Type-2 Fuzzy Braking-Torque Electronic Stability Control for Four-Wheel Independent Drive Electric Vehicles

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1 [ DOI:./ijae... ] Type- Fuzzy Brakig-Torque Electroic Stability Cotrol for Four-Wheel Idepedet Drive Electric Vehicles J. Sharifi* ad A. Amirjamshidy, Electrical ad Computer Egieerig Departmet, Qom Uiversity of Techology, Qom, Ira, sharifi@qut.ac.ir Dowloaded from at : IRST o Saturday October th Abstract The electroic stability cotrol (ESC) system is oe of the most importat active safety systems i vehicles. Here, we ited to improve the Electroic stability of four i-wheel motor drive electric vehicles. We will desig a electroic stability cotrol system based o Type- fuzzy logic cotroller. Sice, Type- fuzzy cotroller has ucertaity i iput iterval furthermore of output fuzziess, it behaves like a robust cotrol, hece it is suitable for cotrol of oliear ucertai systems which ucertaity may be due to parameter variatio or u-modeled dyamics. The cotroller output for stabilizatio of vehicle is corrective yaw momet. Cotroller output is the torque that distribute by brakig ad acceleratio o both sides of the vehicle. We simulate our desigs o MATLAB software. Some drive maeuvers will be carry to validate system performace i vehicle stability maiteace. Simulatio results idicate that distributed torque-brake cotrol strategy based o Type- fuzzy logic cotroller ca improve the stability ad maeuverability of vehicle, sigificatly i compariso with ucotrolled vehicle ad Type- fuzzy ESC. Furthermore, we compare the covetioal brakig ESC with our desiged ESC, i.e. distributed exertio of torque ESC ad brakig ESC i view poit of both stabilizatio ad performace. As we will see, proposed ESC ca decrease vehicle speed reductio, i additio to better vehicle stability maiteace. Keywords: Type- Fuzzy Cotrol, Electroic Stability Cotrol, Yaw Momet, Side Slip Agle, Torque Cotrol. Itroductio Nowadays, Electric Vehicles (EVs) are receivig attetio because of evirometal cocers such as global warmig, exhaustio of fossil fuels, ad air pollutio. I additio, EVs have remarkable advatages i motio cotrol compared to iteral combustio egie vehicles. Some advatages are foregoig i [9]: ()-The respose to the drivigbrakig force by the electric motor is about times faster tha egies. ()- Developmet of i-wheel motors eable the idividual cotrol of each wheel. () The geerated torque is precisely measurable from the motor curret. () Regeeratio ca geerate Smooth brakig torque. For widespread use of the vehicles, the ext geeratio of them must be safe ad reliable. For example, a three-axle bus rollover threshold ad the effective parameters are studied i [] i which rollover threshold is a speed that automotive is passig without occurrig rollover. The objective is a determiatio of the heavy vehicle rollover critical speed while turig. I additio, a multi-objective desig of experimetal (DOE) optimizatio method are developed for crash safety of a vehicle which the vehicle cotais a viscoelastic body ad wide tapered multi-cell eergy absorber []. Brake system performace sigificatly affects safety, hadlig ad vehicle dyamics. Hece, the researchers of referece [9] had studied a brake system desig based o the method of digital logic especially for sports cars, i.e. Mercedes-AMG SLC-. I additio, the electroic stability cotrol (ESC) i electric vehicles is a safety importat system. By istallatio of heavy boxes of battery, vehicle ceter of gravity iadvertetly moves to aother positio. This lead to vehicle over-steerig ad hece it eeds additioal stabilizig system such as ESC is ecessary. We depicted the electric car structure i Figure (). By this structure, we ca utilize the drivig ad brakig torques i all four wheels idepedetly. I additio, sice each of the motors directly coected to the Vol., Number, March

