An Optimal Slip Ratio-Based Revised Regenerative Braking Control Strategy of Range-Extended Electric Vehicle

energies

Article An Optimal Slip Ratio-Based Revised Regenerative Braking Control Strategy of Range-Extended Electric Vehicle

Hanwu Liu , Yulong Lei, Yao Fu * and Xingzhong Li

State Key Laboratory of Automotive Simulation and Control, School of Automotive Engineering, Jilin University, Changchun 130022, China; [email protected] (H.L.); [email protected] (Y.L.); [email protected] (X.L.) * Correspondence: [email protected]

Received: 2 February 2020; Accepted: 20 March 2020; Published: 24 March 2020

Abstract: The energy recovered with regenerative braking system can greatly improve energy efficiency of range-extended electric vehicle (R-EEV). Nevertheless, maximizing braking energy recovery while maintaining braking performance remains a challenging issue, and it is also difficult to reduce the adverse effects of regenerative current on battery capacity loss rate (Qloss,%) to extend its service life. To solve this problem, a revised regenerative braking control strategy (RRBCS) with the rate and shape of regenerative braking current considerations is proposed. Firstly, the initial regenerative braking control strategy (IRBCS) is researched in this paper. Then, the battery capacity loss model is established by using battery capacity test results. Eventually, RRBCS is obtained based on IRBCS to optimize and modify the allocation logic of braking work-point. The simulation results show that compared with IRBCS, the regenerative braking energy is slightly reduced by 16.6% and Qloss,% is reduced by 79.2%. It means that the RRBCS can reduce Qloss,% at the expense of small braking energy recovery loss. As expected, RRBCS has a positive effect on prolonging the battery service life while ensuring braking safety while maximizing recovery energy. This result can be used to develop regenerative braking control system to improve comprehensive performance levels.

Keywords: range-extended electric vehicle; regenerative braking; optimal slip ratio control; battery capacity loss model; regenerative braking controller; control strategy optimization

1. Introduction With increasingly prominent energy and environmental issues, electric vehicles have developed rapidly in recent years due to their advantages of low pollution-free emission. However, due to the low energy density of battery, short driving range and long charging time, the marketing of battery electric vehicles (BEV) is greatly limited [1,2]. Range-extended electric vehicles (R-EEVs) add auxiliary power units, it can solve the range anxiety from consumers by increasing driving range. In addition, a R-EEV has a certain commercial competitiveness in the future market [3]. The regenerative braking system (RBS) provides an effective way to greatly improve overall electrical performance of R-EEVs [4,5]. Thereby, the regenerative braking control strategy (RBCS) is worthwhile research, and is receiving a good deal of attention. The existing research has focused on RBCS in order to achieve better capacity of the regenerative braking energy. Literature [6] has analyzed the braking force distribution strategy and studied the energy saving potential. Different control strategies are studied to achieve the goals of regeneration efficiency and braking safety in [7–9]. Similar researches also include Literature [10–13], which develop braking torque allocating method to achieve improved braking performance and energy regeneration. In terms of the currently available approaches, it is mainly focused on how to coordinate

Energies 2020, 13, 1526; doi:10.3390/en13061526 www.mdpi.com/journal/energies Energies 2020, 13, 1526 2 of 21

Energies 2019, 12, x FOR PEER REVIEW 2 of 21 the regenerative braking torque and mechanical friction to maximize the braking energy recovery while ensuringrecovery thewhile braking ensurin effig ciency.the braking It should efficiency be noted. It should that the be impact noted ofthat regenerative the impact brakingof regenerative current (RCC)braking on current battery (RCC) health on should battery also health be given should suffi alsocient be attention given sufficient and research. attention and research. TheThe otherother focusfocus isis optimization andand the analysis of braking torque distributions strategiesstrategies underunder extremeextreme adhesion adhesion conditions conditions or an or emergencyan emergency braking braking process. process. A revised A controlrevised strategy control is strategy presented is withpresented the front with wheel the front slip ratio wheel consideration slip ratio consideration in [14] to prevent in [14] a frontto prevent wheel a lock-up front wheel and maximize lock-up and the regenerativemaximize the braking regenerative efficiency braking under efficiency low tire–road under low friction tire– conditions.road friction Literature conditions. [15 Literature] proposed [15] an eproposedfficient RBCS an efficient based on RBCS the modifiedbased on nonlinear the modified model nonlinear predictive model control predictive method control to ensure method braking to safety.ensure Inbraking addition, safety. a study In addition, team [16 a ]study built ateam high-precision [16] built a predictivehigh-precision model predictive based on model the o ffbased-line optimizationon the off-line data optimization of the combined data of modelthe combined to solve model the poor to solve real-time the poor problem real-time of the problem optimization. of the Theoptimization. artificial neural The artificial network-based neural controlnetwork mechanism-based control was utilizedmechanism to optimize was utilized the switching to optimize scheme the ofswitching the vehicular scheme braking of the forcevehicular distribution braking was force proposed distribution [17]. was proposed [17]. TheThe previousprevious studies studies have have focused focused more onmore the brakingon the e brakingfficiency efficiency and maximization and maximization of regenerative of energy,regenerative but the energy, impact but of RCCthe impact on battery of RCC service on battery life is not service considered life is not suffi consideredciently. It meanssufficiently. there isIt stillmeans much there room is still for much optimization room for of optimization RBCS. Therefore, of RBCS. a revised Therefore, regenerative a revised braking regenerative control strategybraking (RRBCS)control strategy is proposed (RRBCS) in this is proposed paper. The in strategy this paper. based The on strategy optimal based slip ratioon optimal (OSR) toslip ensure ratio (OSR) braking to performanceensure braking while performance maximizing while braking maximizing energy recovery braking and energy reducing recovery battery and capacity reducing loss battery rate (capacityQloss,%). loss The restrate of(Q thisloss,%). paper The rest is organized of this paper as follows: is organized as follows: InIn SectionSection2, the 2, initial the initial regenerative regenerative braking braking control strategy control (IRBCS) strategy is given, (IRBCS) and is the given distribution, and the of thedistribution front and rear of the slip front ratios and and rear allocation slip ratio logics ofand the allocationbraking work-point logic of arethe introduced.braking work A simulation-point are modelintroduced. is built A in s Sectionimulation3, and mod theel tire–road is built adhesion in Section coe 3,ffi andcient the recognition tire–road module adhesion (TACRM) coefficient and doublerecognition fuzzy module logic controller (TACRM) (DFLC) and double are verified fuzzy logic by simulation controller test.(DFLC) In Sectionare verified4, battery by simulation capacity losstest. moduleIn section (BCLM) 4, battery is established. capacity loss The module BCLM (BCLM) uses test is results established. of battery The lifeBCLM decay uses test. test Eventually, results of RRCBSbattery islife proposed. decay test. In SectionEventually,5, the RRCBS e ffectiveness is proposed. and feasibility In section of the5, the proposed effectiveness RRBCS and are feasibility validated byof the test proposed under the RRBCS world light are validated vehicle test by procedure test under (WLTP). the world This light is followed vehicle bytest the procedure conclusion (WLTP). in the finalThis section.is followed by the conclusion in the final section.

2.2. IRBCS Based on OSR 2.1. Control Principle Overview of IRBCS 2.1. Control Principle Overview of IRBCS The research object is a medium-sized R-EEV. As shown in Figure1, the R-EEV is driven by the The research object is a medium-sized R-EEV. As shown in Figure 1, the R-EEV is driven by the front axle. The regenerative braking system consists of two systems: hydraulic braking system and front axle. The regenerative braking system consists of two systems: hydraulic braking system and an electric braking system. Four wheels are equipped with regulating valves, so each wheel can be an electric braking system. Four wheels are equipped with regulating valves, so each wheel can be controlled independently by braking controller. controlled independently by braking controller.

Figure 1.1. Structure of range-extendedrange-extended electric vehicle withwith regenerativeregenerative brakingbraking system.system.

The optimal control of braking efficiency and energy recovery cannot be guaranteed with fixed slip ratio on different tire–road adhesion conditions. Through monitoring and identification of tire– road adhesion conditions in real time, the OSR is output as the control target value to ensure braking performance [18,19]. Process of IRBCS based on OSR is shown in Figure 2.

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The optimal control of braking efficiency and energy recovery cannot be guaranteed with fixed slip ratio on different tire–road adhesion conditions. Through monitoring and identification of tire–road adhesion conditions in real time, the OSR is output as the control target value to ensure braking performance [18,19]. Process of IRBCS based on OSR is shown in Figure2. EnergiesEnergies 20192019,, 1212,, xx FORFOR PEERPEER REVIEWREVIEW 33 ofof 2121

Figure 2. Process of regenerative braking control strategy based on optimal slip ratio. Figure 2. ProcessProcess of regenerative braking control strategy based on optimal slip ratio.ratio.

WhenWhen brakingbraking starts,starts, hydraulichydraulic brakebrake controlcontrol unitunit judgesjudges thethe batterybabatteryttery statestate ofof chargecharge (SoC).(SoC). IfIf SoC SoC ≥0.8,≥0.8,0.8, itit meansmeans batterybattery energyenergy is is high, high, the the RBSRBS isis notnot carriedcarried outout andand thethe wheelswheels areare braked braked by by hydraulic hydraulic ≥ braking system. If SoC<0.8 and Vvehic>0, the RBS start to work and braking torque distributed between braking system. If SoCSoC<0.8<0.8 and Vvehic>0,>0, the the RBS RBS start start to to work work and and braking braking torque torque distributed distributed between frontfront wheels wheels wheels with withwith regenerative regenerative regenerative braking braking braking torque torque torque and rear and and wheels rear rear wheels wheels with hydraulic with with hydraulic hydraulic braking torque braking braking provided torque torque byprovidedprovided the motor. byby thethe If the motor.motor. regenerative IfIf thethe regenerativeregenerative braking torque brakingbraking can torquetorque provide cancan su ﬃprovideprovidecient required sufficientsufficient braking requiredrequired torque, brakingbraking the fronttorque,torque, wheel the the front frontbraking wheel wheel torque braking braking is all torque torqueprovided is is all all by provided providedthe regenerative by by the the brakingregenerative regenerative torque. brak brak Ifinging the torque. torque. regenerative If If the the brakingregenerativeregenerative torque braking braking cannot torque torque provide cannotcannot suﬃcient provideprovide required sufficientsufficient braking requiredrequired torque, brakingthe braking front torque, torque,wheel braking the the front front torque wheel wheel is providedbrakingbraking torquetorque by the isis regenerative providedprovided byby braking thethe regenerativeregenerative torque and brakingbraking the hydraulic torquetorque and brakingand thethe hydraulichydraulic torque. brakingbraking torque.torque.

