameter variations along with good

disturbance rejection properties. H-infinity(Ching-

Fang Lin, 1995) controller provides one such

393

G. Anavatti S., J. Young C. and Pischery F. (2004).

AN EXPERIENCE WITH THE NEURAL NETWORK FOR AUTO-LANDING SYSTEM OF AN AIRCRAFT.

In Proceedings of the Sixth International Conference on Enterprise Information Systems, pages 393-400

DOI: 10.5220/0002627603930400

 SciTePress

alternative. However, the complexity of the

controller can deter the implementation in practical

uses.

The present paper looks at the alternate way of

implementing the H-infinity controller by training a

neural network[2,3] to imitate this. In addition to

the imitation, the neural network is shown to have

additional properties like generalization with inputs

and better robustness properties.

Section 2 discusses the auto-landing and the

equations governing the dynamics of the aircraft.

Section 3 discusses the design of neural network to

imitate the H-infinity controller. The details of the

design of H-infinity controller are avoided to reduce

the mathematical complexity of the paper. Section 4

presents the comparison between the H-infinity and

the neural network controllers under various

conditions. The paper is concluded in section 5.

2 AIRCRAFT DYNAMICS AND

AUTO-LANDING SYSTEM

The linearized equations describing the longitudinal

motion of the aircraft are:

MqMMuMqM

ZgZuZZ

XgXuXu

eequ

eeu

rpmrpmu

+++=+−

+Θ−+=

δαα

δθαα

δαα

δα

cos

where, u is the change in airspeed (ft/sec), α is the

angle of attack (deg), θ is the pitch angle (deg), δ

the elevator angle (deg), δ

rpm

is the change in the

rpm of the engine (rpm), and Θ

is the initial Euler

angle relative to the horizontal plane. X

X , Z

, Z ,

, M

. M , M

,, M

, Z

are known as the

stability derivatives. These are functions of the

flight regime like the speed, density, altitude, etc.

These equations can be set in the State-Space form

given by,

BUAXX

where X is the state vector, U is the input vector and

Y is the output vector.

2.1 Basic Autopilot Model

The basic autopilot is actually the pitch angle control

system. The error on θ goes through a transfer

function that stands for electronics and hydraulics.

The result is δ

, the elevator deflection. Then the

aircraft equations compute the associated reaction.

The outputs of the aircraft block are the change in

airspeed (u) and the pitch rate (q).

The basic autopilot includes a velocity control

system (VCS). It uses the throttle to correct the

change in airspeed (Fig. 2). The input is the change

in airspeed (u) and the output is the engine rpm

correction.

In the following,

(deg) is the flight path angle.

It is actually the parameter that is being controlled

but it is never measured directly. It is linked to

and

by:

−=

The following simulation results were obtained

with a 1 deg step command input on

. The velocity

control system ensures that the direction of the flight

path angle is in the same direction as the pitching

angle (otherwise, when the aircraft is commanded to

descend, it would actually have a shallow glide up).

2.2 Glide slope control system

The glide slope controller surrounds the basic

autopilot. It computes the right input θ

comm

for the

basic autopilot so the aircraft stays on the predefined

flight path. The task of the glide slope control

system is to keep Γ = 0 so that the aircraft descends

along the desired path.

2.3 Flare Control System

As the glide slope controller, the flare controller

surrounds the aircraft/autopilot model and computes

the input

comm

so the aircraft sticks with the

predetermined flight path.

Flight test data has shown that when a pilot

performs the flare from the approach glide to the

final touchdown he generally decreases his rate of

descent in an exponential manner, thus tending to

make the aircraft fly an exponential path.

For the automatic flare control, then, the aircraft

is commanded to fly an exponential path from the

initiation of the flare until touchdown. The height

above runway (h) is given by :

ehh

−

h is the height (ft).

is the height at the start of the flare (ft).

is the time constant (sec).

and h

are calculated by making assumptions on

the distance between the touchdown point and the

transmitter and on the time the aircraft will take to

reach to touchdown.

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Figure 1: Basic autopilot block diagram

Figure 2: Velocity control system.

