Aterriza Je

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Application of Type-1 and Type-2 Fuzzy CMAC to AutomaticLanding System

Journal: Transactions on Industrial Electronics

Manuscript ID: 10-1315-TIE

Manuscript Type: Regular paper

Manuscript Subject: Control and Signal Processing

Keywords: Intelligent control, Control systems, Fuzzy control

Are any of authors IEEEMember?:

Yes

Are any of authors IESMember?:

No

Transactions on Industrial Electronics


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Application of Type-1 and Type-2 Fuzzy CMAC to Automatic Landing System

AbstractIntelligent control scheme that utilizes

adaptive fuzzy cerebellar model articulation controller

(FCMAC) to aircraft automatic landing system is proposed

in this paper. The control scheme uses CMAC and type-1

and type-2 fuzzy systems. Current flight control law is

adopted in the controller design. Lyapunov stability theory is

applied to obtain adaptive learning rule and to guarantee

stability of the control system. Performance on tracking

desired landing path and environment adaptive capability are

demonstrated through software simulations. The proposed

intelligent controllers can guide the aircraft to a safe landing

in severe turbulence condition and act as an experienced

pilot.

I. INTRODUCTIONOn March 23, 2009 a FedEx cargo plane crashed and burst

into flame as it landed at Narita Airport, Tokyo's main

international airport, killing the American pilot and copilot.

The plane bounced twice on the runway and veered to left as

it turned on its side before bursting into flames. The fire

destroyed the aircraft [1]. Investigators believe wind shear,

or a sudden gust of wind, may have been a factor. An

accident survey of 1,300 aircraft accidents from 1950

through 2008 classified the causes into several categories asshown in Table 1. Weather was a main contributing factor of

the causes. The percentage of weather related to total

accidents was 22%. Conventional automatic landing systems

(ALS) can provide a smooth landing, which is essential to

the comfort of passengers. However, these systems work

only within a specified operational safety envelope. When

the conditions, such as turbulence or wind shear, are beyond

the envelope, they often cannot be used. The ALS relies on

the Instrument Landing System (ILS) to guide the aircraft

into the proper altitude, position, and approach angle during

the landing phase. The atmospheric disturbances affect not

only fly qualities of an airplane but also flight safety. Most

conventional control laws generated by the ALS are basedon the gain scheduling method [2]. Control parameters are

preset for different flight conditions within a specified safety

envelope, which is relatively defined by the Federal Aviation

Administration (FAA) regulations [3]. Environmental

conditions considered in the determination of dispersion

limits are: headwinds up to 25 knots, tailwinds up to 10 knots,

crosswinds up to 15 knots, moderate turbulence, and wind

shear of 8 knots per 100 feet from 200 feet to touchdown.

When the conditions, such as turbulence, are beyond the

envelope, the ALS often is disabled. It is therefore desirable

to develop an intelligent ALS that expands the operational

envelope to include more safe responses under a wider range

of conditions.

In recent years, modern control techniques and intelligent

concepts such as neural networks, fuzzy systems, genetic

algorithms, and mixed intelligent schemes have been applied

to various scientific and engineering researches [4]-[7].

There are also obvious achievements in flight control

domain [8]-[17]. In 1975, the cercbellar model articulation

controller (CMAC) was first introduced by J.S. Albus. It is

neural nwtworks inspired by the cercbellar [18]. It imitates

the structure of human cerebellum, which is a kind of

associative memory neural network. Unlike the

back-propagation based neural network which is using the

global weight updating rule, CMAC is distinguished by the

constant local weight updating rule. CMAC not only

combines the advantages of rapid convergence speed and

low computation but also can be realized easily by hardware.

With these attractive characters, the CMAC can be used to

approximate a wide variety of nonlinear functions and was

widely applied in real time automatic control, signal

processing, image coding and pattern recognition [19]-[22].

Currently, many approaches have been introduced to

improve the performance of CMAC. In 2000, a fuzzy

CMAC was developed by Zhang and Qian [23]. The

characteristics of fuzzy system are human-like reasoning and

expert knowledge. Therefore, fuzzy CMAC includes thelearning ability of neural networks and the advantages of

fuzzy system. Fuzzy logic was first proposed by Zadeh [24].

