Optimal Design of the Aircraft ABS Controller

ELSEVIER

Copyright © IFAC Control Applications of Optimisation. VisegrM, Hungary. 2003

IFAC PUBLICATIONS www.elsevier.comllocatelifac

OPTIMAL DESIGN OF THE AIRCRAFT ABS CONTROLLER Han Young Ko, Deok Ju Ha, Nak Yun Choi Agency for Defense Development, P.O. Box 35-3, Yusung, 305-600, Republic of Korea

Abstract: The main control objective of an aircraft ABS(Anti-skid Brake System) is to continuously adjust brake pressure to maintain optimum brake torque. This optimum level should balance tire and runway friction at its peak value, which is conveniently done by controlling the wheel slip ratio around the peak of the friction coefficient(~)-slip ratio(s) curve during ABS maneuvers. It influences not only the taxing distance of an aircraft, but also the strength and the fatigue life of the landing gear system. Difficulties in designing an ABS controller are due to the nonlinear characteristics of braking system dynamics, the time-varying nature of the system components, and the unknown environmental parameters. Furthermore, as an optimal control problem, this is currently intractable because of the large uncertainty in the dynamics. In this paper, an ABS control algorithm is developed with a 5-D.O.F. aircraft dynamics model based on the landing dynamic equations and the ABS digital control unit(DCU) is designed to accommodate the anti-skid control algorithm. Also the design and implementation of real-time HILS system for development of the aircraft ABS DCU are presented. Developed ABS DCU is evaluated and tested with proposed HILS system on the several runway conditions. Copyright@2003 IFAC Keywords: Aircraft, Antiskid, Control, Digital, HILS, Optimization

dynamics model based on the landing dynamic equations. The dynamic model is composed of a aircraft system block(named big contour) and a brake module(named little contour) by simulation s/w. The big contour represents the interactions of forces in airframe, nose and main landing gear, and engines on the e.G. The little contour represents interactions of wheel, braking units, hydraulic systems and a controller. The DCU is constructed to accommodate the ABS control algorithm. HILS applications in the aircraft industry are becoming popular due to the push to reduce development time and cost for air vehicles by providing a real-time coupling of the physical hlw and computer simulation(Svaricek, 1998). In this framework, h/w components are interchangeable with S/W models allowing experiments to be run to study a particular subsystem without requiring an aircraft to run the real test. In this paper, the design and implementation of real-time HILS system with MatLab/Simulink for development of the aircraft ABS DCU are also presented. Developed ABS DCU is evaluated and tested with proposed HILS system on the several runway conditions.

I . INTRODUCTION An aircraft has a large amount of kinetic energy on landing. When the brakes are applied, the kinetic energy of the aircraft is dissipated as heat energy in the brake disks, and between the tire and the ground. In the past few decades, ABS systems and electronic control units of many different designs have been mounted in many types of aircrafts. The aim of an aircraft ABS is to improve the braking performance by maintaining the tire braking torque at or near its maximum value. Especially a maximum braking force is of major importance when the runway is slippery and/or very short. On a dry runway, wheel skidding must be avoided in order to minimize the wear of the tires and prevent them from bursting. The objective of this paper is to develop an ABS DCU and a related HILS system for the newly developed trainer aircraft. The design of an anti-skid controller requires a model of the braking system dynamics under realistic operating conditions(Somakumar and Chandrasekhar, 1999). In this paper, an ABS control algorithm is introduced with a 5-D.0 .F. aircraft

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The horizontal and vertical projections of aircraft aerodynamic forces and the aerodynamic pitch moment can be described by non-linear equations as follows :

2. AIRCRAFT LANDING DYNAMICS The design of an anti-skid controller requires a model of the braking system dynamics under realistic operating conditions. The dynamics of the braking system are mainly influenced by the frictional characteristics between the tire and the runway. In this paper, a dynamic model of 5-D.O.F. for aircraft braking is developed. The dynamic model is composed of an aircraft system block(named big contour) and a brake module(named little contour).

= X: COS r - Z: sin r Z A = X: sin r + Z: cos r MA = CmbaSwng XA

(4) (5) (6)

z:

where, x: and is the drag and lift, ris the angle, Cm is the coefficient of the pitching moment, ba is the characteristic length and Swng is the wing area.

2.1 The big contour and aircraft dynamics The horizontal and vertical projections of the aircraft engine thrust vector and its pitch moment are described by equations:

The big contour that is shown in Fig.l represents the interactions of forces in airframe, nose and main landing gear and engines on the c.G.(Papadopoulos and Kapadoukas, 1998).

