CONTENTS

S.NO.
1. 2. 3.

TOPIC
ABSTRACT LIST OF FIGURES Chapter 1 - INTRODUCTION 1.1 Importance Of Antilock Braking Systems 1.2 Literature Review 1. Scope ! O"#ective Of $resent %ork 1.4 Organi'ation Of ()esis

PAGES
i ii 1 1 4 & * ! 0 3 13

4.

Chapter 2 - MAT EMATICAL MODELLING 2.1 +e)icle ,ynamics 2.2 $ro"lem .ormulation 2. /ontrol System 2.4 Simulink 1o2els

".

Chapter 3 - RESULTS # DISCUSSION

1 .1 Input $arameters 4se2 .2 Straig)t Line Braking Of +e)icle %it)out 1 .ee2"ack 1* . $roportional /ontrol .4 $roportional ,erivative /ontrol .& $roportional Integral /ontrol .* $roportional Integral ,erivative /ontrol .- ,iscussion $. !. Chapter 4 - CONCLUSION 4.1 .uture Scope REFERENCES 11113 2% 25
21

ABSTARCT
Antilock "raking systems are use2 in mo2ern cars to prevent t)e w)eels from locking after "rakes are applie2. ()e 2ynamics of t)e controller nee2e2 for antilock "raking system 2epen2s on various factors. ()e ve)icle mo2el often is in nonlinear form. /ontroller nee2s to provi2e a controlle2 tor6ue necessary to maintain optimum value of t)e w)eel slip ratio. ()e slip ratio is represente2 in terms of ve)icle spee2 an2 w)eel rotation. In present work first of all system 2ynamic e6uations are e7plaine2 an2 a slip ratio is e7presse2 in terms of system varia"les namely ve)icle linear velocity an2 angular velocity of t)e w)eel. By applying a "ias "raking force system8 response is o"taine2 using Simulink mo2els. 4sing t)e linear control strategies like $ 9 type8 $, 9 type8 $I 9 type8 $I, 9 type t)e effectiveness of maintaining 2esire2 slip ratio is teste2. It is always o"serve2 t)at a stea2y state error of 15: occurring in all t)e control system mo2els.

Li&t '( Fi)*re&

S.N'. 1 2 3 4 " $ ! , 1% 11 12 13 14 1" 1$ 1! 1, 12% 21 22 23 24 2" 2$

Fi)*re N'.

Fi)*re Na+e

Pa)e N'.

1.1 2.1 2.2 2. 2.4 2.& 2.* 2.2.0 2.3 2.15 2.11 2.12 2.1 .1 a .1 " .2 a .2 " . .4 .& a .& " .* a .* " .- a .- "

Sc)eme of ABS ;uarter +e)icle 1o2el .rictional /oefficient of Roa2 Surface v<s %)eel Slip Ratio Block ,iagram of .ee2"ack /ontrol System Block ,iagram Representing ,ynamics of =6uations Su"group of Slip Ratio /alculation Su"group of > /alculation

4 3 1 14 110 10

+e)icle 1o2el %it)out .ee2"ack 13 /ontrol 1o2ifie2 +e)icle 1o2el %it)out 25 .ee2"ack /ontrol Su"group of System 25 $9type .ee2"ack control $,9type .ee2"ack control $I9type .ee2"ack control $I,9type .ee2"ack control w)eel angular spee2 v<s time stopping 2istance v<s time ? 1 ve)icle linear velocity v<s time slip ratio v<s time ? 1 slip ratio v<s time @Ap B 2&5C ? 2 stopping 2istance v<s time ? 2 slip ratio v<s time ? stopping 2istance v<s time ? slip ratio v<s time ? 4 stopping 2istance v<s time ? 4 slip ratio v<s time ? & stopping 2istance v<s time ? & 21 21 22 2 2& 2& 2* 2* 220 23 23 23 23 5 5

