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1 INTRODUCTIONAircraft landing gear is one of the important component

parts of aircraft. As the traditional passive gear has its own

limitations (the damping parameter cannot be adjusted), itcould only make a response in accordance with the shocks

of landing gear and the vibration of track. These

disadvantages cause to the low performance of landing

gear, and they will easily cause problems. At present, the

technology of main landing gear on the application of

control technology is a semi-autonomous control Techno-

logy. Semi-active control is a kind of control method which

is between the active control method and passive control

method, and its control performance is close to full active

control technology, but it has no additional power source.

It only needs the weak power control system according to

the load, speed and road conditions changes to adjust the

internal parameter of structure, making the structuralparameters the best condition. It is a kind of control method

of parameter [1] to [4].

Magnet-orheological fluid (Magnet-orhelological Fluids,

referred to as MRF) is a kind of controllable fluids.

Recently, it is a kind of new materials. Without the effect of

external magnetic field, the magneto-rheological fluid will

have good mobility. With the strong effect of magnetic

field, the magnetic-orheology liquids can be continuous and

reversibly change in a high viscosity, low flow of Bingham

Body at the millisecond level time, and makes its apparent

viscosity increases in more than two orders of magnitude.

Magnetic field will appear similar to the solid mechanics

properties. The MR damper which makes use of this

magnet-orheological fluids nature is a very promising

development direction of the semi-active control damper

[5][6]. Themagneto-rheological damper has been used in

China and other countriesnow. For example, MR damper

This work was supported in part by Program for the Funds of NationalScience of China (Grant Nos. 61203087), the Liaoning EducationDepartment Plan Project of China (No. L2010426), and the Liaoning

Students Innovation Training Plan Project of China (Nos. 201210143012,2012106).

can be served as the structural anti-seismic damper. The

anti-seismic damper and car seat shock absorber are all

developed by American Rhodes company [7]. Because MR

damper has shown good performance, it has been applied in

the field of Aeronautics for many times and has obtained

good damping effect. And some foreign countries have

applied it in the helicopter rotor system [8].

Fault tolerant control is a kind of technology that is

developed for improving the reliability of systems.

Fault-tolerant control idea was first proposed in 1971 by

Niederlinski [9]. In 1980, Siljak published articles about

reliable stabilization, and it had the extremely vital

significance for the development and promotion of

fault-tolerant control research [10]. Now, the fault-tolerant

problem is divided into two research directions, which are

active fault-tolerant control and passive fault-tolerant

control [11]. In 1993 and 1997, Professor Patton has written

two representative articles about the fault-tolerant control.

In the articles, the fault-tolerant control is to be in the faceof the problems which have been analyzed, and put forward

the methods to solve the problem [12][13]. In the domestic

research, Professor Ye Yinzhong first published and

summaried fault-tolerant control [14][15]. Then, in China,

The scholar have published a series of articles on

fault-tolerant control [16]~[19]. Now, fault-tolerance

control has been widely used in many industries including

chemistry, aviation technology, aerospace technology,

robot technology, and so on.

Due to good controllability, magnet-orheological damper

has already been used for aircraft landing gear in foreign

countries, and it achieves good damping effect in the

take-off and landing. But the aircraft landing gear oftenworks in larger impact load and components structure

approach or exceed the design limits of the state, so the

landing gear is easily to cause malfunctions.

The main types of landing gear failure has included the

component deformation, the parts in larger impact load

causes by partial loss of actuator, and the oil cylinder

damages to cause MRF fluid leaks , etc. When a fault

occurs, the performance of landing gear will be severely

Fault-tolerant Control for Semi-autonomous DamperYi-bo Li

1, Bin-Bin Gao

1, Wei Guan

1

1. School of automation, Shenyang Aerospace University,110136E-mail: [email protected]

Abstract: This paper studies the problem of designing adaptive fault-tolerant controller for semi-autonomous control

aircraft landing gear, and the magneto-rheological damper is used as shock absorber of aircraft landing gear. Thedampening system adjusts damping force to reduce aircraft landing impact load and oscillation frequency according tothe real-time feedback to ground. When the plane lands, the plane often makes a big impact load, It is very easy to causethe damage of actuator unit and important for the safety of the aircraft. This paper uses H-infinity and fault-tolerantcontrol to reduce influence of landing gear actuator fault and have ability of anti-disturbance, And good control effect canget from the simulation.