2.2.2.2.22.. T Tire–RoadTireire––RRoadoad AdhesionAdhesion CoeCoefficientCoefficientfficient RecognitionRecognition ModuleModuleModule (TACRM)(TACRM)(TACRM) ThroughThrough TACRM,TACRM, thethe the ttireire tire–road––roadroad adhesionadhesion adhesion coefficientcoefficient coefficient (TAC)(TAC) (TAC) isis estimatedestimated is estimated inin realreal in real timetime time andand the andthe realreal the-- real-timetimetime optimaloptimal optimal slipslip slip ratioratio ratio ((ssosrosr ( s(t)(t)osr)) (t)andand) and realreal real-time--timetime ttireire tire–road––roadroad adhesionadhesion adhesion coefficientcoefficient coefficient ((μ (μµosrosrosr (t)(t)(t))) )areare are outputoutput outputted.tedted.. SeveralSeveraSeverall maturematurematuretire–road ttireire––roadroad models modelsmodels based basedbased on onon empirical empiricalempirical and andand analytical analyticalanalytical can can becan selected bebe selectedselected [13]. [13]. A[13]. braking AA brakingbraking force distributionforceforce distribution distribution strategy strategy strategy is proposed is is proposed proposed in [19] based in in [19] [19] on based based the estimation on on the the estimation estimation of the tire–road of of the the friction t tireire––roadroad coe frictionffifrictioncient usingcoefficientcoefficient a fuzzy usingusing logic aa fuzzyfuzzy estimation logiclogic estimation approach.estimation Inapproach.approach. this paper, InIn this thethis empiricalpaperpaper,, thethe model empiricalempirical ‘Burckhardt modelmodel ‘Burckhardt‘Burckhardt tire model’ istiretire selected model’model’ because isis selectedselected of itsbecausebecause suitability ofof itsits for suitabilitysuitability tire behavior forfor tiretire simulation, behaviorbehavior simulation,simulation, as shown in asas Figure shownshown3 a inin and FigureFigure Table 3(a)3(a)1. Theandand equationTableTable 1.1. TheThe of the equationequation ‘Burckhardt ofof thethe tire ‘Burckhardt‘Burckhardt model’ is tiretire expressed model’model’ as isis follows:expressedexpressed asas follows:follows: Cs CCs22s µ(((sss) ) ) =C C C13( (1 (11  e e− 2 ) ) )  C Cs s s ((11(1))) 113− − 3

FigureFigure 3.3. SlipSlip ratio ratio and and frictionfriction adhesionadhesion coecoefficientcoefficientfficient relationshiprelationship inin BurckhardtBurckhardt tiretire model:model:model: ( (aa)) fivefivefive typicaltypical roads; roads; roads; ( b ( ()bb identification)) identification identification of parameters of of parameters parameters used used used in tire–road in in tiretire– adhesion–roadroad adhesion adhesion coefficient coefficient coefficient recognition recognition recognition module. modulemodule..

TableTable 1.1. BurckhardtBurckhardt tiretire modemode parameters.parameters.

RoadRoad CC11 CC22 CC33 DryDry asphaltasphalt 1.281.28 23.9923.99 0.520.52 WetWet asphaltasphalt 1.1971.197 25.1725.17 0.540.54

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Table 1. Burckhardt tire mode parameters.

Road C1 C2 C3 Dry asphalt 1.28 23.99 0.52 Wet asphalt 1.197 25.17 0.54 Dry cement 0.857 33.82 0.35 Wet cobblestone 0.4 33.71 0.12 Ice 0.05 306.39 0.001

As shown in Figure3b, the peak tire–road adhesion coe ﬃcient on j-th road (µj(s(t))) can be calculated by substituting the real-time slip ratio (s(t)). The utilization adhesion coeﬃcient (f(t)) is calculated as follows: Fx_adhesion f (t) = (2) Fz_vertical where Fx_adhesion is the wheel longitudinal adhesion force; Fz_vertical is the wheel vertical force. When µj(s(t))>f(t), the upper limit value of TAC (µJ_ul(t)) is calculated as follows:

µJ_ul(t) = min[µj(s(t))] (3)

When µ (s(t)) f(t), the lower limit value of TAC (µ (t)) is calculated as follows: j ≤ J_ll

µJ_ll(t) = max[µj(s(t))] (4)

The upper and lower limit values of OSR (sJ_osr_ul(t), sJ_osr_ll(t)), upper and lower limit value of real-time tire–road adhesion coefficient (µJ_osr_ul(t), µJ_osr_ll(t)) on the j-th road are obtained using a look-up table. Then, the distribution proportion coefficient (kr) is defined as follows:

µJ_osr_ul(t) f (t) kr = − (5) µ (t) µ (t) J_osr_ul − J_osr_ll

Real-time optimal slip ratio (sosr(t)) and corresponded adhesion coeﬃcient (µosr(t)) can be obtained as follows: sosr(t) = s (t) + krs (t) krs (t) (6) J_osr_ul J_osr_ul − J_osr_ll µosr(t) = µ (t) krµ (t) + krµ (t) (7) J_osr_ul − J_osr_ul J_osr_ll 2.3. Distribution of Front and Rear Slip Ratio The braking working point is located on the ideal braking force distribution curve (I curve). Making the best use of the tire–road adhesion conditions can maximize the braking safety [20]. It is certain that the Economic Commission of Europe Regulation 13 needs to be considered for the braking force allocation to ensure braking safety in design process of RBCS. As shown in Figure4a, the left intersection of the ECE regulation line (M curve) and the front wheel braking force axis (x-axis) is the maximum braking force value of working point A, which is also limited by the motor maximum torque (Tmot_max). It can ensure that all the braking working points obtained in RBCS are above the M curve to ensure braking safety. When the braking working point is at point A, the braking strength is deﬁned as the threshold of the low braking intensity (Za_1), and it is calculated as follows:

WTmax_moti Z = (8) a_l mgR where m is the total mass of vehicle; R is the wheelbase; i is the transmission ratio. Energies 2019, 12, x FOR PEER REVIEW 4 of 21

Dry cement 0.857 33.82 0.35 Wet cobblestone 0.4 33.71 0.12 Ice 0.05 306.39 0.001

As shown in Figure 3(b), the peak tire–road adhesion coefficient on j-th road (μj(s(t))) can be calculated by substituting the real-time slip ratio (s(t)). The utilization adhesion coefficient (f(t)) is calculated as follows:

Fxa_ dhesion ft() (2) Fz _ vertical

Where Fx_ adhesion is the wheel longitudinal adhesion force; Fz_ vertical is the wheel vertical force. When μj(s(t))>f(t), the upper limit value of TAC (μJ_ul(t)) is calculated as follows:

J_ ul(t ) min[ j ( s ( t ))] (3)

When μj(s(t))≤f(t), the lower limit value of TAC (μJ_ll(t)) is calculated as follows:

J_ ll(t ) max[ j ( s ( t ))] (4)

The upper and lower limit values of OSR (sJ_osr_ul(t), sJ_osr_ll(t)), upper and lower limit value of real- time tire–road adhesion coefficient (μJ_osr_ul(t), μJ_osr_ll(t)) on the j-th road are obtained using a look-up table. Then, the distribution proportion coefficient (kr) is defined as follows:

J__ osr ul ()()t f t kr  (5) J____ osr ul()()tt J osr ll

Real-time optimal slip ratio (sosr(t)) and corresponded adhesion coefficient (μosr(t)) can be obtained as follows:

sosr()()()() t s J______osr ul t  k r s J osr ul t  k r s J osr ll t (6)

osr()()()()t  J______osr ul t  k r  J osr ul t  k r  J osr ll t (7)

Energies 2020, 13, 1526 5 of 21 2.3. Distribution of Front and Rear Slip Ratio

TheW is braking the correction working factor point with is thelocated tire–road on the adhesion ideal braking condition force consideration, distribution and curve it is calculated(I curve). Makingas follows: the best use of the tire–road adhesion conditions can maximize the braking safety [20]. It is  certain that the Economic Commission 0, of Europe 0 Regulationµmax µw _13l needs to be considered for the  ( ) ≤ ≤ braking force allocation to ensure braking µmax safetyµw_l in design process of RBCS. As shown in Figure 4(a), W = − , µw_l µmax µw_h (9)  (µw_h µw_l) ≤ ≤ the left intersection of the ECE regulation − line (M curve) and the front wheel braking force axis (x- 1, µw_h µmax axis) is the maximum braking force value of working point≤ A，which is also limited by the motor where µ is the threshold value of the high TAC; µ is the threshold value of the low TAC; µ is maximumw_h torque (Tmot_max). It can ensure that all thew_l braking working points obtained in RBCSmax are abovethe peak the tire–road M curve adhesionto ensure coebrakingﬃcient safety. (PTAC).

Figure 4. Coordinate system conversion: ( (aa)) braking braking force; force; ( (b)) slip slip ratio.

When the required braking strength (Zreq) is less than Za_l, the front wheel braking torque is provided by the regenerative braking torque totally. If the regenerative braking torque provides insufficient required braking torque, the motor remains at the maximum torque, and the insufficient braking force would be compensated by the hydraulic braking system until reaching point B on I curve. As shown in Figure4a, When the braking working point is at point B, the braking strength is defined as the threshold of the high braking intensity (Zb_h), which is calculated as follows: q 2 m + 4Z hg/l m f a_l − f Zb_h = (10) 2hg/l where mf is the front axle mass distribution coefficient; hg is the centroid height. If Zreq> Zb_h, the front and rear wheel braking force distribution is performed according to the I curve, that is, the BC segment coincides with the I curve. The ideal braking force distribution control is realized by controlling the front and rear slip ratio under braking process [6]. As shown in Figure4b, the relationship between braking force and the slip ratio is derived according to the braking dynamics theory. The distribution values of front wheel slip rate slip ratio (sf) and rear wheel slip rate slip ratio (sr) in three braking stages are described as follows:

(1) OA stage: full regenerative braking

1 Za_l s f = µ−f [ ], sr = 0 (11) m f + Zreqhg/l

(2) AB stage: hydraulic braking compensation

Z Zreq Z 1 a_l 1 − a_l s f = µ−f [ ], sr = µr− [ ] (12) m + Zreqhg/l m Zreqhg/l f f − (3) BC stage: coordination braking on the I curve

1 1 s f = µ−f [Zreq], sr = µr− [Zreq] (13) Energies 2020, 13, 1526 6 of 21

Energies 2019, 12, x FOR PEER REVIEW 6 of 21 2.4. Allocation of Braking Work-Point The allocation logic of braking work-point is a major part of IRBCS, and it determines the The allocation logic of braking work-point is a major part of IRBCS, and it determines the eﬃciency efficiency of IRBCS. The braking work-point in IRBCS is divided into five types in this paper, as of IRBCS. The braking work-point in IRBCS is divided into ﬁve types in this paper, as shown in Figure5. shown in Figure 5.