Figure 4: Geometry of Glide Slope Problem

Figure 3: Simulation Results of basic autopilot

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395

Figure 5: Geometry of the Glide Slope

As the path equation is known, the value of

(rate of descent) is known at any time :

−=−=

− /

This is the command signal for the outer loop.

The coupler shown above is a conventional one that

does not have the properties of robustness. One can

design a better controller that has better robustness

properties. One such controller is the H-infinity

controller.

The H

∞

control design approach consists in

modeling uncertainties as a separate transfer

function that is combined with the plant model in a

multiplicative or additive way. This way the H

∞

controller is able to stabilize not only the nominal

model but a whole family of systems which exist in

the uncertainty region around the nominal model.

However, the complexity of the controller deters the

implementation in the practical systems.

3 NEURAL NETWORK

A feedforward network is employed in the present

work. The training of the network was performed

using the back propagation algorithm.

MATLAB(Howard Demuth et al., 2000) was

employed for doing the same. For the sake of

completeness, the training algorithm is summarized

below;

The backpropagation algorithm used in this

study was the Levenberg-Marquardt algorithm

(trainlm in MATLAB). It is one of the many

variations of the backpropagation algorithm. It was

chosen for its speed of convergence in function

approximation problems. It is inspired by the

Newton method for which the basic step is:

kkkk

gHxx

−

−=

where H is the Hessian matrix of the performance

index at the current values of the weights and biases

and g is the current gradient of the performance

function.

It is often complex and expensive to compute the

Hessian matrix. The Levenberg-Marquardt

algorithm avoids this calculation by approximating

the Hessian matrix as:

JJH

and by computing the gradient as:

eJg

where J is the Jacobian matrix that contains first

derivatives of the network errors with respect to the

weights and biases, and e is a vector of network

errors. The Jacobian matrix can be computed

through a standard backpropagation technique

(much less complex than computing the Hessian

matrix).

The Levenberg_Marquardt algorithm then uses

this approximation in the following Newton-like

update;

[]

eJIJJxx

−

+−=

When the scalar

µ is zero, this is just Newton’s

method, using the approximate Hessian Matrix.

When

µ is large, this becomes gradient descent with

a small step size. Newton’s method is faster and

more accurate near an error minimum, so the aim is

to shift towards Newton’s method as quickly as

possible. Thus,

µ is decreased after each successful

step and increased only when a tentative step would

increase the performance function.

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Figure 6: Flare control system

3.1 First attempt in training

Since, the network is supposed to imitate the H-

infinity controller, the training data employed was

the input and out of the H-infinity controller,as

shown in the block diagram (Figure 7).

Figure 7: Block diagram for the first configuration

At this stage, the neural network is a 3-layer

feedforward network, with the hidden layer

consisting of 5 and 3 neurons. The training set

consists of the input vector d, the distance between

the aircraft center of gravity and the ideal glide slope

and output vector, the H

∞

controller output.

The performance function did not achieve the

targeted minimum with any number of epochs.

Increasing the number of layers and neurons also did

not help the cause. Due to the ambiguity in the

relation between the input and the output, this was

happening.

3.2 Second attempt in training:

In order to remove the ambiguity, the network will

now receive two inputs: u (the airspeed change) and

γ (the flight path angle). θ

comm

∞

controller output)

is still the target. In this configuration, the network is

meant to replace both the “d” block and the H

∞

controller.

This time, convergence was achieved and the

desired performance level was achieved during the

training. The numerical simulations with this

network showed that the response matches very well

with that obtained by the H-infinity controller. Since

the network was trained for a particular initial

condition (distance between the aircraft centre of

gravity and the ideal glide slope line)(in this case d

= 70m), when this initial condition was modified,

the network did not perform according to the

expectations. The graphs below show the evolution

of d during the landing phase: the shape stays

exactly the same and the error is brought back to

zero in the first case; in the second case the aircraft

flies along its glide slope but 30m away from it

(Figure 8). In order to correct this, the network has

to be trained with not only one set of data but several

data sets each corresponding to a different initial

condition.

As the final step in training, an extra input

neuron for the initial condition with 9 and 7 neurons

in the hidden layer were employed.