C APTER 1
INTRODUCTION Anti9lock "rake systems @ABSC prevent "rakes from locking 2uring "raking. 4n2er normal "raking con2itions t)e 2river controls t)e "rakes. Dowever8 2uring severe "raking or on slippery roa2ways8 w)en t)e 2river causes t)e w)eels to approac) lockup8 t)e antilock system takes over. ABS mo2ulates t)e "rake line pressure in2epen2ent of t)e pe2al force8 to "ring t)e w)eel spee2 "ack to t)e slip level range t)at is necessary for optimal "raking performance. An antilock system consists of w)eel spee2 sensors8 a )y2raulic mo2ulator8 an2 an electronic control unit. ()e ABS )as a fee2"ack control system t)at mo2ulates t)e "rake pressure in response to w)eel 2eceleration an2 w)eel angular velocity to prevent t)econtrolle2 w)eel from locking. ()e system s)uts 2own w)en t)e ve)icle spee2 is "elow a pre9set t)res)ol2.

1.1 IMPORTANCE OF ANTILOC. BRA.ING S/STEMS ()e o"#ectives of antilock systems are t)reefol2E 1. to re2uce stopping 2istances8 2. to improve sta"ility8 an2 . to improve steera"ility 2uring "raking.

()ese are e7plaine2 "elow St'ppi0) Di&ta01e ()e 2istance to stop is a function of t)e mass of t)e ve)icle8 t)e initial velocity8 an2 t)e "raking force. By ma7imi'ing t)e "raking force t)e stopping 2istance will "e minimi'e2 if all ot)er factors remain constant. Dowever8 on all types of surfaces8 to a greater or lesser e7tent8 t)ere e7ists a peak in fiction coefficient. It follows t)at "y keeping all of t)e w)eels of a ve)icle near t)e peak8 an antilock system can attain ma7imum fictionalforce an28 t)erefore8 minimum stopping 2istance. ()is o"#ective of antilock systems )owever8 is tempere2 "y t)e nee2 for ve)icle sta"ility an2 steera"ility. Sta2i3it4 Alt)oug) 2ecelerating an2 stopping ve)icles constitutes a fun2amental purpose of "raking systems8 ma7imum friction force may not "e 2esira"le in all cases8 for e7ample not if t)e ve)icle is on a so9calle2 p9split surface @asp)alt an2 ice8 for e7ampleC8 suc) t)at significantly more "raking force is o"taina"le on one si2e of t)e ve)icle t)an on t)e ot)er si2e. Applying ma7imum "raking force on "ot) si2es will result in a yaw moment t)at will ten2 to pull t)e ve)icle to t)e )ig) friction si2e an2 contri"ute to ve)icle insta"ility8 an2 forces t)e operator to make e7cessive steering corrections to counteract t)e yaw moment. If an antilock system can maintain t)e slip of "ot) rear w)eels at t)e level w)ere t)e lower of t)e two friction coefficients peaks8 t)en lateral force is reasona"ly )ig)8 t)oug) not ma7imi'e2. ()is contri"utes to sta"ility an2 is an o"#ective of antilock systems. Steera2i3it4 Foo2 peak frictional force control is necessary in or2er to ac)ieve satisfactory lateral forces an28 t)erefore8 satisfactory steera"ility. Steera"ility w)ile "raking is important not only for minor course corrections "ut also for t)e possi"ility of steering aroun2 an o"stacle. (ire c)aracteristics play an important role in t)e "raking an2 steering response of a ve)icle. .or ABS9e6uippe2 ve)icles t)e tire performance is of critical significance. All "raking an2 steering forces must "e generate2 wit)in t)e small tire contact patc) "etween t)e ve)icle an2 t)e roa2. (ire traction forces as well as si2e forces can only "e pro2uce2 w)en a 2ifference e7ists "etween t)e spee2 of t)e tire circumference an2 t)e spee2 of t)e ve)icle relative to t)e roa2 surface. ()is 2ifference is 2enote2 as slip. It is common to relate t)e tire "raking force to t)e tire "raking slip. After t)e peak value )as "een reac)e28 increase2 tire slip causes re2uction of tire9roa2 friction coefficient. ABS )as to limit t)e slip to values "elow t)e peak value to prevent w)eel from locking. (ires wit) a )ig) peak friction point ac)ieve ma7imum friction at 15 to 25: slip. ()e optimum slip value 2ecreases as tire9roa2 friction 2ecreases. ()e ABS system consists of t)e following ma#or su"systemsE 5hee3-Spee6 Se0&'r& =lectro9magnetic or Dall9effect pulse pickups wit) toot)e2 w)eels mounte2 2irectly on t)e rotating components of t)e 2rivetrain or w)eel )u"s. As t)e w)eel turns t)e toot)e2

