A Multiple Data Fusion Approach to Wheel Slip ... - Semantic Scholar

energies Article

A Multiple Data Fusion Approach to Wheel Slip Control for Decentralized Electric Vehicles Dejun Yin 1 , Nan Sun 1 , Danfeng Shan 1 and Jia-Sheng Hu 2, * 1 2

*

School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China; [email protected] (D.Y.); [email protected] (N.S.); [email protected] (D.S.) Department of Greenergy, National University of Tainan, No. 33, Section 2, Shu-Lin Street, Tainan 700, Taiwan Correspondence: [email protected]; Tel.: +886-6-260-5051

Academic Editor: Joeri Van Mierlo Received: 29 January 2017; Accepted: 27 March 2017; Published: 2 April 2017

Abstract: Currently, active safety control methods for cars, i.e., the antilock braking system (ABS), the traction control system (TCS), and electronic stability control (ESC), govern the wheel slip control based on the wheel slip ratio, which relies on the information from non-driven wheels. However, these methods are not applicable in the cases without non-driven wheels, e.g., a four-wheel decentralized electric vehicle. Therefore, this paper proposes a new wheel slip control approach based on a novel data fusion method to ensure good traction performance in any driving condition. Firstly, with the proposed data fusion algorithm, the acceleration estimator makes use of the data measured by the sensor installed near the vehicle center of mass (CM) to calculate the reference acceleration of each wheel center. Then, the wheel slip is constrained by controlling the acceleration deviation between the actual wheel and the reference wheel center. By comparison with non-control and model following control (MFC) cases in double lane change tests, the simulation results demonstrate that the proposed control method has significant anti-slip effectiveness and stabilizing control performance. Keywords: wheel slip control; data fusion; active safety control; power decentralized electric vehicle

1. Introduction Recently, electric and hybrid vehicles have become more and more popular because of their internal electric motors. The electric motor can provide propulsion and regenerative braking in a unified mechanism [1,2]. Consequently, the transportation efficiency is better than conventional gasoline engine cars. Due to the merits of independent control for each motor, active safety control systems have made significant innovated decentralized electric vehicles in recent years [3–7]. The power decentralized electric vehicle employs the independent drive motors to propel the vehicle system. This freedom makes wheel slip control a crucial issue. Wheel slip control is a key foundation to the vehicle active safety control system, especially for electronic stability control (ESC), because compared with the antilock braking system (ABS) and traction control system (TCS), the ESC needs wheel slip control to generate longitudinal tire force, as well as lateral tire force. The intrinsic explanation of wheel slip is that the output torque of the actuator exceeds the maximum friction force between the tire and the road surface [8–11]. However, the friction force cannot be measured directly, and there are changes with regards to the road surface and vehicle states. In order to solve this problem faced in vehicle dynamic control, the implementations available for wheel slip control fall into two classes: indirect torque control methods based on wheel slip ratio and direct torque control ones based on the vehicle or wheel model. According to the µ − λ curve, the former methods maintain the optimal wheel slip ratio in a stable adhesion region to obtain the maximum friction force. To calculate the wheel slip ratio, the wheel speed is easily detected by a Energies 2017, 10, 461; doi:10.3390/en10040461

