development of antilock braking system using electronic wedge brake ...

Development of Antilock Braking System using Electronic Wedge Brake Model

DEVELOPMENT OF ANTILOCK BRAKING SYSTEM USING ELECTRONIC WEDGE BRAKE MODEL V. R. Aparow1*, K. Hudha2, F. Ahmad3, H. Jamaluddin4 , Department of Mechanical Engineering, Faculty of Engineering, Universiti Pertahanan Nasional Malaysia, Kem Sungai Besi, 57000 Kuala Lumpur, Malaysia

1 2

Smart Material and Automotive Control (SMAC) Group, Department of Automotive Engineering, Faculty of Mechanical Engineering, Universiti Teknikal Malaysia Melaka, 76109 Durian Tunggal, Melaka, Malaysia

3

Faculty of Mechanical Engineering, Universiti Teknologi Malaysia (UTM), 81310 UTM Skudai, Johor Bahru, Malaysia 4

ABSTRACT The development of an Antilock Braking System (ABS) using a quarter vehicle brake model and electronic wedge brake (EWB) actuator is presented. A quarter-vehicle model is derived and simulated in the longitudinal direction. The quarter vehicle brake model is then used to develop an outer loop control structure. Three types of controller are proposed for the outer loop controller. These are conventional PID, adaptive PID and fuzzy logic controller. The adaptive PID controller is developed based on model reference adaptive control (MRAC) scheme. Meanwhile, fuzzy logic controller is developed based on Takagi-Sugeno technique. A brake actuator model based on Gaussian cumulative distribution technique, known as Bell-Shaped curve is used to represent the real actuator. The inner loop controls the EWB model within the ABS control system. The performance of the ABS system is evaluated on stopping distance and longitudinal slip of vehicle. Fuzzy Logic controller shows good performance for ABS model by reducing the stopping distance up to 17.4% compared to the conventional PID and Adaptive PID control which are only 7.38% and 12.08%. KEYWORDS: Anti-lock braking system; Electronic wedge brake; MRAC; Adaptive PID control; Fuzzy logic

* Corresponding author email: [email protected]

ISSN: 2180-1053

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January - June 2014

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Journal of Mechanical Engineering and Technology

1.0 INTRODUCTION Currently, vehicles have become major assets for every human in their daily life usage. Owning personal vehicles will tend to reduce time and save energy for humans to travel from one place to another, but this has significantly increased the risks to the human’s life. According to the Malaysian Institute of Road Safety Research (MIROS), there were 3.55 deaths per 10,000 vehicles and 28.8 deaths for 100,000 populations in Malaysia every year (MROADS, 2009; Ghani & Musa, 2011). Based on statistical analysis by MIROS, the main cause of vehicle accidents is instability condition in which drivers lost control of the vehicle by steering, throttle or braking input (Ghani & Musa, 2011). The major effects of driver losing control of the vehicle are rollover and skidding effect during cornering and braking input. Furthermore, vehicle skidding may cause oversteer where the rear end of vehicle slides out of the road or understeer, a condition where the front vehicle turns over outside the road without following the curve of the road. Other major skid effect is called four wheels skid where all the four wheels lock up and the vehicles starts to slip in the direction of forward momentum of the vehicle. During this condition occurring, there is a high possibility for the wheels to stop from rotating before the vehicle approaches to a halt. This process is known as ‘locking up’ where the braking force on the wheel is not being transferred efficiently to stop the vehicle because of the wheels skid on the road surface (Li & Yang, 2012). This leads to increase in the stopping distance of a vehicle since the grip between the wheel and the road has reduced drastically. Hence, it leads to high risk for a driver to lose control of the vehicle and unable to avoid the disturbance (Cabrera et al., 2005). Henceforth, a new type of braking technology has been designed and developed by automotive designers by considering after effects of vehicle skidding. A wide range of controllable braking technology has been invented by including the conventional braking system with electrical and electronics components (Aparow et al., 2013a). This type of braking technology is commonly known as active braking system such as electronic brake distribution (Laine & Andreasson, 2007), electronic stability control (Zhao et al., 2006; Piyabongkarn et al., 2007), automatic braking system (Littlejohn et al., 2004; Avery & Weekes, 2009) and also antilock braking system (Oudghiri et al., 2007; Aparow et al., 2013a). All this controllable braking system has been enhanced by automotive designers as part of safety system in vehicle. However, automotive designers have focused more on antilock braking system (ABS) since this active braking system has high potential to avoid wheel lock up and reduce stopping distance once emergency brake is applied. 38

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Basically, active braking known as antilock braking system was first introduced in aircraft technology to reduce the stopping distance of an aircraft. However, automotive researchers have adopted the knowledge of this active braking to ground vehicle design as vehicle safety system. Automotive researchers realized the capability of this system to reduce stopping distance in a safer method (Oniz et al., 2009; Aparow et al., 2013a). This active braking system was developed in order to control locking of the wheel during sudden braking (Oudghiri et al., 2007). In general, this type of active braking can be classified into three categories. Firstly, ABS via hydraulic system which is developed using hydraulic fluid used as a medium to transfer brake force from brake pedal to brake pad and rotors (Junxia & Ziming, 2010). Secondly, ABS via pneumatic system is designed by using air as a medium to transfer brake pressure which has been implemented in early 60’s. Unfortunately, this type of active braking system is applied mainly in commercial heavy vehicle such as truck, lorry and bus (Zhang et al., 2009; Zhang et al., 2010). Thirdly, ABS via combination of electronic and mechanical system is invented which used combination of electronic and mechanical systems (Yang et al., 2006). This type of braking system is the latest technology which is also invented based on aircraft and this technology is known as brake-by-wire. Many types of control strategies have been developed as the results of extensive research on antilock braking system (ABS). Control strategies used in order to control the ABS using electro hydro brake (EHB) and recently introduced for electronic wedge brake (EWB). Intelligent control strategies that have been applied for ABS using EHB are adaptive fuzzy-PID controller (Li et al., 2010), fuzzy logic control used by Aly et al., (2011), fuzzy sliding mode controller proposed by Oudghiri et al., (2007) and PID-particle swarm optimization (PSO) control technique proposed by Li and Yang (2012). Since ABS via EWB is still a new technology, many researchers such as Nantais and Minaker (2008) and Kim et al. (2010) have put their effort in designing ABS using simulation and applied in passenger vehicle. Moreover, Han et al. (2012) has initiated the controller research using sliding mode control using EWB actuator to estimate clamping force for braking. Most of the researchers used basic control algorithm such as PID to control ABS via EWB. However, the researchers do not identify a suitable controller by studying different controllers and make evaluation of their performance. Based on previous research works such as by Oudghiri et al. (2007), (Li et al., 2010) and Aly et al., (2011) for ABS using electro hydro brake and Nantaiz and Minaker (2008), Kim et al. (2010), Han et al. (2012) ISSN: 2180-1053

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for ABS using electronic wedge brake, an antilock braking system is proposed in this study. The antilock braking system was developed using electronic wedge brake model using Bell-Shaped curve. The proposed ABS-EWB model is a hydraulic free active braking system where this system tends to help humans to control vehicle steering and stability under heavy braking by preventing the wheels from locking up. Moreover, the proposed ABS-EWB model represents an active braking system based on brake-by-wire technology. Meanwhile, three types of control strategy are proposed and compared in this study for ABS-EWB model. The controllers are conventional PID, adaptive PID and fuzzy logic controller. The main purpose of proposing these types of controller is to identify a suitable control scheme for ABS-EWB by evaluating the performance of the model in terms of wheel longitudinal slip and also stopping distance of a vehicle. Adaptive PID control is developed using model reference adaptive control (MRAC) technique based on MIT rule while fuzzy logic is developed using Takagi-Sugeno configuration method. The paper is organized as follows: The second section presents the dynamic model of the vehicle in longitudinal direction. The following section presents the proposed control structure for the ABS inner loop control using EWB model and outer loop control using validated quarter vehicle model. The next section describes the integration of both outer loop and inner loop control structures to develop an ABS control scheme using PID, adaptive PID, fuzzy logic as the closed loop controller. The sixth section presents the performance evaluation of the proposed ABS control systems. The last section contains the conclusions of this study. 2.0

DEVELOPMENT OF A QUARTER VEHICLE BRAKE MODELING

Referring to works done by Oniz et al. (2009) and Li and Yang (2012), the brake modeling for a single wheel with quarter vehicle mass can be derived as mathematical equations. There are few types of responses of the vehicle due to brake input from driver and one of the response analyze in this study is skidding due to excessive braking. Four types of output response can be obtained using quarter vehicle brake model which are vehicle velocity, wheel velocity, longitudinal slip and stopping distance of a vehicle. The following section describes in detail on the development of the quarter vehicle model.

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2.1

Quarter Vehicle Brake Mathematical Modeling

The free body diagram a quarter vehicle modelThe is as shownsection in Figure wheel velocity, longitudinal slip and of stopping distance of a vehicle. following describes detail on the of themotion quarter vehicle 1 in describes thedevelopment longitudinal of themodel. vehicle and angular motion of the wheel during braking. Even though the model is quite general

wheel velocity, slip and stopping distance of a vehicle. The following section 2.1 Quarter Vehiclelongitudinal Brake Mathematical Modeling but it can sufficiently represent the actual vehicle system’s fundamental describes in detail on the development of the quarter vehicle model. et al., 2009). There several assumptions made The freecharacteristics body diagram of(Oniz a quarter vehicle model is as are shown in Figure 1 describes the wheel velocity, longitudinal slip and stopping distance of a vehicle. The following section deriving dynamic of of the First,braking. the vehicle 2.1 in Quarter Vehicle Mathematical Modeling longitudinal motion of the theBrake vehicle and equations angular motion thesystem. wheel during Even is describes in detail on thegeneral development ofcan the quarter vehicle wheel slip but and it stopping distance ofrepresent a model. vehicle. Theactual following section though the velocity, model islongitudinal quite sufficiently the vehicle considered in a longitudinal direction. The lateral and vertical motion describes in detail on the development of the quarter vehicle model. Theoffree body diagram of a quarter vehicle model is as shown in Figure 1 describes system’s fundamental characteristics (Oniz et al., 2009). There are several assumptions the vehicle is neglected. Secondly, the rolling resistance forcethe is Vehicle Brake Mathematical Modeling longitudinal of theequations vehicle and angular motion wheelisduring braking. made2.1 in Quarter deriving motion the dynamic of the system. First,ofthethevehicle considered in aEven ignored since itlateral is very small during braking. Thirdly, it actual is assumed 2.1 Quarter Vehicle though the model isBrake quite Mathematical general but motion it Modeling can of sufficiently the Secondly, vehicle longitudinal direction. The and vertical the vehiclerepresent is neglected. The free body diagram of a quarter vehicle model is as shown in Figure 1 describes that there is no interaction between four wheels of the vehicle (Oniz et system’s fundamental al.,small 2009). Therebraking. are several assumptions the rolling resistance force characteristics is ignored since(Oniz it is et very during Thirdly, it is the longitudinal motion of the and angular motion of the wheel during braking. Theal., free body diagram of avehicle quarter vehicle model isofas shown in (Oniz Figure describes Li &interaction Yang, 2012). Figure 1system. shows non-braking condition made in2009; deriving the dynamic equations of the First, the vehicle iset1considered inthea assumed that there is no between four wheels thethe vehicle al., 2009;Even though model isofThe general but it can sufficiently represent the actual motion the vehicle angular motion wheel braking. direction. lateral vertical motion ofof thethe vehicle isduring neglected. Secondly, Li &longitudinal Yang, 2012). Figure 1quite shows theand non-braking condition and braking condition ofvehicle aEven and the braking condition of aand quarter vehicle model. system’s fundamental characteristics (Oniz et al., 2009). There are several assumptions though themodel. model is force quite isgeneral it can represent the actual vehicle the rolling resistance ignoredbut since it is sufficiently very small during braking. Thirdly, it is quarter vehicle made in deriving equations of the system. First, thevehicle vehicle is considered in a system’s fundamental (Oniz et al.,wheels 2009). are several assumptions assumed that therethe is dynamic nocharacteristics interaction between four ofThere the (Oniz et al., 2009; longitudinal direction. The lateral andthe vertical ofFirst, the vehicle is neglected. Secondly, made in deriving theFigure dynamic equations of themotion system. theand vehicle is considered in a Li & Yang, 2012). 1 shows non-braking condition braking condition of the rolling resistance force is ignored since itmotion is veryofsmall during isbraking. Thirdly, it is longitudinal direction. The lateral and vertical the vehicle neglected. Secondly, 𝑀𝑀 𝑀𝑀 quarter vehicle model. 𝑣𝑣 𝑣𝑣 𝑉𝑉𝑉𝑉 𝑉𝑉𝑉𝑉 assumed that there is no interaction between wheels of the vehicle (OnizThirdly, et al., 2009; the rolling resistance force is ignored since itfour is very small during braking. it is Li & Yang, 1 shows between the non-braking condition braking condition of a assumed that2012). there isFigure no interaction four wheels of theand vehicle (Oniz et al., 2009; quarter vehicle model. 𝑚𝑚 𝑤𝑤 𝑀𝑀 Li 𝑚𝑚 &𝑊𝑊Yang, 2012). Figure 1 shows the non-braking condition and braking condition of a 𝑉𝑉 𝑀𝑀 𝑣𝑣 𝑣𝑣 𝑇𝑇𝑏𝑏 𝑉𝑉 𝑉𝑉𝑉𝑉 𝜔𝜔 quarter vehicle model. 𝑤𝑤 R R 𝜔𝜔𝑊𝑊 𝑀𝑀𝑣𝑣 𝑀𝑀𝑣𝑣 𝑚𝑚𝑤𝑤 𝑉𝑉𝑉𝑉 𝑚𝑚𝑊𝑊 𝑉𝑉𝑉𝑉 𝑇𝑇𝑏𝑏 𝑇𝑇𝑡𝑡 𝑇𝑇𝑡𝑡 𝜔𝜔 𝑀𝑀 𝑀𝑀 𝑤𝑤 𝑣𝑣 𝑣𝑣 R 𝑉𝑉 R 𝑉𝑉𝑉𝑉 𝐹𝐹𝑓𝑓 𝜔𝜔 𝑉𝑉 𝑊𝑊 𝑚𝑚 𝑚𝑚𝑊𝑊 𝑤𝑤 𝑇𝑇𝑏𝑏 (a) (b) 𝜔𝜔𝑤𝑤 𝑚𝑚𝑤𝑤 𝑚𝑚𝑇𝑇 R 𝑡𝑡𝑇𝑇al., 2009) 𝑊𝑊𝑡𝑡 1(a). R Figure Non-braking condition and (b) braking condition (Ahmad𝑇𝑇et 𝑏𝑏 condition Figure 1(a). Non-braking condition and (b) braking 𝜔𝜔𝐹𝐹𝑊𝑊 𝜔𝜔𝑤𝑤 𝑓𝑓 R R (Ahmad et al., 2009) Based on Newton’s second law, the equation of motion for the simplified vehicle model 𝜔𝜔 (a) (b) 𝑊𝑊 𝑇𝑇𝑡𝑡 𝑇𝑇𝑡𝑡 can be expressed as: 1(a). Non-braking condition and (b) braking condition (Ahmad Figure et al., 2009) 𝐹𝐹 𝑇𝑇𝑡𝑡 Based𝑇𝑇𝑡𝑡on Newton’s second law, the equation of motion for the simplified𝑓𝑓 𝐹𝐹𝑓𝑓 (a) (b) Based on Newton’s law, the model 𝐹𝐹𝑓𝑓 =be −((𝑀𝑀 𝑚𝑚𝑤𝑤 ) × vehicle model second can expressed as:𝑎𝑎𝑣𝑣of) motion for the simplified vehicle(1) 𝑣𝑣 + equation Figure 1(a). Non-braking condition and (b) braking condition (Ahmad et al., 2009) can be expressed(a) as: (b) Figurethe 1(a). Non-braking and (b) braking condition (Ahmad et al.,mass 2009) and 𝑎𝑎 where 𝑀𝑀𝑣𝑣 represents total mass ofcondition a vehicle body, 𝑚𝑚𝑤𝑤 represents the wheel 𝑣𝑣 Based on Newton’s second𝐹𝐹 law, the equation of motion for the simplified vehicle model = −((𝑀𝑀 + 𝑚𝑚 ) × 𝑎𝑎 ) represents the acceleration of the the tire friction force and (1) 𝑓𝑓 vehicle 𝑣𝑣while𝑤𝑤𝐹𝐹𝑓𝑓 represents 𝑣𝑣 can be expressed as: Newton’s second law, the equation of motion for the simplified vehicle model basedBased on theonlaw of Coulomb is represented by: can be 𝑀𝑀 expressed as: where represents the total mass of a vehicle body, 𝑚𝑚𝑤𝑤 represents the wheel mass and 𝑎𝑎𝑣𝑣 𝑣𝑣 (1) 𝐹𝐹𝑓𝑓 =the −((𝑀𝑀 𝑚𝑚𝑤𝑤 ) × of 𝑎𝑎𝑣𝑣 )a vehicle body, m represents where Mvacceleration represents total 𝑣𝑣 + mass w represents the of𝐹𝐹𝑓𝑓the= vehicle while 𝐹𝐹𝑓𝑓 represents the tire friction force (2) and 𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁 (1) 𝐹𝐹 = −((𝑀𝑀 + 𝑚𝑚 ) × 𝑎𝑎 ) the wheel mass and a represents the acceleration of the vehicle while 𝑣𝑣 𝑤𝑤 𝑣𝑣 based on the law of Coulomb𝑓𝑓 isv represented by: where 𝑀𝑀 represents the total mass of a vehicle body, 𝑚𝑚 represents the wheel mass and 𝑣𝑣 𝑤𝑤 𝑣𝑣 Ff represents the tire friction force and based on the law of Coulomb𝑎𝑎is Thusrepresents the acceleration of the vehicle while 𝐹𝐹 represents the tire friction force and 𝑓𝑓 where 𝑀𝑀 represents the total mass of a vehicle body, 𝑚𝑚 represents the wheel mass and 𝑎𝑎 𝑣𝑣 𝑤𝑤 represented by:−(𝑀𝑀𝑣𝑣 + 𝑚𝑚𝑤𝑤𝐹𝐹)𝑓𝑓×=𝑎𝑎𝑣𝑣 𝜇𝜇=𝑠𝑠 𝐹𝐹𝜇𝜇𝑁𝑁𝑠𝑠 𝐹𝐹𝑁𝑁 (3) (2)𝑣𝑣 based on thethelaw of Coulomb represented by: 𝐹𝐹𝑓𝑓 represents the tire friction force and represents acceleration ofis the vehicle while based on the law of Coulomb is represented by: Thus (2) 𝐹𝐹 = 𝜇𝜇 𝐹𝐹 (3) −(𝑀𝑀𝑣𝑣 + 𝑓𝑓𝑚𝑚𝑤𝑤 ) ×𝑠𝑠𝑎𝑎𝑣𝑣𝑁𝑁 = 𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁 (2) 𝐹𝐹𝑓𝑓 = 𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁 Thus Thus (3) −(𝑀𝑀𝑣𝑣 + 𝑚𝑚𝑤𝑤 ) × 𝑎𝑎𝑣𝑣 = 𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁 Thus (3) −(𝑀𝑀𝑣𝑣 + 𝑚𝑚𝑤𝑤 ) × 𝑎𝑎𝑣𝑣 = 𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁 ISSN: 2180-1053