XE =Fcosp.n

-

= Fsinp.n

ZE

ME =FLn

FoIC'ZS'lotJIpa'ItS

(7) (8)

(9)

where, F is the engine force, P is the thrust vector angle, n is the number of engines and L is the arm of the thrust vector from the e.G. Nose and main landing gear show a non-linear characteristics because of the oleo-pneumatic shock-absorber damping features. The responses are calculated according to expressions: Fig. 1. Aircraft system block(big contour)

X

ng

= Fam(sin 0 + f.1 cos 0)

g

zn = Fam cosO g ng M ng = X z + Zn Xng

At the braking stage, the aircraft is loaded by aerodynamic forces and moments (XA, ZA, MA), total aircraft engine thrust forces and moments (XE, ZE, ME), nose landing gear response forces and moments (X ng , Zng, Mng) and main landing gear response forces and moments (X mg , Zmg, Mmg). The airframe dynamic model is described by the system of 6-order differential equations as follows (Stubbs and Tanner, 1980): 2

d

:

dt

=_l_[X A+XE +xmg +xng]

(11 ) (12) (13)

(14) (15)

where, Fam is the nonlinear shock-absorber force and ng , mg is the abscissa of the NLG and MLG

x x

(1)

attaching point.

mp!

d 2z 1 _=_[ZA +Z£ +zmg +zng]_g

dt

xmg = Fam (sin 0 + f.1 cos 0) g Zm = Fam cos 0 g M mg = X mg z+Zm xmg

(10)

2

2.2 The little contour and braking dynamics (2)

m p!

(3)

The little contour that is shown in Fig.2 represents interactions of wheel, braking units, pressure control system(RPCS) and ABS control unit.

where, x and z are horizontal and vertical coordinates, () is the pitch angle, mp! is the aircraft mass, Jp! is the aircraft MOl relative to the lateral axis.

A reflection force on contacts between a tire and a runway is shown in Fig.3. Here, The Fb is brake force and the Fs is friction force . The friction force of the wheel is described as :

d2~ =_l_[M A+ME +Mmg +Mng] dr

Jp!

220

Fs

= JisZ

mg

module is composed by electro-hydraulic control valve, pipeline and hydraulic cylinder like Fig. 5.

(16)

,·c · . ' ~:E " """ " '- ~

where, j.J. is the friction coefficient.

07

- - • . . _., : "- - , - _.

06

:'

OS

-

- - - -

.L

::IlD4 / DJ , o 2 - ~'. - o~ ' . _..

-'

-

;

...;

' .4

: : •

~03

;

02

11',

_. - - - - - . - _..... . _;

0'

- . . _.

. . ..

- . - • _.

- -- .•

-

..

,

I

- - - - - - . .. . --: ,"-;- .......- - ---: - - . . . - ". .. .. :

- -

• -

- -

•

'.

-

-

-;

:

o

' ,

I

= 0.8

(b) Ilmax = 0.6

(c) Ilmax = 0.4

(d) Ilmax = 0.2

(a) Ilmax

-

-,' "

l~okh,

IOKe

13ig Conlour

Fig. 4. The curves of friction coefficient Fig. 2. Brake module(little contour) Simple models of the hydraulic system are used for the study of the entire aircraft control system. The flow rate in the hydraulic cylinders of the brake is defined by equation:

The friction coefficient is a function ofthe wheel slip ratio(s), which is defined as the relative difference between the aircraft speed and the translational wheel speed(Padovan and Padovan, 1994):

(l8)

(17) where, Sbr is the area and Xbr is the displacement of the hydraulic cylinder piston. where, (J)fr

{J)w

is the braking wheel angular velocity and The piston dynamic model in cylinder can be described by the second-order ordinary non-linear differential equation:

is the angular velocity of non-braking wheel

~ ~

where, hbr

mbr

is the mass of the brake movable parts,

is the viscous friction factor,

F, (Ph,)

is the

non-linear brake pressure, F2 (xbr) is the brake disk placement and Rbr is the dry friction force.

Fig. 3. Friction force between a tire and runway

ElectrcrHydraulic Conlr~ Valve

Experimental data show that the friction coefficient depends on the condition of the runway surface. If the runway is dry the maximum value of the friction coefficient is about 0.7 - 0.8 and wet or icy it is about 0.2 - 0.3. Generally, as the slip ratio increases from zero, the friction coefficient first ascends and then proceeds to descend. The stopping distance can be shortened effectively if the slip ratio is kept between 0.05 and 0.2. In this paper, the curves of friction coefficient are presented like Fig. 4. (a)-(d).

