energies

Article Torque Coordination Control during Braking Mode Switch for a Plug-in Hybrid

Yang Yang 1,2,*, Chao Wang 2, Quanrang Zhang 2 and Xiaolong He 2

1 State Key Laboratory of Mechanical , Chongqing University, Chongqing 400044, China 2 School of Automotive Engineering, Chongqing University, Chongqing 400044, China; [email protected] (C.W.); [email protected] (Q.Z.); [email protected] (X.H.) * Correspondence: [email protected]; Tel.: +86-136-0831-1819

Received: 15 September 2017; Accepted: 16 October 2017; Published: 25 October 2017

Abstract: Hybrid vehicles usually have several braking systems, and braking mode switches are significant events during braking. It is difficult to coordinate torque fluctuations caused by mode switches because the dynamic characteristics of braking systems are different. In this study, a new type of plug-in is taken as the research object, and braking mode switches are divided into two types. The control strategy of type one is achieved by controlling the change rates of hold-down and motor braking forces. The control strategy of type two is achieved by simultaneously changing the target braking torque during different mode switch stages and controlling the motor to participate in active coordination control. Finally, the torque coordination control strategy is modeled in MATLAB/Simulink, and the results show that the proposed control strategy has a good effect in reducing the braking torque fluctuation and vehicle shocks during braking mode switches.

Keywords: (HEV); braking; mode switch; coordinated control; ride comfort

1. Introduction Hybrid electric vehicles (HEVs) have attracted significant research attention because they can effectively reduce fuel consumption and emissions [1–3]. HEVs usually have several braking systems such as hydraulic and motor braking systems. Hydraulic braking systems can provide a stable and efficient braking force for a vehicle, and motor braking systems make energy recovery possible, thus expanding the driving range. Engine braking systems, which use engine drag resistance force during braking, can reduce the wear on a hydraulic braking system, thus saving maintenance expenses [4,5]. There are several braking modes during braking because of the existence of different braking systems. The different dynamic characteristics of hydraulic, motor, and engine braking systems cause torque fluctuations during braking mode switch, which deteriorates the riding comfort and the vehicle safety. Currently, existing research on mode switching is mostly concentrated with the driving and less on the braking mode switch [6–8]. Zhang of Ji Lin University adopted a hierarchical control strategy in braking mode switches, then he designed a coordinated controller, based on a forward-feedback algorithm, to control the pneumatic braking system in order to compensate for errors of the motor braking force [9]. Fu of Tsinghua University analyzed the dynamic characteristics of the motor and the electronic vacuum booster (EVB) of a hybrid vehicle. The braking modes were divided into economic braking mode, safe braking mode with low state of charge (SOC), and safe braking mode with high SOC. Based on expected braking torque predictions, he proposed an electro-hydraulic coordinated braking control strategy [10]. Zhu of Tongji University designed a force distribution correction module and a motor force compensation module for transition conditions. These included force intervention conditions, hydraulic brake force evacuation conditions, and force evacuation conditions with low speed. Those studies investigated the coordination control

Energies 2017, 10, 1684; doi:10.3390/en10111684 www.mdpi.com/journal/energies Energies 2017, 10, 1684 2 of 16

Energiesconditions,2017, 10and, 1684 regenerative brake force evacuation conditions with low speed. Those studies2 of 16 investigated the coordination control between the motor and the mechanical braking system [11]. betweenHowever, the they motor did andnot themake mechanical full use of braking the dynami systemc [characteristics11]. However, of they the did hydraulic, not make motor, full use and of theengine characteristics systems. of the hydraulic, motor, and engine braking systems. In this study, aa newnew typetype of plug-inplug-in hybrid vehicle is taken as the research object, and the braking force distributiondistribution controlcontrol strategy,strategy, which which involves involves the the engine engine drag drag resistance resistance force, force, is is developed. developed. It isIt wellis well known known that that the the dynamic dynamic response response of of hydraulic hydraulic braking braking systems systemsis isslow slow andand stable,stable, whilewhile the response of motor braking systems is fastfast andand accurateaccurate [[12].12]. The control strategystrategy uses thethe hydraulichydraulic braking system to provide the required braking force, the motor to coordinate torque fluctuation, fluctuation, and the clutch to coordinate the engine drag force as a response to the problems of torque fluctuationfluctuation during braking mode switch.

2. HEV Structure and Dynamic Model

2.1. HEV Structure The structurestructure ofof aa plug-in plug-in hybrid hybrid vehicle, vehicle, as as shown show inn in Figure Figure1, mainly 1, mainly includes includes an engine, an engine, an ISG an motor,ISG motor, a permanent a permanent magnet magnet synchronous synchronous motor motor (PMSM), (PMSM), a duala dual clutch, clutch, and and an an infinitelyinfinitely variablevariable transmission (CVT). The front is driven by th thee engine and the integrated starter generator (ISG), the rear axleaxle isis drivendriven byby thethe PMSM,PMSM, andand thethe dualdual clutchclutch isis mountedmounted onon bothboth endsends ofof thethe ISGISG motor.motor.

Figure 1. Structure of a plug-inplug-in hybrid vehicle.

2.2. Dynamic Model

2.2.1. Motor Dynamic Model The three-phasethree-phase PMSMPMSM isis a a strongly strongly coupled coupled and and multivariable multivariable nonlinear nonlinear system system [13 [13].]. In In order order to accuratelyto accurately reflect reflect the the dynamic dynamic response response characteristics characteristics of the of motor the motor during during braking, braking, a dynamic a dynamic model ismodel established is established based on based the mathematicalon the mathematical model of mo thedel three-phase of the three-phase PMSM. InPMSM. the synchronous In the synchronous rotating coordinaterotating coordinate system ( dsystem-q axis), (d the-q axis), ideal the PMSM ideal voltage PMSM equation voltage equation [14] is: [14] is:  d ( u uRiLi==+Ri + L d i − −ω LiL i d ddddeqqd d dtdt d e q q  (1)(1) u = Ri + L d i + ω (L i + ψ ) quRiLi=+q q dt q +ω e() Lid d +ψ f  qqqqeddf  dt The electromagnetic torque equation is: The electromagnetic torque equation is: 3 h i Te = 3pniq i (L − Lq) + ψ (2) =−+2 d d ψ f TpiiLLenqddqf () (2) 2 where ud, uq respectively represent the stator voltage d-q axis component; id, iq respectively represent where ud, uq respectively represent the stator voltage d-q axis component; id, iq respectively represent the stator current d-q axis component; R is stator resistance; ωe is electrical angular velocity; Ld, Lq the stator current d-q axis component; R is stator resistance; ωe is electrical angular velocity; Ld, Lq respectively represent inductance d-q axis component; ψf is permanent magnet flux chain; pn is motor respectively represent inductance d-q axis component; ψf is permanent magnet flux chain; pn is motor pole pairs. pole pairs.