Key Words:Landing gear, MR fluid damper system, fault-tolerant, semi-autonomous control, H-infinity control

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affected. Take-off and landing of aircraft often requiredamping system with high control accuracy, otherwise itwill easily cause the crash accidents. So, for the safety ofthe aircraft, the anti-disturbance ability of landing gear hasa very important meaning. The application of fault-tolerantcontrol in aircraft landing gear is very important for thestudy of taking-off and landing planes.

The first part of this paper is mathematical modeling of theaircraft landing gear. The second part is semi-autonomous

control of the landing gear model which had been builtgoes on with fault-tolerant control. Through detects realtime values of the state variables to estimate the adaptivelaw, the actuator adjusts parameters to make the systemstable performance. The third part is simulation results and

principle analysis of the system.

2 MECHANICAL MODEL OF MR DAMPERON THE AIRCRAFT LANGING GEAR

The buffer and tire of landing gear are important parts ofbuffer units, when the plane takes off and lands. Gooddamping performance and control performance aredemanded by the plane. As magneto-rheological damper

shows good shock absorption and control characteristic, itis applied in the landing gear shock absorption device.Here, the magneto-rheological damper and spring serve asthe damping device. Damping device consisting ofdamping system must be used with good control algorithmto ensure the safety of aircraft landing, so the research ofcontrol algorithm becomes a very important problem forlanding gear system with shock absorption. Controlalgorithm that needs to be used on the accurate model canguarantee good performance for closed-loop system. Here,the first step is to be modeling precise landing gear dynamicmode [19]. System dynamic model is given by usingdynamics and kinematical principle. The differentialequation is obtained and processed from the model. Firstly,

conduct the classification according to the stress andmotion characteristics of the landing gear parts. Then, makean introduction to establish the model of landing gearaccording to the mechanics of relevant modelcharacteristics.

First of all, Classification and equivalent model are neededto deal with according to their mechanical characteristicsand movement features.

Fig 1. Half autonomous landing gear the linearization of the simplifiedmodel

In figure 11M is the mass which is above buffer barrel

wall of the air spring ( including fuselage, wing, buffer

barrel wall, etc.).2M is the mass which is below air spring

on the landing gear ( including landing gear tires, pistonrod, support frame, etc. ).

Here, some mechanical model assumptions is needed tosimplified the model.

(1) All of the force which effect on the landing gear partscanbe equivalent to effect in vertical direction.

(2) Neglect the length, which deviates from the center lineof haft and bumpers.

(3) The gravity center of Buffer to with stand mass isdetermined by intersection of the buffer and trunnioncenterline.

(4) 1 can be idealized to concentrate on the rigid bodynearby the trunnion.

(5) Here, only consider the level deflection deformation ofthe buffer structure (anteroposterior direction), and theother deformation of the buffer structure ignores.

(6)2M concentrates on the axle in ideal condition. Bogie

landing gear concentrates on the frame beam.(7) Multiple tire characteristic are equivalent to one tire

characteristic in ideal condition.(8) Regard stiffness of the frame beams and tire stiffness

together.For modeling of aircraft landing gear, this article willconsider the following aspects of the force: all the forcewhich is generated by buffer pillar in the axial direction, theforce which is generated by air spring, the damping forcewhich is generated by hydraulic oil, the frictional forcewhich is generated by the buffer, The restricted force whichis generated by the buffer structure, the force which isgenerated by tire in the vertical direction, the force which isgenerated by tire in the horizontal direction.Analyze the simplified model of the landing gear. Thefollowing the differential equations of damping system can

be given

1 1 1 2 1 1 2 1

2 2 1 2 1 1 2 1 2 2

( ) ( )

- ( )- ( )-K Z -

M Z C Z Z K Z Z U

Z C Z Z K Z Z U

= + +

=

(1)

5 4

1 17 10 / ; 5 10 sec/K N m C N m= = 6

2 3.2 10 /K N m=

1 2 1, ,K K C are the constant which are obtained from the

landing gear system model.1

U and2

U are the

semi-autonomous control force. Here,1

Z and2Z are the

displacements of1M and 2 in the vertical direction

separately, when the plane lands.

The landing gear system is single input and multiple output.

The input is the semi-active control U .The output are

1Z ,

1Z ( the speed of 1M ), 2Z and 2Z

( the speed of2

).

Then, It can be expressed by using the following system.

Z AZ BU

Y CZ

= +

=

(2)

And, applies parameters of the formulaError! Reference source not found. to the equation ofstate (2), the following equations can be obtained.

1 1 2 1 2

2 1 2 1

2

2 2 28 28

60.5327 60.5327 847.4576

4721.5496

Z Z Z Z Z U

Z Z Z Z

Z U

= + + +

=

+

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The following downgrade process is needed to apply thestate of the equation (2). Then, the state of equation can bewritten

( ) ( )x t Ax t Bu

y Cx

= +-

=

(3).