The main idea of fuzzy set is to imitate human experiences to

fuzzy rules applied in fuzzy inference system. And type-2

fuzzy logic [25] is based on the extension principle proposed

by Zadeh. A fuzzy system that uses type-2 fuzzy sets and

type-2 fuzzy logic and inference is called a type-2 fuzzy

system. In contrast, a fuzzy system uses traditional fuzzy sets,

logic, and inference is called type-1 fuzzy system. In

traditional fuzzy system models, the structure is

characterized by using type-1 fuzzy sets. Type-1 fuzzy sets,

defined on a universe of discourse, map an element of the

universe of discourse onto a crisp number in the unit interval[0, 1]. However, type-2 fuzzy can translate the linguistic and

numerical uncertainty from original data into fuzzy rule

uncertainty, while the type-1 cannot.

Another improvement effect is to develop adaptive

learning rule for the CMAC. In 2004, C.M. Lin proposed

adaptive method of CMAC for linear piezoelectric ceramic

motor [26]. After four years, he designed a robust adaptive

CMAC system for BLDC motors [27], which adds an

improved adaptive method into CMAC and obtains better

result. In this paper, we propose an intelligent aircraft

automatic landing control system that uses type-1 fuzzy

CMAC and type-2 fuzzy CMAC with adaptive learning rule

to improve the performance of conventional ALS and guide

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the aircraft to a safe landing. Some researchers have applied

intelligent concepts to the problem of landing control

[10]-[17], but these intelligent concepts are not adaptive to

severe disturbance environment. This paper presents

adaptive learning rule to the control scheme. This approach

can overcome those problems in [10]-[17] and make thecontroller more robust and adaptive to various wind

disturbance conditions.

Table 1. Causes of fatal accidents by decade (%), 1950

through 2008 [1]

Cause 50s 60s 70s80s

90s00s

Pilot Error 40 32 24 25 27 25Pilot Error

(weather related)11 18 14 17 21 17

Pilot Error(mechanical related)

7 5 4 2 4 3

Total Pilot Error 58 57 42 44 53 45Other Human Error 0 8 9 6 8 9

Weather 16 10 13 15 9 8Mechanical Failure 21 20 23 21 21 28

Sabotage 5 5 11 13 10 9Other Cause 0 2 2 1 0 1

II. SYSTEM DESCRIPTIONAt the aircraft landing phase, the pilot descends from the

cruise altitude to an altitude of approximately 1200 ft above

the ground. The pilot then positions the aircraft so that the

aircraft is on a heading towards the runway centerline. When

the aircraft approaches the outer airport marker, which is

about 4 nautical miles from the runway, the glide path signal

is intercepted, as shown in Fig. 1 [28]. As the airplanedescends along the glide path, its pitch, attitude, and speed

must be controlled. The descent rate is about 10 ft/sec and

the pitch angle is between -5 to +5 degrees. Finally, as the

airplane descends 20 to 70 feet above the ground, the glide

path control system is disengaged and a flare maneuver is

executed. The vertical descent rate is decreased to 2 ft/sec so

that the landing gear may be able to dissipate the energy of

the impact at landing. The pitch angle of the airplane is then

adjusted, between 0 to 5 degrees for most aircraft, which

allows a soft touchdown on the runway surface.

~

~

0 ft

50 ft

touchdown

1200 ftglide path

flare ath

Altitude

Fig. 1. Glide path and flare path

A simplified model of a commercial aircraft that moves

only in the longitudinal and vertical plane is used in the

simulations for implementation ease [12]. The motion

equations of the aircraft are given as follows:

( ) ( )

( ) cos( )0180

u X u u X w w X qu g w g q

g X XE E T T

(1)

TTEEqgwgu MMqMwwMuuMq )()( (2)

( ) ( ) ( )0180

( ) sin( )0180

w Z u u Z w w Z U qu g w g q

g Z ZE E T T

(3)

q (4)

0180

Uwh (5)

where u is the aircraft longitudinal velocity (ft/sec), w is

the aircraft vertical velocity (ft/sec), q is the pitch rate

(rate/sec), is the pitch angle (deg), h is the aircraft

altitude (ft),E is the incremental elevator angle (deg), T

is the throttle setting (ft/sec), o is the flight path angle

(-3deg), and g is the gravity (32.2 ft/sec2). The

parameters ii ZX , and iM are the stability and control

derivatives.

To make the ALS more intelligent, reliable wind profiles

are necessary. Two spectral turbulence forms models by von

Karman and Dryden are mostly used for aircraft response

studies. In this study the Dryden form [12] was used for its

demonstration ease. Fig. 2 shows a turbulence profile with a

wind speed of 30 ft/sec at 510 ft altitude.