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In Equations (2) and (3), FN represents the total normal load while the road adhesion coefficient, μs is a function of vehicle velocity and wheel slip. In Equations (2) and (3), 𝐹𝐹𝑁𝑁 represents the total normal load while the road adhesion During𝜇𝜇𝑠𝑠deceleration, torque iswheel applied coefficient, is a function ofbraking vehicle velocity and slip. to the wheels to reduce

wheel speed and vehicle speed. The rolling resistance force occurred at

During braking torque to much the wheels to reduce speedforce and the deceleration, wheel is neglected sinceisitapplied is very smaller thanwheel friction vehicle speed. The rolling resistance force occurred at the wheel is neglected since it is very between (2) theand wheel road (Oniz et al., 2009). According Newton’s In Equations (3), and 𝐹𝐹𝑁𝑁 represents the total normal load while the to road adhesion much smaller than friction force between the wheel and road (Oniz et al., 2009). According coefficient, 𝜇𝜇 is a function of vehicle velocity and wheel slip. second law, the equation of motion of the wheel can be written as: 𝑠𝑠 In Newton’s Equationssecond (2) and (3), the total normal while the as: road adhesion 𝑁𝑁 represents to law, the𝐹𝐹equation of motion of the wheelload can be written coefficient, 𝜇𝜇𝑠𝑠 (2) is aand function vehicle velocity and wheel slip. In Equations (3), 𝐹𝐹of𝑁𝑁torque represents the total normal loadto while roadspeed adhesion During deceleration, braking is applied to the wheels reducethe wheel and (4) ∑ 𝑇𝑇 = 𝑇𝑇 − 𝑇𝑇 𝑤𝑤 𝑡𝑡 𝑏𝑏 coefficient, 𝜇𝜇 is a function of vehicle velocity and wheel slip. is neglected since it is very 𝑠𝑠 The rolling resistance force occurred at the wheel vehicle speed. During deceleration, is applied to the wheels reducethe wheel and In Equations (2) andbraking (3), 𝐹𝐹𝑁𝑁torque represents the total normal loadto while roadspeed adhesion much smaller than friction force between the wheel and road (Oniz et al., 2009). According vehicle The rolling resistance occurred at the wheel neglected since it is very coefficient, 𝜇𝜇𝑠𝑠wheel is aand function vehicle velocity and wheel slip. where 𝑇𝑇speed. torque, while 𝑇𝑇force 𝑇𝑇𝑡𝑡 total represent the brake torque and torque During deceleration, braking applied to the the wheels toisbe reduce wheel speed and 𝑤𝑤 issecond 𝑏𝑏is In Equations (2) (3), 𝐹𝐹of represents the normal load while the roadtire adhesion to Newton’s law, theforce equation ofand motion of wheel can written as: 𝑁𝑁torque much smaller than friction between the wheel and road (Oniz et al., 2009). According respectively, Based on Equation (4), the following equations are derived as: vehicle speed. resistance force occurred at the since ittorque is very where wheel torque, while Tband and Tt wheel represent the brake coefficient, 𝜇𝜇T𝑠𝑠wThe isisa rolling function of vehicle velocity wheel slip. is neglected to Newton’s second law, theforce equation of applied motion of written as: According During deceleration, braking torque is to the the wheels tobereduce wheel speed and where the wheel torque, 𝑇𝑇respectively, much smaller than friction between andwheel road can (Oniz et al., 2009). 𝑤𝑤 , is ∑ and tire torque Equation (4), thesince following (4) 𝑇𝑇𝑤𝑤force = 𝑇𝑇the − wheel 𝑇𝑇𝑏𝑏 on 𝑡𝑡Based vehicle speed. The rolling resistance occurred at the wheel is neglected it is very to Newton’s second law, the equation of applied motion of cantobereduce writtenwheel as: speed During deceleration, braking torque is to the thewheel wheels and equations are derived as: (4) ∑between much smaller than friction force∑ and road (Oniz et al., 2009). According 𝑇𝑇𝑤𝑤 = = 𝐼𝐼𝑇𝑇the − wheel 𝑇𝑇𝑏𝑏 at 𝑡𝑡 × (5) vehicle The rolling resistance the the wheel is neglected since very 𝜔𝜔occurred 𝜔𝜔 where 𝑇𝑇speed. wheel torque, while𝑇𝑇𝑤𝑤𝑇𝑇force 𝑇𝑇𝑡𝑡 𝛼𝛼represent brake torque and tireit is torque 𝑤𝑤 issecond 𝑏𝑏ofand to Newton’s law, the equation motion of the wheel can be written as: (4) much smallerBased than friction force∑ between and road are (Oniz et al.,as: 2009). According 𝑇𝑇𝑤𝑤the = following 𝑇𝑇the 𝑇𝑇𝑏𝑏 equations 𝑡𝑡 − wheel respectively, on Equation (4), derived where wheel torque, while 𝑇𝑇𝑡𝑡 represent the can brake torque tire the torque where wheel torque, T𝑇𝑇w𝑏𝑏,ofand ismotion where I𝑇𝑇ω𝑤𝑤 wheel isisthe the wheel inertia, angular acceleration represented by 𝛼𝛼𝜔𝜔 ,and tire to Newton’s second law, the, equation of theiswheel be written as:while where the torque, 𝑇𝑇 is 𝑤𝑤 (4) respectively, on Equation (4), the ∑ 𝑇𝑇𝑤𝑤are = following 𝑇𝑇𝑡𝑡 − 𝑇𝑇𝑏𝑏 equations are derived as: torque, tire friction force, 𝐹𝐹 where 𝑇𝑇𝑇𝑇𝑤𝑤𝑡𝑡 and is Based wheel torque, while 𝑓𝑓 , 𝑇𝑇 𝑏𝑏 and 𝑇𝑇𝑡𝑡 represent the brake torque and tire torque , is where the wheel torque, 𝑇𝑇 𝑤𝑤 respectively, Based on Equation∑ (4), (4) ∑ 𝑇𝑇 the = following − 𝛼𝛼 𝑇𝑇𝑏𝑏 equations are derived as: (5) 𝐼𝐼𝑇𝑇𝜔𝜔𝑡𝑡 × 𝜔𝜔 where the 𝑇𝑇𝑤𝑤 wheel is wheel torque, while𝑇𝑇𝑤𝑤𝑤𝑤𝑇𝑇𝑏𝑏= and 𝑇𝑇 represent the brake torque and tire torque where torque, 𝑇𝑇𝑤𝑤 , is (6) 𝑇𝑇𝑡𝑡 = 𝐹𝐹𝑓𝑓𝑡𝑡 × 𝑅𝑅𝑟𝑟 (5) respectively, Based on Equation∑(4), the following equations are derived as: 𝑇𝑇 = 𝐼𝐼 × 𝛼𝛼 𝑤𝑤𝑇𝑇 and 𝜔𝜔 𝑇𝑇 represent 𝜔𝜔 where 𝑇𝑇𝑤𝑤 isis the wheel torque, while the brake torque and tire the torque 𝑏𝑏 𝑡𝑡 where I wheel inertia, angular acceleration is represented by 𝛼𝛼 , while tire ω wheel torque, 𝑇𝑇𝑤𝑤 , is 𝜔𝜔 where the (5), ∑𝐹𝐹 respectively, Based onwheel Equation (4), following equations are derived as: 𝑇𝑇𝑤𝑤 the = angular 𝐼𝐼𝜔𝜔 × 𝛼𝛼𝜔𝜔 acceleration and where is wheel the inertia, is represented by α torque, tire friction force, 𝑓𝑓 , are acceleration is represented by 𝛼𝛼𝜔𝜔 , while the tire ω where I𝑇𝑇ω𝑡𝑡 and isIωthe inertia, angular where the wheel torque, 𝑇𝑇 , is 𝑤𝑤 while thetire tire torque, T∑t𝐹𝐹𝑓𝑓and tire friction force, Ff, are (5) 𝑇𝑇 = 𝐼𝐼 × 𝛼𝛼 torque, 𝑇𝑇 and friction force, , are 𝑤𝑤 𝜔𝜔 𝜔𝜔 𝑡𝑡 where Iω is the wheel inertia, angular𝐹𝐹𝑓𝑓acceleration is represented by 𝛼𝛼𝜔𝜔 , while the tire (7) (6) 𝑇𝑇𝑡𝑡 == 𝐹𝐹𝑓𝑓𝜇𝜇𝑠𝑠×𝐹𝐹𝑁𝑁𝑅𝑅𝑟𝑟 (5) torque, 𝑇𝑇𝑡𝑡 and tire friction force,∑𝐹𝐹𝑓𝑓𝑇𝑇,𝑤𝑤are = 𝐼𝐼𝜔𝜔 × 𝛼𝛼𝜔𝜔 where Iω is the wheel inertia, angular acceleration is represented by 𝛼𝛼 , while the tire (6) 𝑇𝑇𝑡𝑡 = 𝐹𝐹𝑓𝑓 × 𝑅𝑅𝑟𝑟 𝜔𝜔 where 𝑅𝑅 is the radius of the wheel. By substituting Equations (5), (6) and (7) into (4), and torque, I𝑇𝑇𝑟𝑟𝑡𝑡 and tirewheel frictioninertia, force, angular 𝐹𝐹𝑓𝑓 , are acceleration is represented by 𝛼𝛼 , while the tire where is the (6) 𝑇𝑇𝑡𝑡 = 𝐹𝐹𝑓𝑓 × 𝑅𝑅𝑟𝑟 𝜔𝜔 Equationω (8) can be obtained as and torque, 𝑇𝑇𝑡𝑡 and tire friction force, 𝐹𝐹𝑓𝑓 , are (7) 𝐹𝐹 = 𝜇𝜇 𝐹𝐹 (6) 𝑇𝑇 𝑓𝑓= 𝐹𝐹 𝑠𝑠× 𝑁𝑁𝑅𝑅 (8) andand 𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁 × 𝑅𝑅𝑡𝑡 𝑟𝑟 − 𝑇𝑇𝑓𝑓𝑏𝑏 = 𝑟𝑟𝐼𝐼𝜔𝜔 × 𝛼𝛼𝜔𝜔 (7) 𝐹𝐹 = 𝜇𝜇 𝐹𝐹 (6) 𝑇𝑇𝑡𝑡 𝑓𝑓= 𝐹𝐹𝑓𝑓 𝑠𝑠× 𝑁𝑁𝑅𝑅𝑟𝑟 where By substituting Equations (5), (6) and (7) into (4), and 𝑅𝑅𝑟𝑟 is the radius of the wheel. 𝐹𝐹 (7) = 𝜇𝜇 𝐹𝐹 , is where the total normal load, 𝐹𝐹 𝑓𝑓 𝑠𝑠 𝑁𝑁 𝑁𝑁 Equation (8) can be obtained as where and 𝑅𝑅𝑟𝑟 is the radius of the wheel. By substituting Equations (5), (6) and (7) into (4), (7) = 𝜇𝜇+𝑠𝑠 𝐹𝐹𝑚𝑚 Equation obtained 𝑓𝑓(𝑀𝑀 𝑁𝑁 )𝑔𝑔 (9) =𝐹𝐹 where 𝑅𝑅𝑟𝑟(8) is can the be radius of theas By substituting Equations (5), (6) and (7) into (4), 𝑁𝑁 𝑅𝑅 𝑣𝑣 𝑤𝑤 (8) 𝜇𝜇𝑠𝑠wheel. 𝐹𝐹𝑁𝑁𝐹𝐹× 𝑟𝑟 − 𝑇𝑇𝑏𝑏 = 𝐼𝐼𝜔𝜔 × 𝛼𝛼𝜔𝜔 = 𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁 By substituting Equations (5), (7) where is the radius of the𝐹𝐹𝑓𝑓wheel. (6) Equation (8)Rcan r be obtained as where 𝑅𝑅 is the radius of the wheel. By substituting Equations (5), (6) and (7) into (4), 𝜇𝜇 𝐹𝐹 × 𝑅𝑅 − 𝑇𝑇 = 𝐼𝐼 × 𝛼𝛼 𝑟𝑟 Equation (9) into Equation 𝑠𝑠 𝑁𝑁 (8)𝑟𝑟 and rearrange 𝑏𝑏 𝜔𝜔 to𝜔𝜔obtain angular acceleration, 𝛼𝛼 (8) substitute 𝜔𝜔 , and into (4), load, Equation (8) can be obtained as where the(7) total 𝐹𝐹as 𝑁𝑁 , is Equation (8) cannormal be obtained (8) 𝐹𝐹𝑁𝑁 × 𝑅𝑅By − 𝑇𝑇 = 𝐼𝐼 × 𝛼𝛼 where 𝑅𝑅𝑟𝑟 is the radius of the𝜇𝜇𝑠𝑠wheel. substituting Equations (5), (6) and (7) into (4), 𝑟𝑟 𝑏𝑏 𝜔𝜔 𝜔𝜔 where the(8) total load, 𝐹𝐹as [𝜇𝜇 (𝑀𝑀 +𝑚𝑚 )𝑔𝑔×𝑅𝑅𝑟𝑟 ]− 𝑇𝑇𝑏𝑏 𝑁𝑁 , is Equation cannormal be obtained 𝛼𝛼𝜔𝜔 𝐹𝐹 =𝑁𝑁 =𝑠𝑠 (𝑀𝑀𝑣𝑣𝑣𝑣 +𝑤𝑤𝑚𝑚𝑤𝑤 )𝑔𝑔 (10) (9) (8) 𝜔𝜔 𝐼𝐼𝜔𝜔 × 𝛼𝛼𝜔𝜔 is𝑁𝑁 × 𝑅𝑅𝑟𝑟 − 𝑇𝑇𝑏𝑏 𝐼𝐼= where the total normal load, 𝐹𝐹𝑁𝑁𝜇𝜇,𝑠𝑠 𝐹𝐹 (9) 𝐹𝐹 = (𝑀𝑀 + 𝑚𝑚 )𝑔𝑔 𝑁𝑁 𝑣𝑣 𝑤𝑤 𝜇𝜇 𝐹𝐹𝑁𝑁 ×(8) 𝑅𝑅𝑟𝑟 and − 𝑇𝑇rearrange 𝛼𝛼𝜔𝜔obtain angular acceleration, 𝛼𝛼 (8) 𝑏𝑏 = 𝐼𝐼𝜔𝜔 × to substitute (9) load, into Equation , 𝜔𝜔 The longitudinal wheel speed, , and vehicle speed, 𝑉𝑉 , is represented in Equations (11) where the Equation total normal 𝐹𝐹𝑁𝑁 ,𝑠𝑠𝑉𝑉is 𝑤𝑤 𝐹𝐹 = (𝑀𝑀 + 𝑚𝑚 )𝑔𝑔 𝑣𝑣 (9) 𝑁𝑁 𝑣𝑣 𝑤𝑤 and (12): the total where normal load,[𝜇𝜇 F(𝑀𝑀 , isrearrange to obtain angular acceleration, 𝛼𝛼𝜔𝜔 , substitute (9) load, into Equation and N +𝑚𝑚 )𝑔𝑔×𝑅𝑅𝑟𝑟 ]− 𝑇𝑇 where the Equation total normal 𝐹𝐹𝑁𝑁 , is (8) 𝑏𝑏 𝛼𝛼𝜔𝜔 𝐹𝐹 =𝑁𝑁 =𝑠𝑠 (𝑀𝑀𝑣𝑣𝑣𝑣 +𝑤𝑤𝑚𝑚𝑤𝑤 )𝑔𝑔 (9) (10) 𝐼𝐼𝜔𝜔 substitute Equation (9) into Equation (8) and𝐹𝐹rearrange to obtain angular acceleration, 𝛼𝛼𝜔𝜔 , [𝜇𝜇𝑠𝑠 (𝑀𝑀𝑣𝑣 +𝑚𝑚 𝑓𝑓 𝑤𝑤 )𝑔𝑔×𝑅𝑅𝑟𝑟 ]− 𝑇𝑇𝑏𝑏 (11) 𝛼𝛼𝜔𝜔=𝐹𝐹 =𝑁𝑁∫ = 𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑 −(𝑀𝑀 𝑑𝑑𝑑𝑑 (vehicle speed) (10) (9) + 𝑚𝑚 )𝑔𝑔 𝑣𝑣 𝑤𝑤 𝐼𝐼 (𝑀𝑀𝑣𝑣 +𝑚𝑚 𝜔𝜔 𝑤𝑤 ) substitute Equation (9) into Equation (8) and rearrange to angular acceleration, 𝛼𝛼𝜔𝜔 , [𝜇𝜇𝑠𝑠vehicle (𝑀𝑀 𝑇𝑇𝑏𝑏,obtain 𝑣𝑣 +𝑚𝑚𝑤𝑤 )𝑔𝑔×𝑅𝑅 𝑟𝑟 ]− 𝑉𝑉 The longitudinal wheel speed, , and speed, (11) 𝑣𝑣 is represented in Equations (10) and 𝛼𝛼𝑉𝑉𝑤𝑤 𝜔𝜔 = 𝐼𝐼 𝜔𝜔 and substitute Equation (9) into Equation (8) and rearrange to obtain angular acceleration, 𝛼𝛼 (11) , The (12): longitudinal wheel speed, 𝑉𝑉𝑤𝑤 , and speed, [𝜇𝜇𝑠𝑠vehicle (𝑀𝑀𝑣𝑣 +𝑚𝑚𝑤𝑤 )𝑔𝑔×𝑅𝑅 𝑇𝑇𝑣𝑣𝑏𝑏, is represented in Equations 𝜔𝜔 𝑟𝑟 ]− 𝑉𝑉 𝛼𝛼 = (10) substitute Equation (9) into Equation (8) and rearrange to obtain 𝜔𝜔 and 𝐼𝐼 The (12): longitudinal wheel speed, 𝑉𝑉𝑤𝑤 , and vehicle 𝐹𝐹 𝜔𝜔speed, ]− 𝑉𝑉 𝑇𝑇𝑣𝑣𝑏𝑏, is represented in Equations (11) acceleration, α𝛼𝛼ω𝜔𝜔,==∫[𝜇𝜇−𝑠𝑠(𝑀𝑀𝑣𝑣 +𝑚𝑚𝑓𝑓𝑤𝑤)𝑔𝑔×𝑅𝑅 (11) 𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑟𝑟 (vehicle speed) (10) andangular (12): 𝐼𝐼𝜔𝜔𝑤𝑤 ) (𝑀𝑀𝑣𝑣𝐹𝐹 +𝑚𝑚 𝑓𝑓 The longitudinal wheel speed, 𝑉𝑉 , and vehicle speed, 𝑉𝑉 , is represented in Equations (11) 𝑣𝑣 (11) 𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑𝑤𝑤= ∫ − (𝑀𝑀 +𝑚𝑚 ) 𝑑𝑑𝑑𝑑 (vehicle speed) and 𝑣𝑣𝐹𝐹 𝑤𝑤 and (12): 𝑓𝑓 speed, 𝑉𝑉 , is represented in Equations (11) The longitudinal wheel speed, 𝑉𝑉 , and vehicle 𝑣𝑣 and (11) 𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑𝑤𝑤= ∫ − (𝑀𝑀 +𝑚𝑚 ) 𝑑𝑑𝑑𝑑 (vehicle speed) and42(12): ISSN: 2180-1053 Vol.𝑣𝑣𝐹𝐹6 𝑤𝑤 No. 1 January - June 2014 𝑓𝑓 and (11) 𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑 = ∫ − 𝑑𝑑𝑑𝑑 (vehicle speed) (𝑀𝑀 +𝑚𝑚 ) 𝑣𝑣𝐹𝐹