Here,Zof formula (2) is replaced by x , U of formula (2)is replaced by u .

0 1 0 0

28 2 28 2

0 0 0 1

847.4576 60.5327 4721.5496 60.5327

A

=

0

1.0000

0

1.0000

B

=

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

C

=

, ,A B C are based on the parameters derived from the

formula (2).

3 CONTROLLER DESIGNWhen the plane lands, the Landing gear often produces astrong impact load so that it likely causes damage to theparts of the landing gear actuator. For example, as theimpact load causes damage to the magneto-rheologicalbarrel wall, the magneto-rheological oil will leak out. Theshock load causes damage to the mechanical componentsparts. Then, the aircraft landing gear cans not be normal towork and the loop-system may be not stable. Aircraftlanding gear is the most accident-prone, so it needs a highdemands for gear failure-resistant capability.When the actuator fault occurs, the aircraft can landnormally and have a strong ability of the anti-disturbanceat the same time. Through detects of the real-time state

variable of the damping system, controller regulates themethod of adaptive law to adjust the control algorithm tominimize impacting. The actuator will ensure the systemstable.First, systematic influence is considered to the landing gearshock .The following state of the system equations can beget:

1

21

( ) ( ) ( ) ( )

( ) ( ) ( )

x t Ax t B w t Bu t

y t Cx t D w t

= + +

= +

(4)

Where, ( )x t represents the system state of the landing gear.

( )u t is the semi-autonomous control force of landing gear

damping system. ( )w t is the disturbance inputs2[0, ]L ,

which is generated by the landing gear damping system.And the disturbance is inevitable, when the plane lands.

Because the system is not general, let21 0D = . At the same

time, make [ ]1 1 1 1 1T

B = , to verify that the

disturbance signal effects on the stability of the system. Theparameters of the system matrix A, B, C are the coefficientmatrix A, B and C of the system (3).The actuator fault model should be considered that thedamper system may produce.

( ) ( ) ( )F ji i iu t I u t = 0j j j

i i i

1i m= " , 1j L= " (5)j

i represents the fault occurs in the i actuator and in the

j fault mode. L is the total number of the possible failure

mode ,such as landing gear oil spills or actuator component

damage. and are the upper and lower bound of the

failure degree of actuator.

The problem which is in the normal working state, or in astate of partial failure. It is not including completely failure

situation of the actuator ( 1ji ) . Here, the signal is

obtained by the landing gear actuator in fault mode. Theformula can express:

( ) ( ) ( )Fu t I u t = , 1[ ]m " (6),

andcan represent the 1[ ]mdiag = "

The state equation of actuator of the failure mode can be gotfrom (5) and (6),

1

1 12

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

x t Ax t B w t B I u t

z t C x t D I u t

= + +

= +

(7)

His used to design feedback controller for aircraft landinggear fault-tolerant state. The structure of the landing gearshock absorbers is designed so that closed-loop system isnot only can be kept stable in the normal state, but also canbe kept stable in the fault state.Controller reorganization becomes as follows:

0( ) ( ( )) ( ) ( ( ( )) ( ( ))) ( )a bu t K t x t K K t K t x t = = + +

(8)

1 1 ( ( )) ( )a aK t K t = and 1 ` ( ( )) ( )b bK t K t =

where1

( )t is used to estimate of 1 the parameters ( 0K

1aK and

1bK of controller gain are needed to design.

The following equations of damping system can be

rewritten:

1

1

0 1

1 12

( ) ( ) ( ) ( ) ( )

( ) ( )

( ( ) ( )) ( )

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

a b

x t Ax t B w t B I u t

Ax t B w B I

K K t K t x t B w

t C x t D I K t x t

= + +

= + +

+ + +

= +

(9)

At the same time, the equation can be obtained too.

0

0

( ) ( )

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

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

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

a b

a

a b

I u t

I K K t K t x t

I K K t x t I t x t

I K x t I K x t

= + +

= + +

+ +

(10)

where ( ) ( )t t

= .Though ( ( ))aK t

and ( ( ))bK t

have the same forms, we deal with them in different way,which gives more freedom and less conservativeness.