2 Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] J. Sharifi ad A. Amirjamshidy wheels, removes vehicle differetial system for torque trasmissio []. A ESC system is a active-safety techology, which proactively help driver to maitai cotrol of vehicle directioal stability. This system cotiuously moitors the dyamics of the vehicle ad detects the loss of cotrol, such as over steerig or uder steerig. After detectig istability, ESC system returs the vehicle to the desired path automatically by producig a ati-yaw momet via drivig or brakig torque distributio i vehicle wheels. I referece [] a ESC cotrol strategy is proposed based o slidig mode. I additio, a vehicle yaw cotroller via secod-order slidig mode techique was desiged that guaratee robust stability i frot of disturbaces ad model H ucertaities []. Based o cotrol theory, the referece [] achieved to both vehicle yaw rate trackig through a sigle wheel brake ad vehicle stability cotrol. Referece [], had ivestigated a ESC cotrol base o fuzzy logic. A ESC cotrol base o geetic fuzzy algorithm is developed [] ad i referece [] ESC system based o Fuzzy PID cotroller are proposed. A two-surfaces slidig mode cotroller (TSSMC) is proposed for the voltage trackig cotrol of a two iput DC-DC coverter i applicatio of electric vehicles i []. Systems i which determiatio of exact fuzzy membership fuctio are difficult ad there are several ucertaities, Type- fuzzy systems has better performace vs Type- fuzzy systems. Ulike previous ESC desigs based o Type- fuzzy cotrol, the Type- fuzzy ESC cotrol lead to more robustess ad compesatio ability of automotive systems i spite of multiple ucertaities such as vehicle weight, wheels, road, etc. Hece, we desig a electroic stability cotrol system for electric vehicles with idepedet torques i each wheels. This system cosist of a type- fuzzy logic cotroller that realize vehicle istability coditios, by exertig a correctigyaw momet to restore vehicle o desired directio. I additio, we desig a torque distributio algorithm for distributio of corrective torque output of the previous stage to the appropriate wheel accordig to vehicle situatio such as oversteer ad udersteer ad driver steerig agle. I additio to the exertio of maximum yaw torque producible by vehicle, simultaeously beefits from brakig ad acceleratio torque o both sides of the vehicle, it maitai vehicle stability, ulike covetioal ESC systems that oly apply brakig torque to maitai vehicle stability. Briefly, this paper cotributio is obtaiig the state-space models for four i-wheel EV ad the desig of type- fuzzy ESP cotrol for these type of vehicles based o both acceleratio torque ad brakig cotrol o both sides of vehicle. Our paper orgaized as follows: Sectio () describes the vehicle model. Sectio () describes iterval type-, fuzzy mathematics. I sectio (), we desig ESC cotrol system. I sectio (), we will preset our simulatio results ad fially Sectio (), is coclusio ad remarks.. VEHICLE DYNAMIC AND STATE-SPACE MODEL ESC system desig eeds a simple vehicle model with importat essetial dyamics. Here, we use a degree of freedom model from referece []. The lateral ad logitudial velocities of the vehicle (vx ad vy) ad the yaw rate ( ) costitute three degrees of freedom (DOF) related to the vehicle body. The velocity of four wheels costitute the other four degrees of freedoms. The equatio of motio for DOF model ca be obtai from figure (): Fig. The structure of a electric vehicle with four electric motors i the wheels [] Vol., Number, March

3 Type- Fuzzy Brakig-Torque Electroic Stability.. [ DOI:./ijae... ] Dowloaded from at : IRST o Saturday October th Fig. Parameters i the DOF vehicle model dv d m( x v y ) (Fxfl Fxfr )cos (Fyfl Fyfr )si Fxrl Fxrr dt dt dv d m( y v x ) (Fxfl Fxfr )si (Fyfl Fyfr ) cos Fyrl Fyrr dt dt () () d L f ( Fxfl Fxfr ) si L f ( Fyfl Fyfr ) cos Lr ( Fyrl Fyrr ) dt L L L w ( Fxfl Fxfr ) cos w ( Fyfl Fyfr ) si w ( Fxrr Fxrl ) Iz () Where m is the vehicle mass, Iz is the momet of iertia aroud z-axis, Iw is wheel base momet, Lf ad Lr are the distaces betwee vehicle ceter of gravity ad the frot ad rear axles respectively. Fx ad Fy are logitudial ad lateral tire forces. Four vehicle wheels are defie as: frot-left (fl), frot-right (fr), rear-left (rl), rear-right (rr). δ is frot steerig agle, φ is vehicle yaw agle, ad β is vehicle sideslip agle which is defied as: vy vx arcta () Wheels rotatioal motio is: d J Td i, j Tbi, j Fx i, j.reff ; (i f, r ; j l, r ) dt () Here Tdi,j refer to trasmitted drive torque ad Tbi,j to brake torque. reff is tire effective radius, is the tire agular velocity ad Jw is wheel iertia. Durig motio, vehicle vertical load chages betwee frot ad rear axles. For istace by brakig, vertical load eters o the vehicle frot axle. Vertical load trasfer equatios o the frot ad rear axles are as follows: mglr cos max hcog mghcog si Fzf (L f L r ) () Fzr mgl f cos max hcog mghcog si (L f L r ) () hcog is height of gravity ceter, ax is logitudial acceleratio, is path slope agle, Fzf ad Fzr is vertical force o the frot axle ad the rear axle respectively. For simulatio of vehicle wheels, we use from Dugoff tire model i []. To obtai the state space model, let us defie the state variables as follows: x vx x v y x X x w fl x w fr x wrl x w rr () We will obtai the oliear state-space model as: x (t) x (t ) X (t) x (t ) x (t ) W (t ) F (t) J w T (9) I which the vectors W ad F are: cos m si m L f si Lw cos Iz reff W (t ) Jw cos m si m L L f si w cos Iz reff Jw T F (t ) Fxfr Fxfl Fxrr Fxrl Fyf Fyr, T T fr m Lw I z Lw I z L f cos reff Jw T fl si m cos m m Trr reff Jw Trl Iz m Lr Iz T I this equatio, the cotrol sigal is the torque ad forces. To calculate the equilibrium poit of a oliear system, both the cotrol sigal ad state derivative must set to zero, hece X E [] F (t ) [], T [] ad which Eidex is the Equilibrium. The the equilibrium of x E above equatios is E meas that vehicle has ot yaw rate. Hece, the equilibrium poit stability of this system meas keepig vehicle yaw rate at zero. Vol., Number, Ju