𝑓𝑓

𝑤𝑤

where the total normal load, 𝐹𝐹𝑁𝑁 , is

(9) (9) 𝐹𝐹𝑁𝑁 = (𝑀𝑀𝑣𝑣 + 𝑚𝑚𝑤𝑤 )𝑔𝑔 substitute Equation (9) into Equation (8) and rearrange to obtain angular acceleration, 𝛼𝛼𝜔𝜔 , substitute Equation (9) into Equation (8) and rearrange to obtain angular acceleration, 𝛼𝛼𝜔𝜔 , [𝜇𝜇 (𝑀𝑀 +𝑚𝑚 )𝑔𝑔×𝑅𝑅𝑟𝑟 ]− 𝑇𝑇𝑏𝑏 𝛼𝛼𝜔𝜔 = 𝑠𝑠 𝑣𝑣 𝑤𝑤𝐼𝐼 (10) 𝜔𝜔 [𝜇𝜇𝑠𝑠 (𝑀𝑀𝑣𝑣 +𝑚𝑚𝑤𝑤 )𝑔𝑔×𝑅𝑅 𝑟𝑟 ]− 𝑇𝑇𝑏𝑏 𝛼𝛼𝜔𝜔 = (10) 𝐼𝐼𝜔𝜔 The longitudinal wheel speed, 𝑉𝑉𝑤𝑤 , and vehicle speed, 𝑉𝑉𝑣𝑣 , is represented in Equations (11) The (12):longitudinal wheel speed, Vw, and vehicle speed, Vv, is represented The and longitudinal wheel speed, 𝑉𝑉 , and vehicle speed, 𝑉𝑉 , is represented in Equations (11) 𝐹𝐹𝑁𝑁 = (𝑀𝑀𝑣𝑣 + 𝑚𝑚𝑤𝑤 )𝑔𝑔


𝑤𝑤

𝑣𝑣

in Equations (11) and (12): and (12): 𝐹𝐹𝑓𝑓 𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑 = ∫ − 𝑑𝑑𝑑𝑑 (vehicle speed) (𝑀𝑀 +𝑚𝑚 ) and

and

and

𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑 =

𝑉𝑉𝑤𝑤 = ∫ 𝑎𝑎𝜔𝜔 𝑑𝑑𝑑𝑑 = ∫

𝑣𝑣

𝑤𝑤

𝐹𝐹𝑓𝑓 ∫ − (𝑀𝑀 +𝑚𝑚 ) 𝑑𝑑𝑑𝑑 𝑣𝑣 𝑤𝑤

(vehicle speed)

[𝜇𝜇𝑠𝑠 (𝑀𝑀𝑣𝑣 +𝑚𝑚𝑤𝑤 )𝑔𝑔×𝑅𝑅𝑟𝑟 ]− 𝑇𝑇𝑏𝑏 𝑑𝑑𝑑𝑑 𝐼𝐼𝜔𝜔

(wheel speed)

(11)

(11)

(12)

The rotational velocity of the [𝜇𝜇wheel would be𝑟𝑟 ]− similar with the forward velocity of the )𝑔𝑔×𝑅𝑅 𝑇𝑇𝑏𝑏 The𝑉𝑉rotational of𝑣𝑣+𝑚𝑚 the𝑤𝑤wheel would be similar the forward 𝑠𝑠 (𝑀𝑀 = ∫ 𝑎𝑎𝜔𝜔operating 𝑑𝑑𝑑𝑑velocity = ∫ conditions. 𝑑𝑑𝑑𝑑 (wheel speed)with vehicle under Once the brakes are applied, braking forces(12) are 𝑤𝑤 normal 𝐼𝐼𝜔𝜔 velocity of the vehicle under normal operating conditions. generated at the interface between the wheel and road surface. The braking force will Once cause thetobrakes applied, braking arethegenerated the interface wheel reduce are thethe speed. Increasing theforces forces at wheel will at increase The the rotational velocity of wheel would be similar with the forward velocityslippage of the between the wheel and road surface. The braking force willthan cause between the tire and road surface and this will cause the wheel speed to be lower the vehicle under normal operating conditions. Once the brakes are applied, braking forces are vehicle the speed (Oniz to et al., 2009).the Thespeed. parameter used to obtain the slippage occurring atwill the wheel reduce Increasing the forces at the wheel generated at the interface between the wheel and road surface. The braking force will cause wheel using both vehicle andbetween wheel velocity is known as wheel slip, 𝜆𝜆,and this will cause increase slippage the tire and road surface the wheel to reduce the speed. Increasing the forces at the wheel will increase slippage speed to be than the vehicle speed (Oniz et al., 2009). between thethe tirewheel and road surface andlower this will cause 𝑉𝑉𝑣𝑣 − 𝑉𝑉𝜔𝜔 the wheel speed to be lower than the 𝜆𝜆 = The parameter usedThe to obtain the slippage occurring at the wheel using vehicle speed (Oniz et al., 2009). parameter to obtain the slippage occurring at(13) the 𝑚𝑚𝑚𝑚𝑚𝑚(𝑉𝑉used 𝑣𝑣 ,𝑉𝑉𝜔𝜔) andwheel wheel velocity is known as wheel wheel usingboth both vehicle vehicle and velocity is known as wheel slip, 𝜆𝜆,slip, λ, The forward velocity and tire rolling speed are equal when the slip ratios of the vehicle 𝑉𝑉𝑣𝑣 − 𝑉𝑉𝜔𝜔 of either engine torque or brake torque. A approach zero. Zero slip ratio implies 𝜆𝜆 = absence (13) 𝑚𝑚𝑚𝑚𝑚𝑚(𝑉𝑉𝑣𝑣 ,𝑉𝑉𝜔𝜔)a greater finite forward velocity with the positive slip ratio implies the vehicle approaches tire having a positive finite rolling velocity. While a negative slip ratio implies the tire has a The greater forwardequivalent velocity and tire rolling speed equal when slip ratios the forward vehicle positive velocityaremeanwhile thethe vehicle has a of finite The forward velocity and tire rolling speed are equal when the slip velocity (Short 2004). Two conditions occurred approach zero. Zero et slipal., ratio implies absence of either enginewhen torquetheor longitudinal brake torque.slip A of +1 theorthe vehicle approach zero. Zerofinite ratio implies absence approaches either -1.vehicle The conditions are wheel isslip ‘spinning’ with the vehicle at positive slipratios ratio implies approaches athegreater forward velocity with the either engine torque orzero brake torque. Aslip positive slip ratio implies zero speed or the finite wheel is ‘locked’ at speed. The longitudinal is mathematically tire having aofpositive rolling velocity. While a negative ratioslip implies the tire has a thewhen vehicle approaches a velocities greater finite forward with the the tire undefined both tires and vehicle are equal zero. velocity Figure graph greater equivalent positive rolling velocity meanwhile theto vehicle has 2a shows finite forward having aal.,positive rolling a the negative slip ratio with wheel slip, velocity. 𝜆𝜆 (Aparow et when al., 2013a). relating friction velocity (Short et coefficient, 2004).𝜇𝜇𝑠𝑠 finite Two conditions occurredWhile longitudinal slip a greater equivalent positive with rolling velocity approaches implies either +1 the or -1.tire Thehas conditions are the wheel is ‘spinning’ the vehicle at vehicleathas a finite velocityslip (Short et al., 2004). zero speed meanwhile or the wheel the is ‘locked’ zero speed. forward The longitudinal is mathematically undefined when tires andoccurred vehicle velocities are longitudinal equal to zero. Figure 2 shows theeither graph Twoboth conditions when the slip approaches relating friction coefficient, 𝜇𝜇 with wheel slip, 𝜆𝜆 (Aparow et al., 2013a). +1 or -1. The conditions are the wheel is ‘spinning’ with the vehicle at 𝑠𝑠

zero speed or the wheel is ‘locked’ at zero speed. The longitudinal slip is mathematically undefined when both tires and vehicle velocities are equal to zero. Figure 2 shows the graph relating friction coefficient, μs with wheel slip, λ (Aparow et al., 2013a).

Figure 2. Experiment data for 𝜇𝜇𝑠𝑠 vs slip (Aparow et al., 2013a)

The value of friction coefficient, 𝜇𝜇𝑠𝑠 , is obtained using a lockup table based on the experiment on normal road2180-1053 surface. These gathered from ISSN: Vol. values 6 No.were 1 January - June 2014tire experiment43 conducted on a normal surface road. The response from the variation of friction coefficient

approaches either +1 or -1. The conditions are the wheel is ‘spinning’ with the vehicle at zero speed or the wheel is ‘locked’ at zero speed. The longitudinal slip is mathematically Journal of Mechanical andvelocities Technologyare equal to zero. Figure 2 shows the graph undefined when both tiresEngineering and vehicle relating friction coefficient, 𝜇𝜇𝑠𝑠 with wheel slip, 𝜆𝜆 (Aparow et al., 2013a).