Fig. 2. Turbulence profile

III. CONTROL SCHEMEPID controller is a simplified structure of an aircraft

landing controller as shown in Fig. 3. Its inputs consist of

altitude and altitude rate commands along with aircraft

altitude and altitude rate. Via aircraft landing controller we

can obtain the pitch commandc . Then, the pitch autopilot

is controlled by pitch command. Detail descriptions can be

found in [12]. In order to enable aircraft to land more steady

when an aircraft arrives to the flare path, a constant pitch

0 5 10 15 20 25 30 35 40 45-40

-35

-30

-25

-20

-15

-10

-5

0

5

10Wind Gust velocity components:Longitudinal (Solid) & Vertical (Dashed)

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angle will be added to the controller. In general, the PID

controller is simple and effective but there are some

drawbacks such as apparent overshoot and sensitive to

external noise and disturbance. When severe turbulence is

encountered the PID controller may not be able to guide the

aircraft to land safely. With CMAC compensator theproposed controller can overcome these disadvantages [17].

It uses a traditional PID controller to stabilize the system and

train the CMAC to provide precise control. The gains of PID

controller are adjusted based on experiences, what it

provides are tolerable solutions, not desired solutions. The

CMAC can effectively meliorate these conditions.

s

wh1

pitchuppitchup

ch

ch

h

ch

hk

hk

applied only during flare

typical value : 4pitchup

1.0hw

25.0hk

3.0h

k

Fig. 3. PID controller

The overall control scheme is described in Fig. 4, in which

the control signal U is the sum of the PID controller output

and the fuzzy CMAC output. The inputs for the fuzzy

CMAC and PID controller are: altitude, altitude command,altitude rate, and altitude rate command. The PID controller

provides tolerable solutions. In each time step k, the fuzzy

CMAC involves a recall process and a learning process. In

the recall process, it uses the desired system output of the

next time step and the actual system output as the address to

generate the control signal fuzzyCMACU . In the learning process,

the control signal of the pitch autopilot, U, is treated as a

desired output. It is used to modify the weights of fuzzy

CMAC stored at location which is addressed by the actual

system output and the system output of the next time step.

The output of the fuzzy CMAC is the compensation for pitch

command. When the wind turbulence is too strong, the ALS

can not control the aircraft to land safely. In here we use

fuzzy CMAC control scheme to improve the ability of

turbulence resistance of the ALS.

Fig. 4. The fuzzy CMAC control scheme

A. Type-1 Fuzzy CMAC

The structure of fuzzy CMAC is shown in Fig. 5. fuzzy

CMAC is a kind of associative memory network. Not only it

has faster self learning rate than normal neural network by

quantities with a few adjustments of memory weights, but

also it has good local generalization ability. The function offuzzy CMAC is similar to a look-up table, and the output of

CMAC is figured from a linear combination of weights

which are stored in memory. The concept of fuzzy CMAC is

to store data (knowledge) into overlapped storage

hypercubes (remembering region) in an associative manner

such that the stored data can easily be recalled. Two kinds of

operations are included in the fuzzy CMAC, one is

calculating the output result and the other is learning and

adjusting the weight. The output of fuzzy CMAC can be

obtained by the mapping process XSCWY as

follows.

1x

2x

nx

dY

Fig. 5. Conventional fuzzy CMAC structure

Step 1. Quantization (XS):

X is an n-dimensional input vector. For the givenT

nxxxX ]...[ 21 ,T

nsssS ]...[ 21 represents the

quantization vector of X. It is specified the corresponding

state of each input variable before the fuzzification.

Step 2. Associative Mapping segment (SC):

It is to fuzzify the quantization vector which is quantized

from x . Fuzzy CMAC uses the fuzzification method of the

fuzzy theorem as its addressing scheme. After the inputvector is being fuzzified, the input state values are

transformed to firing strength, which is based on

corresponding membership functions.

Step 3. Memory Weight Mapping (CW):

After fuzzifying block regions, thethi rules firing strength

in fuzzy CMAC could be computed as:

)()(...*)(*)()( 11

2211 ij

n

injnjjj xcxcxcxcxC

(6)

where ( )ij i

c x is theth

j membership function of theth

i

input vector and nis the number of total states. The asterisk

* denotes a fuzzy t-norm operator. And there are several

kinds of t-norms such as the max, min and product operators.