Energies 2017, 10, 1684 33 of of 16 16

2.2.2. Hydraulic Dynamic Model 2.2.2. Hydraulic Dynamic Model The dynamic response characteristics of the hydraulic braking system are related to the hydraulicThe dynamic system structural response characteristicsparameters, duty of the cycle hydraulic and so brakingon. However, system building are related a precise to the hydraulicmodel of thesystem hydraulic structural braking parameters, system dutyis difficult cycle and and so the on. required However, computational building a precise power model is large. of the In hydraulic order to simplifybraking systemthe model is difficult and accurately and the reflect required the computational dynamic characteristics power is large. of the In hydraulic order to simplifysystem, this the studymodel uses and the accurately empirical reflect first-order the dynamic inertia characteristicslink [15]: of the hydraulic system, this study uses the empirical first-order inertia link [15]:  11 TP= π DRB2   hf f f f Ff  = 411 2 sτ +1  Th f Pf 4 πD f R f BF f sτ+1 (3) 112 (3) TP= 1π DRB2 1  Thrhr= P rr πD rr R rr B FrFrτ +  414 s sτ+1 where Thf,, TThrhr areare the the front front and and rear axle brake torque; Pf,, Pr are cylinder pressures; Df,, Drr areare axle cylindercylinder diameter; diameter; RRf,f ,RRr arer are brake brake operating operating radius; radius; BFf,B BFfFr, areBFr brakeare brake efficiency efficiency factors; factors; τ is theτ is first- the orderfirst-order system system time timeconstant, constant, which which can be can obtained be obtained by experience; by experience; s is as variable.is a variable. As shown in Figure 22,, thethe motormotor torquetorque responseresponse isis quickquick andand accurate,accurate, thethe responseresponse timetime isis approximately 0.06 0.06 s, s, and and the overshoot is is 11.12%. Compared Compared with with the the motor, motor, in in order to overcome thethe brake brake clearance and and cylinder cylinder pressurization, pressurization, the the hydraulic system’s system’s torque torque response response is is slow but stablestable and and the response time is approximately 0.17 0.17 s. According According to to [16], [16], the the full full starting starting time time of of the the driving brake isis generallygenerally controlledcontrolled within within 0.2–0.3 0.2–0.3 s; s; thus, thus, the the dynamic dynamic response response characteristics characteristics of theof thehydraulic hydraulic model model constructed constructed in this in this study study satisfies satisfies this this requirement. requirement.

FigureFigure 2. 2. StepStep response response of of motor motor an andd hydraulic hydraulic braking torque.

2.2.3. Engine Engine Drag Drag Model Model When the engine is anti-dragged, the the throttle is is closed and the engine drag resistant torque is relatedrelated toto thethe engine engine speed, speed, as shownas shown in Figure in Figure3. Because 3. Because the engine the hasengine multiple has multiple subsystem subsystem modules, modules,the establishment the establishment of the engine of the model engine is difficult.model is difficult. At the same At the time, same this time, study this does study not does consider not considerthe problem the ofproblem engine of emissions. engine emissions. Therefore, Theref this studyore, this uses study the experimental uses the experimental modeling methodmodeling to methodestablish to the establish engine model,the engine and model, the output and response the output of theresponse engine of drag the resistantengine drag torque resistant is characterized torque is characterizedby a second-order by a transfersecond-order function: transfer function:

2 ω 2 Tfn= ωn n () bICE= 22( e ) (4) TbICE ss2 ++2ζω ω 2 f ne (4) s + 2ζωnnns + ωn where ωn is the natural frequency; ζ is the damping coefficient; ne is the engine speed; TbICE is the where ωn is the natural frequency; ζ is the damping coefficient; ne is the engine speed; TbICE is the engine drag resistant torque; s is a variable.

Energies 2017,, 10,, 16841684 4 of 16

Figure 3. Engine drag resistance torque.

3. Braking Force Distribution Strategy The hybrid electric vehicle mentioned above is equipped with dual motors, and and during during braking, braking, the maximum strength of the motor brake ranges from 0.06 to 0.27 with the speed and CVT ratio changing. Therefore, Therefore, in inorder order to recover to recover as much as much energy energy as possible, as possible, this study this puts study forward puts forward a brake aforce brake distribution force distribution strategy based strategy on basedthe motor on the brak motoring capacity, braking while capacity, taking while the takingengine thebrake engine into brakeconsideration. into consideration. The braking force distributiondistribution curvecurve isis shownshown inin FigureFigure4 .4.V V isis thethe speedspeed ofof thethe vehicle; vehicle;V Vmaxmax and Vmin areare the the maximum maximum and and minimu minimumm vehicle speeds allowed forfor regenerativeregenerative braking;braking; SOCSOChighhigh is the maximum state of chargecharge allowedallowed forfor regenerativeregenerative braking;braking;i oio11 andand iioo2 areare the transmission ratios of finalfinal drive I andand finalfinal drivedrive II;II; iicvtcvt is thethe CVTCVT transmissiontransmission ratio;ratio; zz isis thethe brakingbraking strength;strength;F Fb_reqb_req is the total braking force force the the driver driver demanded; demanded; FFbm_reqbm_req, F,bh_reqFbh_req andand FbICE_reqFbICE_req are theare target the target motor, motor, hydraulic hydraulic and andengine engine braking braking forces; forces; Fbxf_reqF bxf_reqand Fandbxr_reqF arebxr_req theare target the braking target braking forces forcesof the front of the and front rear and rear of axles the ofvehicle; the vehicle; Fbhf_req andFbhf_req Fbhr_reqand areFbhr_req the targetare the hydraulic target hydraulic braking forces braking of the forces front of and the frontrear axles; and rear FbI_req axles; and FbI_reqbP_req areand theFbP_req targetare braking the target forces braking of ISG forces and of ISGPMSM; and PMSM;FbI_max andFbI_ FmaxbP_maxand areFbP_ themax maximumare the maximum braking brakingforces that forces ISGthat and ISG PMSM and can PMSM provide can provide in the current in the current state; F state;bICE isF thebICE engineis the enginedrag resistant drag resistant force; force;Fbm_maxF isbm_ themax maximumis the maximum braking brakingforce that force the thatmotor the can motor provide; can provide;β is the ratioβ is thebetween ratio betweenfront axle front and axletotal andbraking total force. braking force. As seen in Figure4 4,, thethe pointpoint EE isis thethe intersectionintersection ofof lineline z = 0.4 and curve I while the point F is the intersectionintersection ofof linelinez z= = 0.7 0.7 and and curve curve I. I. Therefore, Therefore, the theβ line β line consists consists of theof the OE OE and and EF segmentsEF segments and theand brakingthe braking strengths strengths of A ,ofB Aand, B Candare: C are:

 iFobP2_maxi F zAz()(A)= = o2 bP_max  GG  ( ) =FFbm_max (5) z B = bm _maxG zB() (5)  G ( + )  ( ) = io2 FbP_max 1 β1 z C G()+ β  iFobP2_max11 zC()= The required motor braking force is: G The required motor braking force is: Fbm_req = icvtio1FbI_req + io2FbP_req (6) =+ FiiFiFbm_1_2_ req cvt o bI req o bP req (6) The required hydraulic braking force is: The required hydraulic braking force is: Fbh_req = Fbh f _req + Fbhr_req (7) FF=+ F (7) bh___ req bhf req bhr req The required braking force is: The required braking force is: Fb_req = Gz (8) FGz= (8) breq_

Energies 2017, 10, 1684 5 of 16 Energies 2017, 10, 1684 5 of 16

= Fbxr z 0.7 z = 0.4 Fbreq_ F

E β 2 F F bm _max bICE • D • • • A B C F β bP _max 1

O F bxf

FigureFigure 4.4. The braking forceforce distributiondistribution curve.curve.( (FFbxfbxf) Braking forceforce inin thethe frontfront axle;axle;( (FFbxrbxr) braking force inin thethe rearrear axle;axle; (I(I curve)curve) thethe idealideal brakingbraking forceforce distributiondistribution curve.curve.

TheThe detaileddetailed brakingbraking forceforce distributiondistribution strategiesstrategies areare asas follows:follows: When Vmin < V < Vmax and SOC < SOChigh: When Vmin < V < Vmax and SOC < SOChigh: (1) 0 (1)< z 0≤

Energies 2017, 10, 1684 6 of 16

= FFbI__max req bI  = FFbP__max req bP  =− (12) FFiiFbhf__1_max req bxf req cvt o bI Energies 2017, 10, 1684 FFiF=− 6 of 16  bhr__2_max req bxr req o bP

When V > Vmax or V < Vmin or SOC ≥ SOChigh or z > z(F), the braking force is completely provided When V > Vmax or V < Vmin or SOC ≥ SOChigh or z > z(F), the braking force is completely provided byby thethe hydraulichydraulic brakingbraking system.system. TheThe brakingbraking forcesforces ofof thethe hydraulichydraulic brakingbraking systemsystem are:are: =  FFbhf__ req bxf req =  Fbh f _req = Fbx f _req (13) FFbhr__ req bxr req (13)   Fbhr_req = Fbxr_req

4.4. CoordinatedCoordinated ControlControl StrategyStrategy forfor BrakingBraking ModeMode SwitchSwitch

4.1.4.1. KineticsKinetics AnalysisAnalysis ofof BrakingBraking ModeMode AccordingAccording toto the the braking braking force force distribution distribution control control strategy strategy mentioned mentioned above, above, there there are four are main four brakingmain braking modes: modes: pure electric pure electric braking braking mode, motor mode, and motor engine and braking engine mode, braking motor mode, and motor hydraulic and brakinghydraulic mode, braking and mode, hydraulic and hydraulic braking mode. braking In mode. order toIn facilitateorder to facilitate the kinetic the analysis, kinetic analysis, the hybrid the vehiclehybrid drivevehicle system drive modelsystem is model simplified, is simplified, as illustrated as illustrated in Figure in5 .Figure 5.

J PMSM JO2

J ISG iO2

J J + 2 Je C 2 C1 JCVT JO1 J w mr

iCVT iO1

FigureFigure 5.5. EquivalentEquivalent diagramdiagram ofof thethe systemsystem model.model.

where Je is moment of inertia of the engine; JISG is moment of inertia of the ISG; Jcvt is moment of inertia where Je is moment of inertia of the engine; JISG is moment of inertia of the ISG; Jcvt is moment of inertia of the CVT; JC1 is moment of inertia of the clutch I; JC2 is moment of inertia of the clutch II; JPMSM is of the CVT; JC1 is moment of inertia of the clutch I; JC2 is moment of inertia of the clutch II; JPMSM is moment of inertia of the PMSM; Jw is moment of inertia of the ; JO1 is moment of inertia of the moment of inertia of the PMSM; Jw is moment of inertia of the wheel; JO1 is moment of inertia of the final drive I; JO2 is moment of inertia of the final drive II; m is the vehicle mass; r is the radius. final drive I; JO2 is moment of inertia of the final drive II; m is the vehicle mass; r is the tire radius. (1) Pure Electric Braking Mode (1) Pure Electric Braking Mode When the motor is braking clutch I is engaged and clutch II is disconnected. The engine and the When the motor is braking clutch I is engaged and clutch II is disconnected. The engine and the hydraulic braking systems do not participate in the braking action and the required braking torque hydraulic braking systems do not participate in the braking action and the required braking torque is is provided by the motor. The equivalent to the moment of inertia on the wheel is: provided by the motor. The equivalent to the moment of inertia on the wheel is: =+⋅+⋅+++⋅++2 J v((JJiJiJJJ ISG C11122 ) cvt CVT ) O O O PMSM iJmr O w (14) 2 Jv = ((JISG + JC1) · icvt + JCVT) · iO1 + JO1 + JO2 + JPMSM · iO2 + Jw + mr (14) The dynamic equation of braking is: The dynamic equation of braking is: T = 0  bICE   TbICE ==0  Tbh 0 (15) Tbh= 0 • (15) •  TiiT⋅⋅+ ⋅ i = Jω TbISG bISG· icvt cvt· iO O112+ T bPMSMbPMSM O· iO2 = vJ wvω w where TbICE is the engine drag resistance torque, Tbh is the hydraulic braking torque, TbISG is the ISG . braking torque, TbPMSM is the PMSM braking torque, and ωw is the wheel angular acceleration. (2) Motor and Engine Braking Mode Energies 2017, 10, 1684 7 of 16