FigureFigure 2. Experiment data for μ vs slip (Aparow et al., 2013a) 2. Experiment data for 𝜇𝜇 s vs slip (Aparow et al., 2013a) 𝑠𝑠

The value of friction coefficient, μs, is obtained lockup table The value of friction coefficient, 𝜇𝜇𝑠𝑠 , is obtained using a using lockupa table based on the basedononnormal the experiment onThese normal roadwere surface. These values were experiment road surface. values gathered from tire experiment gathered from surface tire experiment conducted normalofsurface conducted on a normal road. The response fromon theavariation friction road. coefficient with slip ratio is used as the input for quarterofvehicle brake model. with slip ratio is The response from the variation friction coefficient used as the input for quarter vehicle brake model. 2.2

Description of Simulation Model

The vehicle dynamics model is developed based on the mathematical equations from the previous quarter vehicle model by using MATLAB SIMULINK. Figure thebased simulation model of the quarter The vehicle dynamics model3 isshows developed on the mathematical equations from the vehiclequarter brakevehicle modelmodel withbya step the brakeFigure input.3 The step previous using function MATLABas SIMULINK. shows the simulation model of the quarter model with afrom step function the brake input. response represents thevehicle brakebrake torque input brake aspedal during The step response brakeintorque input fromvehicle brake pedal during This braking. Thisrepresents signal isthe used the quarter model forbraking. dynamic signal is used in the quarter vehicle model for dynamic performance analysis in performance analysis in longitudinal direction only. Meanwhile, the longitudinal direction only. Meanwhile, the parameters for the quarter vehicle model are parameters listed in the Tablefor 1. the quarter vehicle model are listed in the Table 1. 2.2 Description of Simulation Model

Figure 3. Quarter vehicle Matlab SIMULINK Figure 3. Quarter vehiclemodel model in in Matlab SIMULINK Table 1. Simulation model parameters for the vehicle model (Ahmad et al., 2009)

44

Description Wheel Inertia ISSN: 2180-1053 Brake coefficient Vehicle mass

Vol. 6

No. 1

Symbol Value 5 kgm2 𝐼𝐼𝜔𝜔 January - June 2014 0.8 𝐾𝐾𝑏𝑏 690 kg 𝑀𝑀𝑣𝑣

Development of Antilock Braking System using Electronic Wedge Brake Model Figure 3. Quarter vehicle model in Matlab SIMULINK

Table 1. Simulation model parameters for the vehicle model Table 1. Simulation model parameters foret theal., vehicle model (Ahmad et al., 2009) (Ahmad 2009) Description Wheel Inertia Brake coefficient Vehicle mass Wheel mass Tire radius Gravitational acceleration Coefficient of friction Vehicle speed

3.0

Symbol 𝐼𝐼𝜔𝜔 𝐾𝐾𝑏𝑏 𝑀𝑀𝑣𝑣 𝑚𝑚𝑤𝑤 𝑅𝑅𝑡𝑡 g 𝜇𝜇 v0

Value 5 kgm2 0.8 690 kg 50 kg 285 mm 9.81 m/s 2 0.4 25 m/s

EWB MODELING USING BELL-SHAPED CURVE 3.0 EWB MODELING USING BELL-SHAPED CURVE

By refering to Aparowto et Aparow al. (2013b),et a mathematical using Bell-Shaped curve has been By refering al. (2013b),equation a mathematical equation using used toBell-Shaped developed electronic equation can represent the curvewedge has brake beenmodel. usedThetomathematical developed electronic wedge actual force and brake torque produced by a real EWB actuator. The derived mathematical equation

brake model. The mathematical equation can represent the actual force and brake torque produced by a real EWB actuator. The derived mathematical equation using trigonometric function such as tangential function (Aparow et al., 2013b). In this study, Bell-Shaped curve, a nonusing trigonometric function such asdescribed tangential function linear equation is used by (Aparow et al., 2013b). In this study, BellShaped curve, a non-linear equation is used described by

𝑥𝑥−𝑐𝑐 2𝑏𝑏

where

𝐹𝐹𝑀𝑀 = 𝐹𝐹𝑐𝑐𝑐𝑐 [1/(1 + �

𝑎𝑎

� )

(14)

𝐹𝐹𝑀𝑀 where is the maximum clamping force for EWB system (output) 𝐹𝐹𝑐𝑐𝑐𝑐 is clamping force of EWB system FMthe isreal thetime maximum clamping force for EWB system (output) 𝑥𝑥 is the piston displacement (input) F is the real time clamping force of EWB system 𝑎𝑎 andcsb are the width of the curve the ofpiston 𝑐𝑐 isxtheiscenter the curvedisplacement (input)

a and b are the width of the curve

Thecparameters used in is the center ofthe theEquation curve (14) such as a, b and c are estimated to sufficiently the behaviour of EWB simulation model to replace an EWB actuator. The parameters of a, b and c are

estimated through trial and error technique and the data has been analyzed using root mean Theerror parameters used in The the Equation (14)Equation such as(14) a, bisand c arebased estimated square (RMSE) technique. parameters for obtained on the sufficiently of The EWB simulation model an leasttoerror results fromthe the behaviour RMSE analysis. parameters is listed in Tableto2 replace based on the simulation and experiment work of EWB.ofAccording Equation (14), the input oftrial the EWB actuator. The parameters a, b and to c are estimated through proposed equation is obtainedand fromthe the data worm has pinion displacement while the output of this and error technique been analyzed using root mean model represents the clamping force of EWB model. Hence, brake torque of the EWB square error (RMSE) technique. The parameters for Equation (14) is model using Bell-Shaped curve can be obtained using Equation (15) which was obtained obtained on the least error results from the RMSE analysis. The from Rahman etbased al., (2012)

parameters is listed in Table 2 based on the simulation and experiment = 𝐹𝐹𝑓𝑓𝑓𝑓 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒 (14), the input of the proposed work of EWB. According to𝑇𝑇𝑏𝑏Equation where 𝐹𝐹𝑓𝑓𝑓𝑓 = 2𝜇𝜇is𝑓𝑓 𝐹𝐹obtained equation from the worm pinion displacement while the 𝑁𝑁 output of this model represents the clamping force of EWB model. Hence it can be conclude that of the EWB model using Bell-Shaped curve can Hence, brake torque ISSN: 2180-1053

where

𝑇𝑇𝑏𝑏 = 2𝜇𝜇𝑓𝑓 𝐹𝐹𝑁𝑁 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒 Vol. 6

No. 1

January - June 2014

(15)

45

estimated through trial and error technique and the data has been analyzed using root mean

The square parameters in theintechnique. Equation (14) such as a,asbfor andbEquation cand arec estimated to sufficiently errorused (RMSE) The(14) parameters (14) is obtained basedthe on the The parameters used the Equation such a, are estimated to sufficiently the behaviour of EWB simulation model to replace an EWB actuator. Theisparameters of a, of b2 and cand are behaviour of EWB simulation model to replace an EWB actuator. The parameters a, b are least error results from the RMSE analysis. The parameters listed in Table based onc the Journal of Mechanical Engineering and Technology estimated through trial and error technique and the data has been analyzed using root mean

estimated trial and error the data to hasEquation been analyzed using rootof mean simulationthrough and experiment worktechnique of EWB.and According (14), the input the square errorerror (RMSE) technique. The parameters forpinion Equation (14) (14) is obtained based on the square (RMSE) technique. The parameters for Equation iswhile obtained based on this the proposed equation is obtained from the worm displacement the output of leastleast errorerror results fromfrom the RMSE analysis. TheEWB parameters listed inbrake Table 2 based on results the RMSE analysis. The parameters is listed in Table 2 of based on the model represents the clamping force of model.isHence, torque thethe EWB be using obtained using Equation (15) which obtained from Rahman et simulation experiment work of can EWB. According towas Equation (14), the input ofobtained the simulation and experiment work of be EWB. According to Equation thewas input of the model and Bell-Shaped curve obtained using Equation (15)(14), which al., (2012) proposed equation is obtained from the worm pinion displacement while the output of this proposed equation obtained from the worm pinion displacement while the output of this from Rahman et al.,is(2012) model represents the clamping forceforce of EWB model. Hence, brakebrake torque of the model represents the clamping of EWB model. Hence, torque of EWB the EWB model usingusing Bell-Shaped curvecurve can be using Equation (15) which was obtained model Bell-Shaped canobtained be obtained using Equation (15) which was obtained 𝑇𝑇𝑏𝑏 = 𝐹𝐹𝑓𝑓𝑓𝑓 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒 fromfrom Rahman et al., (2012) Rahman et al., (2012) where 𝐹𝐹𝑓𝑓𝑓𝑓 = 2𝜇𝜇𝑓𝑓 𝐹𝐹𝑁𝑁

where

Hence conclude that where 𝐹𝐹𝑓𝑓𝑓𝑓 it=𝐹𝐹can 2𝜇𝜇𝑓𝑓be 𝐹𝐹2𝜇𝜇 𝑁𝑁 𝑓𝑓 𝐹𝐹𝑁𝑁 where 𝑓𝑓𝑓𝑓 =

𝑇𝑇𝑏𝑏 =𝑇𝑇𝐹𝐹𝑏𝑏𝑓𝑓𝑓𝑓=𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒 𝐹𝐹𝑓𝑓𝑓𝑓 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒

𝑇𝑇𝑏𝑏 = 2𝜇𝜇𝑓𝑓 𝐹𝐹𝑁𝑁 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒 Hence itHence canit be that Hence canconclude conclude that itbecan be conclude that

(15)

where 𝑇𝑇 = 2𝜇𝜇 𝐹𝐹𝑁𝑁 𝑓𝑓𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒 (15) (15) 𝐹𝐹𝑁𝑁 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒 𝑇𝑇𝑏𝑏 is the brake torque produced 𝑏𝑏 𝑇𝑇𝑏𝑏 =𝑓𝑓 2𝜇𝜇 𝐹𝐹𝑓𝑓𝑓𝑓 is the friction force generated at the contact interface where 𝑟𝑟where is the effective pad radius 𝑒𝑒𝑒𝑒𝑒𝑒where 𝑇𝑇𝑏𝑏 is𝑇𝑇the brakebrake torque produced 𝐹𝐹𝑏𝑏𝑁𝑁 is is the the normaltorque forceproduced 𝐹𝐹𝑓𝑓𝑓𝑓 is𝐹𝐹𝑓𝑓𝑓𝑓 theisfriction forceforce generated at the contact interface the friction generated contact interface 𝜇𝜇𝑓𝑓 is the friction coefficient of on at thethe surface 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒 𝑟𝑟is𝑒𝑒𝑒𝑒𝑒𝑒 the pad radius Tisbeffective is the brake torque produced the effective pad radius force 𝐹𝐹𝑁𝑁 isIt Fnormal the friction force generated at of thefriction contact interface is theisnormal forceto define 𝐹𝐹the necessary the coefficient between disc and pad contact 𝑁𝑁 is fcalso 𝜇𝜇𝑓𝑓 is𝜇𝜇 the friction ofpad on surface coefficient ofthe on the surface interface to calculate the brake torque. The coefficient of friction is dependent on the refftheisfriction thecoefficient effective radius 𝑓𝑓 is braking such force as disc speed, temperature of the disc, brake line pressure and other F isconditions the normal It is It also necessary to define theAparow coefficient friction between disc disc and and pad pad contact is Nalso necessary to2012; define the coefficient friction between contact factors (Rahman et al., et al., of 2013b). μftoiscalculate the friction coefficient of theofsurface interface the brake torque. Theon coefficient of friction is dependent on the interface to calculate the brake torque. The coefficient of friction is dependent on the braking conditions suchsuch as disc speed, temperature of theofdisc, brakebrake line pressure and other braking conditions as disc speed, temperature the disc, line pressure and other factors (Rahman al.,et2012; Aparow et al.,etthe 2013b). It is(Rahman alsoet necessary toAparow define of friction between disc and factors al., 2012; al., coefficient 2013b).

pad contact interface to calculate the brake torque. The coefficient of friction is dependent on the braking conditions such as disc speed, temperature of the disc, brake line pressure and other factors (Rahman et al., 2012; Aparow et al., 2013b). Table 2. Simulation parameters for bell-shaped curve and brake torque

Table 2. Simulation parameters for bell-shaped curve and brake torque Description 𝐹𝐹𝑐𝑐𝑐𝑐 𝜇𝜇𝑓𝑓 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒 a b c

4.0

Value 3500 N 0.45 0.15 m 6.295×10−4 m 2.820×10−4 m 9.570×10−4 m

CONTROL STRUCTURE DESIGN

4.0

CONTROL STRCTURE DESIGN

In the previous section, the development of a quarter vehicle model and electronic wedge brake model using Bell-Shaped curve has been discussed in detail. In this section, an active braking system, Anti-lock Brakingthe System (ABS) is developed usingvehicle the quarter vehicle In the previous section, development of a quarter model brakeand model and EWB model. Figure 4 shows the proposed outer and inner loop control electronic wedge brake model using Bell-Shaped curve has been for ABS model. Two control loops are needed to be designed in developing an ABS model discussed in detail. In this section, an active braking system, Anticontrol scheme using both quarter vehicle model and EWB model. These control loops are lock Braking System is developed theloop quarter known as an inner loop control(ABS) and outer loop control.using The inner controlvehicle is used to control the actuator of the proposed system. In this study, EWB model is also used as the actuator for the ABS control system. 46

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January - June 2014

The actuator model is the focus of on electronic wedge brake mechanism (EWB) (Rahman

a 6.295×10−4 m b 2.820×10−4 m −4 Development of Antilock Braking System using Electronic c 9.570×10 m Wedge Brake Model

brake CONTROL model andSTRUCTURE EWB model. DESIGN Figure 4 shows the proposed outer and 4.0

inner loop control for ABS model. Two control loops are needed to In previous section, the development a quarter vehiclescheme model and electronic bethe designed in developing an ABSofmodel control using both wedge brake model using model Bell-Shaped been discussed in detail. In this an active quarter vehicle and curve EWBhas model. These control loops aresection, known braking system, Anti-lock Braking System (ABS) is developed using the quarter as an inner loop control and outer loop control. The inner loop control vehicle brake model EWBthe model. Figure 4ofshows the proposed outer and control for is used to and control actuator the proposed system. Ininner this loop study, ABS model. Two control loops are needed to be designed in developing an ABS model EWB model is also used as the actuator for the ABS control system.

control scheme using both quarter vehicle model and EWB model. These control loops are known as an inner loop control and outer loop control. The inner loop control is used to The actuator model is the focus of on electronic wedge brake mechanism control the actuator of the proposed system. In this study, EWB model is also used as the (EWB) for (Rahman al., 2012) actuator the ABS et control system.system since the brake actuator model is

developed based on brake-by-wire concept. Meanwhile, the outer loop control for ABS system is to control the quarter vehicle model. Initially, The actuator model is the focus of on electronic wedge brake mechanism (EWB) (Rahman the longitudinal slip for quarter vehicle model is controlled without et al., 2012) system since the brake actuator model is developed based on brake-by-wire involving brake actuator model or inner loop control. The controller concept. Meanwhile, the outer loop control for ABS system is to control the quarter vehicle for this model will control the quarter vehicle model’s slipwithout model. Initially, the longitudinal slip for quarter vehicle model is wheel controlled directly brake without any model interference the actual longitudinal involving actuator or inner until loop control. The wheel controller for this model will control quarter that vehicle model’s wheel slip the directly without any longitudinal interference until the slip is the obtained closely follow with desired wheel actual wheel longitudinal slip is obtained that closely follow with the desired slip (Aparow et al., 2013a). Similar procedure is applied for inner loop wheel longitudinal slip (Aparow al.,control 2013a).brake Similartorque. procedure is applied for inner loop control control model in orderetto model in order to control brake torque.

Figure 4.outer Proposed outer and loop inner loop controls forABS ABS model model Figure 4. Proposed and inner controls for

Then, both loop controls are integrated to become a closed loop model known as ABSThen, both loop controls are integrated to become a closed loop model EWB model to control the wheel longitudinal slip and stopping distance of quarter vehicle known asproposed ABS-EWB modelfortoinner control wheel longitudinal slipthree andtypes of model. The controller loop the control is PID controller while stopping distance of quarter vehicle model. The proposed controller controller, namely PID, adaptive PID and fuzzy logic controllers are proposed for the

for inner loop control is PID controller while three types of controller, namely PID, adaptive PID and fuzzy logic controllers are proposed for the overall ABS-EWB control structure. The results using all three controllers are compared and most optimum controller is proposed for ABS-EWB model. 4.1

PID controller

PID algorithm stil is remain as one of the most widely used controller in industrial process control. It is not only because PID algorithm has a simple structure whereby easy to implement but also provides adequate performance in most applications. PID controller may also be considered as a phase lead-lag compensator with one pole formation ISSN: 2180-1053

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47

4.1 PID controller


PID algorithm stil is remain as one of the most widely used controller in industrial process control. It is not only because PID algorithm has a simple structure whereby easy to at twobut points which is at the performance origin andinother infinity. PID A standard implement also provides adequate most at applications. controller is as known “ three-term” controller the transfer mayPID also controller be considered a phaseaslead-lag compensator with one where pole formation at two points which is at the origin and other at infinity. A standard PID controller is known as “ function of PID is generally written in the “parallel form” or “ideal three-term” controller where the transfer function of PID is generally written in the form” “parallel form” or “ideal form” 𝑈𝑈(𝑠𝑠)

𝐺𝐺𝑃𝑃𝑃𝑃𝑃𝑃 (𝑠𝑠) = 𝐸𝐸(𝑠𝑠) = 𝐾𝐾𝑝𝑝 + 𝐾𝐾𝑖𝑖 /𝑠𝑠 + 𝐾𝐾𝑑𝑑 𝑠𝑠 𝐺𝐺𝑃𝑃𝑃𝑃𝑃𝑃 (𝑠𝑠) = 𝐾𝐾𝑝𝑝 (1 +

1 𝑇𝑇𝑖𝑖 𝑠𝑠

+ 𝑇𝑇𝑑𝑑 𝑠𝑠)

(16) (17)

where U(s) is the control signal acting on the error signal E(s), 𝐾𝐾𝑝𝑝 is the proportional gain, where U(s) gain, is the𝐾𝐾𝑑𝑑control signalgain, acting onintergal the error signal E(s), is 𝐾𝐾𝑖𝑖 is the intergal the derivative 𝑇𝑇𝑖𝑖 the time constant and 𝑇𝑇𝑑𝑑Kpthe derivative time constant. gain, In thisKstudy, PIDintergal controllergain, is used inthe thederivative inner loop system to the proportional is the K gain, T i d i regulate the brake time torqueconstant from the electronic wedge brake (EWB). output from the the intergal and Td the derivative timeThe constant. In this inner loop control is used as an input for the outer loop control.The output from the outer controller is used in innerthe loop system regulate the loopstudy, controlPID is the wheel longitudinal slipthe to avoid vehicle fromtoskidding during brake torque from the electronic wedge brake (EWB). The output from braking. The PID parameter are tuned using Knowledge Based Tuning (KBT) method the inneret loop control is used as torque an input for the outermodel loopis control. (Calvo-Rolle al., 2011) until actual brake produced by EWB same as desired torque in order to control wheel is longitudinal sliplongitudinal of quarter vehicle Thebrake output from the outer loopthe control the wheel slip model. to avoid the vehicle from skidding during braking. The PID parameter

are tuned using Knowledge Based Tuning (KBT) method (Calvo-Rolle et al., 2011) until actual brake torque produced by EWB model is same desired brake torque in to order the wheel longitudinal slip An as adaptive mechansim is needed tune to thecontrol PID parameters to make overall system behaves as the reference of quarter vehicle model. model.Therefore, a model reference adaptive control (MRAC) 4.2 Outer loop Control Design using Adaptive PID controller

using MIT rule is proposed as an adaptive mechanism for PID controller (Adrian et al., 2008). The adaptive PID controller which is applied in the outer loop model is shown in 4.2 Outer loop Control Design using Adaptive PID controller Figure 5 while mathematical derivations is described by the following equations.