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sensor installed on the rotational wheel axle, and the speed of non-driven wheels replace chassis speed for physical and economic reasons. Clearly, this replacement is not applicable in the cases without non-driven wheels for 4-Wheel Drive (4WD) systems. No matter how ingenious the chassis speed acquisition is, the result of this indirect method is inherently inaccurate. Although some dedicated sensors can measure the chassis speed directly [12], they are too sensitive to the environment and too expensive for commercial applications. Therefore, some researchers focus on designing the estimators without the chassis speed [13,14]. However, these methods are difficult for practical use, and their control robustness is still challenging against the significant variation in tire-road conditions because they only consider typical road conditions. On the other hand, distinguished from indirect methods based on wheel slip ratio, direct methods based on the model of vehicle or wheel do not need information on the chassis speed. The model following control (MFC) method only makes use of the wheel speed and the motor torque to determine the maximum feedback gain for anti-slip control [15–17]. Fewer control inputs with a simple control structure facilitate the practicability, low cost, and higher reliability of this method. However, considering the worst stability situation, such a method impairs the control performance to determine the compensation gain. Additionally, the tuned algorithms and parameters are specific for established vehicles or wheel models such that the MFC cannot adapt to the variation in vehicle mass or equivalent vehicle mass transfer. Vehicle wheel slip caused by tire traction deterioration can be compensated by many approaches, such as sliding model control, robust control, fuzzy control, and adaptive control [18–22]. The maximum transmissible torque estimation (MTTE) method requires neither the chassis speed nor the tire-road information and takes advantage of a relaxation factor (i.e., the ratio of the vehicle acceleration to wheel acceleration) to estimate the maximum transmissible torque as the limitation of the motor torque [6,23,24]. The MTTE, irrespective of the vehicle mass and road conditions, can restrain the wheel slip effectively. Nevertheless, the increased motor cost charged by excessively precise torque output limits the practical use of this method. Consequently, different from the methods above, this paper proposes a novel wheel slip control method by eliminating the acceleration deviation between the actual wheel and the reference wheel center to suppress the wheel slip trend at the initial stage. The rest of this paper is organized as follows. Section 2 introduces the proposed wheel slip control system, including a one-wheel vehicle model, dynamic analysis, and detailed controller design. Section 3 gives the evaluation setups. The simulation results and discussions are offered in Section 4. Finally, Section 5 gives some concluding remarks. 2. Proposed Approach This section discusses the methodologies implemented in the study. Note that the proposed approach is designed for power decentralized electric vehicles. Additionally, the vehicle system is assumed to adhere to rigid body dynamics. 2.1. One-Wheel Vehicle Model In this subsection, the dynamics analysis of vehicle longitudinal motion is discussed based on the one-wheel vehicle model, which can be described as in Figure 1. Table 1 lists the parameter definitions. The dynamics equations for the calculation of the longitudinal vehicle motions are described as follows: .

Fx − Fdr = MV

(1)

Fx = µFz

(2)

Fz = Mg

(3) .

T − RFx = Jw ω

(4)

Vw = Rω

(5)

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Note that the “propulsion torque” and “braking torque” are amalgamated as “driving torque T”. Note that the “propulsion torque” and “braking torque” are amalgamated as “driving torque T ”.

V Fdr

M

TV



J w Vw R

Fx Figure 1. 1. Longitudinal Longitudinal dynamics dynamics of of one-wheel one-wheel vehicle vehicle model. model. Figure Table 1. 1. Parameter Parameter definitions. definitions. Table Symbol Symbol M M Jw T Fdr Fx Fz V Vw ω R µ

Jw

T Fdr Fx

Fz

V Vw 

R 

Definition Definition Vehicle mass (for Quarter Car) Vehicle mass (forinertia Quarter Car) Wheel Wheel inertia Driving torque Driving torque Driving resistance Driving resistance Frictionforce force Friction Normal force Normal force Chassis speed Chassis speed Wheel speed (Circumferential Speed) Wheel speed Wheel(Circumferential rotation speed Speed ) Wheel radius Wheel rotation speed Friction coefficient Wheel radius Friction coefficient

2.2. Dynamic Analysis for Anti-Slip 2.2. Dynamic Analysis for Anti-Slip Substituting Equation (5) into Equation (4), the friction force, Fx , can be expressed as: Substituting Equation (5) into Equation (4), the friction force, Fx , can be expressed as: . T Jw V w Fx = T− J wV2w (6) (6) Fx R  R2 R R Assuming that the driving torque T is constant, then, it can be found that the higher the wheel . Assuming that the driving torque T is constant, then, it can be found that the higher the wheel circumferential acceleration V w , the lower the friction force Fx that can be obtained.  circumferential acceleration Vw , the lower the friction force Fx that can be obtained. Generally, the friction force is less than the maximum value that the road surface can provide Generally, force is lessup. than the maximum value that the roadbefore surface provide and increases asthe thefriction drive torque goes Based on the tire–friction relations, thecan maximum and increases as the drive torque goes up. Based on the tire–friction relations, before the maximum traction force is achieved, the friction force is proportional to the slip ratio. After that, when the slip traction force is achieved, the friction force is proportional to the slip ratio. After that, when the slip ratio continues to increase given lateral or longitudinal force, both of them will deteriorate quickly due ratio continues to increase given lateral or longitudinal force, both of them will deteriorate quickly to the saturation of the traction force. due to the saturation of the traction force. Substituting Fx in Equation (1) into Equation (4), the driving torque, including two movements, Substituting Fx in Equation (1) into Equation (4), the driving torque, including two i.e., the body longitudinal motion and wheel rotation, can be expressed as: movements, i.e., the body longitudinal motion and wheel rotation, can be expressed as: . Jw . T = RFdr + MRV + J w V w (7) T  RFdr  MRV  R Vw (7) R