FigureFigure 5.5. AllocationAllocation logic of braking work work-point-point in in initial initial regenerative regenerative braking braking control control strategy: strategy: (a ()a ) area schematic; (b) logic schematic.area schematic; (b) logic schematic.

AsAs shown shown in in Figure Figure 5a, (a),µ µμ_hμ_hand andµ μµμ_l_l areare thethe highhigh tire–roadtire–road adhesion threshold value and the lowlow t tire–roadire–road adhesion adhesion threshold threshold value, value, respectively. respectively. The The allocation allocation logic logic of ofbraking braking work work-point-point in IRBCSin IRBCS is as is follows: as follows: (1) Mild (1) Mild braking braking (Zreq_l (μ isμ_l), better the braking (µmax>µ workµ_l), the-point braking should work-point follow the should “OA” followcurve on the work “OA-”point curve 2 on(WC2 work-point). The front 2 wheel(WC2). braking The front torque wheel is brakingprovided torque by the is motor provided and by the the rear motor wheel and hydraulic the rear wheelforce is hydraulic 0. (2) Moderate force is braking0. (2) Moderate (Zb_h>Zreq_m braking>Za_l), (whenZb_h> theZreq_m PTAC>Za_l is), not when high the enough PTAC ( isμmax not<μ highμ_h), there enough is also (µmax a μ PTACμ_h), the is brakinghigh (µmax work>µµ-point_h), the should braking follow work-point the “AB should” curve follow on work the-point “AB” 4 curve (WC4) onto work-pointachieve good 4 (brakingWC4) to efficiencyachieve good while braking maximizing efficiency braking while energy maximizing recovery. braking (3) energy In the recovery.emergency (3) braking In the emergency condition (brakingZreq_h>Zb_h condition), there is (aZ riskreq_h of>Z lockingb_h), there slip is due a risk to the of lockingsignificant slip braking due to thestrength. significant Therefore, braking the strength.braking workTherefore,-point theshould braking follow work-point the I curve should on work follow-point the 5 (WI curveC5) to ensure on work-point the braking 5 ( Wefficiency.C5) to ensure The rear the wheelbraking braking efficiency. torque The is rear provided wheel braking by hydraulic torque braking is provided system. by hydraulic The motor braking provides system. its max Theimum motor regenerativeprovides its maximumtorque applied regenerative at the front torque wheels. applied at the front wheels.

3.3. Verification Veriﬁcation and Discussion of IRBCS in Simulation EnvironmentEnvironment 3.1. Simulation Model of R-EEV 3.1. Simulation Model of R-EEV In this section, simulation experiments are performed in MATLAB/Simulink and AVL/Cruise In this section, simulation experiments are performed in MATLAB/Simulink and AVL/Cruise software (version 2014, AVL List GmbH, Austria) to evaluate the control eﬀect of IRBCS. As shown in software (version 2014, AVL List GmbH, Austria) to evaluate the control effect of IRBCS. As shown Figure6, the vehicle dynamics model of R-EEV, including regenerative braking system is established in Figure 6, the vehicle dynamics model of R-EEV, including regenerative braking system is in Cruise software. The vehicle performance simulation calculations are performed in Cruise software. established in Cruise software. The vehicle performance simulation calculations are performed in The IRBCS control strategy is performed on the Simulink software through the API function software Cruise software. The IRBCS control strategy is performed on the Simulink software through the API provided by Cruise. Signals such as traction and braking, battery SoC and Vvehic are transmitted function software provided by Cruise. Signals such as traction and braking, battery SoC and Vvehic are between Cruise and Simulink. The main parameters used in the simulation are shown in Table2. transmitted between Cruise and Simulink. The main parameters used in the simulation are shown in Table 2.

Table 2. Vehicle main parameters used in simulation.

Parameter Value Parameter Value Full load weight (kg) 1700 Brake pedal leverage ratio 3.5 Diameter of pedal travel simulator Wheelbase (mm) 2865 15 (mm) Distance from front axle to centroid Battery capacity (kWh) 20 1352 (mm)

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Distance from rear axle to centroid Initial SoC (state of charge) 0.8 1513 (mm) Centroid height (mm) 500 Diameter of front wheel cylinder (mm) 56.95 Drag area (m2) 1.66 Diameter of rear wheel cylinder (mm) 33.82 Correction coefficient of rotating mass 1.1 Diameter of master cylinder (mm) 18 Effective radius of front brake rotor Mechanical efficiency 0.96 0.235 (mm) Energies 2020, 13, 1526 Effective radius of rear brake rotor 7 of 21 Transmission reduction ratio 4.2 0.227 (mm)

Energies 2019, 12, x FOR PEER REVIEW 7 of 21

Distance from rear axle to centroid Initial SoC (state of charge) 0.8 1513 (mm) Centroid height (mm) 500 Diameter of front wheel cylinder (mm) 56.95 Drag area (m2) 1.66 Diameter of rear wheel cylinder (mm) 33.82 Correction coefficient of rotating mass 1.1 Diameter of master cylinder (mm) 18 Effective radius of front brake rotor Mechanical efficiency 0.96 0.235 (mm) Effective radius of rear brake rotor Transmission reduction ratio 4.2 0.227 (mm)

Figure 6. SimulationSimulation platform platform of the R R-EEV.-EEV.

3.2. Verification of TACRM Table 2. Vehicle main parameters used in simulation. The TACRM proposedParameter is verified by Valuesimulation test in this Parameter section. A co-simulation Value test is carried out based on theFull braking load weight system (kg) model 1700of R-EEV in simulation Brake pedal leverage environment. ratio In simulations, 3.5 the Wheelbase (mm) 2865 Diameter of pedal travel simulator (mm) 15 initial braking Batteryspeed capacity is set (kWh)at 80 km/h, and 20 four tire Distance–road fromconditions front axle towere centroid set (mm) with PTAC 1352 of 0.6, 0.45, 0.2, and 0.1, respectively,Initial SoC (state ofas charge) shown in Figure 0.8 7. The Distance braking from strength rear axle to increases centroid (mm) from 0 1513to 0.7 quickly Centroid height (mm) 500 Diameter of front wheel cylinder (mm) 56.95 to simulate emergencyDrag area braking (m2) conditions,1.66 and it stabilizes Diameter of rearat 0.5 wheel until cylinder the (mm) vehicle speed 33.82 is 0. The estimatedCorrection value of coe thefficient PTAC of rotating will mass be output 1.1 in real time Diameter through of master the cylinder TACRM (mm). The effectiveness 18 and Mechanical efficiency 0.96 Effective radius of front brake rotor (mm) 0.235 accuracy of theTransmission TACRM reduction can be ratio seen by comparing 4.2 Ewithffective the radius preset of rear value brake rotor of PTAC. (mm) 0.227 Figure 6. Simulation platform of the R-EEV. 3.2. Verification of TACRM 3.2. Verification of TACRM The TACRM proposed is verified by simulation test in this section. A co-simulation test is carried The TACRM proposed is verified by simulation test in this section. A co-simulation test is carried out based on the braking system model of R-EEV in simulation environment. In simulations, the initial out based on the braking system model of R-EEV in simulation environment. In simulations, the braking speed is set at 80 km/h, and four tire–road conditions were set with PTAC of 0.6, 0.45, 0.2, and initial braking speed is set at 80 km/h, and four tire–road conditions were set with PTAC of 0.6, 0.45, 0.1, respectively, as shown in Figure7. The braking strength increases from 0 to 0.7 quickly to simulate 0.2, and 0.1, respectively, as shown in Figure 7. The braking strength increases from 0 to 0.7 quickly emergency braking conditions, and it stabilizes at 0.5 until the vehicle speed is 0. The estimated value to simulateFigure emergency 7. Simulation braking result ofconditions, TACRM: ( aand) μmax it =stabilizes 0.6; (b) μ maxat =0.5 0.45; until (c) μthemax =vehicle 0.2; (d) speed μmax = 0.1.is 0. The ofestimated the PTAC value will beof the output PTAC in will real be time output through in real the time TACRM. through The the e TACRMffectiveness. The and effectiveness accuracy and of the TACRMaccuracyThe caninterpolation of be the seen TACRM by calculation comparing can be seen method with by comparing the is presetused to valuewith estimate the of PTAC.preset the t valueire–road of PTAC. adhesion condition in the four types of tire–roads, and it can effectively and accurately estimate the PTAC in real time.

3.3. OSR Control Method By DFLC The braking force distribution of the front and rear wheels is different. The membership function of the fuzzy controller and the formulation of the fuzzy rules are also different, which will affect the target slip ratio control result. Considering the difference of braking torque between front and rear wheels, the DFLC for front and rear wheels is designed to ensure OSR tracking control target values FigureFigure 7. Simulation 7. Simulation result resul oftTACRM: of TACRM: (a) (µamax) μmax= =0.6; 0.6; ( b(b))µ μmaxmax == 0.45;0.45; (c ()c )μµmaxmax = 0.2;= 0.2; (d) (d)μmaxµ =max 0.1.= 0.1. effectively, which is different from the fuzzy controllers in [9,13,21–25]. The requirement slip ratio TheThe interpolation interpolation calculation calculation methodmethod isis used to estimate estimate the the tire tire–road–road adhesion adhesion condition condition in inthe the fourfour types types of of tire–roads, tire–roads, and and it it can can e effectivelyﬀectively andand accuratelyaccurately estimate estimate the the PTAC PTAC in in real real time. time.