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5 Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] J. Sharifi ad A. Amirjamshidy Physically it meas that ESC cotrol effort should maitai the vehicle i every yaw directio exerts by driver. This viewpoit may ot explai i may. Fuzzy Set ad Systems. Type Fuzzy Sets Type- fuzzy sets (TFSs) were origially itroduced by Zadeh i 9 []. The successful applicatios of type- fuzzy logic cotrollers (TFLCs) had reported i may researches. For example, i cotrol ad modelig, predictios of time series ad other applicatios [-]. Despite the apparet advatages of TFSs, it had show that it is ot able to hadle the effect of ucertaities completely []. This is because a TFS is certai i the sese that its membership grades are crisp values. I the real world, may of ucertaity exist i the face of fuzzy system such as: ()-Describig parts of the fuzzy rules are ucertai, that is mea the words used i the parts of atecedet ad cosequet of laws ca have differet meaigs for differet people. ()The results obtaied of the group of experts ofte for the law will be differet because experts are ot ecessarily i agreemet with each other. ()Measuremets that activates a fuzzy system may be Noisy ad therefore are ucertai. Thus, there is ofte some ucertaity related to the data. research papers of vehicle ESC stability sice the ultimate goal of ESC cotrol system is the cotrol of yaw agle, for example i this era see [,, ]. To overcome this ucertaity, type- fuzzy sets (TFSs) were itroduced by Zadeh as a extesio of TFSs (Zadeh, 9) []. TFSs have membership fuctios that are fuzzy themselves while TFSs have certai membership fuctios. I the other had, the membership grade of type- membership fuctios are crisp umbers, whereas the membership degree of type- membership fuctios ca be ay subset i the iterval [, ] that are called primary membership fuctio (PMF). I additio, accordig to ay PMF, a value that called secodary membership fuctio (SMF) that defies the probability of PMFs. Sice this improvemet icreases the computatioal burde, iterval type- fuzzy logic cotrollers (ITFLCs) i which SMFs are zero or oe, are developed [9]. ITFSs as a special case of TFSs, are curretly the most widely used to reduce computatioal burde. Figure () illustrates a example of ITFS. Accordig to this figure, the membership degree of each elemet of x i the domai of ITFS is a iterval. For example, as we see i Figure (), the membership degree of. is a iterval betwee [.,.]. ITFSs are bouded from up ad dow with two TFMs that are called upper membership fuctio (UMF) ad lower membership fuctio (LMF). The area betwee UMF ad LMF is footprit of ucertaity (FOU). Fig. (a) Iterval type- fuzzy set ad (b) secodary MF at x=. [] Vol., Number, Ju

6 Type- Fuzzy Brakig-Torque Electroic Stability.. Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] Fig. Structure of type- fuzzy logic system [9] Fig. Upper MF ad Lower MF [] Fig.. Levels of calculatio for type- fuzzy system [] Vol., Number, March