When the motor and engine are involved in braking, I and II are engaged. The required braking torque is provided by the motor and the engine. At this time, the equivalent to the moment of inertia on the wheel is:

2 Jv = ((Je + JISG + JC1 + JC2) · icvt + JCVT) · iO1 + JO1 + JO2 + JPMSM · iO2 + Jw + mr (16)

The dynamic equation of braking is: ( Tbh = 0 • (17) (TbISG + TbICE) · icvt · iO1 + TbPMSM · iO2 = Jvωw

(3) Motor and Hydraulic Braking Mode During motor and hydraulic braking modes, clutch I is engaged and clutch II is disconnected. The required braking torque is provided by the motor and the hydraulic braking system. At this time, the equivalent to the moment of inertia on the wheel is:

2 Jv = ((JISG + JC2) · icvt + JCVT) · iO1 + JO1 + JO2 + JPMSM · iO2 + Jw + mr (18)

The dynamic equation of braking is: ( TbICE = 0 • (19) TbISG · icvt · iO1 + TbPMSM · iO2 + Tbh = Jvωw

(4) Hydraulic Braking Mode During hydraulic braking mode, clutches I and II are disengaged and the required braking torque is provided by the hydraulic braking system. The equivalent to the moment of inertia on the wheel is:

2 Jv = JCVT · iO1 + JO1 + JO2 + JPMSM · iO2 + Jw + mr (20)

The dynamic equation of braking is:  T = 0  bICE TbISG = TbPMSM = 0 (21)  •  Tbh = Jvωw

Based on the kinetics analysis of the braking mode, there are three types of braking torque that need to be coordinated during braking mode switching. The motor, the hydraulic, and the engine braking systems are three different systems with different dynamic response characteristics; therefore, the sequences and moments of the three joint systems are different. Because mode switching is completed instantaneously, the braking torque varies sharply during the intervention and exit from braking. If there is no coordinated control, it will cause torque fluctuation and seriously worsen the ride comfort of the vehicle.

4.2. Coordination Control Strategy for Mode Switch According to whether or not the hydraulic braking system is involved in braking, the braking mode-switch type is divided into two categories (Figure6). Braking mode-switch coordination control strategies are developed for the different braking mode-switch types. Energies 2017, 10, 1684 8 of 16 Energies 2017, 10, 1684 8 of 16 Energies 2017, 10, 1684 8 of 16

Figure 6. Braking mode switch classification. Figure 6.6. Braking mode switch classification.classification. (1) Type one: braking mode switch without hydraulic braking system participation. In this type (1)(1) TypeType one:one: brakingbraking modemode switchswitch withoutwithout hydraulichydraulic brakingbraking systemsystem participation.participation. InIn thisthis typetype of mode switching it is necessary to control the engagement of the clutch and the change rate of the ofof modemode switchingswitching it isis necessarynecessary toto controlcontrol thethe engagementengagement of thethe clutchclutch and thethe changechange rate ofof thethe motor torque. Thus, the fluctuation caused by mode switch can be reduced. motormotor torque.torque. Thus, the fluctuationfluctuation causedcaused byby modemode switchswitch cancan bebe reduced.reduced. (2) Type two: braking mode switch with hydraulic braking system participation. Due to the (2)(2) TypeType two:two: brakingbraking modemode switchswitch withwith hydraulichydraulic brakingbraking systemsystem participation.participation. Due toto thethe different dynamic response characteristics of the motor and the hydraulic braking systems, this different dynamicdynamic response response characteristics characteristics of theof the motor motor and theand hydraulic the hydraulic braking braking systems, systems, this switch this switch mode is difficult to coordinate. The idea of coordinating control is to take full advantage of modeswitchis mode difficult is difficult to coordinate. to coordinate. The idea The ofidea coordinating of coordinating control control is to is take to take full advantagefull advantage of the of the characteristics of the braking systems. The hydraulic system can provide large and stable torque, characteristicsthe characteristics of the of the braking braking systems. systems. The The hydraulic hydraulic system system can can provide provide largelarge andand stablestable torque, and the motor braking system’s torque response is quick and accurate, reducing the fluctuation of and thethe motormotor brakingbraking system’ssystem’s torquetorque responseresponse isis quickquick andand accurate,accurate, reducingreducing thethe fluctuationfluctuation ofof the vehicle. thethe vehicle.vehicle. The overall coordination control flow chart is shown in Figure 7. Tbm_req, Tbh_req and TbICE_req are the The overall coordination controlcontrol flowflow chartchart isis shownshown inin FigureFigure7 7.. Tbm_req, ,TTbh_req andand TbICE_reqT are arethe target motor, hydraulic and engine braking torques allocated by the brakingbm_req forcebh_req control bICE_reqstrategy. thetarget target motor, motor, hydraulic hydraulic and and engine engine braking braking torque torquess allocated allocated by bythe the braking braking force force control control strategy. strategy.

= TfTTTb____ req= (,, bm req bh req bICE req ) TfTTTb____ req(,, bm req bh req bICE req )

Figure 7. Flow chart of overall coordination control. Figure 7. Flow chart of overall coordination control. First, according to current speed, SOC, CVT ratio, and brake pedal, the braking force distribution First, according toto current speed,speed, SOC,SOC, CVT ratio, and brake pedal, the braking force distribution control strategy allocates the target motor, hydraulic and engine braking torques; then, according to controlcontrol strategystrategy allocatesallocates the target motor,motor, hydraulichydraulic andand engineengine brakingbraking torques;torques; then,then, accordingaccording toto the braking mode boundary conditions the vehicle controller determines whether the braking mode thethe brakingbraking modemode boundaryboundary conditionsconditions thethe vehiclevehicle controllercontroller determinesdetermines whetherwhether thethe brakingbraking modemode should switch or not. If mode switching happens, the vehicle controller determines the type of mode shouldshould switchswitch oror not.not. If mode switching happens, the vehicle controller determines thethe typetype ofof modemode switch and then selects the corresponding coordination control strategy and controls the clutch, switchswitch andand then then selects selects the the corresponding corresponding coordination coordination control control strategy strategy and controlsand controls the clutch, the clutch, motor motor and hydraulic torques to reduce the mode switch fluctuation. Finally, the vehicle controller andmotor hydraulic and hydraulic torques torques to reduce to the redu modece the switch mode fluctuation. switch fluctuation. Finally, the Finally, vehicle the controller vehicle determines controller determines whether the coordination control is completed, and if it is completed, the vehicle will whetherdetermines the whether coordination the coordination control is completed, control is andcomp ifleted, it is completed, and if it is thecompleted, vehicle will the entervehicle a newwill enter a new braking mode. brakingenter a new mode. braking mode.