2.3 The pressure control system and brake model Fig. 5, The pressure control system

The hydraulic pressure control system in the brake

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reference (pb·) and the brake pressure (Pb) are fed on Brake Pressure Control block. And the valve current reference (I·) and the valve current (I) are transmitted to Current Control block and then the valve current (I) is fed on Hydraulic Brake System block and finally the brake pressure (Pb) is transferred to Aircraft Dynamics block.

The flow rate at the pipeline inlet is a function of displacement of the electro-hydraulic control valve and can be described as:

_ Qi -

{f(XJ~I- PPi.. . ... ··(X ~ 0) z

(20)

f(X z )5:···· ··(X z < 0)

Table I. The situations for ABS control algorithm

is the displacement of the control valve, f(X z > is the flow rate, p", is the pipeline pressure and Pi is the evaporation pressure.

Situations

Notes

lE

Blocking of pressure feeding until over speeding of the wheels

2E

Forbid of anti-skid working

The brake simulation model represents hysteresis of the brake static characteristic, dynamic loss during pressure feed and release. Fig. 6 shows hysteretic loop of brake characteristics.

3E

Forbid of working by deceleration

4E

Braking operation by deceleration

5E

Braking operation by skidding

6E

Pressure drop to return pressure

7E

Pressure correction

8E

Shelf endurance

9E

Searching pressure increase

IOE

Pressure increase

where,

Xz

.s f1

.. :::. .. cD c:

E

o

~

I / /I

Decrease/

/

Increase

].',.'[1:' ,~.~~

!~; l~~tlj'

Brake Pressure [psi]

. ./

Fig. 6. Hysteretic loop of brake characteristics 3. ABS DCU DESIGN

Fig. 7. Example of applying the situations

3.1 Anti-skid Control Algorithm

The control algorithm determines presentation of the control unit's output signals depending on incoming signals and commands during operation of the unit in brake mode. Several situations (or Events) are defined to depend on conditions of incoming signals and commands in brake mode on runway. The ABS DCU determines a situation and then generates a control signals. The situations for each anti-skid control step are shown in Table I. The ABS control algorithm is composed of 10 situations. Situations of brake prohibition depending on aircraft conditions are lE, 2E and 3E. Situations of braking operation depending on deceleration and slip ratio are 4E and SE. An example of applying the situations is shown in Fig. 7.

Br"

!

i

ABS Control

The control scheme and data transfer between each blocks are shown in Fig. 8. The pilot command (Br·) and wheel velocity (Vw) are firstly transferred to ABS Control block and then the brake pressure

Pb·

I

Brake Pressure Control

I

Valve Current Control

•

+ +

I

Aircraft Dynamics

I

I

I

Hydraulic Brake System

+

I

I·

I

Fig. 8. The control scheme

222

+

X

I

Pb

Vw

I

The loop including the hardware and virtual aircraft model is closed by the use of data acquisition and processing board. To reduce computational burden due to the rigidity of hydraulic unit comprising brake system, the actual hydraulic brake assembly is taken from the target aircraft. And as an efficient simulation platform, the proposed HILS system includes the braking behavior from the pilot for later expansion to the MILS. The proposed HILS system allows the investigation of not only the dynamic behavior, but also hydraulic response of the aircraft with a complete assess to all system parameters and state variables. In this work, DSP and alpha-chip processor board are used to perform real-time simulation.

3.2ABSDCU The ABS digital control unit(DCU) is designed and manufactured to accommodate the anti-skid control algorithm. The main processor of ABS DCU is TMS320C240-20MHz. The control unit has analog I/O to interface speed sensor, pressure sensor and etc. as well as digital I/O to interface 2SVDC-relays. The hardware specifications of ABS DCU are shown in Table 2. Table 2. Specification of ABS DCU Items

Specifications

Main Processor

TMS320F240 - 20MHz

AID

10 bit, 6.1 us, 6 ch.

D/A

8 bit, 7us, 5 ch.

PWM Output

10 KHz, 2 ch.

Speed Sensor Signal Input

400 - 5.2 KHz, sin wave, 2 ch.