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We choose the product inference method as the t-norm

operator because it is easy to implement.

Step 4. Output generation with memory weight learning

(WY):

Due to partial proportional fuzzy rules and existent overlap

situation, more than one fuzzy rules are fired simultaneously.The consequences of multi-rules are merged by a

defuzzification process. The defuzzification approach we

applied is to sum assigned weights of the activated fuzzy

rules on their firing strengths, denoted as )(xCj . The output

of network is,

))(/)((11

xCxCwy i

N

ijj

N

j (7)

The work on learning of fuzzy CMAC is to update the

memory weight according to the error between the desired

output and the actual output. The weight update rule for

fuzzy CMAC is as follows:

)(/)()(1

)1()( xCxCyym

ww iN

ijd

ij

ij

(8)

where is the learning rate, mis the size of floor (called

generalization),ydis the desired output.

The conventional fuzzy CMAC weight updating rule uses

fixed learning rate, which might make the learning process

updating too slow or too fast. In order to improve the

shortcoming of conventional fuzzy CMAC on the learning

process, an adaptive learning rate is introduced. Here, we use

the discrete-time Lyapunov function to define the adaptive

learning rate . Let the tracking errore(t)be

)()( tyyte d (9)

where tis the time index. A discrete-type Lyapunov function

can be expressed as

)(2

1 2teV (10)

Thus, the change in the Lyapunov function is obtained by

)()1(2

1)()1(

22tetetVtVV (11)

The error difference can be represented by [16]

)()(

)( tWW

tete

(12)

Using gradient descent method, we have

)(

)()(

tw

tV

mtw

j

j

(13)

Since

))(/)())((()(

)()(

)(

)(xCxCtyy

tw

tete

tw

tV Td

jj

(14)

Thus

NjtyyxCxCm

tw djj ,.....,2,1)),()((/)(()(

(15)

( ) ( ( ) / ( )1

( ) ( ( ) / ( )2 2( ) ( ( ))

( ) ( ( ) / ( )

w t C x C xi

w t C x C xW t y y t

dm

w t C x C x

N N

( ( ) / ( )( ( ))C x C x y y t dm

(16)

From (7) to (9) we have

)(/)()(

),(/)(

)(

)(xCxC

W

texCxC

tw

te Tj

j

(17)

From (10) to (17) we have

1 12 2( 1) ( ) ( 1) ( ) ( 1) ( )2 2

1 1( ) 2 ( ) ( ) ( ) ( ) ( )

2 2

V e t e t e t e t e t e t

e t e t e t e t e t e t

( )( ( ) / ( )) ( )

1 ( )( ) ( ( ) / ( )) ( )

2

e tC x C x e t

W m

e te t C x C x e t

W m

(18)

Since )(/)(

)(

xCxCW

te T

, we have

( ) / ( ) ( ) / ( ) ( )

1( ) ( ) / ( ) ( ) / ( ) ( )

2

2( )1 ( ) ( )

( ) 2 ( ) ( )2 22 ( ( )) ( ( ))

2 2( ) ( )1 2( ) 2

22 ( ( )) (

TV C x C x C x C x e t m

Te t C x C x C x C x e t m

C xTC x C x

e t e t e t m mC x C x

C x C x

e tm mC x C

2( ))x

(19)

Let 0))((

)(2

2

2

xC

xC

m

then 0V , i.e., select the

learning rate as

0)(

))((2

2

2

xC

xCm (20)

V becomes negative definite. This implies that 0)( te

for t . The convergence of the adaptive type-1 fuzzyCMAC learning process is then guaranteed. The aircraft

landing control system is locally asymptotically stable.

B. Type-2 Fuzzy CMAC

The type-2 fuzzy theorem is utilized into CMAC structure

in order to promote more accurate resolution than

conventional fuzzy CMAC. The mapping procedure of

type-2 fuzzy CMAC is similar as type-1 fuzzy CMAC. The

diagram structure of type-2 fuzzy CMAC is shown in Fig. 6.