Energies 2017, 10, 1684 9 of 16

Energies 2017, 10, 1684 9 of 16 4.2.1. Coordination Control Strategy of Type One 4.2.1. Coordination Control Strategy of Type One In this type of mode switch the motor braking torque and the engine drag resistance torque, In this type of mode switch the motor braking torque and the engine drag resistance torque, transmitted by clutch II, are the main sources of braking torque fluctuation. Therefore, the braking transmitted by clutch II, are the main sources of braking torque fluctuation. Therefore, the braking torque fluctuation is coordinated by controlling the change rate of the clutch hold-down force and the torque fluctuation is coordinated by controlling the change rate of the clutch hold-down force and motor brake force. The torque transmitted by the dry clutch during slipping is: the motor brake force. The torque transmitted by the dry clutch during slipping is:

333 − 3 2 2 RRR−0 R1 Tc =Δ= sign(ωμ∆ω) µF(t)Z 01 (22) Tsignc () FtZ () 222 2 (22) 3 3 RRR−0 − R1 01 wherewhere Δ∆ωω isis the the clutch clutch angular angular velocity velocity difference difference between between the the main main and and driven driven plate; plate; signsign isis symbolic symbolic function;function; μ µisis clutch clutch friction friction factor, factor, which which is is related related to to the the surface surface temperature temperature of of the the plates plates and and Δ∆ωω; ; F(Ft()t is) is the the compression compression force force of of clutch clutch plates; plates; ZZ isis the the clutch clutch friction friction pair pair number; number; RR0,0 R, R1 are1 are the the clutch clutch outerouter and and inner inner friction friction plate plate diameter. diameter. TheThe coordinated coordinated control control flow flow chart chart of of type type one one is is shown shown in in Figure Figure 8,8, kkmm andand kck careare the the change change ratesrates of of motor motor brake brake torque torque and and clutch clutch hold-down hold-down force. force. TTbmbm andand TcT arec are the the actual actual torques torques of of motor motor andand clutch clutch and and TTbmbm = T=bISGTbISGicvtioi1cvt +i oT1bPMSM+ TbPMSMio2. Tb isio2 the. Tb actualis the total actual brake total torque. brake torque.

= TfTTb___ req(, bm req bICE req )

kc km

Tc Tbm

TTbbreq=?_

Figure 8. Flow control chart of the first type mode-switch. Figure 8. Flow control chart of the first type mode-switch.

It is simple to control the motor brake force changing rate, however, it is hard to obtain the target changeIt rate is simple of the to hold-down the motor force. brake Moreover, force changing it is assumed rate, however, that the it istarget hard change to obtain rate the of target the change rate of the clutch hold-down force. Moreover, it is assumed that the target change rate of the total brake force is kreq. Thus: total brake force is kreq. Thus:  FF(t()=)tF = F ++ R kdtk dt   00  c c   TtT(()=) = + + kdtR Tbmbmt bmT0bm0 m k mdt (23)(23)    TTt(()t) ==+ TT + R kk dtdt bbbreqb00  req where F0, Tbm0 and Tb0 are the initial values of the clutch hold-down force, the motor brake torque, where F0, Tbm0 and Tb0 are the initial values of the clutch hold-down force, the motor brake torque, and and the total brake force. the total brake force. Then: Then: Tb(t) = Tbm(t) + Tcicvtio1 (24) + Ttb()= T bm () t Tii c cvt o1 (24) Derivation of the formula above gives: Derivation of the formula above gives: k = k + ai i k (25) req m+ cvt o1 c kkaiikreq= m cvt o1 c (25) and:

Energies 2017, 10, 1684 10 of 16 and: a = sign(∆ω)µZR (26)

Therefore, the change rate of clutch hold-down force is:

kreq − km kc = (27) aicvtio1

4.2.2. Coordination Control Strategy of Type Two The dynamic response of the hydraulic braking system is slow and stable while the response of the motor braking system is fast and accurate. The hydraulic brake system has been developed for a long time, its technology is mature and stable, and its dynamic response characteristics have been well researched [17]. Therefore, in order to make full use of the characteristics of the motor and the hydraulic braking systems, the coordinated control process of braking mode switch is divided into two stages; this is achieved by modifying the target braking torque. 0 0 0 The coordinated control flow chart of type two is shown in Figure9, Tbm , Tbh and TbICE are the modified target braking torques of the motor, the hydraulic and the engine braking system; Tbm0, Tbh0 and TbICE0 are the initial torques of the motor, the hydraulic and the engine braking system when mode is switched; Tc is the transmitted torque of the dry clutch. When mode switch happens, the coordination control process is described as follows: during mode switching, the torques of the motor, the hydraulic and the engine braking system are:

 T = T  bm bm0  Tbh = Tbh0 (28)   TbICE = TbICE0

At that moment, the coordinated control process of the braking mode switch enters into the first stage: it keeps the brake torques of the motor and engine unchanged and modifies the target braking torque of the hydraulic braking system to meet the driver demand. Therefore, the modified torques are:

 0 Tbm = Tbm0   0 Tbh = Tb_req − Tbm0 − icvtio1TbICE0 (29)   0 TbICE = TbICE0

Next, the vehicle controller determines whether Tb is equal to Tb_req, if Tb = Tb_req, the coordinated control process enters into the second stage: it makes full use of the dynamic characteristics of the motor braking system to coordinate the torque fluctuation and modifies the target braking torque of the engine and the hydraulic braking system in order to reach the target value (Tbh_req and TbICE_req)

 0  Tbm = Tb_req − Tbh − icvtio1Tc   0 Tbh = Tbh_req (30)   0  TbICE = TbICE_req

Finally, the vehicle controller evaluates whether Tbm = Tbm_req and TbICE = TbICE_req if so, the current mode is substituted by a new braking mode. A motor torque proportional-integral-derivative (PID) control algorithm was designed in order to improve the hydraulic and clutch torque fluctuation and keep the total braking torque stable during 0 the second stage. The PID algorithm’s control structure is shown in Figure 10. The input is Tbm which Energies 2017, 10, 1684 11 of 16

is the modified target braking torque of the motor while the output is Tbm which is the actual braking torqueEnergies 2017 of the, 10, motor. 1684 11 of 16

Energies 2017, 10, 1684 11 of 16

= TfTTTbreq____(,, bmreqbhreqbICEreq ) = TfTTTbreq____(,, bmreqbhreqbICEreq )

′ ′ TTbm= bm0 TTbICE= bICE0 ′ ′ ′TTbm= bm−−0 TTbICE= bICE0 TTbh= b_010 req T bm iiT cvt o bICE ′ −− TTbh= b_010 req T bm iiT cvt o bICE

TTbbreq=?_ TTbbreq=?_

TT′= TT′= TTbh′= bh_ req TTbICE′= bICE_ req TTbh′= bh_ req −− TiiTbICE bICE_ req bm′ b_1 req−− bh cvt o c TTbm= b_1 req TiiT bh cvt o c

TTbm= bm_ req TTbm= bm_ req &TTbICE= bICE_ req？ &TTbICE= bICE_ req？

FigureFigure 9. 9. Flow Flow control control chart chart ofof thethe second type type mode-switch. mode-switch.