Here, the driving resistance Fdr , which is related to the chassis speed and vehicle shape, is assumed to be zero. Hence:

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Here, the driving resistance Fdr , which is related to the chassis speed and vehicle shape, is assumed to be zero. Hence: . Jw . (8) T = MRV + V w R In some conditions where the vehicle runs at high speeds and thus require higher anti-slip performance, Fdr should be estimated in real time. The regular operation of steering a vehicle can typically be treated as a linear motion [25], excluding the situation of the vehicle always performing turning control. Consequently, it is easy to see if no slip is expected, i.e., λ = 0; the vehicle acceleration in linear motion then can be obtained as . . . . V = ωr = V w . Therefore, in a pure rolling condition where no slip occurs, the wheel acceleration V w . equals that of the chassis V in Equation (8). When slip stars to occur, i.e., part of the output torque cannot be transmitted to the chassis by the tire-road interaction, the driving torque T containing two parts, can be rewritten as: .

.

T=

V V Jw · + MR2 · R R

.

!

+ Jw

where Te f f ective =

.

Vw − V R

!

= Te f f ective + Twaste ,

Jw + MR2 . V. R

(9)

(10)

Here, Te f f ective represents the desired maximum torque to maintain a pure rolling state. Twaste stands for extra torque that exists when the slip ratio is not equal to zero. It is invalid torque that does not contribute to the propulsion. It turns into rotational kinetic energy when the wheel self-spins in skidding scenarios. Note that less of the wasted energy may be stored in different areas, such as potential energy in the suspension. However, most of the wasted energy is directly delivered to the wheels. Consequently, the proposed control method, which makes use of the deviation between the accelerations of the wheel and the chassis directly, adjusts the output driving torque to constrain the wheel slip by: Tc∗ = Th∗ − Twaste . (11) This formula indicates that the calculation of the desired drive torque for anti-slip control requires only the wheel and chassis accelerations. Th ∗ represents the torque distribution command from the upper yaw-moment control, which the driver demands. 2.3. Data Fusion for Reference Acceleration According to classical rigid body dynamics, it is inaccurate for Equation (8) to take the chassis acceleration as the reference for four independent wheels. Thus, in order to ensure the accuracy of the proposed control method, the reference accelerations of each wheel center, which are rigid on the vehicle body, are utilized to replace the chassis acceleration. The reference accelerations are derived from measurable quantities including the chassis longitudinal acceleration, the chassis lateral acceleration, and the yaw rate. In this paper, an inertia sensor is installed at the vehicle center of mass, simultaneously measuring these physical quantities. Taking the front left wheel as an example, as shown in Figure 2, O is the vehicle’s center of mass (CM); a x , ay , and γ the longitudinal acceleration, lateral acceleration, and yaw rate of the chassis, respectively. Let i be FL, FR, RL, or RR, i.e., four wheels; awi represents the wheel acceleration; δ the steer angle of front two wheels; lOi the horizontal distance from the vehicle centroid to the wheel center; θi the intersection angle between lOi and the vehicle body side; and a xi and ayi the longitudinal and lateral reference acceleration at each wheel center, respectively. As shown in Figure 2, the proposed steering kinematics is assumed under a left turn.

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atFL

Y

a yFL

awFL



 RL lORL

ay

ac lOFL

 FL anFL

ax



X

O

lORR

axFL

lOFR

 RR

 FR

Figure 2. 2. Vehicle model used used for for data data fusion fusion analysis. analysis. Figure Vehicle model

For each wheel, due to the rotation of the vehicle body, the reference wheel center acceleration For each wheel, due to the rotation of the vehicle body, the reference wheel center acceleration comprises another two components besides the chassis a x and a y . As shown in Figure 2, they are comprises another two components besides the chassis a x and ay . As shown in Figure 2, they are the ati aand ani , defined as: the tangential normal accelerations, tangential and and normal accelerations, i.e., i.e., ati and ni , defined as: ( a  l  2 ni Oi ani = lOi γ2  a l a ti = lOi γ. ti Oi