7 Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] J. Sharifi ad A. Amirjamshidy. Iterval Type- Fuzzy Logic A type- FL System icludes four stage: (a)-type- fuzzyfier, (b)-rule-base, (c)-iferece egie ad (d)output processor. The output processor icludes a typereducer ad defuzzyfier. Comparig to type- fuzzy system, the mai differece is the type reducer part which it coverts the type- fuzzy set ito the type- fuzzy set. Fially, i defuzzyfier part, type reduced set covert to a crisp umber. Figure () depicts the structure of type- fuzzy logic system. A iterval type- fuzzy set A ca be characterize as: A x, u, u A x, u x X, u J x [,] () Where x is the primary variable ad its measuremet domai deoted by X; u is the secodary domai variable u Jx at each x X, Jx is the primary membership of x. The amplitude of the secodary MF is the "secodary grade." For a iterval type- fuzzy set, the secodary grade equals over the etire of u ( x, u) FOU, A ; hece, the ew third dimesio of a type- fuzzy set does ot covey ay ew iformatio for a iterval type- fuzzy set. So ucertaities i a iterval type- fuzzy set characterizes by FOU completely. Membership fuctio of iterval type- fuzzy set is: ua (x), ua (x) u J X u ua (x) goal, we must covert the first type- fuzzy output i type reducer block to a type- fuzzy set ad the by usig defuzzificatio methods i TFL covert it to a crisp umber. Type reductio i IT FLSs is the most itesive operatio. There are several methods for computig type-reductio. Some methods have high precisio but leads to large computatioal costs ad others have lower computatioal cost but have less accurate. I this article, we use the Karik- Medel (KM) algorithm []. The KM algorithm coverges mootoically ad super-expoetially fast. I this paper, for typereductio from the ceter-of-sets method, we use the method of [9]: N f y f F (x) YCOS (x) N f y Y [yl, y r ] () Where YCOS is a iterval type- fuzzy set determied by its two ed poits yl ad yr. that yl ad yr is Miimum ad maximum this distace respectively. This values ca be computed efficietly usig the Karik-Medel (KM) algorithms as follows [9],[] : L yl f y L f N f y f L N R, yr y R f L I above equatios, f x X f ad N f y f R N () R f are upper ad () IT FS is bouded from the above ad below by lower firig iterval for each output rule ad y ad u ( x) ad ua ( x), which are upper MF two T FSs, A are upper ad lower membership fuctio ceter i the cosequet part respectively. The mai idea of the KM algorithm is to fid the switch poits L ad R for yl ad yr to esure from their miimum ad maximum. The switch poit L ad R i KM algorithm is determied by followig equatio. (UMF) ad lower MF (LMF), respectively. The area u ( x) u ( x) betwee A ad A is the footprit of ucertaity (FOU). Math operatio of ITFL is almost similar to TFL ad the oly differeces is i iput ad output membership fuctios ad output processor. However, i other parts, such as fuzzifier, rule-base ad iferece egie is similar to TFL. Mathematically, istead of computig a area of type- rule output FS, the TFLSs compute two such FSs for each fired rule, oe for the LMF ad oe for the UMF of the fired ruleoutput fuzzy sets. Agai, each of these two calculatios oly ivolves type- FS calculatios. Figure () shows the levels of calculatios to reach to output of type- fuzzy system for a two-fired rules system with two iput-oe output. Type- fuzzy system Output is a type- fuzzy set. While we eed a crisp umber i output, to reach this y y L y l y L y R y r y R () Take yl for example. yl is the miimum of YCOS(x). y Sice icreases from the left to the right alog the horizotal axis of Figure (), we should choose a large y weight (upper membership grade f ) for o the left of switch poit L ad a small weight (lower f y membership grade ) for o the right of switch poit L. The KM algorithm fids the switch poit L. For L, the upper membership grades are used to Vol., Number, Ju

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9 Type- Fuzzy Brakig-Torque Electroic Stability.. Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] 9 calculate yl ; for > L, the lower membership grades are used. This will esure yl be the miimum. After calculatig yl ad yr, must compute the defuzzified (crisp) output as follows: y yl yr () Accordig to beig ew the type- fuzzy logic, few specialized tools desiged for the use of type- fuzzy sets, amog these tools ca be metioed to graphics toolbox that desiged by Taski et al., []. This toolbox has the same eviromet with type- fuzzy graphics toolbox i MATLAB. I simulatio sectio, we will use this toolbox for desigig ITFC.. ESC Cotrol System Desig. ESC system is a vehicle safety active cotrol system. It improves vehicle's lateral stability i emergecies. Two istaces of vehicle directioal istability may occur as follows: Oversteer: the actual path followed by the vehicle moves i towards the ceter of the curvature of tur with respect to the driver s iteded desired path. I other words, the vehicle start spiig. I over-steer situatio, vehicle has higher yaw rate ad larger sideslip agle. Udersteer: whe vehicle is turig, due to slip at the frot axle, it deviates away from the driver s iteded path. A uder-steer vehicle ca be characterized by less yaw rate ad smaller side-slip agle. Both above coditios are udesirable ad it is due to loss of driver cotrol o vehicle, lead to probability icesemet of a accidet. Cotroller should apply a corrective yaw momet i opposite directio to the driver geerated yaw momet to overcome this situatio To create yaw momet o vehicle is equivalet to geerate positive or egative torque o a specific wheel. To check the yaw rate of vehicle d / dt stability, cotrol system must apply ad sideslip agle (B). The, the error betwee them ad desirable values are iputs of fuzzy cotroller. Sice, desired values had obtaied by ormal yaw rate ad sideslip agle, the we expect guide agles ad differet coditios such as turig ad double lae chage maeuver, without vehicle cotrol lose. Figure (9) shows the overall structure of the ESC cotroller. This cotroller icludes two layers: The first layer cotais a fuzzy cotroller for calculatig the correctio torque ad the secod layer cosists of a torque distributor to allocate torque geerated by first layer to appropriate wheels. I this cotrol structure, by comparig yaw rate ad sideslip agle with desirable values (which is obtaied from referece model) to determie error rate as ESC cotroller iput. I additio, the required corrective yaw momet (Mz) is cotroller output. The, the egative or positive torque will distribute by distributor block o electric motors mouted i each wheel. Whe the vehicle moves as expected, the smaller sideslip agle is better. O vehicle dyamics researches, the desired sideslip is geerally cosidered as degree, i.e., Bdes=. Fig. Switch poit i KM algorithm [] Vol., Number, Ju