KK pp ′′′′ ′ ′ TTbmbm TT TTbm bmbm ++ ++ bm KKi _ _ i ++

Kd Kd

Figure 10. Motor torque PID control algorithm. Figure 10. Motor torque PID control algorithm. Figure 10. Motor torque PID control algorithm. TheThe PID PID control control algorithm’s algorithm’s expression expression is: is: The PID control algorithm’s expression is: ( 00 =′′ =+( ) + R ( ) ++ d d ( ) Tbm TbmK Ketpe pt() KK ii etdt ()e t dt K d Kdd et ()e t T ′′ =+ Ket() K etdt () + Kdt dt et () bm p i d (31)(31) ( ) = 0 − dt e tet()T=−bm T′ Tbm (31)  =−bm′ bm et() Tbm T bm wherewheree(t )e( ist) theis the PID PID deviation; deviation;K pK,pK, Ki iand and KKdd are the PID PID ratio, ratio, the the integral integral and and the the differential differential factors. factors. where e(t) is the PID deviation; Kp, Ki and Kd are the PID ratio, the integral and the differential factors. 5. Simulation5. Simulation Results Results and and Analysis Analysis 5. Simulation Results and Analysis In thisIn this study, study, the the simulation simulation model model of of a a plug-in plug-in four-wheelfour-wheel drive hybrid hybrid vehicle vehicle was was established established onon theIn the MATLAB/Simulinkthis MATLAB/Simulink study, the simulation simulation simulation model platform. platform.of a plug-i The n four-wheel parameters parameters drive of of the thehybrid hybrid hybrid vehicle vehicle vehicle was and and established the the key key componentson componentsthe MATLAB/Simulink are are listed listed in in Table Tablesimulation1. The1. The effectiveness platform.effectiveness The of of the parameters the coordinated coordinated of controlthe control hybrid strategy strategy vehicle was was and studied studied the key by comparingcomponentsby comparing the are results listedthe results within Table and with 1. without Theand effectivenesswithout a control a strategy.co ofntrol the strategy.coordinated In the simulation In thecontrol simulation of strategy the non-coordinated of was the studiednon- controlby coordinatedcomparing strategy, controlthe motor, results strategy, hydraulic with motor, and and withouthydraulic clutch torques a ancodntrol clutch are notstrategy. torques intervened areIn thenot during simulationintervened the braking duringof the mode thenon- switchcoordinatedbraking while mode control the switch other strategy, parameters while the motor, othe remainedr hydraulicparameters the same.an remainedd clutch the torques same. are not intervened during the braking mode switch while the othe r parameters remained the same.

Energies 2017, 10, 1684 12 of 16

Energies 2017, 10, 1684 Table 1. The parameters of vehicle and key components. 12 of 16

ComponentsTable 1. The parameters Parametersof vehicle and key components. Value Vehicle Mass/kg 1800 Components Parameters Value Displacement/L 1.597 VehicleEngine Mass/kg 1800 PeakDisplacement/L power/Kw 691.597 Engine ISG PeakPeak power/Kwpower/Kw 28 69 ISGPMSM PeakPeak power/Kwpower/Kw 2728 PMSM Peak power/Kw 27 BatteryBattery Type of battery Lithium Lithium

InIn this this paper, paper, the the forward forward simulation simulation modelmodel of plug-in hybrid hybrid ve vehiclehicle is isestablished established based based on on MATLAB/Simulink,MATLAB/Simulink, asas illustratedillustrated in Figure 11.11. Th Thee vehicle vehicle simulati simulationon model model is iscomposed composed of ofISG ISG model,model, PMSM PMSM model, model, battery battery model, model, hydraulichydraulic braking system system model model and and the the controller controller model. model.

Figure 11. Vehicle simulation model based on Simulink. Figure 11. Vehicle simulation model based on Simulink.

TheThe hybrid hybrid vehicle’s vehicle’s brakebrake mode-switch types types in in this this study study are are complex complex and and numerous numerous and it and itwould require require a alot lot of ofcomputational computational power power for the for simulation the simulation analysis analysis of each brake of each mode brake switch. mode switch.Therefore, Therefore, this study this studysimulated simulated several several typical typicalbraking braking mode-switch mode-switch conditions conditions to verify to verifythe theeffectiveness effectiveness of ofthe the coordinated coordinated control control strategy. strategy. The typical The typical braking braking mode-switch mode-switch conditions conditions were wereas follows: as follows: (1) motor (1) motor braking braking mode mode to motor to motor and andengine engine braking braking mode; mode; (2) motor (2) motor braking braking mode mode to tomotor motor and and hydraulic hydraulic braking braking mode; mode; (3) (3) motor motor and and engine engine braking braking mode mode to tomotor motor and and hydraulic hydraulic brakingbraking mode; mode; (4) (4) motor motor and and hydraulic hydraulic brakingbraking mode to to hydraulic hydraulic braking braking mode. mode. This This paper paper takes takes thethe urgent urgent situation situation into into consideration, consideration, therefore,therefore, th thee step step type type of of target target braking braking force force is isset, set, and and the the simulationsimulation results results were were as as follows: follows: when when the the vehicle vehicle speed speed was was 60 60 km/h km/h and and the the braking braking strength strength was changedwas changed from 0.05 from to 0.05 0.2, to the 0.2, braking the braking mode mode was switched, was switched, at 0.2 at s, 0.2 from s, from the motor the motor brake brake to the to motorthe andmotor engine and brake engine (Figure brake 12 (Figure). In the 12). model In the without model without coordination coordination the motor the quickly motor quickly reached reached the target brakingthe target torque braking due torque to its rapiddue to response its rapid response characteristics. characteristics. The dramatic The dramatic change change of the of motor the motor torque torque had a great impact on the ride comfort of the vehicle, the vehicle jerk caused by the motor had a great impact on the ride comfort of the vehicle, the vehicle jerk caused by the motor reached reached 86.06 m/s3. Because the clutch was engaged in a slower time than the motor response, it took 86.06 m/s3. Because the clutch was engaged in a slower time than the motor response, it took longer longer time for it to reach the target value. In the model with coordination, due to fact that the change