3.3.3.3 OSR. OSR Control Control Method Method By By DFLC DFLC TheThe braking braking force force distribution distribution of of thethe frontfront and rear rear wheels wheels is is different. different. The The membership membership function function ofof the the fuzzy fuzzy controller controller and and the the formulationformulation of the fuzzy fuzzy rules rules are are also also different, different, which which will will affect affect the the targettarget slip slip ratio ratio control control result. result. ConsideringConsidering the difference difference of of braking braking torque torque between between front front and and rear rear wheels, the DFLC for front and rear wheels is designed to ensure OSR tracking control target values effectively, which is different from the fuzzy controllers in [9,13,21–25]. The requirement slip ratio

Energies 2020, 13, 1526 8 of 21 wheels, the DFLC for front and rear wheels is designed to ensure OSR tracking control target values Energies 2019, 12, x FOR PEER REVIEW 8 of 21 eﬀectively, which is diﬀerent from the fuzzy controllers in [9,13,21–25]. The requirement slip ratio (sreq(t)) can be obtained from the requirement braking strength calculation and real-time OSR (sosr(t)) (sreq(t)) can be obtained from the requirement braking strength calculation and real-time OSR (sosr(t)) can be outputted. The determination process of the real-time OSR control target (scsr(t)) of the control can be outputted. The determination process of the real-time OSR control target (scsr(t)) of the control system is as follows: If sreq(t)

Figure 8. Diagram of optimal slip ratio control process: ( (aa)) fuzzy fuzzy controller controller of of front wheel; ( b) fuzzy controller of rear wheel.

The Mamdani method is used to perform the fuzzy logic calculation in this paper. Triangular shapes are selected for the membership functions of the inputs and outputs and five five fuzzy sets are selected. As As shown shown in in Figure Figure 9 9,, in in the the fuzzy fuzzy logic logic controller controller of of front front wheels, wheels, two two inputs inputs are are the the e (t) s (t) differencedifference between the real slip ratio and the target slip ratio (eff(t)) and slip ratio change rate (s0 ́ff(t)).). e (t) ( 0.05, 0.05), s (t) ( 0.2, 0.2). The input universe is divided into 5 membership functions, ef(t) ∈∈ (−−0.05, 0.05), s ́f(t)0f ∈ (∈−0.2,− 0.2). The input universe is divided into 5 membership functions, which whichare negative are negative large (NB), large negative (NB), negative small small(NS), zero (NS), (ZO), zero (ZO),positive positive small small(PS), positive (PS), positive large large(PB). (PB).The T (t) Theoutputs outputs are the are regenerative the regenerative braking braking force force adjustment adjustment value value (ΔTf _e (∆(t))f and _e )the and hydr theaulic hydraulic braking braking force force adjustment value (∆T (t)). ∆T (t) ( 500, 500), ∆T (t) ( 500, 500). The output universe is adjustment value (ΔTf_m (t)).f_m ΔTf_m (t) ∈f_m (−500,∈ 500),− ΔTf _e(t) ∈ (−500,f _e ∈500−). The output universe is divided intodivided 7 membership into 7 membership functions, functions, which are which negative are negative large (NB), large negative (NB), negative medium medium (NM), (NM),negative negative small (NS),small zero (NS), (ZO), zero (ZO),positive positive small small(PS), positive (PS), positive medium medium (PM), (PM),and positive and positive large (PB). large (PB). The fuzzy rules are the key part of the fuzzy controller. Taking the front wheel fuzzy controller as an example, its design principles are as follows: (1) When ef (t)<0: If s0f (t)>0, it means that sact(t) has approached scsr(t), and ∆Tf should be PS or ZO. If s0f (t) = 0, it means that sact(t) is relatively small relative to scsr(t). There is no risk of slipping during braking due to the slip ratio is small, ∆Tf should be PS or PM. if s0f (t)>0, it means that sact(t) has deviated greatly from scsr(t). In order to eliminate the target deviation as soon as possible, ∆T is PB. (2) When e (t) = 0: if s (t) 0, it means that sact(t) is f f 0f ≤ closer to scsr(t), ∆Tf should be PS or ZO. If s0f (t)>0, it means that sact(t) becomes larger, and the front wheel has the risk of slipping. ∆Tf should be NS or NM. (3) When ef (t)>0: If s0f (t)>0, it means that sact(t) has deviated seriously from scsr(t), and the wheel has the risk of slipping. ∆Tf should be NB or NM to reduce the slip ratio as soon as possible. If s0f (t) = 0, it means that sact(t) s relatively large relative to scsr(t). ∆Tf should be NM or NS. If s0f (t)>0, it means that sact(t) is closer to scsr(t). ∆Tf should be NS or ZO. The fuzzy control rules base of front wheel fuzzy controller is shown in Table3.

Figure 9. Membership functions and output surface of the front wheel fuzzy controller: (a) ef (t); (b)

s´f (t); (c) ∆Tf _e(t); (d) ∆Tf_m (t); (e) ∆Tf _e(t); (f) ∆Tf_m (t).

Energies 2019, 12, x FOR PEER REVIEW 8 of 21

(sreq(t)) can be obtained from the requirement braking strength calculation and real-time OSR (sosr(t)) can be outputted. The determination process of the real-time OSR control target (scsr(t)) of the control system is as follows: If sreq(t)

Figure 8. Diagram of optimal slip ratio control process: (a) fuzzy controller of front wheel; (b) fuzzy controller of rear wheel.

The Mamdani method is used to perform the fuzzy logic calculation in this paper. Triangular shapes are selected for the membership functions of the inputs and outputs and five fuzzy sets are selected. As shown in Figure 9, in the fuzzy logic controller of front wheels, two inputs are the diﬀerence between the real slip ratio and the target slip ratio (ef(t)) and slip ratio change rate (s ́f(t)). ef(t) ∈ (−0.05, 0.05), s ́f(t) ∈ (−0.2, 0.2). The input universe is divided into 5 membership functions, which are negative large (NB), negative small (NS), zero (ZO), positive small (PS), positive large (PB). The outputs are the regenerative braking force adjustment value (ΔTf _e(t)) and the hydraulic braking force adjustment value (ΔTf_m (t)). ΔTf_m (t) ∈ (−500, 500), ΔTf _e(t) ∈ (−500, 500). The output universe is divided into 7 membership functions, which are negative large (NB), negative medium (NM), negative small Energies 2020, 13, 1526 9 of 21 (NS), zero (ZO), positive small (PS), positive medium (PM), and positive large (PB).

Energies 2019, 12, x FOR PEER REVIEW 9 of 21

The fuzzy rules are the key part of the fuzzy controller. Taking the front wheel fuzzy controller as an example, its design principles are as follows: (1) When ef (t)<0: If s´f (t)>0, it means that sact(t) has approached scsr(t), and ∆Tf should be PS or ZO. If s´f (t) = 0, it means that sact(t) is relatively small relative to scsr(t). There is no risk of slipping during braking due to the slip ratio is small, ∆Tf should be PS or PM. if s´f (t)>0, it means that sact(t) has deviated greatly from scsr(t). In order to eliminate the target deviation as soon as possible, ∆Tf is PB. (2) When ef (t) = 0: if s´f (t) ≤0, it means that sact(t) is closer to scsr(t), ∆Tf should be PS or ZO. If s´f (t)>0, it means that sact(t) becomes larger, and the front wheel has the risk of slipping. ∆Tf should be NS or NM. (3) When ef (t)>0: If s´f (t)>0, it means that sact(t) has deviated seriously from scsr(t), and the wheel has the risk of slipping. ∆Tf should be NB or NM to

reduce the slip ratio as soon as possible. If s´f (t) = 0, it means that sact(t) s relatively large relative to Figure 9. Membership functions and output surface of the front wheel fuzzy controller: (a) ef (t);(b) s0f scsr(t). ∆FigureTf should 9. Membership be NM or functionsNS. If s´ fand (t)>0, output it means surface that of the sact (t)front is wheelcloser fuzzy to scsr controller(t). ∆Tf should: (a) ef (t) be; (b NS) or (t);(c) ∆Tf _e(t);(d) ∆Tf_m (t);(e) ∆Tf _e(t);(f) ∆Tf_m (t). ZO. Thes´ ffuzzy (t); (c) control∆Tf _e(t); (rulesd) ∆T f_mbase (t); of(e) front∆Tf _e(t) wheel; (f) ∆ Tfuzzyf_m (t). controller is shown in Table 3. Table 3. The fuzzy control rules base of front wheel fuzzy controller. Table 3. The fuzzy control rules base of front wheel fuzzy controller. s0f (t) NB NS ZO PS PB s´f (t) NB NS ZO PS PB NB PB PM PS ZO ZO NB PB PM PS ZO ZO NS PB PS ZO ZO NS ef (t) ZONS PMPB PSPS ZO ZO ZO NSNS NM ef (t) PSZO PSPM ZOPS ZO NS NS NMNM NB

PBPS ZOPS ZOZO NS NM NM NBNB NB PB ZO ZO NM NB NB AsAs shown shown in in Figure Figure 10 10,, in inthe the fuzzy fuzzy controller controller of rear of wheels, rear wheels, two inputs two inputs are the diareff erence the difference between betweenthe real slipthe ratioreal slip and ratio the targetand the slip target ratio slip (er (t)ratio) and (er(t) slip) and ratio slip change ratio change rate (s rrate(t)). (esr ́r(t)(t)). e(r(t)0.05, ∈ (− 0.05),0.05, 0 ∈ − 0.05s r(t)), s (ŕ (t)0.2, ∈ ( 0.2).−0.2, The0.2) output. The output is the hydraulicis the hydraulic braking braking force adjustment force adjustment value of value rear wheel of rear∆ Twheelr_m(t) . 0 ∈ − ΔT∆Tr_mr_m(t)(t). ΔT(r_m500, (t) ∈ 500). (−500, The 500 selection). The selection and definition and definition of the membership of the membership function function are different are different with the ∈ − withfront the wheel front fuzzy wheel controller fuzzy obviously.controller Theobviously. possibility The of possibility sudden changes of sudden in rear changes wheel brakingin rear torquewheel brakingand the risk torque of overshoot and the risk fluctuations of overshoot should fluctuations be considered. should The be principles considered. are roughly The principles the same are in roughlythe formulation the same of in fuzzy the formulation rules. Compared of fuzzy with rules. the front Compared wheel controller, with the front the selection wheel controller, of fuzzy rules the selectionshould be of softer. fuzzy rules should be softer.

Figure 10. Membership functions and output surface of the rear wheel fuzzy controller: (a) er (t);(b) s0r Figure 10. Membership functions and output surface of the rear wheel fuzzy controller: (a) er (t); (t);(c) ∆Tr _m(t);(d) ∆Tr_m (t). (b) s´r (t); (c) ∆Tr _m(t); (d) ∆Tr_m (t). The fuzzy control rules base of rear wheel fuzzy controller after repeated design adjustments is The fuzzy control rules base of rear wheel fuzzy controller after repeated design adjustments is shown in Table4. shown in Table 4.