10 Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] J. Sharifi ad A. Amirjamshidy Fig. Uder-steer ad Over-steer i vehicle Fig9.. Overall structure of our ESC cotrol system. Liear -DOF Referece Model The vehicle desired yaw rate from a simplified DOF liear model are as follows []: d s dt C f C r L () V.ta, Vch m(c r Lr C f L f ) V L. ( ) Vch C C which f ad r are side stiffess of frot ad rear axle. The ormal yaw rate calculate from () may exceeds the max yaw rate that is limited by road adhesio. The max ormal yaw rate should be calculate from the followig equatio: d g () dt VX is the tire-road frictio coefficiet ad g is the earth gravitatioal acceleratio. If the value calculated from equatio () exceeds the value from equatio (), the max value of the ormal yaw rate is the latter.. Type- Fuzzy ESC Desig The mai objective of ESC system is to reduce the yaw rate error ad sideslip error by creatig a Vol., Number, March

11 Type- Fuzzy Brakig-Torque Electroic Stability.. Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] corrective yaw momet, util to maitai the vehicle desired stability. Type- fuzzy ESC cotroller has two iputs cosistig of yaw rate error e( ) des act ad sideslip agle error e(b) Bdes Bact ad Procedure for formig fuzzy cotrol rules ad also torque distributio layer is as follows []: The first mode: to occur uder-steer mode whe the vehicle suddely tur to the left. This mode e( ) e(b) characterized by ad. To cotrol this situatio, the fuzzy cotroller must geerate egative yaw momet i the couterclockwise directio. The i the torque distributor block, this torque distribute i the form of rear-right wheel acceleratig ad rear-left wheel brakig. The secod mode: to occur over-steer mode whe the vehicle suddely tur to left. This mode e( ) e(b) e( ) e(b) e( ) e(b) characterized by ad. To cotrol it, fuzzy cotroller must geerate positive yaw momet i the clockwise directio. The i the torque distributor block, this torque distribute i the form of frot-right wheel brakig ad frot-left wheel acceleratig. The third mode: to occur uder-steer mode whe the vehicle suddely tur to right. This mode characterized by ad. To cotrol it, fuzzy cotroller must geerate positive yaw momet i the clockwise directio. The i the torque distributor block, this torque distribute i the form of rear-right wheel brakig ad rear-left wheel acceleratig. The fourth mode: to occur uder-steer mode whe the vehicle suddely tur to right. This mode characterized by ad. To cotrol it, fuzzy cotroller must geerate egative yaw momet i the couterclockwise directio. The i the torque distributor block, this torque distribute i the form of frot-right wheel acceleratig ad frot-left wheel brakig. The ESC cotroller performace for the four metioed modes illustrated i figure (). cotroller output is corrective yaw momet Mz. To provide eough rule coverage for fuzzy cotroller, we cosider five fuzzy sets for each of the yaw rate ad sideslip error variables with liguistic variables {NB, NS, ZE, PS, PB}. I additio, seve fuzzy sets describe the cotroller output by liguistic variables {NB, NM, NS, ZE, PS, PM, PB}. These symbols are acroym of Negative Big (NB), Negative Medium (NM), Negative Small (NS), Zero (ZE), Positive Small (PS), Positive Medium (PM), Positive Big (PB). Accordig to some practical tests, the maximum allowable sideslip agle error ad yaw rate error whe drivig through a severe double-lae-chage maeuver are assumed to be ad /s, respectively[], which correspod well with the limits foud i the literature for ormal passeger cars. Based o this practical iformatio rage of iput variables are: sideslip agle error i.,. rad.,. (rad ad for yaw rate error sec). Moreover, maximum possible torque due to i-wheel motors is N/m. So the rage of chage corrective yaw momet Mz is cosidered to be i iterval [-,]. The membership fuctio iput ad output variables is show i figure (), also the fuzzy cotroller schematic i MATLAB Simulik eviromet is show i figure (). I ITFL we will use the Sugeo fuzzy iferece egie, miimum for AND, maximum for OR, miimum for implicatio, maximum for aggregatio ad fially for type reductio ad deffuzificatio the KM algorithm. We report the rule based fuzzy cotroller i table (). After corrective yaw torque calculatio by fuzzy cotroller i first layer, it distributes to wheel motors. Torque distributor does this task. Torque distributor idetify vehicle situatios such as over-steerig, uder-steerig, steer agle drive, sig of Mz ad etc. based o this iformatio, it will distributes appropriate torque to respective wheels. I torque distributio to acquire maximum possible yaw momet, we will exert the egative torque to wheels of oe side ad the positive torque to cross-wheel of the other side. I fact, after assigmet of corrective torque to a wheel for brakig or acceleratio, reverse of this torque assigs to cross-wheel o the other side. Furthermore, to make torque that is more effective i uder-steerig situatio due to frot axle slip, the system must distributes torque oly to rear axle. Similarly, i over-steerig situatio due to rear axle slip, the torque distributed oly to the frot axle. Table () reports the wheels torque allocatio. Vol., Number, Ju