w)eel @pulse ringC generates an A/ voltage at t)e w)eel9spee2 sensor. ()e voltage fre6uency is 2irectly proportional to t)e w)eelGs rotational spee2. E3e1tr'0i1 C'0tr'3 U0it 7ECU8 ()e electronic control unit receives8 amplifies an2 filters t)e sensor signals for calculating t)e w)eel rotational spee2 an2 acceleration. ()is unit also uses t)e spee2s of two 2iagonally oppose2 w)eels to calculate an estimate for t)e spee2 of t)e ve)icle. ()e slip at eac) w)eel is 2erive2 "y comparing t)is reference spee2 wit) t)e spee2s of t)e in2ivi2ual w)eels. ()e Hw)eel accelerationH an2 Hw)eel slipH signals serve to alert t)e =/4 to any locking ten2ency. ()e microcomputers respon2 to suc) an alert "y sen2ing a signal to trigger t)e pressure control valve solenoi2s of t)e pressure mo2ulator to mo2ulate t)e "rake pressure in t)e in2ivi2ual w)eel9"rake cylin2ers. ()e =/4 also incorporates a num"er of features for error recognition for t)e entire ABS system @w)eel9spee2 sensors8 t)e =/4 itself8 pressure9control valves8 wiring )arnessC. ()e =/4 reacts to a recogni'e2 2efect or error "y switc)ing off t)e malfunctioning part of t)e system or s)utting 2own t)e entire ABS. 46ra*3i1 Pre&&*re M'6*3at'r ()e )y2raulic pressure mo2ulator is an electro9)y2raulic 2evice for re2ucing8 )ol2ing8 an2 restoring t)e pressure of t)e w)eel "rakes "y manipulating t)e solenoi2 valves in t)e )y2raulic "rake system. It forms t)e )y2raulic link "etween t)e "rake master cylin2er an2 t)e w)eel9"rake cylin2ers. ()e )y2raulic mo2ulator is mounte2 in t)e engine compartment to minimi'e t)e lengt) of t)e lines to t)e "rake master cylin2er an2 t)e w)eel9"rake cylin2ers. ,epen2ing on t)e 2esign8 t)is 2evice may inclu2e a pump8 motor assem"ly8 accumulator an2 reservoir. .ig 1 s)ows relations)ip "etween mo2ulator8 2ynamics an2 controller.

.ollowing "rakes are generally use2 in automo"iles.