An adaptive mechansim is needed to tune the PID parameters to make overall system behaves as the reference model. Therefore, a model reference adaptive control (MRAC) using MIT rule is proposed as an adaptive mechanism for PID controller (Adrian et al., 2008). The adaptive PID controller which is applied in the outer loop model is shown in Figure 5 while mathematical derivations is described by the following equations.

Figure 5. Adaptive PID using MIT Rule for outer loop model Figure 5. Adaptive PID using MIT Rule for outer loop model

The adaptive PID controller parameters are adjusted to give desired closed-loop performance for ABS model. The controller parameters are estimated to cause the desired change in plant transfer function so that can- June be made 48 ISSN: 2180-1053 Vol. the 6 actual No. 1 output January 2014 similar to the reference model (Swarnkar et al., 2011).


The adaptive PID controller parameters are adjusted to give desired closed-loop performance for ABS model. The controller parameters are estimated to cause the desired change in plant transfer function so that the actual output can be made similar to the reference model (Swarnkar Figure 5. Adaptive PID using MIT Rule for outer loop model et al., 2011).

The adaptive PID controller parameters are adjusted to give desired closed-loop performance for ABS model. 4.2.1 Reference modelThe controller parameters are estimated to cause the desired change in plant transfer function so that the actual output can be made similar to the reference model (Swarnkar et al., 2011). Normally, the reference model will be the desired overall system’s

performance by the designer. The adaptive mechanism is developed based on the error between the output response of the plant with the reference model. The controller is designed force the by plant Normally, the reference modeladaptive will be the desired overall system’s to performance the modelThe to act similar to reference model. Model output, λm, is compared designer. adaptive mechanism is developed based on the error between the output response the plantoutput, with the λ reference The adaptive designed to force to theof actual , and model. the difference is controller used to is adjust feedback p the PID plantcontroller model to act similar to reference model. Model output, 𝜆𝜆 , is compared to the 𝑚𝑚 parameters. The reference model used for the adjustment actual output, 𝜆𝜆𝑝𝑝 , and the difference is used to adjust feedback PID controller parameters. mechanism is 4.2.1 Reference model

The reference model used for the adjustment mechanism is 𝜆𝜆𝑚𝑚 (𝑠𝑠) 𝜆𝜆𝑝𝑝(𝑠𝑠)

𝐾𝐾𝜔𝜔 2

= 𝑠𝑠2 +2𝜀𝜀𝜀𝜀 𝑛𝑛𝑠𝑠+𝜔𝜔 𝑛𝑛

𝑛𝑛

(18)

2

where, 𝜔𝜔𝑛𝑛 is the undamped natural frequency, 𝜀𝜀, is the damping ratio while K is the gain of is the undamped natural frequency, ε, is the damping ratio the where, system. ω The n value of 𝜔𝜔𝑛𝑛 = 15 rad/s, 𝜀𝜀 = 0.65, K = 1. These values are chosen for the closed loopKsystem haveofmaximum overshoot 5% atofrise s andεpeak timeKat= while is the to gain the system. The ≤ value ωntime = 150.1 rad/s, = 0.65, 0.251.s These when excited with step function. values area chosen for the closed loop system to have maximum

overshoot ≤ 5% at rise time 0.1 s and peak time at 0.25 s when excited with a step function.

4.2.2 Transfer Function for Quarter Vehicle Brake Model

The inner loop model is ignored in this stage in order to develop outer loop ABS model. The4.2.2 purpose of ignoring the inner modelVehicle is to avoid interference Transfer Function forloop Quarter Brake Model during the development of the adaptive control. The Laplace transfer function of the quarter vehicle The𝐺𝐺inner loop model is ignored in this stage in order to develop outer model, 𝑝𝑝 , is needed to derive the adjustment mechanism. This transfer function model is loop ABS Thesingle purpose of ignoring loop model is the to developed usingmodel. single input output (SISO) concept.the Theinner step response is used as brake inputinterference for both quarter vehicle model and first order transfer control. function. The The avoid during thebrake development of the adaptive comparison of the quarter of vehicle brake model and the approximation of the Laplaceresults transfer function the quarter vehicle model, Gp, is needed response as a first order system are shown in Figure 6.

to derive the adjustment mechanism. This transfer function model is developed using single input single output (SISO) concept. The step response is used as the brake input for both quarter vehicle brake model and first order transfer function. The comparison results of the quarter vehicle brake model and the approximation of the response as a first order system are shown in Figure 6.

ISSN: 2180-1053

Vol. 6

No. 1

January - June 2014

49


Graph longitudinal wheel slip versus time 1 2DOF 1st order function

Graph longitudinal wheel slip versus time

0.9 1 0.8

longitudinal longitudinal wheel slip longitudinal wheel slip longitudinal wheel slip wheel slipwheel slip longitudinal

0.9 0.7 1 0.8 0.6 0.9 0.7 0.5 1 0.8 0.6 0.4 0.9 0.7 0.5 0.3 1 0.8 0.6 0.4 0.2 0.9 0.7 0.5 0.3 0.1 0.8 0.6 0.4 0.20 0.7 0 0.5 0.3 0.1 0.6 0.4 0.2 0 0 0.5 0.3 0.1


2DOF 1st order function


2DOF 1st order function


2DOF 1st order function 2DOF 1st order function

0.5

1

1.5

time, t

2

2.5

3

3.5

0.5 1of 1.5 2 function 2.5 and 3 3.5 Figure 6. Comparison order transfer quarter vehicle Figure 6. Comparison of1st 1st order transfer function and quarter vehicle model time, t 0.4 model 0.2 0 0 0.5 1 1.5 2 2.5 3 3.5 Transfer function plant model, quarter vehicle model is model shown in Equation Figureof 6. Comparison of 1st𝐺𝐺order transfer and quarter vehicle 0.3 𝑝𝑝 , using time, function t 0.1 (19) 0.2 0 Transfer function of plant model, Gfunction using quarter vehicle model is 0 2.5 vehicle model 3 3.5 p, 2 vehicle Figure 0.5 6. Comparison1 of 1st order1.5 transfer and quarter Transfer quarter model is shown in Equation t 0.1 function of plant model, 𝐺𝐺𝑝𝑝 , using time, shown in Equation (19) 𝑏𝑏 0.002385 (19) 0 st 𝐺𝐺1𝑝𝑝of=1�𝐺𝐺 � =quarter �function � quarter 0.5 1.5 2 vehicle 2.5 vehicle 3 3.5 (19) Figureof 6. Comparison transfer and model Transfer 0function plant model, ,1 +𝑎𝑎 using model is shown in Equation 𝑎𝑎𝑝𝑝order 𝑠𝑠 0 time, t 1+0.25𝑠𝑠 (19) 𝑏𝑏 0.002385 st (19) 𝐺𝐺𝑝𝑝 of = 1�𝐺𝐺 � =quarter �function � quarter Transfer function of6. Comparison plant , using vehicle model is shown Figure transfer and vehicle model in Equation Meanwhile the output frommodel, plant model, 𝑎𝑎𝑝𝑝order 1 +𝑎𝑎0𝜆𝜆𝑠𝑠𝑝𝑝 , is 1+0.25𝑠𝑠 𝑏𝑏 0.002385 (19) (19) 𝐺𝐺𝑝𝑝 = � � =quarter � 2 vehicle � model is shown in Equation Transfer function of plant 𝐺𝐺𝑎𝑎𝑝𝑝1,+𝑎𝑎 using 0.002385 Meanwhile the output from model, plant model, 𝜆𝜆0𝐾𝐾𝑝𝑝𝑠𝑠𝑝𝑝 𝑠𝑠+𝐾𝐾 , is 𝑖𝑖 +𝐾𝐾1+0.25𝑠𝑠 𝑑𝑑 𝑠𝑠 (20) 𝜆𝜆 = � � � � �𝜆𝜆 − 𝜆𝜆 � 𝑝𝑝 𝑑𝑑 𝑝𝑝 𝑏𝑏 (19)Meanwhile the output 1+0.25𝑠𝑠 𝑠𝑠 0.002385 λp�, is (19) 𝐺𝐺𝑝𝑝 from = � plant =model, � � 2 Meanwhile the output from plant model, , is𝑖𝑖 +𝐾𝐾1+0.25𝑠𝑠 𝑎𝑎1 +𝑎𝑎𝜆𝜆 𝑠𝑠𝑠𝑠+𝐾𝐾 𝐾𝐾 0𝑝𝑝 0.002385 𝑝𝑝 𝑑𝑑 𝑠𝑠 𝜆𝜆𝑝𝑝 =the � difference �� 𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 � and actual response for(20) desired input the where 𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 represents 1+0.25𝑠𝑠 𝑏𝑏 between 𝑠𝑠 0.002385 (19) 𝐺𝐺𝑝𝑝 = � =� 2 � � 𝐾𝐾 𝑠𝑠+𝐾𝐾 +𝐾𝐾 𝑠𝑠 , is Meanwhile output from plant model, outer loop the model. Rearrange Equation (20) to obtain the closed function of outer loop 0.002385 𝑎𝑎1 +𝑎𝑎𝜆𝜆 𝑠𝑠 1+0.25𝑠𝑠 𝑝𝑝 𝑑𝑑 𝑖𝑖 (20) 𝜆𝜆 = � 1+0.25𝑠𝑠 � � 0𝑝𝑝 𝑠𝑠 � �𝜆𝜆 − 𝜆𝜆𝑝𝑝 � between desired𝑑𝑑 input and actual response for the where model 𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 represents𝑝𝑝 the difference 2 𝐾𝐾 , isto Meanwhile the output from plant model, 𝜆𝜆 0.002385 outer loop model. Rearrange Equation (20) the closed function of outer loop 𝑝𝑝 𝑑𝑑 𝑠𝑠 𝑖𝑖 +𝐾𝐾obtain 𝑝𝑝𝑠𝑠+𝐾𝐾 𝜆𝜆𝑝𝑝 = � difference � � between � �𝜆𝜆 − 𝜆𝜆𝑝𝑝 �and actual response for(20) − 𝜆𝜆 represents the desired the where 𝜆𝜆 𝜆𝜆 0.002385(𝐾𝐾 𝑠𝑠+𝐾𝐾 +𝐾𝐾𝑑𝑑 𝑠𝑠2𝑑𝑑) input 1+0.25𝑠𝑠 𝑠𝑠 𝑑𝑑 𝑝𝑝 𝑝𝑝 𝑝𝑝 𝑖𝑖 model = �(0.25+0.002385𝐾𝐾 )𝑠𝑠2 +(1+0.002385𝐾𝐾 � (21) 𝜆𝜆represents )𝑠𝑠+0.002385𝐾𝐾 outer loop λ model. Rearrange Equation (20) closed function outer loop +𝐾𝐾obtain 𝑠𝑠2 where -λ the difference between desired and actual 0.002385 𝑝𝑝the 𝑑𝑑 𝑑𝑑 𝐾𝐾 𝑖𝑖 inputof 𝑝𝑝 𝑠𝑠+𝐾𝐾to 𝑑𝑑 𝑖𝑖 d p 𝜆𝜆𝑝𝑝 = � � between � �𝜆𝜆2𝑑𝑑 − 𝜆𝜆𝑝𝑝 �and actual response for(20) represents the� difference desired input the where 𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 for model 𝜆𝜆𝑝𝑝the outer 1+0.25𝑠𝑠 𝑠𝑠𝑠𝑠+𝐾𝐾 𝑝𝑝 𝑖𝑖 +𝐾𝐾𝑑𝑑 𝑠𝑠 ) response loop0.002385(𝐾𝐾 model. Rearrange Equation (20) to obtain = � � (21) 2 +(1+0.002385𝐾𝐾 outer loop model.𝜆𝜆𝑑𝑑Rearrange Equation𝑑𝑑)𝑠𝑠(20) to obtain 𝑝𝑝the closed function of outer loop (0.25+0.002385𝐾𝐾 )𝑠𝑠+0.002385𝐾𝐾 𝑖𝑖 the𝜆𝜆closed function of difference outer0.002385(𝐾𝐾 loop model 𝜆𝜆MIT +𝐾𝐾𝑑𝑑value 𝑠𝑠2 ) input represents the response for the where model By applying gradient rule, thebetween adaptation for and PIDactual controller parameters 𝑝𝑝 𝑝𝑝 𝑠𝑠+𝐾𝐾𝑖𝑖desired 𝑑𝑑 − 𝜆𝜆𝑝𝑝the =� � (21) 2 +(1+0.002385𝐾𝐾 )𝑠𝑠+0.002385𝐾𝐾 𝜆𝜆𝑑𝑑Rearrange (0.25+0.002385𝐾𝐾 outer model. Equation (20) obtain 𝑝𝑝based the closed function of outer loop 𝑑𝑑 )𝑠𝑠 𝑖𝑖 𝐾𝐾𝑝𝑝 , 𝐾𝐾𝑖𝑖loop and 𝐾𝐾 The parameters aretoderived 𝑑𝑑 are obtained. 𝜆𝜆𝑝𝑝 𝑠𝑠2 ) 𝑝𝑝 𝑠𝑠+𝐾𝐾𝑖𝑖 +𝐾𝐾𝑑𝑑value model By applying the MIT rule,0.002385(𝐾𝐾 the adaptation for PID �controller parameters = gradient �(0.25+0.002385𝐾𝐾 (21) 2 +(1+0.002385𝐾𝐾 𝜆𝜆 )𝑠𝑠 𝑑𝑑𝑑𝑑 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝑝𝑝 )𝑠𝑠+0.002385𝐾𝐾 𝑑𝑑 𝑑𝑑 𝑖𝑖 𝑥𝑥 𝐾𝐾𝑝𝑝 , 𝐾𝐾𝑖𝑖 and 𝐾𝐾𝑑𝑑 are obtained. The parameters are derived based = 𝛾𝛾 ( ) = 𝛾𝛾 [( )( )( )] (22) 𝑝𝑝 𝑥𝑥 2 𝑑𝑑𝑑𝑑 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜆𝜆𝑝𝑝 𝑠𝑠 ) 𝜕𝜕𝜕𝜕for By applying the MIT gradient rule,0.002385(𝐾𝐾 the adaptation PID controller parameters 𝑥𝑥 𝑥𝑥 𝑝𝑝 𝑠𝑠+𝐾𝐾𝜕𝜕𝜕𝜕 𝑖𝑖 +𝐾𝐾𝑑𝑑value = � � (21) 2 𝜆𝜆𝑑𝑑 (0.25+0.002385𝐾𝐾 𝐾𝐾𝑝𝑝 , 𝐾𝐾𝑖𝑖 and 𝐾𝐾𝑑𝑑 are obtained. are derived 𝑑𝑑𝑑𝑑𝑥𝑥The parameters 𝜕𝜕𝜕𝜕 𝑑𝑑 )𝑠𝑠 +(1+0.002385𝐾𝐾 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕based 𝜕𝜕𝜕𝜕 𝑝𝑝 )𝑠𝑠+0.002385𝐾𝐾 𝑖𝑖 =or- Intergral 𝛾𝛾rule, ) =adaptation - 𝛾𝛾 [(𝜕𝜕𝜕𝜕)(𝜕𝜕𝜕𝜕 )(𝜕𝜕𝜕𝜕 )] PID (22) 𝑝𝑝 (𝜕𝜕𝜕𝜕the 𝑥𝑥 Derivative ⁄𝜕𝜕𝜕𝜕controller ⁄𝜕𝜕𝜕𝜕PID where 𝐾𝐾applying (P) or (D), = value 𝑒𝑒 and 𝜕𝜕𝜕𝜕 = 1. By applying the MIT value parameters 𝑑𝑑𝑑𝑑 𝑥𝑥 = Proportional 𝑥𝑥 (I) 𝑥𝑥for 𝜕𝜕𝜕𝜕 By thegradient MIT gradient rule, the adaptation for Equation (22) has been derived mathematically in order to develop an adjustment 𝑑𝑑𝑑𝑑 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝐾𝐾 , 𝐾𝐾 and 𝐾𝐾 are obtained. The parameters are derived based 𝑥𝑥 𝑝𝑝 controller 𝑖𝑖 𝑑𝑑 = -K𝛾𝛾p𝑝𝑝,K ( i and ) = - 𝛾𝛾K𝑥𝑥 d[(are )( obtained. )(𝜕𝜕𝜕𝜕 )] The parameters (22) parameters are 𝑑𝑑𝑑𝑑 or Intergral 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 mechanism for controller. ⁄𝜕𝜕𝜕𝜕controller ⁄𝜕𝜕𝜕𝜕 = 1. where 𝐾𝐾𝑥𝑥 = Proportional (P) or Derivative (D), = 𝑒𝑒 and 𝜕𝜕𝜕𝜕 𝑥𝑥 (I) 𝑥𝑥for𝜕𝜕𝜕𝜕 By applying thePID MIT gradient rule,𝜕𝜕𝜕𝜕 the adaptation value PID parameters derived 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 in 𝜕𝜕𝜕𝜕 order 𝜕𝜕𝜕𝜕 Equation has been𝑑𝑑𝑑𝑑derived mathematically to develop an adjustment 𝑥𝑥The parameters 𝐾𝐾 𝐾𝐾𝑑𝑑based are obtained. 𝑝𝑝 , 𝐾𝐾𝑖𝑖 and(22) = - 𝛾𝛾𝑝𝑝 ( ) = -are 𝛾𝛾 derived [( )( based )( (D),)] 𝜕𝜕𝜕𝜕⁄𝜕𝜕𝜕𝜕 = 𝑒𝑒 and 𝜕𝜕𝜕𝜕⁄𝜕𝜕𝜕𝜕 (22) where 𝐾𝐾𝑥𝑥 = for Proportional (P) = 1. 𝑑𝑑𝑑𝑑 or Intergral 𝜕𝜕𝜕𝜕𝑥𝑥 (I) or𝑥𝑥 Derivative 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 mechanism PID controller. 𝑥𝑥 Equation (22) has been𝑑𝑑𝑑𝑑derived mathematically to develop an adjustment 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 in 𝜕𝜕𝜕𝜕 order 𝜕𝜕𝜕𝜕 𝑥𝑥 = - 𝛾𝛾𝑝𝑝 ( ) = - 𝛾𝛾 [( )( )( (D),)] 𝜕𝜕𝜕𝜕⁄𝜕𝜕𝜕𝜕 = 𝑒𝑒 and 𝜕𝜕𝜕𝜕⁄𝜕𝜕𝜕𝜕 (22) where 𝐾𝐾𝑥𝑥 = for Proportional (P) = 1. mechanism PID controller. 𝑑𝑑𝑑𝑑 or Intergral 𝜕𝜕𝜕𝜕𝑥𝑥 (I) or𝑥𝑥 Derivative 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕𝑥𝑥 Equation (22) has been derived mathematically in order to develop an adjustment mechanism PID controller. where 𝐾𝐾𝑥𝑥 = for Proportional (P) or Intergral (I) or Derivative (D), 𝜕𝜕𝜕𝜕⁄𝜕𝜕𝜕𝜕 = 𝑒𝑒 and 𝜕𝜕𝜕𝜕⁄𝜕𝜕𝜕𝜕 = 1. Equation (22) has been derived mathematically in order to develop an adjustment mechanism for PID controller.