12 Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] J. Sharifi ad A. Amirjamshidy Fig. Fig. Our Iterval type- membership fuctios of iputs ad output variables Fuzzy cotroller schematic i our MATLAB Simulik eviromet Table. Rule base the fuzzy cotroller Vol., Number, March

13 Type- Fuzzy Brakig-Torque Electroic Stability.. [ DOI:./ijae... ] Dowloaded from at : IRST o Saturday October th Table. : Allocatio torque table to the wheels Fig. The ESC cotroller performace i differet models [ Vol., Number, Ju

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15 Table. Vehicle Specificatios Fig. The path of the car ad the car steer agle yaw rate Desire type fuzzy ESC type fuzzy ESC No Cotrol Degree/S - - (a) Side slip Agle Degree Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] J. Sharifi ad A. Amirjamshidy type fuzzy ESC Desire type fuzzy ESC No Cotrol - - (b) Vol., Number, Ju

16 Type- Fuzzy Brakig-Torque Electroic Stability.. [ DOI:./ijae... ]. type fuzzy ESC type fuzzy ESC No Cotrol Y [m] X [m] Speed 9 type fuzzy ESC type fuzzy ESC 9 Km/h 9 Fig. (d) (a) respose of yaw rate. (b) Respose of side slip agle. (c) Displacemet of vehicle i the coordiate plae. (d) Chages of vehicle speed type fuzzy ESC type fuzzy ESC Torque [Nm] (a) FR RR FL Torque [Nm] - RL FR - - Fig. FL RR RL Torque [Nm] Dowloaded from at : IRST o Saturday October th (c) (b) T ime (a) Corrective yaw momet output of the fuzzy cotroller. (b) Output torque distributio of ITFL cotroller to i-wheel motors 9. Simulatio ad Aalysis Performace of ESC cotrol system evaluate with a double lae chage maeuver that i this test. The vehicle parameters i this paper is reported i table.. Double Lae Chage Maeuver Vol., Number, March

17 Type- Fuzzy Brakig-Torque Electroic Stability.. For simulatio vehicle rus at costat speed of 9 system completely lose cotrol. The vehicle with ESC system ca track desired yaw rate ad keeps sideslip agle withi stable rage. Hece, driver ca cotrol the vehicle. km/h i the dry road with frictio coefficiet.. Figure () depicts the steerig wheel iput at double lae chage. The resposes of vehicle with iterval type- fuzzy ESC cotrol are compared to type- fuzzy ESC cotrol with the same rules ad membership fuctios ad with without cotrol. The test results are i Figures -. The results show that the vehicle ca track desired yaw rate ad keeps sideslip agle withi stable rage, ad driver ca cotrol the vehicle. I additio, the respose of vehicle with ITFL ESC cotrol ad TFL ESC cotrol ca track the ideal output of the referece model compared to without ESC cotrol. However, i compariso with TFL ESC cotrol, the vehicle with ITFL ESC cotrol has better performace ad stability. Step steerig test Step steerig experimet adopted to validate the performace of ESC cotroller. I this corerig test, the vehicle rus at costat speed of 9 km/h i sowy road with frictio coefficiet., ad the driver iput steerig wheel agle is degrees. We will compare the resposes of vehicle with iterval type- fuzzy ESC cotrol to system without ay cotrol ad type- fuzzy ESC cotrol with same rules ad membership fuctios. After sudde chage i steerig, the vehicle get a oversteerig i the couterclockwise directio ad vehicle goes out of the way i a ucotrolled maer. Now to restore the car to the desire directio, fuzzy cotroller must geerate positive yaw momet i the clockwise directio. The i the torque distributor block, this torque distribute i the form of frot-right wheel brakig ad frot-left wheel acceleratig as show that i figure(). We ca see i figure () that the yaw velocity ad sideslip agle covergece rapidly. The yaw velocity of ESC cotrol system ca also track the dof ideal referece model closely.. The effect of ESC cotroller o a low frictio road surface I this sectio, we evaluate the performace of ESC cotrol system with a double lae chage maeuver i sowy road with frictio coefficiet of.. Drivig coditios ad vehicle steer agle is like the previous sectio. Figure () depicts the test results ad Table () reports the umerical compariso of experimets. The test result imply that i double lae chage maeuver i sowy road, the vehicle without ESC yaw rate Side Slip Agle desire type fuzzy ESC type fuzzy ESC No Cotrol Degree Degree/s - type fuzzy ESC desire type fuzzy ESC No Cotrol - (a) (b) Positio No Cotrol type fuzzy ESC type fuzzy ESC Y[m] Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] - (c) Fig. X[m]. (a) respose of yaw rate. (b) Respose of side slip agle. (c) Displacemet of vehicle i the coordiate plae Vol., Number, March