Denote ( ){ } { }1 1 : min( ) min( )j j

p m = = "

n is H 's performance index ,when the actuator of

dampening system works normally or faultily.Theorem 1 [21]

Let 0f> and n 0> . If there exist 0X > 0Y , aiY , biY

1i m= " and a symmetric matrix with

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11 12

12 22

T

=

and11 , 22

n NnR , such that following inequalities

hold:

22 0, 1ii i m = " (11)

11 12 12 22( ) ( ( )) ( ) ( ) 0T + + +

(12)when the system is in normal work and 0 =

0 1

1 2

0a T T

T

N ZU U G G

Z Z

+ + = " is constant. Pr { }oj isprojectionoperator.The projection operator estimates value of ( )i t to

project into the[ , ]i i

.

When the system is in normal circumstances work, the

closed-loop system (7) is asymptotically stable. 0= and

(0) 0x = 2

2

010

(0)

( ) ( ) ( ) ( )

mT T i

ni i

z t z t dt w t w t dt l

= +

.

When the system is in abnormal circumstances work,

where { 1 L = " and (0) 0x = .2

2

010

(0)( ) ( ) ( ) ( )

mT T i

f

i i

z t z t dt w t w t dtl

=

+

The parameter is

1( ) [ ( ) ( )] ( ) ( )m i i it diag t t t t = = "

Then the controller gain is given by

0 1 ( ) ai biK K K K = + + (24)

Algorithm 1Step 1 Solve the following optimization problem:

min n fa b +

. .s t (13) (25)

Here, 2n n = and

2

f f = . a and b are weighted

coefficient. The normal working time of system is more

than the fault time, so a b> . With the optimal solutions

n , f , optX X= , 0 0optY Y= , ai aiopt Y Y= and bi biopt Y Y= ,go

to step 2.Step 2 Determine the controller parameter matrices

1

0K XY

= ,1K Xai aiY

= and

1K Xbi biY

= .

Step 3 Determine the adaptive law (24).

Then, an adaptive fault-tolerrant controller is designed.The formula (15), (16) of theorem 1 is used to the aircraftlanding gear system.

T

0 0 0( ) ( ( ) )aN AX B I Y A X B I Y = + + +

1 1 1 12

1( )

T T

a a

n

B Y B Y B B

+ + + (26)

T

0 0 0( ) ( ( ) )N AX B I Y AX B I Y = + + +

1 1 1 12

1( )

T T

a a

f

B Y B Y B B

+ + + (27)

The system model is used in the formula (16) to (21) ofTheorem. And the following matrices can be given out.

1 0 0 00 1 0 0

0 0 1 0

0 0 0 1

G

=

1 1 1[ ]a bZ B Y BY= +

1[ ]U C X= 1 4 4 ( ) [ ]diag I =


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1 1 1 4

1 1 4 1

2

4 1 4 4

1 4 4 4

( ) ( )

( ) ( )

T T

b b b b

T T

b b b b

B Y B Y B Y B Y

Z

B Y B Y B Y B Y

=

"

# # #

"

and

0 1 0 0

28 2 28 2

0 0 0 1847.4576 60.5327 4721.5496 60.5327

A

=

0

1.0000

0

1.0000

B

=

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

C

=

X Y ,1aY and 1bY are that seeking unknown parameter.

Set 10a = and 1b = in the algorithm in LMI Toolkit, theoptimum solutions are

0.3187 1.0491 0.0423 0.0705

1.0491 92.5463 0.4135 114.33760.0423 0.4135 0.0256 0.5361

0.0705 114.3376 0.5361 188.6121

X

=

[ ]0.0000 6.2088 0.0000 6.2088Y = 1P X=

1

0K XY

= 1a1K Ya1*X

= 1b1K Yb1*X

=

After calculates the above formula, the parameters can beobtained.

5.6318 0.3063 10.9423 0.1567

0.3063 0.0603 0.7553 0.0345

10.9423 0.7553 63.3028 0.28200.1567 0.0345 0.2820 0.0255

P

=

0 [-0.9317 -0.1603 2.9513 -0.0562]K =

1K =[-0.2273 -0.0391 0.7200 -0.0137]a

1K =[-1.2150 -0.2090 3.8487 -0.0733]b

The controller parameters can be got

0 1 1 1 1 ( ) a bK K K k = + + (28).

il is constant of the control gain,and let 1000l =

The formula (23) can be expressed as1

11 a1L ( )[ + ] ( )Ti bl x t PB K PBK x t = (29)

Pis the value of the formula (28),1

B is state B of thedampening system.

,

1 [-0.2273 -0.0391 0.7200 -0.0137]aK =

1 [-1.2150 -0.2090 3.8487 -0.0733]bK =

4 ANALYSIS OF SIMULATION RESULTSBecause the system function is include ( ) ( )y t Cx t= with

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

C

=

,

four states variables system can be observed.