Each phase of mapping is described as follows. TheXis an

n-dimensional input space, as shown in Fig 7. Type-2 fuzzy

CMAC uses the interval type-2 fuzzification method of the

fuzzy theorem as its addressing scheme. After the input

vector to the interval type-2 fuzzy set is being fuzzified, the

input state values are transformed to upper firing strength


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and lower firing strength, which is based on corresponding

interval type-2 membership functions. We choose the

product inference method as the t-norm operator. The jth

rules upper firing strength jc and lower firing strength

firing strengthj

c in type-2 fuzzy CMAC could becomputed as:

)()(......*)(*)()(1

21 21 ij

n

i

njjjj

xcxcxcxcxcin

(21)

)()(......*)(*)()(1

2121

ij

n

i

njjj

jxcxcxcxcxc

in

(22)

1S

2

S

Fig. 6. Diagram of type-2 fuzzy CMAC in 3-D

1x

2x

nx

dY

Fig. 7. Architecture of type-2 fuzzy CMAC network

The type-reduced set of the type-2 fuzzy CMAC using the

center of sets type reduction :

11 1[ , ]

1 11[ , ] ....[ , ] [ , ]cos

1.... 1/[ , ]

1

...c c c

N NMy y y w w w w w wl r

nj jc w

jM NMc c c n

jc

j

(23)

It is an interval type-1 set determined by its left and right end

points ly and ry , which can be written as follows [29]:

N

Rj

jR

j

j

N

Rj

jjR

j

jj

N

j

j

N

j

jj

r

cc

wcwc

c

wc

y

11

11

1

1 (24)

N

Lj

jL

j

j

N

Lj

jjL

j

jj

N

j

j

N

j

jj

l

cc

wcwc

c

wc

y

11

11

1

1 (25)

w and w are the corresponding weights of c and c ,

respectively. L and R can be obtained as follows:

Step 1.Assume that the pre-computed jw are arranged in

ascending order, i.e., Nwww ...21

Step 2.Compute ry by initially setting 2/)(jjj ccc

for Nj ,....2,1 and let rr yy

Step 3.Find )11( NRR such that 1 RrR wyw

Step 4. Compute ry withjj

cc for Rj and jj cc

for Rj and let rr yy

Step 5. If rr yy then go to step 6. If rr yy then stop

and set rr yy

Step 6. Set rr yy and return to Step 3.

The procedure for computing ly is very similar to the one

just given for ry . In Step 3, find )11( NLL such

that1 Ll

Lwyw . Additionally, in Step 2 compute ly

initially setting 2/)(

jjj

ccc

for Nj ,....2,1

and inStep 4 compute ly with

jjcc for Lj and jj cc

for Lj . The defuzzified output is simply the average ofyr

andylas

lr yyy (26)

The work on learning of type-2 fuzzy CMAC is to update the

memory weight according to the error between the desired

output and the actual output. The learning rules for type-2

fuzzy CMAC is as follows:

N

j

jjd

i

j

i

j xcxcyym

ww1

1)1()( )(/)()(

(27)

N

j

jjdi

ji

j xcxcyym

ww1

2)1()( )(/)()( (28)

where 1 and 2 are the learning rates, m is the size of

floor (called generalization) , dy is the desired output.

The conventional type-2 fuzzy CMAC weight updating

rule uses fixed learning rate, which might make the learning

process too slow or too fast. In order to improve the

shortcoming of conventional type-2 fuzzy CMAC, adaptive

learning rule is introduced. Here, we use the discrete-time

Lyapunov function to define the adaptive learning rate .

The tracking error e(t) is given in (9). A discrete-type

Lyapunov function can be expressed in (10). The change in

the Lyapunov function is given in (11). The error difference


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can be represented by (12). Using gradient descent method,

we have

N

j

jjdj xcxcyym

tw1

1 )(/)()()(

(29)

N

j

jjdjxcxcyy

mtw

1

2 )(/)()()( (30)

Since

( ) ( ) ( ) ( )( )

( ) ( ) ( ) ( )

( ) ( ) / ( )1

V t V t e t e t e t

w t e t w t w t j j j

Ny y c x c xjd j

j

(31)

( ) ( ) ( ) ( ) ( )( )

( ) ( ) ( ) ( )

( ) ( ) / ( )1

V t V t e t e t ie t wjw t e t w t w t j j j

N

y y c x c xj jdj

(32)

Thus

Njxcxcyym

twN

j

jjdj ,.....,2,1,)(/)()()(1

1

(33)

Njxcxcyym

twN

j

jjdj ,.....,2,1,)(/)()()(1

2

(34)

( ) / ( )11

( )1

( ) / ( )2( )2 1( ) ( ( ))1

( )

( ) / ( )