Digital Input

28 VDC, II ch.

Digital Output

28 VDC, 5 ch.

Control Period

< 2 ms

Power Consumption

< 50 W

The s/w part of the HILS system is mainly composed of MatLab and ControlDesk packages. Several initial data is applied to test. The friction coefficient is the most important parameter among initial data. The developed system is simulated to depend on some friction coefficients from dry runway (~== O.S) to wet or icy runway (Ilmax == 0.2). At touchdown, the model aircraft has a speed of about SO knots, and the maximum speed for braking is about 60 knots. So a beginning velocity of ABS control algorithm is 60 knots and the ending velocity is 10 knots. Test results are presented in Fig. 10 - 13 . A phenomenon of wheel skid is more occurred on wet or icy runway than dry runway. Total time for brake is more needed on wet or icy runway than dry runway.

4. HILS SIMULATION The HILS system makes it possible for designers to assess the capabilities of the control scheme long before the actual tests are carried out, boosting the grade of innovativeness and providing more flexibility incorporating various control techniques. Fig. 9 shows the h/w composition of real-time ABS HILS system, which includes a host PC, a simulation system, an 110 interface, an ABS DCU, and a brake system.

1.0

90

BO

0.8

2io 70 ~ 60

0.6

Z;50 ~ 40 ~30

20

0.2

u...__.......-'-__........ -. .- ......._ _ 0.0 2 3 456 7 8 9 10111213141415161718 Trne Cs]

Simulation System

Host PC

• os I003 OSP Board • OSIOO4 Alpha-chip Board • DS2302 Signal Generator Board • OS2201 110 Board

(lntel Pentium 111.5(0)

Fig. 10. Results on Ilmax = O.S

so

• Hydraulic Brake System • ABS control Valve

• Pressure Sensor

~L-

___

VII •• coalrol

hII

1.0

Ell

Bnk.

Brake System

.~

(jj

0.4

-::~ D

uno

08

.><

06

g9)

_ _ _--'

Z;5J

04

~3J

~________~~L-____A_B_S_D_C_U____--,

02

aJ 10

o

I 2 3 4 5 6 7 8 9 101 I 12131415 1617 1819 Trne [s)

Fig. 9. Configuration ofHILS system Fig. 11. Results on Ilmax = 0.6

223

.~

(jj

g40

Wheel speed signal

1.0

90 80

~8


g6Q

~6

~

~50

g 40 ~30

Control Scheme. International Conference on SIMULATION, Conference Publication No.457, pp. 176-181 Somakumar, R. and 1. Chandrasekhar (1999). Intelligent anti-skid brake controller using a neural network. Control Engineering Practice, Vo!. 7. pp. 611-621 Stubbs, S.M. and 1.A. Tanner (1980). Review of Antiskid and Brake Dynamics Research. Aircraft Safety and Operating Problems Conference, Wallops, Flight Center Svaricek, F. (1998). Automatic Valuation and Verification of ABS Controllers by Using a HILS. SAE Paper No. 980241

.~

iZi

~----------~~".------h~ ~4 ~2

20 10

o

1 2 3 456 7 8 910111314151617181920

Trne [51

Fig. 12. Results on Ilmax = 0.4 90

1.0

80 (i)

70 H-R~-------------------+--l 0.8

g6Q .><

;

~r--~~r-----------'-~ ~6

50

g 40

.~

iZi 1--i1------t--....;..&II'I"Hlk---,--H+t-+---I 0.4

g?30

0.2

20 10

0.0

o

1 2 4 56 7 91011121315161718aJ212223

Tine [51

Fig. 13. Results on Ilmax = 0.2

5. CONCLUSIONS The design of an aircraft anti-skid controller requires a model of the braking system dynamics under realistic operating conditions and the dynamics of the braking system are mainly influenced by the frictional characteristics between the tire and the runway. In this paper, an ABS control algorithm is developed with a 5-D.O.F. aircraft dynamics model based on the landing-braking dynamic equations, and the ABS DCU is designed to acconunodate the anti-skid control algorithm for the newly developed trainer aircraft. Also the design and implementation of real-time HILS system for development of the aircraft ABS DCU are presented. Developed ABS DCU is evaluated and tested with proposed HILS system on the several runway conditions by changing the friction coefficient. ABS DCU on wet or icy runway as well as dry runway very well protects wheel skid.

REFERENCES Padovan, 1. and P. Padovan (1994). Modeling Wear at Intermittently Slipping High Speed Interfaces. Computers & Structures, Vo!. 52. No. 4 pp. 795-812 Papadopoulos, C. and G. Kapadoukas (1998). The Development of a Total System Aircraft Landing

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