Inputs

Targets

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397

Figure 8: Neural Network behaviour for two different initial conditions

This network was trained with three data sets

corresponding to three different initial conditions: d

equals to 100, 50 and -20m. After 500 epochs, the

mean square error is equal to 2.4e-6. The simulation

shows that the neural networks behavior is

satisfactory for the initial conditions included in the

training.

Figure 9: Neural Network results for two different initial conditions (final network).

However, when other initial conditions were tried

out, the performance was not good. Once again this

is attributed to the ambiguity and hence, an

additional input (the integrated value of distance, d)

was employed. With this, the final training was

carried out with data for initial conditions of d

= -

100, -90, -80, …, 90, 100m. The final network was a

four layer network with 10 neurons per hidden layer.

In addition, another network with 11 neurons per

hidden layer was also trained. The results of

comparison of these two networks with H-infinity

controller indicate the generalization property of the

network as well as the effect of architecture on the

robustness.

4 PERFORMANCE AND

ROBUSTNESS

The performance of the controller for auto-landing is

measured through the global accuracy of the landing

system. Robustness evaluation is based on three

tests: sensitivity to modeling errors, disturbance

rejection and sensitivity to sensor noise. The

following paragraphs compare the results for the

three controllers. For convenience, the H-infinity

controller and the neural networks will respectively

be called H

∞

, NN

and NN

here afterwards.

4.1 Accuracy

The neural networks were trained for initial

conditions varying within [-100;+100]. For several

initial conditions from this range and for each

controller, d

touchdown

is measured (Figure 10). For

each controller, the maximum gap, the average gap

and the standard deviation of the values were

computed. The results are given by;

Hinf NN10 NN11

Maximum (m)

0.272 0.346

0.209

Average (m)

-0.042

0.038

-0.148

Stand. Dev.

0.101 0.146

0.078

These values show that even though NN

has

the highest average gap, it is the most interesting

controller here. It is very constant (low standard

deviation) and its maximum error is smaller.

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Figure 10 Controller Accuracy as a function of simulation initial conditions.

4.2 Sensitivity to uncertainty and

modeling errors

Modeling errors arise due to the simplifying

assumptions in mathematical modelling. Along with

this, due to the variations in the flight conditions, the

stability derivatives governing the dynamics of the

aircraft change. Hence, there is a necessity to

validate the controller against these.

Numerical simulations were carried out by

varying all the parameters of the A matrix by a

certain percentage indicating the worst case scenario

The controllers were tested in the following

configurations:

 the stability derivatives are 5, 8, 10 and 11%

bigger,

 the stability derivatives are 10, 15, 16 and

17% smaller.

For a certain amount of change in the A matrix,

the natural frequencies governing the dynamics of

the aircraft change. The aim is to define the range

of natural frequencies in which each controller stays

effective. Like before, the effectiveness is measured

through d

touchdown

It is assumed that 50cm is the maximum

acceptable d

touchdown

. With a glide slope angle ( ) of

4°, that would mean a ground distance of about 7m

between ideal and actual touchdown points. So the

net would have to be 14m long which seems about

right. The green zones indicate that according to this

criteria, the controller kept the aircraft in the net.

The red zones means the aircraft would have missed

it.

Change -17% -16% -15% -10% 0% 5% 8% 10% 11%

Max (m)

0.427 0.468 0.516 0.272 0.506 0.897 1.278 1.508

Avg (m)

-0.017 -0.034

-0.088 -0.042 -0.062 -0.137 -0.223 -0.279

Hinf

Std

0.122 0.132 0.144 0.101 0.133 0.215 0.302 0.356

Max (m)

7.541 5.986 2.166 0.346 0.239 0.809 1.404 1.697

Avg (m)

-4.895 -4.021

-1.610

0.038 -0.037

-0.115 -0.202 -0.259

NN10

Std

1.659 1.344 0.299 0.146 0.090 0.140 0.266 0.343

Max (m)

24.406

0.101 0.109 0.140 0.209 0.136 0.477 1.036 1.457

Avg (m)