50

ISSN: 2180-1053

Vol. 6

No. 1

January - June 2014


where Kx = Proportional (P) or Intergral (I) or Derivative (D), ∂J⁄∂e= e and ∂e⁄∂y = 1. Equation (22) has been derived mathematically in order to develop an adjustment mechanism for PID controller. 𝜕𝜕𝜕𝜕𝑝𝑝

𝜕𝜕𝜕𝜕𝑝𝑝

𝜕𝜕𝜕𝜕𝑖𝑖

𝜕𝜕𝜕𝜕𝑝𝑝

𝜕𝜕𝜕𝜕𝑝𝑝 𝜕𝜕𝜕𝜕= 𝑝𝑝 𝜕𝜕𝜕𝜕𝑑𝑑 𝜕𝜕𝜕𝜕𝑖𝑖

= �(0.25+0.002385𝐾𝐾

𝑑𝑑 )𝑠𝑠

= 𝑝𝑝 𝜕𝜕𝜕𝜕

𝜕𝜕𝜕𝜕𝑝𝑝

0.002385𝑠𝑠

2 +(1+0.002385𝐾𝐾 )𝑠𝑠+0.002385𝐾𝐾 𝑝𝑝 𝑖𝑖

0.002385

�(𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 )

� �(𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 ) 0.002385𝑠𝑠 i 𝑑𝑑 − 𝜆𝜆𝑝𝑝 ) = � (0.25+0.002385Kd)s2 2 +(1+0.002385Kp)s+0.002385K �(𝜆𝜆 (0.25+0.002385𝐾𝐾𝑑𝑑 )𝑠𝑠 +(1+0.002385𝐾𝐾𝑝𝑝 )𝑠𝑠+0.002385𝐾𝐾𝑖𝑖

0.002385s2

�(0.25+0.002385K )s2 +(1+0.002385K �(𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 ) 0.002385 = �(0.25+0.002385K �(𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 ) p )s+0.002385Ki d )s2 +(1+0.002385K )s+0.002385K p

d

i

(23) (24) (23) (25) (24)

By refering to𝜕𝜕𝜕𝜕Equations (23) to (25),0.002385s the adaptation value for PID parameters are obtained 2 𝑝𝑝 = � �(𝜆𝜆equations (25) as Equations (26) to (28) using 1st order transfer function. This will be used as By refering to Equations (23) to (25), the adaptation for PID 𝑑𝑑 − 𝜆𝜆𝑝𝑝 )value 2 𝜕𝜕𝜕𝜕𝑑𝑑 (0.25+0.002385Kd )s +(1+0.002385Kp )s+0.002385K i adjustment mechanism for the PID of outer loop control to 1st develop antransfer adaptive parameters are obtained ascontroller Equations (26) to (28) using order controller usingThis By refering toPID. Equations (23) towill (25),be theused adaptation value for PIDmechanism parameters arefor obtained function. equations as adjustment the as Equations (26) to (28) using 1st order transfer function. This equations will be used as PID controller of outer loop control to develop an adaptive controller 𝑑𝑑𝑑𝑑𝑝𝑝 𝜕𝜕𝜕𝜕 0.002385𝑠𝑠 adjustment the PID controller of outer loop control to� (𝜆𝜆 develop an adaptive = - 𝛾𝛾𝑝𝑝 PID. (𝜕𝜕𝜕𝜕 mechanism ) = - 𝛾𝛾𝑝𝑝 𝑒𝑒[�for (26) 𝑑𝑑 − 𝜆𝜆𝑝𝑝 )] 2 𝑑𝑑𝑑𝑑using 𝑝𝑝 controller using PID. (0.25+0.002385𝐾𝐾𝑑𝑑)𝑠𝑠 +(1+0.002385𝐾𝐾𝑝𝑝 )𝑠𝑠+0.002385𝐾𝐾𝑖𝑖 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 ∂J 0.002385 𝑖𝑖 𝑝𝑝 0.002385𝑠𝑠 = - γ ( 𝑝𝑝 () 𝜕𝜕𝜕𝜕 = -) = γi -e[� � (λ�d(𝜆𝜆−𝑑𝑑 λ−p )] 𝛾𝛾𝑝𝑝(0.25+0.002385𝐾𝐾 𝑒𝑒[�(0.25+0.002385𝐾𝐾 𝜆𝜆𝑝𝑝 )] 2 +(1+0.002385𝐾𝐾 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 = i- 𝛾𝛾∂K 𝑝𝑝 )𝑠𝑠+0.002385𝐾𝐾 𝑑𝑑 )𝑠𝑠 𝑑𝑑 i 𝜕𝜕𝜕𝜕𝑝𝑝 𝑖𝑖 )𝑠𝑠2 +(1+0.002385𝐾𝐾 𝑝𝑝 )𝑠𝑠+0.002385𝐾𝐾 𝑖𝑖

2 𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑖𝑖 𝜕𝜕𝜕𝜕 ∂J 0.002385𝑠𝑠 0.002385 = - 𝛾𝛾=𝑑𝑑 -(𝜕𝜕𝜕𝜕 ) = )- =𝛾𝛾𝑑𝑑- γ𝑒𝑒[� �� (𝜆𝜆 γ ( e[� (λ𝑑𝑑d − 𝜆𝜆λp𝑝𝑝)] 2 +(1+0.002385𝐾𝐾 2 i i 𝑑𝑑𝑑𝑑 (0.25+0.002385𝐾𝐾 )𝑠𝑠 )𝑠𝑠+0.002385𝐾𝐾 𝑑𝑑𝑑𝑑 (0.25+0.002385𝐾𝐾 )𝑠𝑠+0.002385𝐾𝐾𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝 𝑑𝑑 ∂Ki 𝑑𝑑 𝑑𝑑 )𝑠𝑠 +(1+0.002385𝐾𝐾

(27) (26)

(28) (27)

𝑑𝑑𝑑𝑑𝑑𝑑𝛾𝛾 represents 𝜕𝜕𝜕𝜕 the learning rate of the adaptation 0.002385𝑠𝑠2 mechanism and 𝜀𝜀 are the defined where = - 𝛾𝛾𝑑𝑑 ( ) = - 𝛾𝛾𝑑𝑑 𝑒𝑒[� � (𝜆𝜆 − 𝜆𝜆𝑝𝑝 )] (28) 2 +(1+0.002385𝐾𝐾 )𝑠𝑠+0.002385𝐾𝐾 𝑑𝑑𝑑𝑑 𝜕𝜕𝜕𝜕 (0.25+0.002385𝐾𝐾 )𝑠𝑠 𝑝𝑝 error based on the𝑑𝑑 difference between actual𝑑𝑑 output and desired output. 𝑖𝑖The 𝑑𝑑parameters for the adjustment mechanism in the Equations (18) to (28) are obtained from linearization of 𝛾𝛾 represents rate value of theofadaptation mechanism and 𝜀𝜀 linearization are the defined the where controller gain with the the learning desired slip antilock braking, 𝜆𝜆. Before is error based on the to difference output and desired The parameters for made, it is necessary identify between the PID actual controller parameter for output. the braking model using where γ represents the rate of adaptation mechanism and the adjustment mechanism in learning the Equations (18) tothe (28) areis obtained linearization sudden braking test input. The identified PID controller used asfrom a bench mark inof εtheare the defined error based theofdifference between actual output controller gain with the desired slipon value antilockThe braking, 𝜆𝜆. Before linearization developing adaptation mechanism for MRAC model. initial values of the PIDis made,desired it is necessary identify the PID in controller for the braking and output. Therate parameters forparameter the adjustment mechanism controller parameters andtolearning used this model are shown in Table 3. model using sudden test input. identified PID controller is used as a bench of mark in the braking Equations (18) The to (28) are obtained from linearization thein developing adaptationTable mechanism forandMRAC The initial values of the PID 3. Controller learning model. rate parameters controller gain with desired slipinvalue of antilock controller parameters and the learning rate used this model are shownbraking, in Table 3.λ. Before

linearization is made, it is necessary to identify Value the PID controller Description Symbol P 3. Controller 550 Table and learning parametersbraking 𝐾𝐾𝑝𝑝sudden parameter Proportional for the gain, braking model usingrate test input. Intergal gain, I 2950 𝐾𝐾𝑖𝑖 The identified PID controller is used as Symbol a bench mark Description Valuein developing Derivative gain, D 10 𝐾𝐾 𝑑𝑑 Proportional P MRAC model.𝛾𝛾The 550 𝐾𝐾 adaptationLearning mechanism initial values of the PID rate of gain, P for 0.001 𝑝𝑝 𝑝𝑝 Intergal gain, I 2950 𝐾𝐾 𝑖𝑖 Learning rate of I and learning rate used 0.05 𝛾𝛾𝑖𝑖 controller parameters in this model are shown Derivative gain, 10 Learning rate of D D 0.05 𝛾𝛾𝑑𝑑𝐾𝐾𝑑𝑑 in Table 3. Learning rate of P 0.001 𝛾𝛾𝑝𝑝 Learning rate of I

𝛾𝛾𝑖𝑖 4.3 Outer loop Control Design using Fuzzy Logic controller Learning rate of D 𝛾𝛾𝑑𝑑

0.05 0.05

Another advance fuzzyusing logic,Fuzzy was developed in this study based on Takagi4.3 Outer loopcontroller, Control Design Logic controller Sugeno method for the outer loop control system besides adaptive PID controller. In this Another advance controller, fuzzy logic, was developed in this study based on TakagiSugeno method for the outer loop control system besides adaptive PID controller. In this

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made, it is necessary to identify the PID controller parameter for the braking model using sudden braking test input. The identified PID controller is used as a bench mark in developing mechanismand forTechnology MRAC model. The initial values of the PID Journal ofadaptation Mechanical Engineering controller parameters and learning rate used in this model are shown in Table 3. 3. Controller and learning rate parameters Table Table 3. Controller and learning rate parameters Description Proportional gain, P Intergal gain, I Derivative gain, D Learning rate of P Learning rate of I Learning rate of D

Symbol 𝐾𝐾𝑝𝑝 𝐾𝐾𝑖𝑖 𝐾𝐾𝑑𝑑 𝛾𝛾𝑝𝑝 𝛾𝛾𝑖𝑖 𝛾𝛾𝑑𝑑

Value 550 2950 10 0.001 0.05 0.05

4.3 Outer loop Control Design using Fuzzy Logic controller

4.3

Outer loop Control Design using Fuzzy Logic controller

Another advance controller, fuzzy logic, was developed in this study based on TakagiAnother advance controller, fuzzy logic, was developed in this study Sugeno method for the outer loop control system besides adaptive PID controller. In this

0.2 Desired input, 𝜆𝜆𝑑𝑑

+ _

𝑑𝑑⁄𝑑𝑑𝑑𝑑

Inference

Rule Base

Defuzzificatio

Error

Fuzzification

based on Takagi-Sugeno method for the outer loop control system besides adaptive PID controller. In this network model, the controller consists of three stages which are known as fuzzification, rule base and defuzzification (Ping et al., 2010). Figure 7 shows the overall control structure of fuzzy logic control using Gaussian membership function for the outer loop. The inputs to the fuzzy controller are error and error rate. These fuzzy or linguistic variables are obtained through network model, the controller of three of stages known as fuzzification, fuzzification process.consists The output the which fuzzyarecontroller is gap control rule of base and defuzzification (Ping et al., 2010). Figure 7 shows the overall brake piston in EWB actuator. Membership functions of control the input structure of fuzzy logic control using Gaussian membership function for the outer loop. The and outpu fuzzy variables are defined. The output-input variables inputs to the fuzzy controller are error and error rate. These fuzzy or linguistic variables are are through linkedfuzzification by rules. process. The membership functions and rules are defined obtained The output of the fuzzy controller is gap control of brakebased piston in EWB actuator. Membership functions of the input and outpu fuzzy variables on expert experinece. Finally, defuzzification method converts are defined. The output-input variables are linked by rules. The membership functions and the fuzzy output into a crisp signal and become the command input for rules are defined based on expert experinece. Finally, defuzzification method converts the plant fuzzythe output intomodel. a crisp signal and become the command input for the plant model.