18 Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ]

19 Table. Quatitative compariso amog type ad type fuzzy ESC ad without cotrol i double lae chage maeuver o (Itel Core i,. GHZ) yaw rate Steer Agle desire type fuzzy ESC No Cotrol Degree/s Degree (a) - (b) Side Slip Agle Positio - - Y[m] Degree type fuzzy ESC desire No Cotrol (c) Fig. type fuzzy ESC No Cotrol type fuzzy ESC (d) X[m] (a) vehicle steer agle. (b) Respose of yaw rate. (c) Vehicle sideslip agle. (d) Displacemet of vehicle i the coordiate plat Torque [Nm] (a) FL FR - RL - (b) Fig. Torque [Nm] Torque [NM] Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] J. Sharifi ad A. Amirjamshidy RR - (a) Corrective yaw momet output of the fuzzy cotroller. (b) Output torque distributio of ITFL cotroller to i-wheel motors Vol., Number, Ju

20 Type- Fuzzy Brakig-Torque Electroic Stability.. Table. Quatitative compariso amog type ad type fuzzy ESC ad without cotrol i step steerig test o (Itel Core i,. GHZ) yaw rate desire ESC accelerate ESC brake Degree/S - - (a) speed km/h Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] 9 ESC brake ESC accelerate (b) Fig9. (a) Respose of yaw rate ad (b) chages of vehicle speed Table. Quatitative Compariso betwee Desiged ESC ad Covetioal ESC Vol., Number, March

21 Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] J. Sharifi ad A. Amirjamshidy. Compariso betwee our New Desiged ESC ad Covetioal ESC I covetioal ESC, which oly use brakig torque to make corrective yaw momet, i oemergecy situatios due to brakig itervetio at work driver, lead to further reductio of vehicle speed. This type of ESC beget a upleasat feelig i the driver. However, i ESC system that desiged i this article, due to simultaeous exertio of brakig ad acceleratig torque, reduce vehicle speed less. Meawhile, i emergecies, vehicle stability well maitaied. Figure (9) depicts the compariso of speed ad yaw rate betwee ESC desiged i this article ad ESC that use oly brakig torque with the same fuzzy cotroller i a double lae chage test with the same specificatio. Coclusio I this work a Electroic Stability Cotrol system based o type- fuzzy logic theory for electric vehicles with idepedet torque at each wheel for trackig desired vehicle behavior is developed. The proposed cotroller improved hadlig ad stability of the vehicle by cotrollig the parameters yaw rate ad sideslip agle of vehicle. The results show that the proposed system clearly improves the vehicle stability compared with the ucotrolled vehicle, ad has a better performace compared with type- fuzzy cotroller. However, accordig to table(), yaw rate error ad side slip error from their optimal value i type fuzzy cotroller is better tha type fuzzy cotroller ad type fuzzy ESC cotrol system ca also track the dof ideal referece model closely. However, because of more computatioal complexity, ru time simulatio i It also uses a torque distributor that use brakig ad acceleratig o both sides of the vehicle, which cause Reduce vehicle speed less tha ESC cotrol system that use oly itervetio brakig to maitai vehicle stability ad yaw rate error i desiged cotroller is less. Refereces []. LiQiag Ji ad Yue Liu, Study o Adaptive Slid Mode Cotroller for Improvig Hadlig Stability of Motorized Electric Vehicles, IEEE []. Massimo Caale, Lorezo Fagiao, Vehicle Yaw Cotrol via Secod-Order Slidig-Mode Techique. IEEE Trasactio o Idustrial Electroic, VOL., NO. -. []. Jog Hyeo P, Woo Sug A, H yaw momet cotrol with brakes for imp rovig drivig performace ad stability, [C] USA, 999, 9:. []. Li, Bi, Daofei Li., ad Fa Yu, Vehicle Yaw Stability Cotrol Usig the Fuzzy-Logic Cotroller, IEEE []. Kiumars Jalili, Stability Cotrol of Electric Vehicles With I-Wheel Motors, Doctoral thesis,uiversity of Waterloo,Otario,Caada. []. Li Zhai, Tiami Su ad Jie Wag, Electroic Stability Cotrol Based o Motor Drivig ad Brakig Torque Distributio for a Four I-Wheel Motor Drive Electric Vehicle, IEEE DOI.9/TVT... []. L. A. Zadeh,. Fuzzy sets. Iformatio ad cotrol, (),. 9. []. L. A. Zadeh, The Cocept of a Liguistic Variable ad Its Applicatio to Approximate Reasoig I. Iformatio Scieces, Vol., pp. 99-9, 9. [9]. Medel, J. M, Ucertai rule-based fuzzy logic system: Itroductio ad ew directios, Upper Saddle River, NJ: Pretice Hall.. []. Dugoff, H., Facher, P.S. ad Segal, L, Tire performace characteristics affectig vehicle respose to steerig ad brakig cotrol iputs, Fial Report, Cotract CST-, Office of Vehicle Systems Research, US Natioal Bureau of Stadards, 99. []. J. M. Medel, O a % Savigs i The Computatio of The Cetroid of a symmetrical Iterval Type- Fuzzy Set, Iformatio Scieces, Vol., pp. -,. []. Ahmet Taski, Tufa Kumbasar, Digital sigle sidebad detectio for iterferometric sesors, A Ope Source Matlab/Simulik Toolbox for Iterval Type- Fuzzy Logic Systems-. []. Hogwe He, Jiaku Peg, Rui Xiog ad Hao Fa, A Acceleratio Slip Regulatio Strategy for Four-Wheel Drive Electric Vehicles Based o Slidig Mode Cotrol, Eergies,, ; doi:.9/e Vol., Number, March