1

1 ( ( ) / ( ))( ( )1

Nc x c xj

jw t

N

c x c xw t jW t y y t j dm

w tNN

c x c xN jj

NC x c x y y t j dm j

(35)

( ) / ( )11

( )1( ) / ( )( ) 22 2( ) ( ( ))1

( )

( ) / ( )

1

2 ( ( ) / ( ))( ( )1

Nc x c xj

j

w t Nc x c xw t j

W t y y t j dm

w tNN

c x c xN jj

NC x c x y y t j dm j

(36)

From (21, (22), (27), and (28) we have

N

j

jT

N

j

jj

j

xcxCW

te

xcxctw

te

1

1

)(/)()(

)(/)()(

)(

(37)

N

j

j

T

N

j

jj

j

xcxCW

te

xcxctw

te

1

1

)(/)()(

)(/)()(

)(

(38)

From (9) to (12) and (29) to (38), with respect to W , we

have

1 12 2( 1) ( ) ( 1) ( ) ( 1) ( )2 2

1 1( ) 2 ( ) ( ) ( ) ( ) ( )

2 2

( ) 1( ( )/ ( )) ( )

1

1 ( ) 1( ) ( ( ) / ( )) ( )2 1



Ne tC x c x e t j

mW j

Ne te t C x c x e t j

mW j

(39)

Since

N

j

jT xcxC

W

te

1

)(/)()(

, we have

1( ( ) / ( )) ( ( ) / ( )) ( )

1 1

1 1( ) ( ( ) / ( )) ( ( ) / ( )) ( )2 1 1

2( )1 ( ) ( )1 1( ) 2 ( ) ( )2 2 2( ( )) ( ( ))

1 1

N NTV C x c x C x c x e t j j

mj j

N NTe t C x c x C x c x e t j j

mj j

C xTC x C xe t e t e t

N Nm mc x c xj j

j j

2 2( ) ( )1 21 1( ) 22 2 2( ( )) ( ( ))

1 1

C x C xe t

N Nm mc x c xj j

j j

(40)

Let 0

))((

)(2

2

1

2

1

N

j

j xc

xC

m

then 0V , i.e., we can

select the learning rate 1 in the following range


0

2

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7

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9

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0)(

))((2

12

2

1

xC

xcmN

j

j

(41)

From (9) to (12) and (29) to (38), with respect to W , wehave

1 12 2( 1) ( ) ( 1) ( ) ( 1) ( )2 2

1 1( ) 2 ( ) ( ) ( ) ( ) ( )

2 2

( ) 2 ( ( ) / ( )) ( )

1

1 ( ) 2( ) ( ( ) / ( )) ( )2 1



Ne tC x c x e t jW m j

Ne te t C x c x e t jW m j

(42)

Since

N

j

j

T xcxCW

te

1

)(/)()(

, we have

2( ( ) / ( )) ( ( ) / ( )) ( )

1 1

1 2( ) ( ( ) / ( )) ( ( ) / ( )) ( )2 1 1

2( )1 ( ) ( )2 2( ) 2 ( ) ( )2 2 2( ( )) ( ( ))

1 1

N NTV C x c x C x c x e t j jmj j

N NTe t C x c x C x c x e t j jmj j

C xTC x C xe t e t e t

N Nm mc x c xj j

j j

2 2( ) ( )1 22 2( ) 22 2 2( ( )) ( ( ))

1 1

C x C x

e tN Nm m

c x c xj jj j

(43)

Let 0

))((

)(22

1

2

2

N

j

jxc

xC

m

then 0V , i.e., we can

select the learning rate 2 in the following range

0)(

))((2

22

2

1

xC

xcmN

j

j

(44)

V becomes negative definite. This implies that 0)( te

for t . The convergence of the adaptive type-2 fuzzyCMAC learning process is then guaranteed. The aircraft

landing control system is locally asymptotically stable.

The four inputs of the aircraft are altitude, altitude rate,

altitude command, and altitude rate command and also are

the inputs for the PID controller and type-2 fuzzy CMAC.

The input of pitch autopilot U, which is the control signal of

aircraft model,is the summation of the PID controller output

PIDU and the type-2 fuzzy CMAC output fuzzyCMACU . The

conventional PID controller is used to stabilize the aircraft

and to help type-2 fuzzy CMAC in learning process, then the

type-2 fuzzy CMAC improves the performance of the

intelligent controller in severe wind disturbance condition.