In 2isk "rake8 a force is applie2 to "ot) si2es of a rotor an2 "raking action is ac)ieve2 t)roug) t)e frictional action of in"oar2 an2 out"oar2 "rake pa2s against t)e rotor. In 2rum "rakes8 a force is applie2 to a pair of "rake s)oes. A variety of configurations e7ists8 inclu2ing 1ea2ing8 trailing s)oe @simple7C8 2uo92uple78 an2 2uo9servo. ,rum "rakes feature )ig) gains compare2 to 2isk "rakes8 "ut some configurations ten2 to "e more nonlinear an2 sensitive to fa2ing. 1.2 LITERATURE RE9IE5 .ollowing literature is surveye2 relating to ABS. Mir:aei0e;a6 a06 Mir:aei I1J )ave applie2 a pre2ictive approac) to 2esign a non9 linear mo2el9"ase2 controller for t)e w)eel slip. ()e integral fee2"ack tec)ni6ue is also employe2 to increase t)e ro"ustness of t)e 2esigne2 controller. ()erefore8 t)e control law is 2evelope2 "y minimi'ing t)e 2ifference "etween t)e pre2icte2 an2 2esire2 responses of t)e w)eel slip an2 itKs integral. Ba&3a+i&3iet al. I2J propose2 a static9state fee2"ack control algorit)m for ABS control. ()e ro"ustness of t)e controller against mo2el uncertainties suc) as tire longitu2inal force an2 roa2 a2)esion coefficient )as "een guarantee2 t)roug) t)e satisfaction of a set of linear matri7 ine6ualities. Ro"ustness of t)e controller against actuator time 2elays along wit) a met)o2 for tuning controller gains )as "een a22resse2. .urt)er tuning strategies )ave "een given t)roug) a general ro"ustness analysis8 w)ere especially t)e 2esign conflict impose2 "y noise re#ection an2 actuator time 2elay )as "een a22resse2. Ch'i I J )as 2evelope2 a new continuous w)eel slip ABS algorit)m. )ere ABS algorit)m8 rule9"ase2 control of w)eel velocity is re2uce2 to t)e minimum. Rear w)eels cycles in2epen2ently t)roug) pressure apply8 )ol28 an2 2ump mo2es8 "ut t)e cycling is 2one "y continuous fee2"ack control. %)ile cycling rear w)eel spee2s8 t)e w)eel peak slips t)at ma7imi'e tire9to9roa2 friction are estimate2. .rom t)e estimate2 peak slips8 reference velocities of front w)eels are calculate2. ()e front w)eels are controlle2 continuously to track t)e reference velocities. By t)e continuous tracking control of front w)eels wit)out cycling8 "raking performance is ma7imi'e2. Ra0)e3'< I4J 2escri"e2 t)e mo2el of a 6uarter9ve)icle an2 an ABS in 1A(LAB9 SI14LILA. In t)is report8 to mo2el t)e tire c)aracteristics an2 t)e 2ynamic "e)avior on a flat as well as an uneven roa28 t)e S%I.(9tire mo2el is employe2. Shar=a>4 I&J stu2ie2 t)e performance of ABS wit) variation of weig)t8 friction coefficient of roa28 roa2 inclination etc. A self9tuning $I, control sc)eme to overcome t)ese effects via fu''y FA is 2evelope2M wit) a control o"#ective to minimi'e stopping 2istance w)ile keeping slip ratio of t)e tires wit)in t)e 2esire2 range. P'*r&+a6 I*J )as propose2 an a2aptive LL9 "ase2 controller for ABS. ()e propose2 controller is 2esigne2 to tackle t)e 2raw"acks of fee2"ack lineari'ation controller for ABS.