Table 4. The fuzzy control rules base of rear wheel fuzzy controller.

s´r (t) NB NS ZO PS PB er (t) NB PM PM PS ZO ZO NS PM PS ZO ZO NS

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Table 4. The fuzzy control rules base of rear wheel fuzzy controller.

s0r (t) NB NS ZO PS PB NB PM PM PS ZO ZO NS PM PS ZO ZO NS er (t) ZO PS ZO ZO NS NM PS PS ZO NS NM NM PB ZO ZO NS NM NB

Defuzzification is an important step in fuzzy inference system. There are many methods of defuzzification. The most common used methods are the maximum membership method, the center of gravity method, and the weighted average method. The weighted average method is selected in fuzzy controller for defuzzification, which is widely used in industrial control. The off-line calculation method is adopted to ensure the control accuracy and calculation speed, and the corresponding relationship between the observed value and the actual control value can be calculated using following equation:

Pn ωi Xi i=1 · X = (14) Pn ωi i=1 where X is the ﬁnal value; n is the number of elements, ωi is the membership.

3.4. Simulation Analysis of IRBCS Based on the simulation model of the regenerative braking system, the braking performance was tested to verify the effectiveness of IRBCS and detect the control effect of the DFLC on the target slip ratio. In simulations, three different roads are set up, namely dry asphalt surface (µmax_h = 0.8), dry cement surface (µmax_m = 0.6) and wet cobblestone surface (µmax_l = 0.35). The initial braking speed is set at 80 km/h. The braking strength increases from 0 to 0.2 and then increases to 0.7 to simulate emergency braking conditions, and it stabilizes at 0.5 until the Vvehic = 0. Two evaluation indexes are used to evaluate the energy recovery performance of IRBCS. Evaluation parameter of regenerative braking efficiency (ηb) and energy recovery ratio (Cb_cyc) can be calculated using following equation:

F f _e ηb = 100% (15) Ftotal ×

Eregen_o f f Eregen_on Cb_cyc = − 100% (16) Eregen_o f f × where Ff_e is the regenerative braking force; Ftotal is the total demand force; Eregen_on is the energy consumed with RBS under the single braking test; Eregen_off is the energy consumed without RBS under the single braking test. Cb_cyc can be expressed as the contribution rate of regenerative braking to the reduction of energy consumption. In order to make the simulation more realistic, the research uses the use of real-like sensor signals affected by errors. During the simulation process, the effects of errors are simulated by adding noise signals.

3.4.1. High Tire–Road Adhesion Condition

As shown in the Figure 11a, IRBCS tries to stop the car and the actual braking strength (Zact) can reach the required braking strength (Zreq). The battery SoC increases from 0.4 to 0.4053, and Cb-cyc is about 61.325%. The speed and slip ratio of front and rear wheel with IRBCS are shown in Figure 11b,c, respectively. Energies 2020, 13, 1526 11 of 21 Energies 2019, 12, x FOR PEER REVIEW 11 of 21

Figure 11. Simulation result of the RBCS under high tire–road adhesion condition (μmax = 0.8): (a) Figure 11. Simulation result of the RBCS under high tire–road adhesion condition (µmax = 0.8): braking strength, TAC and SoC; (b) front wheel slip rate and speed; (c) rear wheel slip rate and (a) braking strength, TAC and SoC; (b) front wheel slip rate and speed; (c) rear wheel slip rate and speed; (d) braking torque. speed; (d) braking torque.

We can see that the IRBCS keeps the slip ratio at the optimal value. The actual slip ratio sact(t) Weresponses can see in thattime with the IRBCSno oversho keepsoting, the and slip the fluctuation ratio at the is small. optimal It means value. that The the DFLC actual designed slip ratio sact(t) responsesin IRBCS in time can achieve with no good overshooting, follow-up of andthe OSR. the fluctuationThe actual vehicle is small. speed It overlaps means thatwith thethe DFLCdesired designed in IRBCSvehicle can speed. achieve The good difference follow-up between of the the vehicle OSR. speed The actual and the vehicle wheel speed speed is overlapsvery smal withl. Figure the desired vehicle11(d) speed. shows The that di thefference regenerative between braking the vehicleefficiency speed and the and variations the wheel of the speed braking is very torque small. include Figure 11d showshydraulic that the regenerative braking torque braking and regenerative efficiency and braking the variations torque, the of hydraulic the braking braking torque torque include and hydraulic regenerative braking torque can cooperate well under IRBCS. Initially, the braking torque is all braking torque and regenerative braking torque, the hydraulic braking torque and regenerative braking provided by the regenerative braking system and ηb is 1 from 0s to 2.4s to increase regenerative torquebraking can cooperate energy. When well the under braking IRBCS. demand Initially, is increased the braking with braking torque torque is all demand provided value by exceeding the regenerative brakingthe system maximum and motorηb is torque 1 from Tmot_max 0s to, the 2.4s hydraulic to increase braking regenerative torque participates braking in energy.the braking When process the braking demandand is η increasedb∈[0.65, 0.81] with; it shows braking thattorque a large demandregenerative value braking exceeding efficiency the can maximum still be achieved. motor torque Tmot_max, the hydraulic braking torque participates in the braking process and ηb [0.65, 0.81]; it shows that a 3.4.2. Medium Tire–Road Adhesion Condition ∈ large regenerative braking efficiency can still be achieved. Similar analysis with the previous Section 3.4.1 is as follows: Zact can reach the required braking 3.4.2. Mediumstrength well Tire–Road on medium Adhesion PTAC, the Condition SoC is increased from 0.4 to 0.4049, and Cb-cyc is about 56.677%. IRBCS keeps the slip ratio at the optimal value, as shown in Figure 12(b) and 12(c). Figure 12(d) shows Similarthat variations analysis of with the braking the previous torque limitingSection the3.4.1 follow is as-up follows: of the targetZact can braking reach intensity the required when braking strengthZreq>0.6 well after on medium3s-3.8s with PTAC, μmax_h thereaching SoC the is increased upper limitation. from 0.4 The to target 0.4049, slip and ratioC isb-cyc equalis aboutto the 56.677%. IRBCSground keeps best the and slip provides ratio at the the maximum optimal braking value, strength. as shown During in Figure the braking 12b,c. process, Figure ηb is12 ind the shows that range of 0.58 to 1; it shows that a large regenerative braking efficiency can still be achieved. variations of the braking torque limiting the follow-up of the target braking intensity when Zreq>0.6 after 3–3.8 s with µmax_h reaching the upper limitation. The target slip ratio is equal to the ground best and provides the maximum braking strength. During the braking process, ηb is in the range of 0.58 to 1; it shows that a large regenerative braking efficiency can still be achieved.

3.4.3. Low Tire–road Adhesion Condition

As shown in the Figure 13a, Zact can reach the required braking strength well on low adhesion coeﬃcient condition, the SoC is increased from 0.4 to 0.4031, and Cb-cyc is about 32.841%. IRBCS keeps the slip ratio at the optimal value, as shown in Figure 13b,c. Figure 13d shows that variations of the braking torque limiting the follow-up of the target braking intensity when Zreq>0.35 after 2.2 s with µmax_l reaching the upper limitation. The control target slip ratio is equal to the ground best and provides the maximum braking strength. During the braking process, ηb is always 1. Under the Energies 2020, 13, 1526 12 of 21 premise of ensuring the braking eﬃciency, the braking energy is recovered to the greatest extent, and the controlEnergies system2019, 12, x FOR has PEER excellent REVIEW performance. 12 of 21

Figure 12. Simulation result of the RBCS under medium tire–road adhesion condition (μmax = 0.6): (a) Figure 12. Simulation result of the RBCS under medium tire–road adhesion condition (µmax = 0.6): braking strength, TAC and SoC; (b) front wheel slip rate and speed; (c) rear wheel slip rate and (a) braking strength, TAC and SoC; (b) front wheel slip rate and speed; (c) rear wheel slip rate and speed; (d) braking torque. speed;Energies (2019d) braking, 12, x FOR torque. PEER REVIEW 13 of 21 3.4.3. Low Tire–road Adhesion Condition

As shown in the Figure 13(a), Zact can reach the required braking strength well on low adhesion coefficient condition, the SoC is increased from 0.4 to 0.4031, and Cb-cyc is about 32.841%. IRBCS keeps the slip ratio at the optimal value, as shown in Figure 13(b) and 13(c). Figure 13(d) shows that variations of the braking torque limiting the follow-up of the target braking intensity when Zreq>0.35 after 2.2s with μmax_l reaching the upper limitation. The control target slip ratio is equal to the ground best and provides the maximum braking strength. During the braking process, ηb is always 1. Under the premise of ensuring the braking efficiency, the braking energy is recovered to the greatest extent, and the control system has excellent performance.

Figure 13. Simulation result of the RBCS under low tire–road adhesion condition (μmax = 0.35): (a) Figure 13. Simulation result of the RBCS under low tire–road adhesion condition (µmax = 0.35): (a) brakingbraking strength, strength, TAC TAC and and SoC;SoC; (b (b) )front front wheel wheel slip sliprate and rate speed; and speed;(c) rear wheel (c) rear slip wheel rate and slip rate and speed; (d) braking torque. speed; (d) braking torque. In summary: as the braking control intervenes, the wheel speed decreases smoothly, and the slip In summary: as the braking control intervenes, the wheel speed decreases smoothly, and the slip ratio maintains the ideal value while in deceleration process. As shown in Figure 11- Figure 13, the ratio maintainswheels actual the slip ideal ratio value can achieve while a good in deceleration tracking of the process. target slip As ratio shown on various in Figures TAC conditions. 11–13, the wheels actualIt slip means ratio that can the achieve IRBCS can a good prevent tracking the wheel of the from target locking slip to ratio ensure on braking various safety. TAC By conditions. using the It means proposed IRBCS, the accumulated Cb_cyc on the three types of roads are 61.325%, 56.677%, 32.841%, respectively. Thereby, tire–road adhesion is fully utilized and the regenerative braking performance of R-EEV is assured, testifying the effectiveness and adaption of the developed control strategy.