At each sampling instant k, the function of type-2 fuzzyCMAC includes two phases, which are recall process and

learning process. First, type-2 fuzzy CMAC will utilize

)1( kYd and )(kY to address the corresponding memory

weights in order to generate an output fuzzyCMACU in the

recall process, where the )(kY is the output of the dynamic

aircraft model at sampling instant k and the )1( kYd represents the desired dynamic aircraft model output at the

next time step, as shown in Fig. 8. fuzzyCMACU in the recall

process is taken to be an calculation of the demanded control

signal U. And then it is integrated with the output of PID

controller PIDU to form the demanded control signal U. In

the learning process, as shown in Fig. 9, Uobtained in the

recall process is regarded as the desired output. The error we

get from fuzzyCMACUU is used to update the corresponding

memory weights stored at location )(kY and )1( kY . The

error will converge after several iterations, then the type-2

fuzzy CMAC network can compensate for the PID

controller.

type-2 fuzzy CMACU

Fig. 8. The control process of type-2 fuzzy CMAC

( 1)Y k

( )Y k

U

type-2 fuzzy CMACU

Fig. 9. The learning process of type-2 fuzzy CMAC

IV. SIMULATIONSThe aircraft starts the initial states of the ALS as follows:

the flight height is 500 ft, the horizontal position before

touching the ground is 9240 ft, the flight angle is -3 degrees,

the speed of the aircraft is 234.7 ft/sec. Successful

touchdown landing conditions are defined as follows:

-3 )(Th ft/sec 0, 200 )(Tx ft/sec 270,

-300 )(Tx ft 1000, -10 )(T degree 5,


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where T is the time at touchdown, )(Th is vertical speed of

the aircraft at touchdown, )(Tx is the horizontal position at

touchdown, )(Tx is the horizontal speed, )(T is the pitch

angle at touchdown.

Table 2 shows the results from using PID controller withdifferent turbulence speeds [15]. The conventional controller

with original control gains can only successfully guide an

aircraft flying through wind speeds of 0 ft/sec to 30 ft/sec.

The situations at turbulence 30 ft/sec are that the pitch angle

is -0.17 degrees, vertical speed is -2.19 ft/sec, horizontal

velocity is 234.7 ft/sec, and horizontal position at touchdown

is 844 ft as show in Fig. 10 to Fig. 12 . If the wind speed is

higher than 30 ft/sec, the ALS will be unable to guide an

aircraft to land safely.

Table2.Result from using conventional PIDWind speed

(ft/sec)

Landing

point (ft)

Aircraft vertical

speed (ft/sec)

Pitch angle

(degree)0 797 -2.83 -1.41

10 910 -2.55 -0.85

20 809 -2.38 -0.59

30 844 -2.19 -0.17

40 1020 -1.72 0.44

0 5 10 15 20 25 30 35 40 45-5

-4

-3

-2

-1

0

1

2

Time (sec.)

de

g.

Pitch (Solid) & Pitch Command (Dashed)

Fig. 10. Aircraft pitch and pitch command at turbulence 30

ft/sec

0 5 10 15 20 25 30 35 40 45-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

Time (sec.)

ft.

/sec.

Vertical Velocity (Solid) & Vertical V elocity Command (Dashed)

Fig. 11. Aircraft vertical velocity and command at turbulence

30 ft/sec

5 10 15 20 25 30 35 40 450

50

100

150

200

250

300

350

400

450

500

Time (sec.)

ft.

Altit ude (Solid) & Altit ude Command (Dashed)

Fig. 12. Aircraft altitude and command at turbulence 30

ft/sec

Table 3 shows the results from using type-1 fuzzy CMAC

with different turbulence speeds. This controller can guidethe aircraft to land safely through wind speed at 10 ft/sec to

90 ft/sec.

Table 3.Result from using type-1 fuzzy CMACWindspeed

(ft/sec)

Landingpoint (ft)

Aircraftvertical

speed (ft/sec

Pitch angle(degree)

10 656.1882 -1.5376 -0.878720 574.0509 -1.8942 -0.409430 855.6644 -2.5421 -0.182240 656.1882 -2.2989 0.062550 515.3814 -2.2081 0.676560 421.5102 -1.2063 2.22

70 773.5271 -1.6393 1.365980 468.4458 -2.5756 1.255990 808.7288 -2.4467 2.2739

Table 4 shows the results from using adaptive type-1 fuzzy

CMAC with adaptive learning rate. Simulations are done by

using original control parameters of pitch autopilot. The

learning rate is2

2

)(

))((

xC

xCm and the number of blocks m

is 10. This controller can successfully guide the aircraft

flying through wind speeds to 100 ft/sec as shown in Fig. 13

to Fig. 15.