(12) (12)

By the geometric relations, the reference acceleration a xi and a yi of each wheel center can be By the geometric relations, the reference acceleration a xi and ayi of each wheel center can be calculated as: calculated as:   a  1 0 sin( )l  cos( )lOFL   ax  FL OFL a xFL  xFL  1  0 − sin(θ FL )lOFL − cosFL(θ FL )lOFL ax    a a  lOFR)l  a y  a  1 0 sin( )lOFR − cos(  FR cos (θ)FR  xFR  xFR 1  0 sin(θ FRFR)lOFR OFR ,  y  (13) (13)   a=  1 0 sin( )l   . ,  cos( ) l  RL ORL RL ORL xRL  a xRL   1 0 − sin(θ RL )lORL    cos(θ RL )lORL γ     2 sin( cos( )lORR  RR))llORR a xRR  axRR  1 10 0 sin (θ RR cos(RRθ RR )lORR γ2 ORR          ax  cos(  FL)l)OFL sin(  FL(θ)FL lOFL − lOFL)lOFL ayFL  a yFL  0 01 1 cos (θ FL sin ax  a    a    a  (θ FR sin )lOFR  y   yFR  a yFR 0 01 1 cos cos(  FR)l)OFR sin( (FRθ FR )lOFR lOFR   y  (14) =  .  . .  (14)  ayRL  a  0 01 1− cos  ( θ ) l − sin ( θ ) l   ORL sin( RL )RL cos(RL lORL ORL   γ  RL )lORL yRL     2 ayRR  (θRR ))llORR sin( sin(θ RR )lORR γ2 cos(  0 01 1− cos a RR ORR RR )lORR      yRR   Here, for a certain vehicle, the body parameters, e.g., lOi and θi , are fixed such that the precision for a acceleration certain vehicle, parameters, lOi and i , are fixed such that the of theHere, calculated only the has body a relationship with e.g., the inertia sensor, which is installed at the precision of the calculated acceleration a relationship with theininertia sensor, whichthe is vehicle center of mass. Additionally, the only data has fusion algorithm proposed this paper ignores installed atofthe of mass. Additionally, data fusion algorithm proposed in this paper influences thevehicle chassiscenter vertical, pitching, and rollingthe motions. However, if higher calculation accuracy ignores the all influences of the chassis and synthetically, rolling motions. However, if higher is required, related quantities shouldvertical, be takenpitching, into account which can be actualized calculation accuracy is required, all related quantities should be taken into account synthetically, by a sensor with six degrees of freedom. which can be actualized by a sensor with six degrees of freedom. 2.4. Proposed Control Scheme 2.4. Proposed Control Scheme The proposed wheel slip control system is illustrated in Figure 3. Based on the proposed data fusion algorithm forwheel the reference acceleration, mechanism obtains the longitudinal and lateral The proposed slip control system is the illustrated in Figure 3. Based on the proposed data components of thefor reference acceleration. As shown in Figure 2,obtains the resultant reference acceleration fusion algorithm the reference acceleration, the mechanism the longitudinal and lateral has a differentofdirection with the actual wheel acceleration, which indicates the wheel travel direction. components the reference acceleration. As shown in Figure 2, the resultant reference acceleration Therefore, the reference ofwheel each wheel center should be rewritten according to:direction. has a different direction accelerations with the actual acceleration, which indicates the wheel travel Therefore, the reference accelerations of each wheel center should be rewritten according to:

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acFL  axFL cos( )  a yFL sin( )  acFR  axFR cos ( )  a yFR sin( )   (15) acRL= aaxFL  acFL xRL cos ( δ ) + a yFL sin ( δ )    a = a cos(δ) + ayFR sin(δ) acRR  axFR xRR cFR (15)  a = a cRL xRL    front wheels, which is measured by an angular sensor. where  represents the steer anglea of both cRR = a xRR The slight toe-out difference is neglected. where δ represents theacceleration steer angle of front wheels, which is measured byofanthe angular awiboth , achieved by taking the time derivative wheel sensor. speed The actual wheel The slight toe-out difference is neglected. Ri , which is measured directly, should be equal or very close to aci , in the complete adhesion The actual wheel acceleration awi , achieved by taking the time derivative of the wheel speed Rωi , condition. Then, the eventual output torque is constrained by: which is measured directly, should be equal or very close to aci , in the complete adhesion condition. Then, the eventual output torque by: J   1  is constrained T  min  Th*   K p  K i   awi  aci  w  , Teffective   min Tc* , Teffective  , (16) s        R  n o  Jw 1 , Te f f ective = min Tc ∗ , Te f f ective , (16) T = min Th ∗ − K p + Ki ( awi − aci ) s R in which, K p and K i denote the PI compensator gains that ensure the wheel slip being controlled; is the non-slip torque that the wheel can provide; herein is acontrolled; reference Th * slip Teffective in which, K p maximum and Ki denote the output PI compensator gains that ensure the wheel being * ∗ Te f f ective is that the maximum output the wheel Th herein reference  isisathe command representsnon-slip the initial inputtorque torquethat requests fromcan the provide; driver. Herein, actual ∗ is the actual command that represents the initial input torque requests from the driver. Herein, δ steering angle command given from the operator. From Equations (9) and (11), we can have steering angle* command given from the operator. From Equations * (9) *and (11), we can have the manipulation of the PI compensator, Th  T∗c  0∗. Consequently, the T T  (Th  Tc*∗) . Under ∗ ). Under the manipulation of the PI compensator, T = Teffective + ( T − T Th − Tc ≈ 0. Consequently, e f f ective c h propulsion torque leads to TtoTTeffective the propulsion torque leads = Te f. f ective . * V Tc

CM Sensors

T

 ax , a y , 

*

*

Th 

Wheel Speed Steering Wheel Sensor Sensor

 Tˆ

i

waste

PI Compensator

axi cos( )  a yi sin( )

Rs

Jw R

a yi

axi



awi Te

Data Fusion for Acceleration



 e

aci Note i =FL, FR, RL, RR

Figure 3. Proposed wheel slip control scheme (based on data fusion). Figure 3. Proposed wheel slip control scheme (based on data fusion).

Basically, the proposed wheel slip control is a kind of disturbance estimation. Its stability Basically, proposed control is acontrol kind of block disturbance estimation. stability analysis analysis is the the same in each wheel wheel.slip Based on the diagram of FigureIts 3 and the relevant is the same in eachthe wheel. BasedFigure on the 4control block diagram of Figure and the relevant control. motion motion equations, following illustrates the equivalent model3 of the proposed equations, the following Figure 4 illustrates the equivalent model of the proposed control. Note Note that the driving resistance Fdr is assumed to be zero. 1 and  2 are the time constantsthat for the driving resistance Fdr is assumed to be zero. τ1 and τ2 are the time constants for low-pass filters. low-pass filters. V stands for the deterioration of wheel skidding. Vxi is the linear velocity of a ∆V stands for the deterioration of wheel skidding. Vxi is the linear velocity of a quarter car. According quarter car. According to Mason’s gain formula, the following transfer functions can be obtained. to Mason’s gain formula, the following transfer functions can be obtained. V G ( s )  − G (s) ∆V 4 2 = F   3 1K  3 1)is21+KK Fx x JwJM [τ1 τ2s14+2 s[(Kp + i s ]p  1 s  K i s  wM  )τp1 +τ12]s 1+(K2i τ1 s+Kp + K  2 3 2 (17) G (s) = R 2 Mτ1 τ2 s3 + Jw Ki (τ1 − τ2 ) +2 R M + Jw s (17) ( s ) 2 R M  1 2 s   J wK i  1   2   R M
 J w 2 s  2 G + R M + Jw (K p +1) τ1 + Jw 1 − K p + R M τ2 + Jw τ1 τ2 s





  R 2 M  J w ( K p  1)   1   J w 1  K p   R 2 M   2  J w 1 2 s 2 R(τ2 s + 1) ∆V
= Th∗ Jw [τ2 s2 + K p + 1 s + Ki ]

(18)

V 2  Th* J w [ 2 s 2   K p  1 s  Ki ]

(18)