4. Revised Regenerative Braking Control Strategy (RRBCS)

4.1. Battery Capacity Loss Model (BCLM) Relevant research shows that the better charging capacity and the better health state of the battery can be obtained by controlling the charging current profiles [26]. In this paper, the Li-ion cylindrical batteries with model M18650 have been selected to study the impact of charging profiles on battery performance. The battery storage systems were subjected to repeat operations of charging and discharging profiles, and the rate and shape of RCC indubitably affected the charging time and the aging rate of a battery. In this section, we reveal the relationship and establish the coupling relationship model between the battery current (I(t)) and the battery capacity loss rate (Qloss,%). The battery model and the measurements of battery capacity fading are proposed in [26–28]. Under a comprehensive driving cycle, the BCLM can be established as follows:

Qloss,%   N cyc  DOD  Ah cell (17) It()  BBCBB1 exp( 2n )  1  exp( 2 ) (18) Ahcell

Energies 2020, 13, 1526 13 of 21

that the IRBCS can prevent the wheel from locking to ensure braking safety. By using the proposed IRBCS, the accumulated Cb_cyc on the three types of roads are 61.325%, 56.677%, 32.841%, respectively. Thereby, tire–road adhesion is fully utilized and the regenerative braking performance of R-EEV is assured, testifying the eﬀectiveness and adaption of the developed control strategy.

4. Revised Regenerative Braking Control Strategy (RRBCS)

4.1. Battery Capacity Loss Model (BCLM) Relevant research shows that the better charging capacity and the better health state of the battery can be obtained by controlling the charging current profiles [26]. In this paper, the Li-ion cylindrical batteries with model M18650 have been selected to study the impact of charging profiles on battery performance. The battery storage systems were subjected to repeat operations of charging and discharging profiles, and the rate and shape of RCC indubitably affected the charging time and the aging rate of a battery. In this section, we reveal the relationship and establish the coupling relationship model between the battery current (I(t)) and the battery capacity loss rate (Qloss,%). The battery model Energiesand the 2019 measurements, 12, x FOR PEER ofREVIEW battery capacity fading are proposed in [26–28]. Under a comprehensive14 of 21 driving cycle, the BCLM can be established as follows:

Tcyc It() Q B  B  I( t )  exp( B )  N  DODdt (19) loss,%0 Q 1loss,% 2= α Ncyc DOD 2 Ahcell cyc (17) × × Ah×cell I(t) Where α is the capacity attenuation coefficient; DOD is the depth of discharge; Ahcell is the α = B1 exp(B2Cn) = B1 exp(B2 ) (18) cumulative capacity of the battery; B1× and B2 are fitting parameters,× Ah cellwhich can be calculated through Z the least square method; Cn is theT cyccharging rate; I(t) is the batteryI(t) current; Tcyc is the total cycle time. It is difficult to Qevaluateloss,% = the impactB1 Bof2 dischargeI0(t) exp profiles(B2 on) batteryNcyc performance,DODdt because most(19) 0 × × × Ahcell × × discharge conditions are multifarious based on the load itself [26], and it is necessary to correct the where α is the capacity attenuation coefficient; DOD is the depth of discharge; Ah is the cumulative original equation of BCLM with rate and current shape characteristic index. In ordercell to evaluate the capacity of the battery; B and B are fitting parameters, which can be calculated through the least capacity fading of the cells1 during2 their service life, multi-stage constant current–constant voltage square method; C is the charging rate; I(t) is the battery current; T is the total cycle time. with a negative pulsen (MCC-CVNP) is selected to simulate thecyc battery current shape during It is difficult to evaluate the impact of discharge profiles on battery performance, because most operation, and the reference performance test was carried out regularly (every 1700 cycles). As shown discharge conditions are multifarious based on the load itself [26], and it is necessary to correct the in Figure 14, six cases have been selected in this paper to investigate the impact of the battery current original equation of BCLM with rate and current shape characteristic index. In order to evaluate the curve on the lithium-ion battery: capacity fading of the cells during their service life, multi-stage constant current–constant voltage with Case 1 (CC-CVNP): constant current discharging at current rate Id for Td and constant current a negative pulse (MCC-CVNP) is selected to simulate the battery current shape during operation, and charging at current rate Ich for Tch, followed by rest time Ts were applied. the reference performance test was carried out regularly (every 1700 cycles). As shown in Figure 14, Cases 2–6 (CC-CVNP): initial constant current discharging at current rate I ⃰d for Td and initial six cases have been selected in this paper to investigate the impact of the battery current curve on the constant current charging at current rate I ⃰ch for Tch, followed by rest time Ts were applied. Each pulse lithium-ion battery: decreases in sequence of ∆Id.

FigureFigure 14. 14. ExampleExample of of the the current current profiles proﬁles of of six six cases: cases: ( (aa)) case case 1; 1; ( (bb)) case case 2 2 to to case case 6. 6.

UnderCase 1 the (CC-CVNP): same discharge constant rate current Cn, the dischargingparameters of at six current cases rateare designedId for Td andas follows: constant current

charging at current rate Ich for Tch, followed by rest timeTTTs were applied. ()()()TT  T  Ah  C d Itdt  ch Itdt d ch s cell n00 d ch

nnTT (20) ((())((())dI t  i  I  ch I t  i  I 00d d ch ch ii00

Where ∆Id is the decrement of discharging current; ∆Ich is the decrement of charging current. As shown in Figure 14 (b), each pulse decreases in sequence of ΔId. The reduced current value becomes equal difference series size relationship, which increases in sequence (ΔId, 2ΔId, 3ΔId…). The relationship between ∆Id, ∆Ich, I ⃰d, and I ⃰ch needs to satisfy the Equation 20 to ensure that maintain the same charging rate under the shape of pulse current. Sc2 is defined to characterize the fluctuation of current shape under cycle condition and is calculated as follows:

T 22cyc S(()) I t C Ah dt (21) c0 n cell

The related research results reveal that the dynamic discharging–charging profile has a significant impact on reducing the capacity fade of the lithium-ion battery cells compared with the static profile [26]. Therefore, case 1 is selected as reference scheme because of their minimum Sc2 in this paper, and ks2 is defined as follows:

Energies 2020, 13, 1526 14 of 21

Cases 2–6 (CC-CVNP): initial constant current discharging at current rate I*d for Td and initial constant current charging at current rate I*ch for Tch, followed by rest time Ts were applied. Each pulse decreases in sequence of ∆Id. Under the same discharge rate Cn, the parameters of six cases are designed as follows:

R T R T (T + T + T ) Ah C = d I (t)dt ch I (t)dt d ch s cell n 0 d 0 ch n × × n − P R T∗ R T∗ (20) = ( d (I (t) i ∆I ) P ( ch ( ( ) ) 0 d∗ d 0 Ich∗ t i ∆Ich i=0 − × − i=0 − × where ∆Id is the decrement of discharging current; ∆Ich is the decrement of charging current. As shown in Figure 14b, each pulse decreases in sequence of ∆Id. The reduced current value becomes equal difference series size relationship, which increases in sequence (∆Id, 2∆Id, 3∆Id ... ). The relationship between ∆Id, ∆Ich, I*d, and I*ch needs to satisfy the Equation (20) to ensure that maintain the same charging rate under the shape of pulse current. 2 Sc is defined to characterize the fluctuation of current shape under cycle condition and is calculated as follows: Z Tcyc 2 2 Sc = (I(t) CnAhcell) dt (21) 0 − The related research results reveal that the dynamic discharging–charging profile has a significant impact on reducing the capacity fade of the lithium-ion battery cells compared with the static profile [26]. 2 Therefore, case 1 is selected as reference scheme because of their minimum Sc in this paper, and ks2 is defined as follows: Q loss∗ ,% ks2 = (22) Qloss,% 2 To characterize the fluctuation of current shape under cycle condition, Swc (t) can be calculated as follows: 2 2 S = (I(t) Iwc) ∆t (23) wc − × Commercial lithium-ion M18650 cells has been used to study the battery capacity loss rate Qloss,%. Table5 shows the electrical parameters of battery cells.

Table 5. Electrical parameters of battery cells.

Electrical Parameters Value Electrical Parameters Value Typical capacity (Ah) 3.65 End-of-charge voltage (V) 4.20 0.05 ± Minimum capacity (Ah) 3.60 End-of-discharge voltage (V) 3.00 Nominal voltage (V) 3.7 Energy density (Wh/kg) 150

Six cases of the applied charging process are shown in Table6.

Table 6. Six cases of the applied discharging process of Cn = 0.5C.

I T I T I* I* ∆I ∆I T C = 1C d d ch ch d ch d ch s f n (A) (s) (A) (s) (A) (A) (A) (A) (s) p Case 1 28 12 14 2 0.5 21 − − − − Case 2 12 2 30 15 0.2 0.1 0.5 21 − − Case 3 12 2 32 16 0.4 0.2 0.5 21 − − Case 4 12 2 34 17 0.6 0.3 0.5 21 − − Case 5 12 2 36 18 0.8 0.4 0.5 21 − − Case 6 12 2 38 19 1.0 0.5 0.5 21 − −

The same test procedure can be performed in the case of Cn = 1.0C, Cn = 2.0C and Cn = 3.0C. 2 The relationship of correction factor ks2(t) and Swc (t) can be computed and concluded as shown in Figure 15. Energies 2019, 12, x FOR PEER REVIEW 15 of 21

Q k  loss,% s2 (22) Qloss,%

To characterize the fluctuation of current shape under cycle condition, Swc2(t) can be calculated as follows:

22 Swc(()) I t  I wc  t (23)

Commercial lithium-ion M18650 cells has been used to study the battery capacity loss rate Qloss,%. Table 5 shows the electrical parameters of battery cells.

Table 5. Electrical parameters of battery cells.

Electrical Parameters Value Electrical Parameters Value Typical capacity (Ah) 3.65 End-of-charge voltage (V) 4.20±0.05 End-of-discharge voltage Minimum capacity (Ah) 3.60 3.00 (V) Nominal voltage (V) 3.7 Energy density (Wh/kg) 150 Six cases of the applied charging process are shown in Table 6.

Table 6. Six cases of the applied discharging process of Cn = 0.5C.

Id Td Ich Tch I ⃰d I ⃰ch ∆Id ∆Ich Ts Cn = 1C fp (A) (s) (A) (s) (A) (A) (A) (A) (s) Case 1 28 12 14 2 − − − − 0.5 21 Case 2 − 12 − 2 30 15 0.2 0.1 0.5 21 Case 3 − 12 − 2 32 16 0.4 0.2 0.5 21 Case 4 − 12 − 2 34 17 0.6 0.3 0.5 21 Case 5 − 12 − 2 36 18 0.8 0.4 0.5 21 Case 6 − 12 − 2 38 19 1.0 0.5 0.5 21

The same test procedure can be performed in the case of Cn = 1.0C, Cn = 2.0C and Cn = 3.0C. The 2 relationshipEnergies 2020, 13 of, 1526correction factor ks2(t) and Swc (t) can be computed and concluded as shown in Figure15 of 21 15.