Two DOF vehicle model

Actual output, 𝜆𝜆𝑝𝑝

Error rate

Fuzzy Logic controller

Figure 7. Fuzzy logic controller Gaussian membership Figure 7. Fuzzy logic controller using Gaussianusing membership function for outer loop modelfunction for outer loop model

In the Figure 7, the inputs of the fuzzy controller i.e. slip error and slip error rate are defined duringFigure the initialization stage andofallthe fuzzy membership functions defined in In the 7, the inputs fuzzy controller i.e.areslip error order to form the complete rules. A Gaussian membership function is used and defined by

and slip error rate are defined during the initialization stage and all fuzzy 𝑥𝑥 − 𝑐𝑐in order to form the complete rules. membership functions are defined (29) 𝜇𝜇 = 𝑒𝑒 −0.5( 𝜎𝜎 ) A Gaussian membership function is used and defined by

where x is the Gaussian input from error and error rate c is the center of the curve 𝜎𝜎 is the spread of the curve

The52 fuzzy logic network model used a singleton Gaussian membership input ISSN: 2180-1053 Vol. 6fuzzification, No. 1 January - June 2014 using two variables such as centers, 𝑐𝑐𝑗𝑗𝑖𝑖 , and spreads, 𝜎𝜎𝑗𝑗𝑖𝑖 , output membership function uses

Figure 7. Fuzzy logic controller using Gaussian membe

y logic controller using Gaussian membership function for outer loop model In the Figure 7, the inputs of the fuzzy controller i.e. slip error and slip error rate are of Antilock System using7, Electronic Wedge Brake In the Figure the ofdefined the Model fuzzy 7. Fuzzy logicDevelopment controllerstage using Gaussian membership function for outerinputs loop model definedFigure during the initialization and all Braking fuzzy membership functions are in

controller defined during the initialization stage and all fuzzy order to form the complete rules. A Gaussian membership function is used and defined by e inputs of the fuzzy controller i.e. slip error and slip error rate are order to form the complete rules. A Gaussian member In the Figure 7, the inputs of the fuzzy controller i.e. slip error and slip error rate are initialization stage and all fuzzy membership functions𝑥𝑥 −are defined in 𝑐𝑐 defined during the initialization stage and all fuzzy membership functions are defined in −0.5( ) (29) omplete rules. A Gaussian membership function is 𝑒𝑒used and 𝜎𝜎 defined by 𝜇𝜇 = 𝑥𝑥 − 𝑐𝑐 order to form the complete rules. A Gaussian membership function is used and defined by 𝜇𝜇 = 𝑒𝑒 −0.5( 𝜎𝜎 ) where 𝜇𝜇 = 𝑒𝑒 −0.5( 𝑥𝑥 𝜎𝜎− 𝑐𝑐) (29) 𝑥𝑥 − 𝑐𝑐 where ) (29) = 𝑒𝑒 −0.5( x is the Gaussian input from error and𝜇𝜇 error rate 𝜎𝜎where x is the Gaussian input from error and error rate c is the center of the curve x is the Gaussian input from error and error rate is theofcenter of the curve where 𝜎𝜎 is thecspread the curve c is the center of the curve put from error andσGaussian error is therate spread of the x is the input from errorcurve and error rate 𝜎𝜎 is the spread of the curve e curve cThe fuzzy logic is the center of network the curvemodel used a singleton fuzzification, Gaussian membership input 𝑖𝑖 he curve 𝜎𝜎 is the spread of thesuch curve using two variables as centers, 𝑐𝑐𝑗𝑗𝑖𝑖 , and spreads, 𝜎𝜎fuzzy membership function The fuzzy logic network model used alogic singleton The network fuzzification, model useduses a singleton fuzz 𝑗𝑗 , output 𝑖𝑖 , product for the implication and also center average defuzzification. The final center 𝑏𝑏 𝑖𝑖 using two variables such as centers, 𝑐𝑐 Gaussian membership input using two variables such as centers, 𝑗𝑗 , and spreads, work model used a singleton fuzzification, Gaussian membership inputGaussian membership input The fuzzy logic network model used a singleton fuzzification, equation representing the network model is 𝑖𝑖 𝑖𝑖 output membership 𝑖𝑖 𝑏𝑏𝑖𝑖 , uses center product the implication ,𝑐𝑐and usesfor center bi, product such as centers, andspreads, spreads, output membership function using two such 𝜎𝜎as 𝑐𝑐𝑗𝑗𝑖𝑖 , and spreads, 𝜎𝜎function usesand also cent 𝑗𝑗 , variables 𝑗𝑗 , centers, 𝑗𝑗 , output membership function equation representing the network model is 𝑖𝑖 𝑖𝑖 for the implication and also center average defuzzification. The final for the implication alsofor center average defuzzification. 𝑥𝑥𝑗𝑗average −𝑐𝑐𝑗𝑗 final defuzzification. The final product the implication and also centerThe center 𝑏𝑏𝑖𝑖 , and ∑𝑅𝑅 𝑏𝑏𝑖𝑖 ∏𝑛𝑛 𝑒𝑒𝑒𝑒𝑒𝑒 [−0.5 𝑖𝑖 ] 𝑖𝑖=1 𝑗𝑗=1 equation representing network model𝜎𝜎𝑗𝑗is ng the network model is equation representing the network the model is (30) f(x|𝜃𝜃) = 𝑅𝑅 𝑛𝑛 𝑥𝑥𝑖𝑖 −𝑐𝑐𝑖𝑖 f(x|𝜃𝜃) =

𝑥𝑥𝑖𝑖𝑗𝑗−𝑐𝑐𝑖𝑖𝑗𝑗 𝑛𝑛 ∑𝑅𝑅 ] 𝑖𝑖=1 𝑏𝑏𝑖𝑖 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0.5 𝜎𝜎𝑖𝑖𝑗𝑗 𝑥𝑥𝑖𝑖𝑗𝑗−𝑐𝑐𝑖𝑖𝑗𝑗 𝑛𝑛 ∑𝑅𝑅 𝑖𝑖=1 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0.5 𝜎𝜎𝑖𝑖 ] 𝑗𝑗

f(x|𝜃𝜃) =

𝑗𝑗

𝑗𝑗

𝑛𝑛 ∑𝑅𝑅 𝑖𝑖=1 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0.5 𝑥𝑥𝑖𝑖𝑖𝑖−𝑐𝑐𝑖𝑖] 𝜎𝜎𝑗𝑗𝑗𝑗 𝑗𝑗 𝑛𝑛 ∑𝑅𝑅 𝑖𝑖=1 𝑏𝑏𝑖𝑖 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0.5 𝑖𝑖 ] 𝜎𝜎𝑗𝑗

𝑥𝑥𝑖𝑖𝑗𝑗−𝑐𝑐𝑖𝑖𝑗𝑗

𝑛𝑛 ∑𝑅𝑅 𝑖𝑖=1 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0.5

𝜎𝜎𝑖𝑖𝑗𝑗

(30)

]

f(x|𝜃𝜃) =

∑𝑖𝑖=1 𝑏𝑏𝑖𝑖 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0 𝑅𝑅

𝑛𝑛

∑𝑖𝑖=1 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0. (30)

where inputtotothe thefuzzy fuzzynetwork, network, number where 𝑥𝑥𝑗𝑗𝑖𝑖 is input j =j =1,1,…,…,n n(n(nis is thethe number of inputs) and 𝑖𝑖 where 𝑥𝑥 is input to the fuzzy network, j = 1, …, n (n is the number of inputs) and of inputs) and i = 1, …, R (R is the number of rules and it will be 𝑗𝑗 R (R is the number of rules and it will be determined during the initialization determined the initialization stage fixed during Rfixed (R isduring the during number ofstage). rules and parameter it will beand duringlearning the initialization learning The 𝑏𝑏determined 𝑖𝑖 is the center of i th consequent fuz stage). The b is the center of i th consequent fuzzy set andfunctionsfuzz 𝑖𝑖 𝑖𝑖 parameter fixed during learning stage). The parameter 𝑏𝑏 is the center of i th consequent 𝑖𝑖 membership at 𝑐𝑐𝑗𝑗 and σ𝑗𝑗 are center andi spread of Gaussian antecedent 𝑖𝑖 𝑖𝑖 center and spread of Gaussian antecedent membership and σ are center and spread of Gaussian antecedent membership functions at 𝑐𝑐input 𝑗𝑗 j, 𝑗𝑗respectively. In order to develop the Fuzzy Logic controller, slip error an functions at rule as i and input j, respectively. Invariables order toreflect develop input j, respectively. In order develop These the Fuzzy Logic controller, slip error error are chosen the input to variables. thethe fuzzy inputand se Fuzzy Logic controller, slip error and slip rate variables error are reflect chosen the as the error are chosen as the input variables. These fuzzy input se closed loop model which is shown in Figures 8 and 9. The parameter of cen input variables. These variables reflect in theFigures fuzzy input sets9.for theparameter closed closed which is shown and The spread,loop 𝜎𝜎 aremodel determined based on the range of 8maximum and minimumofofcent the loop model which is shown in Figures 8 and 9. The parameter of center, spread, 𝜎𝜎 are determined based on the range of maximum and minimum of the error rate values. The range is measured from the outer loop control structure u cerror and rate spread, σ areThe determined based on the range of maximum and structure u values. range is structure measured from theasouter loop control controller since this control is used the benchmark to develop minimum of the error and error rate values. The range is measured from controller since this control structure is used as the benchmark to develop controllers. the parameter is determined based on the maxi the outer loopMeanwhile, control structure using PID bcontroller since this control controllers. Meanwhile, the parameter b braking is determined based on the maxim minimum brake torque required during a vehicle in order to avoid structure is used as the benchmark to develop advance controllers. minimum brake torque required during braking a vehicle in order to avoid disturbance. Meanwhile, the parameter b is determined based on the maximum and disturbance. minimum brake torque required during braking a vehicle in order to In order to improve fuzzification speed, Gaussian function is proposed as the me avoid skidding disturbance.

In order to improve speed, Gaussian is proposed as theofme function (Ping et al.,fuzzification 2010). Figures 8 and 9 show function the membership functions in function (Ping et al., 2010). Figures 8 and 9 show the membership functions of in variables Figurefuzzification 10 for the output variable where the range of slip erro In order toand improve speed, fuzzy Gaussian function is proposed variables 10 foristhe output fuzzy variable where the slip erro 0.01) andand slipFigure rate function error (-0.154, Meanwhile, Figure 119 range shows range as the membership (Ping et 0). al., 2010). Figures 8 and show ofthe 0.01) and slip rate error is (-0.154, 0). Meanwhile, Figure 11 shows the range fuzzy variable is afunctions singleton within to 700 and the relationship between slip the membership of input-700 fuzzy variables and Figure 10 fuzzy variable is a singleton within -700 to 700 and the relationship between slip for therateoutput fuzzy variable where range of slip error is (-0.8, error and brake torque output in 3Dthe surface. error and rate slip and brake torque output in surface. Figure 11 shows the 0.01) rate error is (-0.154, 0).3D Meanwhile, range of output fuzzy variable is a singleton within -700 to 700 and the relationship between slip error, slip error rate and brake torque output in 3D surface. ISSN: 2180-1053

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In order to improve fuzzification speed, Gaussian function is proposed as the membership In order to improve fuzzification speed, Gaussian function is proposed as the membership function (Ping et al., 2010). Figures 8 and 9 show the membership functions of input fuzzy function (Ping et al., 2010). Figures 8 and 9 show the membership functions of input fuzzy variables Figure 10 for the output fuzzy variable where the range of slip error is (-0.8, Journal of and Mechanical and Technology variables and FigureEngineering 10 for the output fuzzy variable where the range of slip error is (-0.8, 0.01) and slip rate error is (-0.154, 0). Meanwhile, Figure 11 shows the range of output 0.01) and slip rate error is (-0.154, 0). Meanwhile, Figure 11 shows the range of output fuzzy variable is a singleton within -700 to 700 and the relationship between slip error, slip fuzzy variable is a singleton within -700 to 700 and the relationship between slip error, slip error rate and brake torque output in 3D surface. error rate and brake torque output in 3D surface.

Figure 8. Slip error variable Figure 8. Slip error input input variable Figure 8. Slip error input variable

FigureFigure 9. Slip error input variable 9. Slip errorrate rate input variable

Figure 10.10. Brake torquetorque output fuzzy variables Figure Brake output fuzzy Figure 10. Brake torque output fuzzy variables

variables

Figure 9. Slip error rate input variable

Figure Output-input relation Figure 11.11. Output-input relation Figure 11. Output-input relation

The fuzzy sets for the input fuzzy variables are defined as positive (POS), zero (ZERO) and negative (NEG). The variables are maintained to initial condition since this inputs itself is sufficient to control the ABS longitudinal slip. Since there are 3 elements of each fuzzy set, the probability of 9 types of fuzzy rules has been used as base rule for this controller. The output fuzzy set representing brake torque is defined as positive big (PB), positive small (PS), zero (ZERO), negative small (NS) and negative big (NB). The rules in Table 4 are derived basically using a combination of experience, trial and error approach and the knowledge of the response of the ABS system. In this study, ABS control system using PID controller is used as a benchmark to develop fuzzy logic rules. The error and error rate from ABS control system using PID controller is used to derive the combinations rules for ABS using fuzzy logic controller. Normally, the rules are determined using “if and then rules” condition. For an example, if slip error is positive and slip error rate is positive then the output is positive big. This means that the output signal is increasing and responding as overshoot response.

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The rules in Table are ABS derived basically combinationNormally, of experience, trial and combinations rules 4for using fuzzyusing logica controller. the rules are error approach and“ifthe knowledge ofcondition. the response ABS system. In this study, ABS determined using and then rules” For of anthe example, if slip error is positive and control system PIDthen controller is used as a benchmark toElectronic develop fuzzy logic rules. slip error rate isusing positive theofoutput is positive big. This means that the output signal is Development Antilock Braking System using Wedge Brake Model The error and rate from control system using PID controller is used to derive the increasing anderror responding as ABS overshoot response. combinations rules for ABS using fuzzy logic controller. Normally, the rules are determined using “if and then rules”Table condition. example, if slip error is positive and FuzzyFor rule an Table 4. 4. Fuzzy rulebase base slip error rate is positive then the output is positive big. This means that the output signal is Input variable increasing and responding as overshoot response. Slip error rate POS ZERO NEG PB (rule 9) PS (rule 8) ZERO (rule 7) Table 4. Fuzzy rule base PS (rule 6) ZERO (rule 5) NS (rule 4) ZERO (rule 3) NS (rule 2) NB (rule 1) Slip error rate POS ZERO NEG 4.4 Inner loop control PBEWB (rule 9)model PS (rule 8) ZERO (rule 7) Slip error design POS using 4.4 Inner loop ZERO control design EWB PS (rule 6)using ZERO (rule model 5) NS (rule 4) ZERO 3) NS (rule 2)brake (EWB) NB (rulemechanism. 1) NEG Inner loop control was developed for the(rule electronic wedge Slip error

POS ZERO NEG Input variable

From Inner loop control was developed for the electronic wedge brake (EWB) the previous section, the Bell-Shaped curve has been used as the model for the EWB mechanism. the previous section, theclosely Bell-Shaped curve has been 4.4 InnerSince loop control design EWB modelcurve actuator. theFrom behaviour ofusing the Bell-Shaped follows the actual behaviour used as the model for the EWB actuator. Since the behaviour of the of the EWB actuator, this mathematical equation is used as the plant model of theBellinner Inner loop control developed for of the electronic wedge brakehas (EWB) mechanism. loop control. The was desired trajectory the inner loop control been set upactuator, to 420From Nm Shaped curve closely follows the actual behaviour of the EWB the previous section, theofBell-Shaped curve has Figure been used as the the model for thecontrol EWB based on brake torque a passenger vehicle. 12 shows proposed this mathematical equation is used as the plant model of the inner loop actuator. behaviour structure Since using the EWB model. of the Bell-Shaped curve closely follows the actual behaviour desired trajectory equation of the inner has ofbeen set ofcontrol. the EWB The actuator, this mathematical is usedloop as thecontrol plant model the inner upcontrol. to 420The Nmdesired basedtrajectory on brake torque a passenger vehicle. 12 loop of the inner of loop control has been set upFigure to 420 Nm based on brake torque of control a passenger vehicle. using Figure EWB 12 shows the proposed control shows the proposed structure model. structure using EWB model.

Figure 12. Proposed control structure using EWB model

Figure 12. Proposed control structure structure using EWB EWB model model Figure 12. Proposed control using

Figure 12 shows the proposed control structure using EWB model to develop an inner loop controller. The reference input to the EWB model is the wheel brake torque. Meanwhile, PID controller is used to control the error of the inner loop control. Refering to Figure 12, there are two PID controllers used in this control structure. The primary PID controller is used to control brake torque obtained from the EWB model as described in Equation (14) and (15). The secondary PID controller is used specifically to command the DC motor to actuate the desired value from the primary PID controller (Aparow et al., 2013c). The rotational displacement from the DC motor is converted to linear displacement (gapping mode). This will be the input to the BellShaped curve which represents the EWB actuator. The EWB force will be converted to wheel brake torque and feedback to the comparator. The actual brake torque is compared with the desired brake torque by measuring the difference between actual and desired values in order to obtain minimum error. The performance of EWB model has been discussed in Aparow et al., (2013c).