T'pa3'<et al. I-J propose2 a neurofu''y a2aptive control approac) for nonlinear system wit) mo2el uncertainties8 in antilock "raking systems. ()e control sc)eme consists of $, controller an2 an inverse reference mo2el of t)e response of controlle2 system. Its output is use2 as an error signal "y an online algorit)m to up2ate t)e parameters of a neuro9 fu''y fee2"ack controller. Pati3 a06 L'0)'riaI0J )ave use2 2ecoupling feature in frictional 2isk "rake mec)anism 2erive2 t)roug) kinematic analysis of ABS to specify reference "raking tor6ue is presente2. 1o2elling of ABS actuator an2 control 2esign are 2escri"e2. La40e et al. I3J )ave illustrate2 t)e fu''y mo2el reference learning control @.1RL/C. Braking effectiveness w)en t)ere are transition "etween icy an2 wet roa2 surfaces is stu2ie2. *a0) a06 Shih I15J )ave use2 t)e fu''y controller to control t)e )y2raulic mo2ulator an2 )ence t)e "rake pressure. ()e performance of controller an2 )y2raulic mo2ulator are assesse2 "y t)e )ar2ware in loop @DILC e7periments. O0itet al. I11J )ave propose2 a novel strategy for t)e 2esign of sli2ing mo2e controller @S1/C. As velocity of t)e ve)icle c)anges8 t)e optimum value of t)e w)eel slip will also alter. Fray pre2ictor is employe2 to anticipate t)e future output of t)e system. 1.3 SCOPE # OB?ECTI9E OF PRESENT 5OR. ,uring t)e 2esign of ABS8 nonlinear ve)icle 2ynamics an2 unknown environment c)aracters as well as parameters8 c)ange 2ue to mec)anical wear )ave to "e consi2ere2. $I, controller are very easy to un2erstan2 an2 easy to implement. Dowever $I, loop re6uire continuous monitoring an2 a2#ustments. In t)is line t)ere is a scope to un2erstan2 improve2 $I, controllers wit) mat)ematical mo2els. ()e present work8 it is planne2 to un2erstan2 an2 o"tain t)e 2ynamic solution of 6uarter car ve)icle mo2el to o"tain t)e time varying ve)icle velocity an2 w)eel. After i2entification of system 2ynamics a slip factor 2efine2 at eac) instance of time will "e mo2ifie2 to 2esire2 value "y means of a control sc)eme. +arious fee2"ack control sc)emes can "e use2 for t)is purpose. Simulation are carrie2 out to ac)ieve a 2esire2 slip factor wit) 2ifferent control sc)eme suc) as 1C $roportional .ee2"ack control 2C $roportional ,erivative .ee2"ack /ontrol C $roportional Integral .ee2"ack /ontrol 4C $roportional Integral ,erivative .ee2"ack /ontrol Frap)s of linear velocity8 stopping 2istance an2 slip ratio for eac) system is plotte2 an2 compare2 wit) eac) ot)er. At t)e en28 possi"le alternate solutions are 2iscusse2.

()e work is inspire2 from t)e 2emo mo2el of ABS provi2e2 in Simulink software. 1.4 ORGANISATION OF T ESIS /)apter 2 2escri"es t)e mat)ematical mo2elling of 6uarter ve)icle an2 ve)icle 2ynamic e6uations use2 to 2escri"e t)e system. .ee2"ack control systems w)ic) are use2 for ABS are e7plaine2. Simulink 1o2els of eac) control system are 2escri"e2. /)apter contains various grap)s o"taine2 from eac) of Simulink mo2els. /omparison an2 2iscussion "etween 2ifferent control sc)emes are s)own. /)apter 4 conclu2es t)e a"ove work. It contains summary of work an2 t)rows lig)t on future scope for furt)er stu2ies an2 2evelopment.

C APTER 2 MAT EMATICAL MODELLING 2.1 9E ICLE D/NAMICS Basically8 a complete ve)icle mo2el t)at inclu2es all relevant c)aracteristics of t)e ve)icle is too complicate2 for use in t)e control system 2esign. ()erefore8 for simplification a mo2el capturing t)e essential features of t)e ve)icle system )as to "e employe2 for t)e controller 2esign. ()e 2esign consi2ere2 )ere "elongs to a 6uarter ve)icle mo2el as s)own in .ig 2.1. ()is mo2el )as "een alrea2y use2 to 2esign t)e controller for ABS.

()e longitu2inal velocity of t)e ve)icle an2 t)e rotational spee2 of t)e w)eel constitute t)e 2egrees of free2om for t)is mo2el. 2.2 PROBLEM FORMULATION ()e relation of t)e frictional coefficient versus w)eel slip ratio 8 provi2es t)e e7planation of t)e a"ility of t)e ABS to maintain ve)icle steera"ility an2 sta"ility8 an2 still pro2uce s)orter stopping 2istances t)an t)ose of locke2 w)eel stop. ()e friction coefficient can vary in a very wi2e range8 2epen2ing on factors likeE @aC Roa2 surface con2itions @2ry or wetC8 @"C (ire si2e9slip angle8 @cC (ire "ran2 @summer tire8 winter tireC8 @2C +e)icle spee28 an2 @eC ()e slip ratio "etween t)e tire an2 t)e roa2.