2 Figure 15. Function relationship of correction factor ks2 andand SSwcwc2. .

AccordingAccording to to equation Equation (21) (21) and and equation Equation (22), (22), Correction Correction factor factor kks2s2 cancan be be calculated calculated as as follows: follows:

22 kk 2 = CC1 + CC2 ln(ln( S ) ) (24) ss2 12 wc (24)

By ﬁtting the experimental data, the following can be acquired: C1 = 1.0419 and C2 = 0.0363. Equation (23) can be calculated as follows:

2 ks2 = 1.0419 + 0.0363 ln(Swc) (25)

2 Finally, according to the above analysis of the relationship between ks2 and Swc , the BCLM with current curve shape considerations under the cycle condition is obtained as follows:

R Tcyc I(t) Qloss,% = B1 B2 I0(t) exp(B2 ) ks2 (t) Ncyc DODdt 0 × × × Ahcell × × × (26) R Tcyc I(t) 2 = 0.495457 I0(t) exp(0.3785 ) [1.0419 + 0.0363 ln(Swc)]dt 0 × × Ahcell × 4.2. Regenerative Braking Work-Point Switching The goal of R-EEV’s regenerative braking control strategy is to ensure comprehensive regenerative braking performance and the OSR-based RRCCS is proposed. The shape and rate of the RCC characterize the details of the battery being charged and discharged during vehicle operation, which can be seen in the battery SoC. In order to control the shape and rate of the battery RCC and reduce the adverse eﬀect of RCC on battery life. The operating point switching mechanism in RRBCS is to conservatively adjust the operating point by referring to the battery SoC characteristics. Through the “conservative braking mode”, the actual SoC will be close to the pre-set value to make full use of the power of the battery pack, while protecting the battery health. As shown in Figure 16, the switching of the braking working point is adjusted in real time according to the vehicle state. WC1 is switched to WC2, and WC4 is switched to WC3. The reference index for braking work-point switching logic is calculated as follows:

(k+1) (k) 1 k = (SoC SoC )∆t− (27) SoC − (k+1) (k) 1 kcr = ζ k = ζ (SoC SoC )∆t− (28) 0 0 0 0 − 0 (k) (k) where kSoC is the SoC change rate; kcr is the change rate discrimination value; SoC and SoC0 are (k + 1)) (k+1) the battery real time SoC and the SoC controls target value at the k instant; SoC and SoC0 are the battery real time SoC and the SoC controls target value at the k+1 instant; k0 and k0_CD are the SoC control target change rate and preset value in charge depletion, and the k0_CS is the SoC preset value in Energies 2019, 12, x FOR PEER REVIEW 16 of 21

By fitting the experimental data, the following can be acquired: C1 = 1.0419 and C2 = 0.0363. Equation (23) can be calculated as follows: kS1.0419 0.0363ln(2 ) s2 wc (25)

Finally, according to the above analysis of the relationship between ks2 and Swc2, the BCLM with current curve shape considerations under the cycle condition is obtained as follows:

Tcyc It() Q BBIt  ( )  exp( B )  ktN2 ( )   DODdt loss,%0 1 2 2 Ah s cyc cell (26) Tcyc It() 0.495457 I ( t )  exp(0.3785 )  [1.0419  0.0363ln( S2 )] dt 0 wc Ahcell

4.2. Regenerative Braking Work-Point Switching The goal of R-EEV's regenerative braking control strategy is to ensure comprehensive regenerative braking performance and the OSR-based RRCCS is proposed. The shape and rate of the RCC characterize the details of the battery being charged and discharged during vehicle operation, which can be seen in the battery SoC. In order to control the shape and rate of the battery RCC and reduce the adverse effect of RCC on battery life. The operating point switching mechanism in RRBCS isEnergies to conservatively2020, 13, 1526 adjust the operating point by referring to the battery SoC characteristics. Through16 of 21 the "conservative braking mode", the actual SoC will be close to the pre-set value to make full use of the power of the battery pack, while protecting the battery health. As shown in Figure 16, the charge sustaining with the value assigned is 0. ζ is a correction coeﬃcient and the value assigned to switching of the braking working point is adjusted0 in real time according to the vehicle state. WC1 is the study is 0.5. switched to WC2, and WC4 is switched to WC3.

FigureFigure 16. 16. SchematicSchematic diagram diagram of of braking braking work work-point-point switching switching logic. logic.

TheThe reference details are index explained for braking as follows: work- (1)point In chargeswitching depletion logic is (CD), calculated when as the follows: SoC>0, if the ksoc is positive and greater than the discrimination value kcr, it means that the SoC has a greater increasing (kk 1) ( ) 1 trend and the possibility of deviationkSoC from() SoC the SoC0,  "conservative SoC  t braking mode" should be adopted.(27)

(2) If kSoC is negative and |kSoC| <|kcr|, it means that the(kk 1) SoC has ( a ) trend 1 of approaching the SoC0, but the “fallback” is slow. At thisk time,cr  a0 “conservative k 0  0() SoC 0 braking  SoC mode” 0 t should be adopted. (3) In charge(28) sustaining (CS), when SoC> 0, it means that the difference between SoC and SoC0 is too large. There is Where kSoC is the SoC change rate; kcr is the change rate discrimination value; SoC (k) and SoC0 (k) a risk of increasing the deviation of the recovered braking energy at this time; thus, the “conservative are the battery real time SoC and the SoC controls target value at the k instant; SoC (k + 1)) and SoC0 (k+1) braking method” should be adopted. are the battery real time SoC and the SoC controls target value at the k+1 instant; k0 and k0_CD are the SoC5. Comparison control target and change Analysis rate of and Three preset Control value Strategiesin charge depletion, and the k0_CS is the SoC preset value in charge sustaining with the value assigned is 0. ζ0 is a correction coefficient and the value assignedThe to world the study light vehicleis 0.5. test procedure (WLTP) is close to actual driving behavior. In this paper, the WLTPThe details driving are cycleexplained is adopted as follows: to carry (1) In out charge the tests depletion for studying (CD), when the comprehensivethe SoC＞0, if the braking ksoc is performance of R-EEV. Under the WLTP driving cycle, the vehicle braking intensity Zreq [0, 0.15], it positive and greater than the discrimination value kcr, it means that the SoC has a greater∈ increasing trendmeans and that the the possibility regenerative of deviation braking work-point from the SoC is W0, "conservativC1 or WC2. Ine addition,braking mode" no braking should work be adopted. condition (2)is definedIf kSoC is asnegative the work-point and |kSoC 0| (<|WkC0cr|,). it means that the SoC has a trend of approaching the SoC0, but the "fallback"Control is strategy slow. At 1 (thethis time, best-braking-performance a "conservative braking strategy) mode" isshould adopted be adopted. to guarantee (3) In thecharge best sustainingbraking performance. (CS), when SoC> The 0, regenerative it means that braking the difference work-point between is always SoC andWC1 SoCin0 Controlis too large. strategy There 1. Control strategy 2 (the maximum-regeneration-efficiency strategy) is the IRBCS proposed mentioned before. The regenerative braking work-point is WC2 in Control strategy 2 to maximize the use of the regenerative braking torque and achieve the maximum regeneration efficiency theoretically. Control strategy 3 (the switchable-work-point strategy) is RRBCS through adding "conservative condition" based on IRBCS. The regenerative braking work-point can be switched from WC2 to WC1 in Control strategy 3 to balance the recovery energy and battery capacity loss rate. Comparative simulations are carried out among three control strategies, as shown in Figure 17. It should be noted that the braking energy recovery will be limited by the motor maximum torque. The motor torque is assumed to provide sufficient required braking torque, and the braking energy is recovered at all braking strengths in theory. This braking recovery is defined as the theoretical maximum regenerative braking to illustrate the contribution of the developed strategy to energy recovery. As depicted in Figure 17a, the vehicle speed can be in good agreement with the target speed under the control strategy 1 and the control strategy 2. It indicated that the IRBCS proposed in this paper can effectively ensure braking efficiency and braking safety. Figure 17b shows that the regenerative braking efficiency of strategy 1 has decreased from 100% to about 56.7%, and the regenerative braking efficiency of strategy 2 has always been 100%. As shown in Figure 17c,d, after a WLTP driving cycle, battery SoC drops from the initial value of 0.8 to 0.671 and 0.683, respectively. The energy recovery ratio Cb-cyc of strategy 1 is above 13.6%. In particular, the energy recovery ratio Cb-cyc even reaches 24.8% for strategy 2, which is a relatively high level. In addition, there are about 37% of the regenerative braking Energies 2019, 12, x FOR PEER REVIEW 17 of 21

is a risk of increasing the deviation of the recovered braking energy at this time; thus, the “conservative braking method” should be adopted.

5. Comparison and Analysis of Three Control Strategies The world light vehicle test procedure (WLTP) is close to actual driving behavior. In this paper, the WLTP driving cycle is adopted to carry out the tests for studying the comprehensive braking performance of R-EEV. Under the WLTP driving cycle, the vehicle braking intensity Zreq ∈ [0, 0.15], it means that the regenerative braking work-point is WC1 or WC2. In addition, no braking work condition is defined as the work-point 0 (WC0). Control strategy 1 (the best-braking-performance strategy) is adopted to guarantee the best braking performance. The regenerative braking work-point is always WC1 in Control strategy 1. Control strategy 2 (the maximum-regeneration-efficiency strategy) is the IRBCS proposed mentioned before. The regenerative braking work-point is WC2 in Control strategy 2 to maximize the use of the regenerative braking torque and achieve the maximum regeneration efficiency theoretically. Control strategy 3 (the switchable-work-point strategy) is RRBCS through adding "conservative condition" based on IRBCS. The regenerative braking work-point can be switched from WC2 to WC1 in Control strategy 3 to balance the recovery energy and battery capacity loss rate. Comparative simulations are Energiescarried2020 ,out13, 1526among three control strategies, as shown in Figure 17. It should be noted that the braking 17 of 21 energy recovery will be limited by the motor maximum torque. The motor torque is assumed to provide sufficient required braking torque, and the braking energy is recovered at all braking work-pointsstrengths switched in theory. from This W brakingc2 to W recoveryc1 in strategy is defined 3 during as the drivingtheoretical cycle; maximum it means regenerative that some of the brakingbraking recovery to illustrate energy the willcontribution not be fully of the utilized, developed as strategy shown into Figureenergy recovery.18.