Equation (17) represents the transfer function of anti-slip control. According to the following Routh table: Energies 2017, 10, 461

s4

K i 1  K p  1 0

 1 2  K p  11   2

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s3 Ki 0 Equation (17) represents the transfer function of anti-slip control. According to the following K i 1 2 Routh table: s 2  K i 1  K p  1  0 (19) 4 K s τ1 τ2  p  1 1   2 Ki τ1 + K p + 1 0
s3s1 K p + 1 0τ1 + τ2 Ki 0
Ki τ1 τ2 2 0 0 s s Ki τ1 + K p + 1 0− (19) (K p +1)τ1 +τ2 1 s 0 Hence, Equation (17)0 is stable if: s 0 K  Hence, Equation (17) is stable  Kiif:1  K p  1  K  i1 1 2    p 1 2
Ki τ1 τ2 Ki τ1 + K  1 − 1K+ Kpi+    τ2 K i 1 2 1  K p ( p 1 1) τ21 +  K p 1 (20) K τ [(K p +1)τ +τ ]−K τ τ = K p + 1 + i 1 K p  111  2 2 i 1 2 (20) (K p +1)τ1 +τ2 Kip(K Ki  K p1+1)12τ1 2 ≥ K pKp1+ 1 + (K p +1)τ1 +τ = 0 0 K 1   2



p



1

2

Clearly, the first column of Routh table reveals that all numbers are positive. Hence, Equation (17) Clearly, the first column of Routh table reveals that all numbers are positive. Hence, Equation (17) is stable. The second transfer function of Equation (18) shows the characteristic equation that: is stable. The second transfer function of Equation (18) shows the characteristic equation that:
2 τ2s22s + (21)  KKpp +  11 ss +KKi i=0 0 (21)

Analyzing Analyzing Equation Equation (21) (21) uncovers uncovers that that the the real real part part of of the the roots roots shall shall be be negative negative numbers. numbers. Equation also stable stablein inconsequence. consequence.Since Sinceboth bothEquations Equations (17) and (18) stable, it leads to Equation (18) is also (17) and (18) areare stable, it leads to the the conclusion proposed wheel control system is stable all the time. conclusion thatthat the the proposed wheel slipslip control system is stable all the time. Single wheel model

1 M

Fx

1 s

Vxi 

V

R



Th

*

Tc 

*

Tˆwaste

1 J ws





i

R

Vwi

1 

K p  Ki

 1s  1

1

 2s 1

1 s

Rs

Jw R

 awi  a xi

Figure Figure 4. 4. Equivalent Equivalentmodel modelof ofthe the proposed proposed control. control.

3. Evaluation Setups In order to evaluate the performance of the proposed approach, this study applied software CarSim with Simulink (Version 8.03, Mechanical Simulation Corporation, Ann Arbor, MI, USA, 2012) to carry out the simulation. Table 2 shows the specifications of the test vehicle, which is a type of sport utility vehicle (SUV). In addition, we have set the powertrain of this vehicle in CarSim as “4-wheel

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3. Evaluation Setups In order to evaluate the performance of the proposed approach, this study applied software CarSim2017, with (Version 8.03, Mechanical Simulation Corporation, Ann Arbor, MI, USA, 82012) Energies 10,Simulink 461 of 24 to carry out the simulation. Table 2 shows the specifications of the test vehicle, which is a type of sport utility vehicle (SUV). In addition, we have set the powertrain of this vehicle in CarSim as drive withdrive all external powertrain components”. Hence, the electric are set in Simulink. “4-wheel with all external powertrain components”. Hence, motors the electric motors are set In in our configuration, the testing electric vehicle is fully power decentralized, which can be used in the Simulink. In our configuration, the testing electric vehicle is fully power decentralized, which can be evaluation the proposed fusion strategy. Note that, in thethat, simulations, the test vehicle is used in the of evaluation of thesensor proposed sensor fusion strategy. Note in the simulations, the test ◦ . Three types of tests are carried regarded as a rigid body and the maximum wheel steering angle is 36 vehicle is regarded as a rigid body and the maximum wheel steering angle is 36°. Three types of tests out for the evaluations. are carried out for the evaluations. Table 2. Vehicle specification. Table 2. Vehicle specification. SprungSprung Mass Mass Unsprung Unsprung mass mass Width DWidth D Height of CM of CM Height Wheelbase L Wheelbase L Front wheel base Front wheel base Rear wheel Rearbase wheel base Unloaded wheel radius Unloaded wheel radius Wheel inertia Wheel inertia