.riction mo2el use2 in I&J is use2 )ere. It gives value of coefficient of friction as a function of linear velocity an2 slip ratio. 2.3 CONTROL S/STEM A fee2"ack control system is a close2 loop control system in w)ic) a sensor monitors t)e output @slip ratioC an2 fee2s 2ata to t)e controller w)ic) a2#usts t)e control @"rake pressure mo2ulatorC as necessary to maintain t)e 2esire2 system output @matc) t)e w)eel slip ratio to t)e reference value of slip ratioC. .ig 2. s)ows t)e "lock 2iagram of fee2"ack control system

()is fee2"ack controller can "e any one of 1C $roportional /ontrol 2C $roportional ,erivative /ontrol C $roportional Integral /ontrol 4C $roportional Integral ,erivative /ontrol

2.4 SIMULIN. MODELS Si+*3i0= +'6e3 '( @*arter <ehi13e In or2er to mo2el t)e ABS wit) 2ifferent controllers system incorporating t)e 2ynamic e6uations is mo2elle2 in Simulink environment. .ig 2.4 s)ows t)e "lock 2iagram of t)e Simulink mo2el representing ve)icle 2ynamics 2uring straig)t line "raking.

(o mo2el t)is system in Simulink8 several su"groups are use2 to avoi2 confusion. Slip ratio calculation given in =6. @3C can "e forme2 as a su"group s)own in fig 2.&

Similarly friction coefficient @>C calculation can "e forme2 in one su"group

Fi) 2.$ S*2)r'*p '( A Ca31*3ati'0 /om"ining su" groups an2 mo2elling remaining e6uations into Simulink mo2el8 we get complete Simulink mo2el of 6uarter ve)icle 2uring straig)t line "raking wit)out fee2"ack control as s)own in .ig 2.-

Fi) 2.! 9ehi13e M'6e3 5ith'*t Fee62a1= C'0tr'3 Si+*3i0= +'6e3 '( ABS *&i0) pr'p'rti'0a3 (ee62a1= 1'0tr'3 Simulink mo2el s)own in .ig 2.- is mo2ifie2 to use it as a system su"group in mo2elling of fee2"ack control system. .ig 2.0 s)ows t)e mo2ifie2 version in w)ic) a S41 "o7 is a22e2 "etween input terminal @w)ic) is control tor6ue uC an2 "rake tor6ue (". So t)e total tor6ue input ( to w)eel is ( B u N (" @1&C ()is su"group forme2 is s)own in .ig 2.3

Fi) 2., M'6i(ie6 9ehi13e M'6e3 5ith'*t Fee62a1= C'0tr'3

Fi) 2.- S*2)r'*p '( S4&te+ Lewly forme2 su"group s)own in .ig 2.0 is integrate2 wit) proportional fee2"ack control wit) proportional gain Ap as s)own in .ig 2.15

Fi) 2.1% P-t4pe Fee62a1= 1'0tr'3 Si+*3i0= +'6e3 '( ABS *&i0) pr'p'rti'0a3 6e(ere0tia3 (ee62a1= 1'0tr'3 In t)is case system is fe2 wit) proportional 2eferential fee2"ack control. %)ere Ap is proportional gain an2 A2 is 2ifferential gain. ()is system is s)own in .ig 2.11

Fi) 2.11 PD-t4pe Fee62a1= 1'0tr'3

Si+*3i0= +'6e3 '( ABS *&i0) pr'p'rti'0a3 i0te)ra3 (ee62a1= 1'0tr'3 System is fe2 wit) proportional integral fee2"ack control w)ere Ap is proportional gain an2 Ai is integral gain. ()is system is s)own in .ig 2.12