1.269

-0.009 -0.010

-0.028

-0.148 -0.084

-0.110 -0.166 -0.216

NN11

Std

5.557

0.031 0.031 0.038 0.078 0.023 0.084 0.203 0.299

These results show the superiority of NN

. Its

maximum distances at touchdown are always

smaller than the others and as shown by the green

zones, its range of effectiveness is wider. NN

valid from –16% to +8%, which gives [1.922;4.303]

as natural frequency validity range, whereas H

∞

not even valid from –10% to +5%, which gives the

validity range [2.059;4.184]. In addition

, NN

average errors are very small and actually

-0,300

-0,200

-0,100

0,000

0,100

0,200

0,300

0,400

-100 -80 -60 -40 -20 0 20 40 60 80 100

Simulation initial condition (m)

Gap @ touchdown (m)

Hinf

NN10

NN11

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399

improve a little bit with parameter variation. Finally,

its standard deviation indicate that it is by far the

most consistent of the tested controllers.

The neural network was trained with samples

created by H

∞

only. So the neural network not only

does the job of what H

∞

’s does, but does it better.

The neural network is able to compensate for a

bigger change. As this result was reached with a

training set including only data for the ideal plant

configuration, it is very possible that additional

training (with data from several controllers and

several plant configurations) enhances the

robustness of NN

4.3 Disturbance rejection

In general, the disturbances can be on the actuator

side or the sensor side. Since the control surfaces (in

this case elevator) are the actuators for an aircraft,

the presence of atmospheric disturbances can be

translated as equivalent disturbances on these

aerodynamic control surfaces. The aircraft should

be able to withstand these disturbances. To model

external disturbances, random signals of various

amplitude were added to δ

, the elevator deflection

and simulations were conducted. Three cases of

10%, 25% and 50% of δ

curent amplitude are

considered. In each of these cases and for each

controller, the entire flight path was compared to the

clean flight path (without disturbances). For each

time step, the difference between the clean and noisy

flight paths was computed. Based on these

difference numbers, an average difference and the

standard deviation were computed. Because this

time the entire flight path is monitored and not just

the gap at touchdown, this test was not run for

several initial conditions but just for d

= 50m. The

table below summarises the results.

∞

appears to have a slightly better resistance to

disturbances when their amplitude grows. But

globally, NN

does not have a bad behavior. Its

numbers are very much comparable to those of H

∞

We believe that by including noise or noisy inputs in

the training set, the neural network should improve

its filtering capabilities significantly. Unfortunately,

the lack of time prevented us from going any further

in this direction.

Hinf NN11

Difference (m) Difference (m)

10%

25%

50%

10%

25%

50%

Average (m)

0,005 0,012

0,032

-0,002 0,016

0,120

Stand. Dev.

0,124

0,294

0,832 0,098 0,329

0,836

5 CONCLUDING REMARKS

This paper discusses the experience in training a

neural network to imitate a complex robust

controller for auto-landing of aircraft, a major

requirement for the present day aircraft. The various

steps in achieving the desired training and the results

of the comparison are presented in graphical as well

as tabular form. To verify the performance of the

controller, both accuracy and robustness are

considered. The neural network seems to do a better

job than the controller used for its training due to the

generalization nature of these networks. Additional

training with noisy data can improve the filtering

characteristics of these networks in a significantly

thus combining the efforts of the filter and the

controller in a single network.

REFERENCES

John H. Blakelock, (1991), Automatic Control of Aircraft

and Missiles.

Marilyn McCord Nelson, W.T. Illingworth, (1991), A

Practical Guide to Neural Nets.

William E. Faller, Scott J. Schreck, (1996), Neural

Networks : Applications and Opportunities in

Aeronautics, Progress in Aerospace Sciences, Vol. 32,

Issue 5.

Howard Demuth, Mark Beale, (2000), Neural Network

Toolbox User’s Guide, Version 4 (Release 12).

Louis V. Schmidt, (1998), Introduction to Aircraft Flight

Dynamics, AIAA Education Series.

Ching-Fang Lin, (1995), Advanced Control Systems

Design, PTR Prentice Hall

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