1429kg kg 1429 360 360kg kg 1565 1565mm mm 670mm mm 670 2619mm mm 2619 1050 mm 1050 mm 1569mm mm 1569 394 mm 394 mm 2 0.9 kg·m 0.9 kg·m2

Steering Angle (rad)

The first test is is the the verification verificationof ofthe theproposed proposeddata datafusion fusionalgorithm. algorithm. The conditions The testtest conditions areare an an initial speed km/h and a roadfriction frictioncoefficient coefficientofof0.85. 0.85.The Thefront front wheel wheel steering steering angle is initial speed of of 5050 km/h and a road maneuvered as seen in Figure Figure 5. 5. In order to evaluate evaluate the effectiveness effectiveness of the the proposed proposed data data fusion fusion algorithm, four acceleration acceleration sensors sensors are are installed installed at at the the center center of of four four wheels wheelsin inCarSim. CarSim. 0.10 0.08 0.06 0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08 -0.10 1

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The second test is made under a defined double lane change (DLC). This test maneuver is The second test is made under a defined double lane change (DLC). This test maneuver is performed to verify the effectiveness of the proposed wheel slip control. The DLC test is recognized performed to verify the effectiveness of the proposed wheel slip control. The DLC test is recognized as as a benchmark for evaluating steering stability, e.g., the international standard ISO 3888-2 [26]. a benchmark for evaluating steering stability, e.g., the international standard ISO 3888-2 [26]. In order In order to eliminate the randomness of the driver’s actions, a built-in UMTRI preview driver, which to eliminate the randomness of the driver’s actions, a built-in UMTRI preview driver, which indicates indicates the most average driver in CarSim, is set to make the steering decision for trajectory tracking; the most average driver in CarSim, is set to make the steering decision for trajectory tracking; the the preview time is 0.5 s. All tests are set to the same value for fair comparison. The initial speed for preview time is 0.5 s. All tests are set to the same value for fair comparison. The initial speed for the the DLC test is 38 km/h, and two road friction coefficients are set to 0.8 and 0.45. The maximum DLC test is 38 km/h, and two road friction coefficients are set to 0.8 and 0.45. The maximum output output torque of each wheel is 500 Nm. Note that the PI compensator gains in Figure 3 are set to torque of each wheel is 500 Nm. Note that the PI compensator gains in Figure 3 are set to K p = 148 K p  148 and K i  0.1 . Note that regardless of the scenario, the PI gains are always set to the same and Ki = 0.1. Note that regardless of the scenario, the PI gains are always set to the same value in value in the evaluations. the evaluations. The third test verifies the robustness of lighter and heavier vehicle masses. This test is carried out on the DLC test with the vehicle weights of 1589 kg and 1939 kg, respectively. The results of this test lead to evaluate the robustness of the proposed approach when the vehicle’s mass is changed.

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The third test verifies the robustness of lighter and heavier vehicle masses. This test is carried out on the DLC test with the vehicle weights of 1589 kg and 1939 kg, respectively. The results of this Energies 2017, 461 9 of 24 test lead to10, evaluate the robustness of the proposed approach when the vehicle’s mass is changed. 4. Results and Discussion 4. Results and Discussion This paper presents a wheel slip control scheme based on the proposed data fusion algorithm. This paper presents a wheel slip control scheme based on the proposed data fusion algorithm. In the following, the aforementioned issues will be verified under the corresponding simulations. In the following, the aforementioned issues will be verified under the corresponding simulations. In order to verify the wheel slip control, the data fusion performance is firstly evaluated. Note that In order to verify the wheel slip control, the data fusion performance is firstly evaluated. Note that based on the steering command of Figure 5, Figure 6 shows the simulation results of data fusion as based on the steering command of Figure 5, Figure 6 shows the simulation results of data fusion as they pertain to the front wheels. Compared to the proposed estimation with the information from they pertain to the front wheels. Compared to the proposed estimation with the information from sensors, as can be seen in this figure, the proposed approach for acceleration estimation is reliable. sensors, as can be seen in this figure, the proposed approach for acceleration estimation is reliable. Additionally, considering the cost of the chassis acceleration sensor, the proposed approach is a costAdditionally, considering the cost of the chassis acceleration sensor, the proposed approach is a effective solution. Moreover, in this simulation, we can also observe the acceleration discrepancy cost-effective solution. Moreover, in this simulation, we can also observe the acceleration discrepancy between the CM and individual wheels. Therefore, without the data fusion from all wheels, using the between the CM and individual wheels. Therefore, without the data fusion from all wheels, using the acceleration information from a single wheel instead of chassis acceleration is not recommended. acceleration information from a single wheel instead of chassis acceleration is not recommended. Longitudinal Acceleration of Front Left Wheel