Table4.Results from using adaptive type-1 fuzzy CMACWindspeed

(ft/sec)

Landingpoint (ft)

Aircraft verticalspeed (ft/sec

Pitch angle(degree)

10 843.9305 -2.5073 -0.90420 879.1322 -2.2857 -0.547130 69.4933 -2.8413 -0.094140 773.5271 -2.0937 0.104450 738.3255 -2.4378 0.255760 656.1882 -2.7763 0.86870 550.5831 -2.362 1.506280 480.1797 -2.0533 1.945790 433.2441 -1.7998 2.3901

100 620.9865 -2.7555 2.3027


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ft/sec

Fig. 14. Aircraft vertical velocity and command atturbulence 100 ft/sec


ft/sec

Table 5 shows the results from using type-2 fuzzy CMAC.

Table 6 shows the results from using adaptive type-2 fuzzy

CMAC. This controller can successfully guide the aircraft

flying through wind speeds to 165 ft/sec as shown in Fig. 16

to Fig. 18.

Table 5. The results from using type-2 fuzzy CMAC

Table 6. The results from using adaptive type-2 fuzzy

CMAC

0 5 10 15 20 25 30 35 40 45-10

-5

0

5

10

15

20

25

30

Time (sec.)

deg.



ft/sec

0 5 10 15 20 25 30 35 40 45-80

-60

-40

-20

0

20

40

Time (sec.)

ft.

/sec.

Vertical Velocity (Solid) & Vertical Velocity Command (Dashed)

Fig. 17. Aircraft vertical velocity and command at

turbulence 165 ft/sec

Wind speed(ft/sec)

Landingpoint (ft)

Aircraft verticalSpeed (ft/sec)

Pitch angle(degree)

30 703.1238 -2.2958 0.0532

50 667.9221 -2.1930 0.191470 644.4543 -2.4343 0.7688

90 562.3170 -2.0297 1.8769110 691.3899 -1.8194 2.8465

130 609.2526 -1.7036 3.6364

Wind speed(ft/sec)

Landingpoint (ft)

Aircraft verticalspeed (ft/sec)

Pitch angle(degree)

10 867.3983 -2.6675 -0.977130 996.4712 -2.473 -0.5183

50 796.9949 -1.9923 0.7827

70 550.5831 -1.9903 1.569290 163.3645 -2.5925 2.7191

110 268.9696 -2.6133 3.5923

130 480.1797 -2.1648 3.8796150 351.1069 -2.9028 3.3518

165 961.2695 -1.4312 4.8714

5 10 15 20 25 30 35 40 450

50

100

150

200

250

300

350

400

450

500

Time (sec.)

ft.

Altitude (Solid) & Altitude Command (Dashed)

0 5 10 15 20 25 30 35 40 45-30

-25

-20

-15

-10

-5

0

5

Time (sec.)

ft.

/sec.

Vertical Velocity (Solid) & Vertical Velocity Command (Dashed)

0 5 10 15 20 25 30 35 40 45-10

-5

0

5

10

15

Time (sec.)

deg.



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5 10 15 20 25 30 35 40 450

50

100

150

200

250

300

350

400

450

500

Time (sec.)

ft.

Altitude (Solid) & Altitude Command (Dashed)


ft/sec

V. CONCLUSIONSThe purpose of this paper is to investigate the use of

intelligent control techniques in the automatic landing

system, which includes the conventional fuzzy CMAC and

the fuzzy CMAC with adaptive learning rule. Tracking

performance and environment adaptive capability are

demonstrated through software simulations. The type-2

fuzzy CMAC has better disturbance adaptive capability than

conventional PID type controller and type-1 fuzzy CMAC, it

can tolerate the turbulence strength to 130 ft/sec. The

performance of the adaptive type-2 fuzzy CMAC is more

robust than type-2 fuzzy CMAC. The adaptive type-2 fuzzy

CMAC can guide the aircraft safely under the turbulence

strength up to 165 ft/sec. Stability of the proposed control

system is guaranteed by using gradient descent method andthe Lyapunov theory.

ACKNOWLEDGEMENT

This work is supported by the National Science Council,

Taiwan, ROC under Grant NSC 97-2221-E- 019-025.

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