Fig 2. state variable (1)x of the system




Obviously under the disturbance signal ( ) 1w t = , the

close-loop system with adaptive H

controller is still

stable. It can be seen from the figure 2 to figure 5, and thesystem will be stable after a period of tme to adjust. The

control effect will be better, when the actuator fault occurs.

5 CONCLUSIONWhen the plane lands, the landing gear often make a bigimpact load. The parts of landing gear are very easy todamage. Such as the leakage of magnet-orheologicaldamper oil cylinder oil, spring damage, etc. Here, the planecan normally land, when the fault occurs. Here the designswere developed in the framework of the LMI approach,which could guarantee disturbance tolerance ability and

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adaptive H

performances of closed-loop systems in the

cases of actuator failures. Fault-tolerant control system will

be able to maintain stability, when there is a disturbance

inputs. Conclusions can be draw from the figure to figure

.What the curve shock a few times and tend to be

convergence can get from the Figure. When the actuator

fault of landing gear occurs, the plane can maintain a good

performance index. The plane can also be safe landing.

REFERENCES

[1] D. Yadav, R. P. Ramamoorthy, Nonliner Landing GearBehavior at Touchdown, Journal of Dynamic System Measurement and Control, Vol.133, 667-682, 1991.

[2] J. R. McGehee, H. D. Carden, Improved aircraft dynamicresponse and fatigue life during g round operations using

anactive control landing gear system, Aircraft Systems andTechnology conference, 1978.

[3] Mehdi, Ahmadian. On the Isolation Properties of SemiactiveDampers. Journal of Vibration and Control, Vol.5, No.2,217- 232, 1995.

[4] J. S. Weng, Fuzzy semi-active control of vehicle suspensionsystem based on magnet-orheological damper, NanjingUniversity of Aeronautics and Astronautics, Nanjing, China,

2001.

[5] J. Li, H. L. Zhang, Study and Application ofMagnetorheological Fluids. Journal of shanghai University,Vol.10, No.1, 21-29, 2004.

[6] S. X. Zhu, P. Jin, Aircraft landing gear on the application ofdamping control technology, Journal of Civil Aviation FlightUniversity of China, Vol.18, No.3, 3-7, 2007.

[7] J. X. Wang, G. Meng, Magnet-orheological fluid devices andtheir applications in mechanical engineering, Mechanicalstrength, Vol.23, No.1, 50-56, 2001.

[8] H. P. Wang, C. H. Cai. Analysis mode of amagnet-orheological damper

Machinery Design &ManufactureVol.2, 33-34, 2006.

[9] A, Niederlinski, A Heuristic approach to the design of linearmultivariable interacting control systems, Automatic, Vol.7,No.6, 691-701, 1971.

[10]D. D. Siljak, Reliable control using multiple control systems,International Journal of Control, Vol.31, No.2, 303-329,1980 .

[11]J. S. Eterno, D. P. Looze, Weiss J. L. Willsky. A. S, Designissues for fault-tolerant restructurable aircraft control,

Proceedings of 24th Conference on Decision & Control, FortLauderdale, 900-905, 1985.

[12]R. J. Patton, Robustness issues in fault tolerant control,Proceedings of International Conference on Fault Diagnosis ,

Toulouse, France, 1081- 1117, 1993.[13]R. J. Patton, Fault-tolerant control: the 1997 Situation,

Proceedings of IFAC/IMACs Symposium on Fault Detection

and Safety for Technical Process, Hull, England, 1033-1055,1997.

[14]Y. Z. Ye, R. F. Pan, J. W. Sun, Design multivariable stablefault-tolerant controller, The collected papers of 1th processcontrol Conference, 203-209, 1987.

[15]Y. Z. Ye, R. F. Pan, W. S. Jiang. Review and prospectcontrol system fault-tolerant controller, The collected papersof 2th process control Conference, 49-61, 1988.

[16]Y. L. Zhang, L. D. Xu, Dynamic system fault diagnosistheory and application, National University of Defense

Technology Press , Beijing, China, 1997.[17]X. Wen, H. Y. Zhang, L. Zhou, Control system fault

diagnosis and fault-tolerant control, China Machine Press,Beijing, China, 2000.

[18]D. H. Zhou, Y. Z. Ye, Modern fault diagnosis andfault-tolerant control, Tsinghua University Press, Beijing,China, 2000.

[19]F. L. Wang, Y. W. Zhang, Fault-tolerant control,Northeastern University Press, Shenyang, China, 2003.

[20]W. Fan, Research on Simulation of Semi-Active Control ForAircraft Landing Gears during Landing Process, Nanjing

University of Aeronautics and Astronautics, Nanjing, China,2006.

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