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Lateral Lateral Acceleration Acceleration of of Front Front Right Right Wheel Wheel

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(d) (d) Figure 6. results of data fusion: (a) longitudinal acceleration of front left wheel; Figure 6. 6. Simulation Simulation Figure Simulation results results of of data data fusion: fusion: (a) (a) longitudinal longitudinal acceleration acceleration of of front front left left wheel; wheel; (b) longitudinal acceleration of front right wheel; (c) lateral acceleration of front left wheel; (b) longitudinal longitudinal acceleration acceleration of of front front right right wheel; wheel; (c) (c) lateral lateral acceleration acceleration of of front front left left wheel; wheel; and and (b) and (d) acceleration of front right wheel. (d) lateral lateral acceleration acceleration of of front front right right wheel. wheel. (d) lateral

SteeringAngle Angle(rad) (rad) Steering

In In order order to to evaluate evaluate performance performance of of the the proposed proposed data data fusion fusion under under aa noisy noisy environment, environment, aa In order to evaluate performance of the proposed data fusion under a noisy environment, a mechanism mechanism of of white white noise noise is is added added in in the the feedback feedback states. states. The The noise noise is is added added on on measured measured data data of of each each mechanism of white noise is added in the feedback states. The noise is added on measured data of each wheel wheel according according to to the the data data from from aa real real sensor: sensor: TAMAGAWA TAMAGAWA AU7428N200 AU7428N200 (TAMAGAWA (TAMAGAWA SEIKI SEIKI Co., Co., wheel according to the data from a real sensor: TAMAGAWA AU7428N200 (TAMAGAWA SEIKI Co., 2 Ltd., noise for Ltd., Nagano Nagano Prefecture, Prefecture, Japan). Japan). The The noise noise for for acceleration acceleration on on the the CM CM is is up up to to 0.049 0.049 m/s m/s2.. The The noise for 2 Ltd.,yaw Nagano Prefecture, Japan). The noise for acceleration on theoccurs CM isup uptoto150.049 m/s . The noise the rate is up to 1 deg/s. The noise effect for the wheel speed rpm. Figure 7 shows the yaw rate is up to 1 deg/s. The noise effect for the wheel speed occurs up to 15 rpm. Figure 7 shows for the yaw rate is up to 1As deg/s.be The noise effectfigure, for the wheel speed occursfusion up to 15 rpm. Figure 7 the the comparative comparative results. results. As can can be seen seen in in this this figure, the the proposed proposed data data fusion algorithm algorithm shows shows shows the comparative results. As can be seen in this figure, the proposed data fusion algorithm shows acceptable acceptable performance performance against against the the effect effect of of noise. noise. acceptable performance against the effect of noise. 0.10 0.10 0.08 0.08 0.06 0.06 0.04 0.04 0.02 0.02 0.00 0.00 -0.02 -0.02 -0.04 -0.04 -0.06 -0.06 -0.08 -0.08 -0.10 -0.10

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Longitudinal Acceleration of Rear Right Wheel

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Time (s) (e) Figure Simulation results of fusion: data fusion: (a) for reference for steering front wheel angle; Figure 7.7.Simulation results of data (a) reference front wheel angle; steering (b) longitudinal (b) longitudinal acceleration of front left wheel; (c) longitudinal acceleration of rear right wheel; acceleration of front left wheel; (c) longitudinal acceleration of rear right wheel; (d) lateral acceleration (d) lateral leftacceleration wheel; and of (e)rear lateral acceleration of rear right wheel. of front leftacceleration wheel; andof (e)front lateral right wheel.

According to [8], a rival MFC approach is employed for performance comparison, whose the According to [8], a rival MFC approach is employed for performance comparison, whose the control block diagram is depicted in Figure 8. In this figure, the K MFC should satisfy the following control block diagram is depicted in Figure 8. In this figure, the K MFC should satisfy the following stability condition: stability condition: h i MR22  K MFC