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4.5 Proposed ABS-EWB closed loop control structure For an ABS-EWB closed loop scheme, the disturbance is measured in the form of wheel slip occurred after brake being applied and a corrective action is taken to maintain the wheel slip to 0.2. The outer loop model is developed using the quarter vehicle model as the plant to be controlled. Meanwhile, EWB model is used as the plant model for inner loop model. Since the outer closed loop is developed using a quarter vehicle brake model, only a single wheel brake torque is needed to be controlled by the controller. Besides, validated electronic wedge brake model is used as an inner loop control. The input for inner loop control is obtained from the controller of the outer loop control. Based on the proposed inner and outer loop controls, an ABS model is developed by integrating both inner loop and outer loop into a system. The desired trajectory used a constant slip value of 0.2. The response from inner loop control is used as brake torque for the plant model and the wheel slip is feedback and compared with the desired trajectory. 4.5.1 Closed Loop Control Design using Quarter Vehicle and EWB Model The ABS control system using three type of controllers which are conventional PID, adaptive PID and fuzzy logic control are studied. For comparison, the adaptive PID and fuzzy logic controller are compared with both conventional PID controller and passive system. The performance of the controllers are evaluated by examining the vehicle braking performance namely vehicle and wheel velocity, stopping distance and vehicle longitudinal slip. Figures 13 and 14 show the closed loop control structure of the proposed ABS model using adaptive PID and fuzzy logic control.

Figure 13. Control structure of ABS-EWB closed loop control using Figure 13. Control structure of ABS-EWB closed loop control using adaptive PID adaptive PID

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Development of Antilock Braking System using Electronic Wedge Brake Model Figure 13. Control structure of ABS-EWB closed loop control using adaptive PID

Figure 14. Control structure of ABS-EWB closed loop control using fuzzy logic Figure 14. Control structure of ABS-EWB closed loop control using fuzzy The actual response of longitudinal slip from thelogic quarter vehicle model will be feedback to

the comparator. The error is obtained from the difference between the predefined trajectory ofThe ABSactual slip andresponse actual longitudinal slip from theslip plantfrom model.the Thequarter error willvehicle be used asmodel the of longitudinal input the feedback controller to to optimize and reduce the error the actual value willfrom closelythe willto be the comparator. Theuntil error is obtained follow the reference value. According to the ABS concept, the wheel of the quarter vehicle difference between slip theinpredefined trajectory of ABS slip andsudden actual should produce longitudinal the range of 0.15 to 0.25. Wheel skidding during longitudinal slip iffrom the plantwheel model. error will be the used asofthe braking can be reduced the longitudinal slip isThe maintained between range 0.15 to 0.25. wheel speed stopping and distance of the vehicle are also determined. input to Further, the controller to and optimize reduce the error until the actual

value will closely follow the reference value. According to the ABS the wheel of the quarter vehicle should produce longitudinal 5.0concept, SIMULATION RESULTS slip in the range of 0.15 to 0.25. Wheel skidding during sudden braking The simulation resultsifofthe thelongitudinal ABS closed loop controlslip structure using PID, adaptive PIDthe can be reduced wheel is maintained between using model reference adaptive control (MRAC) technique, and fuzzy logic control using range of 0.15 to 0.25. Further, wheel speed and stopping distance of the Gaussian membership function compared with conventional braking. This control system vehicle arebased alsoon determined. was developed the outer loop control using quarter vehicle model and inner loop control using electronic wedge brake (EWB) actuator model as shown in Figures 13 and 14. The control structure is analyzed using sudden braking test where the brake is applied when the velocity of the vehicle is 25 m/s and stopping distance, longitudinal slip and velocities 5.0 SIMULATION RESULTS of vehicle and wheel are observed. ABS is developed by controlling the brake torque obtained from the EWB actuator.

The simulation results of the ABS closed loop control structure using PID, adaptive PID using model reference adaptive control (MRAC) technique, and fuzzy logic control using Gaussian membership function compared with conventional braking. This control system was developed based on the outer loop control using quarter vehicle model and inner loop control using electronic wedge brake (EWB) actuator model as shown in Figures 13 and 14. The control structure is analyzed using sudden braking test where the brake is applied when the velocity of the vehicle is 25 m/s and stopping distance, longitudinal slip and velocities of vehicle and wheel are observed. ABS is developed by controlling the brake torque obtained from the EWB actuator. Brake torque from EWB model is used as input to the quarter vehicle model. Conventional PID controller is used as the benchmark for the adaptive PID and fuzzy logic to control the brake torque of a single wheel. The brake torque will control the longitudinal wheel slip to be in between 0.15 to 0.25. This will reduce the stopping distance of the vehicle and managed to halt wheel velocity without skidding. The results of the study are shown in Figures 15 to 18 which compare the ISSN: 2180-1053

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Brake torque from EWB model is used as input to the quarter vehicle model. Conventional PID controller is used as the benchmark for the adaptive PID and fuzzy logic to control the brake torque of a single wheel. The brake torque will control the longitudinal wheel slip to be in between 0.15 to 0.25. This will reduce the stopping distance of the vehicle and vehicle and wheel longitudinal slipresults and the vehicle managed to halt wheelvelocities, velocity without skidding. The of the study stopping are shown in distance. Figures and 16the show theand comparison of vehicle andslip wheel Figures 15 to 18 which15compare vehicle wheel velocities, longitudinal and the vehicle stopping distance. Figures 15 and 16 show the comparison of vehicle and wheel velocity of the quarter vehicle model using conventional PID, adaptive velocity of the quarter vehicle model using conventional PID, adaptive PID, fuzzy logic PID, fuzzy logic and conventional braking. and conventional braking.


Figure Comparison ofof vehicle velocity Figure 16. of wheel Figure 15. 15. Comparison vehicle Figure 16.Comparison Comparison ofvelocity wheel velocity velocity Conventional braking causes the wheel to lock up causing skidding after 0.6 seconds brake is applied. Meanwhile, ABS model using conventional PID, adaptive PID and fuzzy logic Conventional causes the wheel to from lock locking up causing skidding control the brake braking torque in order to avoid the wheel during braking. ABS after 0.6 seconds brake is applied. Meanwhile, ABS model using using conventional PID shows the wheel stops decelerate at 3.65 second and ABS using adaptive PID stops at 3.5adaptive second. However, for ABS-EWB usingcontrol fuzzy logic conventional PID, PID and fuzzy logic thecontrol, brakethe vehicle is able to halt at 3.3 second. ABS-EWB using fuzzy logic control has improve torque in order to avoid the wheel from locking during braking. ABSthe performance of the wheel velocity by reducing jerking motion occurred in a wheel during using conventional PID shows the wheel stops decelerate at 3.65 second braking compared to the other two controllers. Skidding of the wheel has been reduced and andimproving ABS using adaptive PIDofstops at 3.5 second. However, for ABSthus the stopping distance the vehicle.

EWB using fuzzy logic control, the vehicle is able to halt at 3.3 second.

Figure 17 shows the comparison of the response longitudinalthe wheel slip during sudden ABS-EWB using fuzzy logic control hasof improve performance of braking. It canvelocity be seen that braking results approaches +1 in aftera 0.6 second the wheel by conventional reducing jerking motion occurred wheel which represents wheel locking during braking and the vehicle starts to skid until stops at during braking compared to the other two controllers. Skidding of the 3.9 second. Three type of controllers are used to reduce address issue occurring in the wheelbyhas been reduced and thusslip improving the stopping distance wheel controlling wheel longitudinal to 0.2. Conventional PID and adaptiveof PID the vehicle. controllers are used in this study to control longitudinal slip of wheel to be equal to 0.2 once brake is applied. The performance of both controllers is investigated and the responses show that17 ABS usingthe PIDcomparison controller reached settling time condition for longitudinal wheel Figure shows of the response of longitudinal wheel slip within 2.0 second with minor jerk before halt. Meanwhile, ABS using adaptive slip during sudden braking. It can be seen that conventional brakingPID

results approaches +1 after 0.6 second which represents wheel locking during braking and the vehicle starts to skid until stops at 3.9 second. Three type of controllers are used to reduce address issue occurring in the wheel by controlling wheel longitudinal slip to 0.2. Conventional PID and adaptive PID controllers are used in this study to control longitudinal slip of wheel to be equal to 0.2 once brake is applied. The performance of both controllers is investigated and the responses show that ABS using PID controller reached settling time condition for longitudinal wheel slip within 2.0 second with minor jerk before halt. Meanwhile, ABS using adaptive PID controller is also able to reach

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settling time condition within 1.5 second with jerking slighly better than previous controller. Jerking condition as shown in Figure 17 is occurred because of overshoot response in wheel longitudinal slip before approaching steady state conditions.Generally, adaptive PID works better than conventional PID because of the parameter of PID will change by the adjustment controller is also until able to reach time condition within 1.5 second However, with jerking slighly mechanism they settling converge to optimal values. the better than previous controller.for adaptive PID will take some time and this parameter adjustment has been effected the simulation to slow down the longitudinal slip Jerking condition as shown in Figure 17 is occurred because of overshoot response in wheel response slip to before reach approaching 0.2 in shortest time. Even tough theadaptive result PID shows longitudinal steady state conditions.Generally, works overshoot response using both conventional PID and adaptive PIDthe better than conventional PID because of the parameter of PID will change by adjustment mechanism until they values. controllers, the system still converge unable to to optimal produce fast However, responsethetoparameter reach adjustment for adaptive PID will take some time and this has beenas effected simulation steady-state condition. Hence, by using fuzzy logic ABS the controller tothe slow down stopping the longitudinal slip response reach 0.2 in shortest time.This Evensystem tough the wheel capability has to improved drastically. result shows overshoot response using both conventional PID and adaptive PID controllers, is system able tostillreach 0.58 second even tough theby the unablesteady-state to produce fastcondition response toin reach steady-state condition. Hence, wheel longitudinal slip shows overdamped behaviour. Additionally, using fuzzy logic as ABS controller the wheel stopping capability has improved drastically. This is able to reach in 0.58 second evenfor tough the wheel thissystem system is also ablesteady-state to avoid condition jerking which occurred adaptive longitudinal shows overdamped behaviour. thistosystem is also able PID at 0.6slipsecond to 1.5 second andAdditionally, 0.72 second 1.8 second forto avoid jerking which occurred for adaptive PID at 0.6 second to 1.5 second and 0.72 second conventional PID. to 1.8 second for conventional PID.

Jerking

Figure 17. Comparison of Figure 18. Comparison of Figure 18. Comparison of vehicle distance travel longitudinal slip vehicle distance travel Figure 18 shows the distance travelled by the vehicle after the brake input is applied. The figure shows logic is able to reduce travelled vehicle Figure 18 fuzzy shows thecontroller distance travelled bythe thedistance vehicle after by thethebrake compared to other controllers and conventional braking system. The distance travel by the input is applied. The figure shows fuzzy logic controller is able vehicle controlled by fuzzy logic control is about 12.3 meter and the vehicle stops 3.3 to reduce the distance travelled by the vehicle compared to other second after braking. Meanwhile, vehicle with adaptive PID and conventional PID controllers andtoconventional system.travelled The distance travel controllers are able stop 3.5 secondsbraking with the distance of 13.8 meter and by 3.65 the vehicle controlled by fuzzy logic control is about 12.3 meter seconds with the distance travelled of 14.9 meter respectively. By controling the and wheel longitudinal slip, the distance travel after bu the vehicle has been improved significantly the vehicle stops 3.3 second braking. Meanwhile, vehicle with compared conventional braking system. At controllers the same time,are fuzzy logic adaptiveto PID and conventional PID able to controller stop 3.5 is shown to halt the vehicle with the shortest distance compared to other controllers. Figure 17. Comparison of longitudinal slip

seconds with the distance travelled of 13.8 meter and 3.65 seconds with 19 theshows distance travelled of 14.9velocity meterand respectively. Figure the comparison of vehicle wheel velocityBy of acontroling vehicle using

fuzzy logic controller. The ABS-EWB model using fuzzy logic controller shows a good performance by stopping the vehicle and wheel at the same time without any jerking ISSN: 2180-1053

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the wheel longitudinal slip, the distance travel bu the vehicle has been improved significantly compared to conventional braking system. At the same time, fuzzy logic controller is shown to halt the vehicle with the shortest distance compared to other controllers. Figure 19 shows the comparison of vehicle velocity and wheel velocity of a vehicle using fuzzy logic controller. The ABS-EWB model using fuzzy logic controller shows a good performance by stopping the vehicle and wheel at the same time without any jerking problems in the wheel. Besides, the stopping distance has been reduced compared to ABS model using conventional PID and adaptive PID. The proposed problems in the shows wheel. Besides, stopping distance been reduced ABS controller better the performance in has controlling thecompared vehicleto and model using conventional PID and adaptive PID. The proposed controller shows better EWB brake model to produce a good ABS model. performance in controlling the vehicle and EWB brake model to produce a good ABS model. Graph of comparison between vehicle and wheel velocity versus time

Comparison of vehicle and wheel velocity, m/s

90

vehicle wheel

80 70 60 50 40 30 20 10 0 0

2

4

6 time, t

8

10

12

Figure Comparison between vehicle for ABS Figure 19. 19. Comparison between wheel andwheel vehicle and velocity for ABSvelocity using fuzzy logic using fuzzy logic 6.0

CONCLUSION

6.0 CONCLUSION

A comprehensive study of the ABS model using Electronic wedge brake (EWB) A comprehensive of the ABS wedge mechanism and the design study of the conventional PID,model adaptiveusing PID andElectronic fuzzy logic controller have been (EWB) presented.mechanism A quarter vehicle is modeled and validated using CarSim brake and model the design of the conventional PID, simulator. A mathematical model using Bell-Shaped is used represent an A EWB. This adaptive PID and fuzzy logic controller have beentopresented. quarter model is used to represent the actual EWB behaivour. An outer loop model has been vehicle model is modeled and validated using CarSim simulator. A proposed using validated quarter vehicle model and EWB model is used to develop an inner mathematical model using Bell-Shaped to develop represent an EWB. loop model. Both outer and inner loop are integratedisinused order to the overall ABS Thissystem. model used to studies represent the actual EWB behaivour. An outer closed Theissimulation considered three types of controllers for ABS model. Comparison has been the proposed ABSvalidated model to investigate performance of loop model has made beenfor proposed using quarterthe vehicle model theand proposed controllers. From the simulation results, the Fuzzy Logic controller shows EWB model is used to develop an inner loop model. Both outer and good performance forintegrated ABS-EWB control structure by reducing theoverall stoppingABS distance up to inner loop are in order to develop the closed 17.4 % compared to the conventional PID and Adaptive PID control is 7.38% and 12.08 %. system. Thecontrol simulation three types of controllers for The proposed schemestudies is able considered to improve the stopping distance and wheel ABS model. Comparison has been made for the proposed ABS model longitudinal slip of vehicle during braking. Hence, it can be concluded that fuzzy logic controller could provide better active brake performance the adaptive PID the and to investigate the performance of the proposedthan controllers. From conventional PIDresults, control. the Fuzzy Logic controller shows good performance simulation ACKNOWLEDGEMENT 60

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This work is supported by the University Teknikal Malaysia Melaka (UTeM) through short


for ABS-EWB control structure by reducing the stopping distance up to 17.4 % compared to the conventional PID and Adaptive PID control is 7.38% and 12.08 %. The proposed control scheme is able to improve the stopping distance and wheel longitudinal slip of vehicle during braking. Hence, it can be concluded that fuzzy logic controller could provide better active brake performance than the adaptive PID and conventional PID control. ACKNOWLEDGEMENT This work is supported by the University Teknikal Malaysia Melaka (UTeM) through short term grant project entitled “Safety and Stability Enhancement of Automotive Vehicle using ABS with Electronic Wedge Brake Mechanism” led by Fauzi Bin Ahmad at the Universiti Teknikal Malaysia Melaka. This financial support is gratefully acknowledged. REFERENCE Adrian, C., Corneliu, A.and Mircea, B. (2008). The simulation of adaptive systems using the MIT rule. In International Conference on Mathematical Methods and Computational Techniques in Electrical Engineering (pp. 301– 305). Ahmad, F., Hudha, K. & Jamaluddin, H. (2009). Gain scheduling PID control with pitch moment rejection for reducing vehicle dive and squat. International Journal of Vehicle Safety. 4(1), 45–83. Aly, A., Zeidan, E.-S., Hamed, A., & Salem, F. (2011). An antilock-braking systems (ABS) control: a technical review. Intelligent Control and Automation, 2(3), 186–195. Aparow, V. R., Ahmad, F., Hudha, K., & Jamaluddin, H. (2013a). Modeling and PID control of antilock braking system with wheel slip reduction to improve braking performance. International Journal of Vehicle Safety, 6(3), 265–295. Aparow, V. R., Ahmad, F., Hudha, K., Jamaluddin, H., & Dwijotomo, A. (2013b). Modeling and validation of electronic wedge brake mechanism for vehicle safety system. International Journal of Automotive Technology. Accepted. Aparow, V. R., Hudha, K., Ahmad, F., & Jamaluddin. (2013c). Modelin-the-loop simulation of gap and torque tracking control using electronic wedge brake actuator. International Journal of Vehicle Safety. (Forthcoming).

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