Fi) 2.12 PI-t4pe Fee62a1= 1'0tr'3 Si+*3i0= +'6e3 '( ABS *&i0) pr'p'rti'0a3 i0te)ra3 6e(ere0tia3 (ee62a1= 1'0tr'3 By com"ination of a"ove systems we get $I,9 type control system w)ere Ap is proportional gainK A2 is 2ifferential gain an2 Ai is integral gain are use2. ()is system is s)own in .ig 2.1

Fi) 2.13 PID-t4pe Fee62a1= 1'0tr'3

C APTER 3 RESULTS # DISCUSSION ()is c)apter 2escri"es t)e controlle2 slip response outputs using linear control mo2els. 3.1 INPUT PARAMETERS USED (o simulate t)e performance of 2ifferent ve)icle parameters wit) an2 wit)out any fee2"ack control system un2er straig)t line "raking following input parameters are consi2ere2 I&J. RB5. m8 m B 42 kg8 Ow B1.1 kgm28 g B3.01 m<s28 1a7 "raking tor6ue B 1255Lm Initial linear velocity B 2-.-0m<s B 155 km<) Initial rotational spee2 B 2-.-0<5. B 04.10 ra2<s P2B5.2 Ap B 2&5 A2 B & Ai B 15 3.2 STRAIG T LINE BRA.ING OF 9E ICLE 5IT OUT FEEDBAC. .ig .1 an2 .2 s)ows t)e "e)aviour of ve)icle parameters 2uring straig)t line "raking wit)out any controller. .ig .1 a8 " an2 .ig .2 a8 " are plot of ve)icle angular velocity8 stopping 2istance8 ve)icle linear velocity an2 slip ratio respectively versus time.

Fi) 3.1B a8 >hee3 a0)*3ar &pee6 <C& ti+eD 28 &t'ppi0) 6i&ta01e <C& ti+e

Fi) 3.2B a8<ehi13e 3i0ear <e3'1it4 <C& ti+eD 28 &3ip rati' <C& ti+e It is seen t)at slip ratio )as "een varying from 5 to 1 from application of "rakes to t)e w)eel stopping instant. =ven t)e w)eel spee2 is 'ero at .42 secon2s8 t)e stopping 2istance of 4& m occurs at .* secon2s. ()is in2icates t)at w)eel )as "een locke2 "efore ve)icle comes to )alt. ()at means 2uring "raking steera"ility is lost at .42 secon2s 2ue to locking of w)eel

3.3 PROPORTIONAL CONTROL %)en fee2"ack control is incorporate2 in t)e system to maintain constant slip ratio value8 simple linear mo2el calle2 $9 control wit) a constant gain Ap comes first. .ig . an2 .ig .4 s)ows plot of slip ratio versus time an2 stopping 2istance versus time respectively.

Fi) 3.3B &3ip rati' <C& ti+e 7.p E 2"%8

Fi) 3.4B &t'ppi0) 6i&ta01e <C& ti+e /ompare to 4& m stopping 2istance an2 increasing slip ratio in open loop case8 $ ? controller supplies a control force an2 maintain slip ratio wit) 5.51 stea2y state error an2 t)e stopping 2istance re2uce2 to m. /ompare to 4& m stopping 2istance an2 increasing slip ratio in open loop case8 $ ? controller supplies a control force an2 maintain slip ratio wit) 5.51 stea2y state error an2 t)e stopping 2istance re2uce2 to m. 3.4 PROPORTIONAL DERI9ATI9E CONTROL .or $, type fee2"ack control8 plots of slip ratio versus time an2 stopping 2istance versus time are o"taine2. ()ese plots are s)own in .ig .& a an2 ".

Fi) 3."B a8 &3ip rati' <C& ti+eD 28 &t'ppi0) 6i&ta01e <C& ti+e As seen it is similar to $ type controller. In t)is case stopping time is 2.4 secon2s an2 stopping 2istance is 2 m. Stopping time an2 stopping 2istance are 2ecrease2 slig)tly.