Energies 2019,, 12,, xx FORFOR PEERPEER REVIEWREVIEW 18 of 21 recovery ratio Cb--cyccyc even reaches 24.8% for strategy 2, which is a relatively high level. In addition, there are about 37% of the regenerative braking work-points switched from Wc2c2 to Wc1c1 in strategy 3 during the driving cycle; it means that some of the braking recovery energy will not be fully utilized, as shown in Figure 18. as shown in FigureFigure Figure18. 17. 17.Simulation Simulation results results of of control control strategy strategy 1 and 1 and control control strategy strategy 2. 2.

As depicted in Figure 17 (a), the vehicle speed can be in good agreement with the target speed under the control strategy 1 and the control strategy 2. It indicated that the IRBCS proposed in this paper can effectively ensure braking efficiency and braking safety. Figure 17(b) shows that the regenerative braking efficiency of strategy 1 has decreased from 100% to about 56.7%, and the regenerative braking efficiency of strategy 2 has always been 100%. As shown in Figure 17(c), (d), after a WLTP driving cycle, battery SoC drops from the initial value of 0.8 to 0.671 and 0.683, respectively. The energy recovery ratio Cb-cyc of strategy 1 is above 13.6%. In particular, the energy

Figure 18. WorkWork-point-point switching situation of strategy 3.

The battery SoC and current curve in the three braking modes based on the WLTP cycle is shown in FiguresFigure 19 19 and and Figure 20. 20.

Figure 19. VariationVariation of the battery SoC with three control strategies.

Through the SoC comparison of the three strategies, it is not hard to discover that the IRBCS (strategy 2) and RRBCS (strategy 3) possess a more superior economy and reduces electricity consumption as much as possible.

Figure 20. Variation of the current with three control strategies.

Compared with Control strategy 2, the change of energy recovery ratio ∆Cb_cyc and the change of battery capacity loss rate ∆Qloss,%loss,% are calculated as follows:

Energies 2019, 12, x FOR PEER REVIEW 18 of 21

recovery ratio Cb-cyc even reaches 24.8% for strategy 2, which is a relatively high level. In addition, there are about 37% of the regenerative braking work-points switched from Wc2 to Wc1 in strategy 3 during the driving cycle; it means that some of the braking recovery energy will not be fully utilized, as shown in Figure 18.

Figure 18. Work-point switching situation of strategy 3.

The battery SoC and current curve in the three braking modes based on the WLTP cycle is shown in Figure 19 and Figure 20.

Figure 19. Variation of the battery SoC with three control strategies.

Figure 20. Variation of the current with three control strategies. Figure 20. Variation of the current with three control strategies. Through the SoC comparison of the three strategies, it is not hard to discover that the IRBCS Compared with Control strategy 2, the change of energy recovery ratio ∆Cb_cyc and the change of (strategy 2) and RRBCS (strategy 3) possess a more superior economy and reduces electricity battery capacity loss rate ∆Qloss,% are calculated as follows: consumption as much as possible. Compared with Control strategy 2, the change of energy recovery ratio ∆C and the change of b_cyc battery capacity loss rate ∆Qloss,% are calculated as follows:

Ci C2 b_cyc − b_cyc ∆Cb_cyc = 100% (29) C2 C1 × b_cyc − b_cyc

Qi Q2 loss,% − loss,% ∆Qloss,% = 100% (30) Q2 Q1 × loss,% − loss,% i i where C b_cyc is the energy recovery ratio Cb_cyc of control strategy i (I = 1, 2, 3); Q loss,% is the battery capacity loss rate Qloss,% of control strategy i (i = 1, 2, 3). The comparison results of regenerative braking performance among the three strategies are listed in Table7.

Table 7. Comparative results regenerative braking performance with three control strategies.

Control Strategy Cb_cyc (%) ηb (%) Qloss,% (%) ∆Cb_cyc (%) ∆Qloss,% (%) Strategy 1 8.5 49.59 0.00176 100 100 − − Strategy 2 24.8 84.43 0.00325 0 0 Strategy 3 22.1 76.51 0.00207 16.6 79.2 − −

As depicted in Figure 21, regenerative braking eﬃciency ηb under three control strategies are 49.59%, 84.43% and 76.51%, respectively. The energy recovery ratio Cb_cyc under three control strategies are 8.5%, 24.8% and 22.1%, respectively. The Cb_cyc slightly reduced by 16.6% and the Qloss,% reduced by 79.2%. It infers that the strategy 3 can improve battery life to a certain extent with less loss of braking energy recovery. This means that strategy 3 balances the regenerative braking energy and the battery capacity attenuation as much as possible. The mitigation eﬀect of the strategy 3 on the battery capacity loss should be more clearly presented, especially during the entire battery life. Therefore, the results of Qloss,% after 1000–10,000 times under WLTP driving cycles are shown in Table8. Energies 2019, 12, x FOR PEER REVIEW 19 of 21

i 2 CCb__ cyc b cyc Cb_ cyc 21 100% (29) CCb__ cyc b cyc

i 2 QQloss,%,% loss Qloss,% 21 100% (30) QQloss,%,% loss

Where Cib_cyc is the energy recovery ratio Cb_cyc of control strategy i (I = 1, 2, 3); Qiloss,% is the battery capacity loss rate Qloss,% of control strategy i (i = 1, 2, 3). The comparison results of regenerative braking performance among the three strategies are listed in Table 7.

Table 7. Comparative results regenerative braking performance with three control strategies.

Control Cb_cyc (%) ηb (%) Qloss,% (%) ∆Cb_cyc (%) ∆Qloss,% (%) Strategy Strategy 1 8.5 49.59 0.00176 −100 −100 Strategy 2 24.8 84.43 0.00325 0 0 Strategy 3 22.1 76.51 0.00207 −16.6 −79.2

As depicted in Figure 21, regenerative braking efficiency ηb under three control strategies are

49.59%,Energies 2020 84.43%, 13, 1526 and 76.51%, respectively. The energy recovery ratio Cb_cyc under three control19 of 21 strategies are 8.5%, 24.8% and 22.1%, respectively.

FigureFigure 21. 21. BarBar chart chart of of regenerative regenerative braking braking performance performance with with three three control control strategies.

Table 8. Comparative results of Qloss,% on three control strategies. The Cb_cyc slightly reduced by 16.6% and the Qloss,% reduced by 79.2%. It infers that the strategy 3 can improve batteryCycles life to a certain 1000 extent with less 2000 loss of braking 5000 energy recovery. 10000 This means that strategy 3 balancesStrategy the regenerative 1 1.77 braking energy 3.89 and the battery 10.27 capacity attenuation 19.64 as much as possible. The mitigatStrategyion 2 effect of 3.29the strategy 3 on 7.24 the battery 19.08capacity loss should 36.52 be more clearly presented, especiallyStrategy during 3 the 2.25entire battery life. 4.95 Therefore, 13.05the results of Q 24.97loss,% after 1000-10000 times under WLTP driving cycles are shown in Table 8.

As shown in Table8, the battery Qloss,% gradually increases with the number of WLTP driving cycles. Table 8. Comparative results of Qloss,% on three control strategies. After 10,000 WLTP driving cycles, Qloss,% under control strategy 1 is 19.64%. By comparison, Qloss,% under control strategy 2 andCycles control strategy1000 3 are2000 36.52% and5000 24.97%, 10000 respectively. It can indicate that the proposed control strategyStrategy 3 avoids 1 the1.77 negative 3.89 impact 10.27 of the large19.64 braking feedback of strategy 2 on battery life and inheritsStrategy the battery 2 friendliness3.29 of7.24 control 19.08 strategy 1.36.52 Therefore, the proposed control strategy 3, namely the switchable-work-pointStrategy 3 2.25 strategy,4.95 has better13.05 comprehensive24.97 braking performance, whichAs can shown provide in Table a feasible 8, the reference battery Q forloss,% regenerative gradually brakingincreases control with the strategy number development. of WLTP driving cycles. After 10,000 WLTP driving cycles, Qloss,% under control strategy 1 is 19.64%. By comparison, 6. Conclusions Qloss,% under control strategy 2 and control strategy 3 are 36.52% and 24.97%, respectively. It can indicateIn thisthat paper, the proposed a RRBCS control with thestrategy rate and3 avoids shape the of negative battery currentimpact of consideration the large braking is proposed feedback to ofbalance strategy the 2 comprehensive on battery life regenerativeand inherits brakingthe battery performance friendliness and of battery control service strategy life. 1. TheTherefore, test results the validate the effectiveness and feasibility of the proposed control strategy. Firstly, The IRBCS based on OSR is introduced, and the aim anti-lock control braking torque based on OSR is provided to improve braking performance while maximizing braking energy recovery. It has been shown that, as expected, IRBCS can achieve good follow-up control of the target slip ratio by DFLC. During the control process, the actual slip ratio responds quickly without overshooting. At the same time, under the three types of tire–road adhesion conditions, IRBCS can maximize the braking energy regenerative efficiency while guaranteeing good braking efficiency with the energy regenerative ratio is 82.46%, 86.43% and 100%, respectively. Moreover, three different braking energy recovery strategies, namely the best-braking-performance strategy (Control strategy 1), the maximum-regeneration-efficiency strategy (Control strategy 2, IRBCS), and the switchable-work-point strategy (Control strategy 3, RRCBS) are implemented and analyzed during WLTP driving cycle. The experimental results indicate the effectiveness and adaptability of the RRBCS. About 37% of work-points are switched from Wc2 to WC1 under strategy 3, with regenerative brake efficiency slightly reduced by 16.6% and the decline in the battery’s capacity reduced by 79.2%, it infers that the RRBCS can reduce Qloss,% to extend its service life significantly with less loss of braking energy recovery. The research methods and conclusions proposed in this paper can provide a powerful reference for regenerative braking control strategy design of R-EEVs.

Author Contributions: Y.L. managed the project; Y.F. conceptualized the scheme; H.L. conceived the control method, completed the modeling, performed the simulation experiments, and ﬁnished the manuscript; X.L. collected the data and reviewed the paper. All authors have read and agreed to the published version of the manuscript. Energies 2020, 13, 1526 20 of 21

Funding: This research was funded by 1. [Project of The National Key Research and Development Program of China] grant number [2016YFB0101402-21]; 2. [Science and Technology Project of Qingdao] grant number [18-1-2-17-zhc]; 3. [Science and Technology Planning Project of Jilin Province] grant number [20180520071JH]. Conﬂicts of Interest: The authors declare no conﬂicts of interest.

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