22 Dowloaded from at : IRST o Saturday October th [ DOI:./ijae... ] 9 Type- Fuzzy Brakig-Torque Electroic Stability.. []. Kiecke, U. ad Nielse, L, Automotive Cotrol Systems for Egie, Drivelie, ad Vehicle, d editio, Spriger,. []. Rajesh Rajamai, vehicle dyamics ad cotrol, Spriger Sciece ad Busiess Media Ic, pp-,. []. Jerry M. Medel, Why Type- Fuzzy Sets Should be Used ad How They Ca be Used, Uiversity of Souther Califoria Los Ageles, CA 99-;. []. D. Wu ad M. Nie, Compariso ad practical implemetatio of type-reductio algorithms for type- fuzzy sets ad systems. I Proc, IEEE It l Cof. o Fuzzy Systems, Taipei, Taiwa, Jue. []. J. M. Medel ad D. Wu, Perceptual Computig: Aidig People i Makig Subjective Judgmets, Hoboke, NJ: Wiley-IEEE Press,. [9]. Hiroshi Fujimoto ad Shigo Harada, Field ad Bech Test Evaluatio of Rage Extesio Cotrol System for Electric Vehicles Based o Frot ad Rear Drivig-Brakig Force Distributios, The Iteratioal Power Electroics Coferece. []. Regaraj, Chadrasekara, Itegratio of Active Chassis Cotrol Systems for Improved Vehicle Hadlig Performace, Doctoral thesis, Uiversity of Suderlad. []. N. Mutoh, H. Akashi, K. Suzuki, T. Takayaagi, Frot ad Rear Wheel Idepedet Drive Type Electric Vehicles (FRID EVs) with Outstadig Ruig Performace Suitable for NextGeeratio Electric Vehicles, Graduate School, Tokyo Metropolita Uiversity - Asahigaoka Hio-shi, Tokyo, 9- Japa. []. A. Amirjamshidy, J. Sharifi, Developmet of Electroic Stability Cotrol System for Electric Vehicle with Four i Wheel Motors, Joural of Cotrol, Witer. []. Kasabov, N. K., & Sog, Q, Defis: dyamic evolvig eural-fuzzy iferece system ad its applicatio for time-series predictio, IEEE Trasactios o Fuzzy Systems,. (),. []. Wag, L. X, A course i fuzzy systems, Hog Kog: Pretice-Hall Press 999. []. Hagras, H., Type- FLCs: A ew geeratio of fuzzy cotrollers, IEEE Computatioal Itelligece Magazie,. (),. []. P. Bayat, H. Mojallali, A. Baghramia, P. Bayat, wo-surfaces Slidig Mode Cotroller for Eergy Maagemet of Electric Vehicle Based o Multi Iput DCDC Coverter, Iteratioal []. []. [9]. []. Joural of Automotive Egieerig Vol., Number, Jue. A. Otadi M.Masih-Tehrai S.M. Boluhari A.Darvish-Damavadi, Determiatio of the three-axle bus critical speed i the sese of rollover stability respect to the driver commad ad the road coditios, Iteratioal Joural of Automotive Egieerig Vol., Number, March M. Pasadidehpour, M. Shariyat, Multi-objective desig optimizatio for crash safety of a vehicle with a viscoelastic body ad wide tapered multicell eergy absorber usig DOE method, Vol., Number, Sept S.Ebrahimi-Nejad, M.Kheybari, Brake System Desig for Sports Cars usig Digital Logic Method, Iteratioal Joural of Automotive Egieerig Vol., Number, Dec Web available at: eer-ad-udersteer-explaied/ Vol., Number, Ju