Energies 2017, 10, 1684 13 of 16 Energies 2017, 10, 1684 13 of 16 rate of the motor was limited, the impact caused by the motor torque was significantly improved and the value of vehicle jerk was less than 15.18 m/s3. Therefore, the coordinated control strategy time for it to reach the target value. In the model with coordination, due to fact that the change rate of significantly improved the vehicle’s ride comfort. the motorEnergies was 2017 limited,, 10, 1684 the impact caused by the motor torque was significantly improved13 of 16 and the As shown in Figure 13, when the braking strength is changed from 0.1 to 0.3, the braking mode value of vehicle jerk was less than 15.18 m/s3. Therefore, the coordinated control strategy significantly is switchedrate of the from motor the was motor limited, brake the impact to the caused moto by rthe and motor hydraulic torque was brake. significantly In the improved results andwithout improvedcoordinationthe thevalue vehicle’s the of hydraulicvehicle ride jerk comfort. system was less response than 15.18 was m/s slower3. Therefore, and the the hydraulic coordinated braking control system strategy reached theAs targetsignificantly shown braking inFigure improved torque 13 after ,the when vehicle’s the the motor, brakingride therefore,comfort. strength it had is changed a large impact from 0.1on the to 0.3, vehicle. the braking In the results mode is switchedwith coordination fromAs shown the motor thein Figure vehicle brake 13, fluctuation towhen the the motor braking was and significantly strength hydraulic is changed improved brake. from In theby 0.1 coordinating to results 0.3, the without braking the coordinationmotormode and is switched from the motor brake to the motor and hydraulic brake. In the results without thethe hydraulic hydraulic system braking response torque. was However, slower a and small the fluctuation hydraulic brakingoccurred system at 0.42 reacheds because the the target motor braking did coordination the hydraulic system response was slower and the hydraulic braking system reached torquenot have after enough the motor, ability therefore, to coordinate it had the a large change impact of the on hydraulic the vehicle. braking In the torque. results The with jerk coordination of a small the target braking torque after the motor, therefore, it had a large impact on the vehicle. In the results 3 thefluctuation vehiclewith fluctuation coordination was less than was the vehicle significantly1.57 m/s fluctuation and improved the was effect significantly of by the coordinating coordinated improved the bycontrol motorcoordinating is and pretty the the good. hydraulic motor and braking torque.the However, hydraulic a braking small fluctuation torque. However, occurred a small at 0.42fluctuation s because occurred the at motor 0.42 s did because not havethe motor enough did ability to coordinatenot have the enough change ability of theto coordinate hydraulic the braking change torque.of the hydraulic The jerk braking of asmall torque. fluctuation The jerk of a was small less than 1.57 m/sfluctuation3 and the was effect less ofthan the 1.57 coordinated m/s3 and the control effect of isthe pretty coordinated good. control is pretty good.

(a) (b)

(a) (b)

(c)

FigureFigure 12.Figure 12.Simulation Simulation 12. Simulation results results resultsof of motorofmotor motor brakingbraking braking mo modemode toto to motor motor motor and and and engine engine engine braking braking braking mode. mode. mode.(a) Total (a)( aTotal) Total brakingbrakingbraking torque; torque; torque; (b ()b Motor) Motor(b) Motor and and and engine engine engine braking braking braking torque; torque;torque; ( (cc)) Vehicle Vehicle jerk. jerk. jerk.

(a) (b)

(a) (b)

Figure 13. Cont. Energies 2017, 10, 1684 14 of 16 Energies 2017, 10, 1684 14 of 16 Energies 2017, 10, 1684 14 of 16

(c) (c) FigureFigure 13. 13.Simulation Simulation results results of of motor motor braking braking mode mode to to motor motor andand hydraulichydraulic braking braking mode. mode. (a ()a )Total Total brakingFigurebraking torque;13. torque;Simulation (b) ( Motorb) Motor results and and of hydraulic motorhydraulic braking braking braking mode torque; torque; to motor ( c()c) Vehicle Vehicleand hydraulic jerk. jerk. braking mode. (a) Total braking torque; (b) Motor and hydraulic braking torque; (c) Vehicle jerk. Figure 14 shows that the braking mode changes from motor and engine brake to motor and Figure 14 shows that the braking mode changes from motor and engine brake to motor and hydraulicFigure brake.14 shows During that mode the braking switch, modethe engine change exitss from the anti-drag motor and brake, engine and brake the hydraulic to motor system and hydraulic brake. During mode switch, the engine exits the anti-drag brake, and the hydraulic system hydraulicis involved brake. in Duringbraking. mode Figure switch, 14a the shows engine that exits the the totalanti-drag braking brake, torque and the fluctuation hydraulic systemwithout isis involvedcoordination involved in braking.in is braking.very Figureintense. Figure 14 Meanwhile,a shows14a shows that the the torqthat totalue the brakingfluctuation total torquebraking with fluctuation coordinationtorque fluctuation without is smaller. coordination without iscoordination very intense.When theis Meanwhile, very mode intense. is switched the Meanwhile, torque from fluctuation motor the torq andue withhydraulic fluctuation coordination brake with to coordination ishydraulic smaller. brake is smaller. (Figure 15), the motorWhenWhen exits the the the modemode regenerative is switched brake from from mode, motor motor the and moto and hydraulicr hydraulicbraking brake torque brake to drops hydraulic to hydraulic suddenly brake and brake(Figure the (Figure hydraulic 15), the 15 ), themotorbraking motor exits exitstorque the regenerative the rises regenerative slowly. brake The brake mode,vehicle mode,the jerk moto without ther braking motor coordination torque braking drops can torque suddenlyreach drops 138.4 and suddenlym/s the3 and hydraulic the and ride the 3 3 hydraulicbrakingcomfort torque braking is seriously rises torque slowly. worsened. rises The slowly. However,vehicle The jerk vehicle the without jerk jerk with coordination without coordination coordination can is reach less than can138.4 reach95 m/s m/s 138.43and. the m/s rideand thecomfort ride comfort is seriously is seriously worsened. worsened. However, However, the jerk with the jerk coordination with coordination is less than is 95 less m/s than3. 95 m/s3.