3." PROPORTIONAL INTEGRAL CONTROL In t)is case also t)e plots of slip ratio versus time an2 stopping 2istance versus time are o"taine2. ()ese plots are s)own in .ig .* a an2 "

Fi) 3.$B a8 &3ip rati' <C& ti+eD 28 &t'ppi0) 6i&ta01e <C& ti+e ()ere is no muc) variation. ()is time stopping 2istance foun2 to "e m an2 stopping time foun2 to "e 2.& secon2s. 3.$ PROPORTIONAL INTEGRAL DERI9ATI9E CONTROL Similarly in case of $I, type fee2"ack control plots of slip ratio versus time an2 stopping 2istanceversus time are o"taine2.

Fi) 3.!B a8 &3ip rati' <C& ti+eD 28 &t'ppi0) 6i&ta01e <C& ti+e Dere t)e stopping time an2 stopping 2istance are slig)tly re2uce2. Stopping time is 2. secon2s an2 stopping 2istance is 1 m. Overall /omparisons are ta"ulate2 in (a"le .1. Ta23e 3.1 Bra=i0) Per('r+a01e Re&*3t& ABS /ontroller Braking %it)out controller $9type $,9type 2 2.4 Stopping time @metersC 4& Stopping 2istance @secon2sC .*

$I9type

2.&

$I,9type

2.

3.! DISCUSSION .rom (a"le .18 it is clear t)at ABS improves "raking performance of ve)icle. /omparing slip ratio v<s time grap)s of 2ifferent control sc)emes suggests t)at a proportional controller @ApC will )ave t)e effect of re2ucing t)e rise time an2 will re2uce "ut never eliminate t)e stea2y9state error. An integral control @AiC will )ave t)e effect of eliminating t)e stea2y9state error8 "ut it may make t)e transient response worse. A 2erivative control @A2C will )ave t)e effect of increasing t)e sta"ility of t)e system8 re2ucing t)e overs)oot8 an2 improving t)e transient response. =ffects of eac) of controllers Ap8 A28 an2 Ai on a close29loop system are summari'e2 in t)e ta"le s)own "elow.

Ta23e 3.2 Ge0era3 E((e1t& Fain Response Ap Ai A2 Rise time ,ecrease ,ecrease Small /)ange Over s)oot Increase Increase ,ecrease Settling time Small /)ange =liminate ,ecrease

C APTER 4 CONCLUSION In t)is t)esis an attempt is ma2e to un2erstan2 t)e application of various type of linear controller use2 for antilock "raking systems. ()e system was mo2ele2 wit) a 6uarter ve)icle 2ynamics an2 2ifferential e6uation of motion was formulate2. ()e slip ratio is use2 control as a criterion for t)is control work. .riction force an2 normal reaction are function of slip ratio an2 in turn entire e6uations were nonlinear. ()e secon2 or2er 2ifferential e6uations were written as t)ree state space e6uations @1st or2er e6uationsC an2 solutions are o"taine2 "y time integration met)o2 an2 are 2irectly ac)ieve2 wit) 1A(LAB(1 Simulink "lock 2iagrams. ()e time )istories of t)e w)eel8 stopping 2istance of t)e ve)icle8 an2 slip factor variation are o"taine2 for "enc)mark pro"lem availa"le in literature. +arious central strategies like $9type8 $,9type8 $I9type8 an2 $I,9 type )ave "een implemente2 to augment t)e constant "raking tor6ue so as to control t)e slip ratio. 4.1 FUTURE SCOPE In t)is work system is nonlinear mo2el an2 controller is a linear type )ence t)e effectiveness of t)e controller may not "e goo2. In t)is line8 as a future scope of t)e work well known linear controllers like neural networks8 neuro9fu''y8 an2 fu''y $I, systems may "e employe2. Also8 real time implementation of t)e control logic is nee2e2 wit) a on "oar2 micro9controller mounte2 over a small scale2 mo2el of t)e ve)icle.

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