(a) (b) (a) (b)

(c) (c) Figure 14. Simulation results of motor and engine braking mode to motor and hydraulic braking FigureFiguremode. 14. 14. (Simulationa )Simulation Total braking results results torque; of of motor motor(b) Motor, and and engine engineengine braking and braking hydraulic mode mode to braking motorto motor andtorque; and hydraulic hydraulic(c) Vehicle braking braking jerk.mode. (a)mode. Total ( brakinga) Total torque;braking (torque;b) Motor, (b) engineMotor, andengine hydraulic and hydraulic braking braking torque; torque; (c) Vehicle (c) Vehicle jerk. jerk.

Energies 20172017,, 1010,, 16841684 15 of 16

(a) (b)

(c)

Figure 15.15. SimulationSimulation results results of of motor motor and and hydraulic hydraulic braking braking mode mode to hydraulic to hydraulic braking braking mode. mode. (a) Total (a) brakingTotal braking torque; torque; (b) Motor (b) Motor and hydraulic and hydraulic braking braking torque; torque; (c) Vehicle (c) Vehicle jerk. jerk.

6. Conclusions 6. Conclusions In this study, a new type of plug-in hybrid was taken as the research object and the braking force In this study, a new type of plug-in hybrid was taken as the research object and the braking force distribution strategy which takes the engine drag resistance torque into consideration was put distribution strategy which takes the engine drag resistance torque into consideration was put forward. forward. The types of braking mode switches were divided into two types, aimed at the problem of The types of braking mode switches were divided into two types, aimed at the problem of torque torque fluctuation during the braking mode switch. Two coordinated control strategies which fluctuation during the braking mode switch. Two coordinated control strategies which correspond to correspond to the two types were developed by analyzing the clutch and the characteristics of the the two types were developed by analyzing the clutch and the characteristics of the hydraulic and the hydraulic and the motor braking systems. The coordination control strategy of type one was achieved motor braking systems. The coordination control strategy of type one was achieved by controlling by controlling the change rates of the clutch hold-down force and the motor braking force. By the change rates of the clutch hold-down force and the motor braking force. By comparing the comparing the characteristics of the motor and the hydraulic braking systems, it was found that the characteristics of the motor and the hydraulic braking systems, it was found that the dynamic response dynamic response of the hydraulic braking system is slow and stable, while the response of the motor of the hydraulic braking system is slow and stable, while the response of the motor braking system braking system is fast and accurate. Therefore, the strategy of type two was coordinated by modifying is fast and accurate. Therefore, the strategy of type two was coordinated by modifying the target the target braking torque during the braking mode switch. Meanwhile, control of the motor braking braking torque during the braking mode switch. Meanwhile, control of the motor braking system system was utilized to actively improve the torque fluctuation and a motor torque PID control was utilized to actively improve the torque fluctuation and a motor torque PID control algorithm was algorithm was designed for this purpose. Finally, a coordination control strategy simulation was designed for this purpose. Finally, a coordination control strategy simulation was performed on the performed on the MATLAB/Simulink platform; the simulation results showed that the coordination MATLAB/Simulink platform; the simulation results showed that the coordination control strategy can control strategy can effectively reduce the vehicle jerk under specific conditions during a typical effectively reduce the vehicle jerk under specific road conditions during a typical braking mode switch. braking mode switch. These promising results are meaningful for further research on the torque These promising results are meaningful for further research on the torque coordination of the braking coordination of the braking mode switch. mode switch. Acknowledgments: The research is supported by: (1) the National Natural Science Foundation of China Acknowledgments:(51575063); (2) the ChongqingThe research Significant is supported Application by: an (1)d theDevelopment National NaturalPlanning Science Project (cstc2015yykfC60003). Foundation of China (51575063); (2) the Chongqing Significant Application and Development Planning Project (cstc2015yykfC60003). The authors would also like to acknowledge the support from the State Key Laboratory of Mechanical Transmission of Chongqing University, China. The authors are indebted to the people who have helped to improve the paper.

Energies 2017, 10, 1684 16 of 16

The authors would also like to acknowledge the support from the State Key Laboratory of Mechanical Transmission of Chongqing University, China. The authors are indebted to the people who have helped to improve the paper. Author Contributions: Yang Yang designed the structure of hybrid vehicle system and proposed the coordination control strategies; Chao Wang built the simulation model based on Simulink and acquired the simulation data. Xiaolong He and Quanrang Zhang participated in data processing. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Zhao, Z.; He, N.; Zhu, Y.; Yu, Z. Mode Transition Control for Four Wheel Drive Hybrid Electric . J. Mech. Eng. 2011, 47, 100–101. [CrossRef] 2. Kerem, K. Modeling and Control of a Hybrid-Electric Vehicle for Drivability and Fuel Economy Improvements. Ph.D. Thesis, Ohio State University, Columbus, OH, USA, May 2008. 3. Steven, M. Mechanical and Regenerative Braking Integration for a Hybrid Electric Vehicle. Ph.D. Thesis, University of Waterloo, Waterloo, ON, Canada, August 2008. 4. Zhang, J.; Lu, C.; Li, Y.; He, C. Status quo and prospect of regenerative braking technology in electric . Automot. Eng. 2014, 36, 911–917. 5. Zheng, Z. Research of Brake Pedal Stroke Simulator and Braking Smoothness Based on Electric-Wheel Vehicle. Ph.D. Thesis, Jilin University, Changchun, China, June 2013. 6. Korowais, K.; Westervelt, E.R.; Rizzoni, G. Toward the systematic Design of Controllers for Smooth Hybrid Electric Vehicle Mode Changes. In Proceedings of the 2007 American Control Conference, New York, NY, USA, 9–13 July 2007. 7. Yang, Y.; Huang, J.; Qin, D.; Duan, Z. Control Strategy for Operation Mode Switch of Dual-Clutch Hybrid Electric Vehicle. Automot. Eng. 2013, 35, 723–730. 8. Yang, Y.; Huang, J.; Qin, D.; Yang, W. Coordinated Torque Control for Model-switch between Motor and Engine Driving in Heavy Hybrid Electric Vehicle. Appl. Mech. Mater. 2011, 86, 779–783. [CrossRef] 9. Zhang, T. Study on the Coordination Control Algorithm of Braking Force for HEV Bus. Master’s Thesis, Jilin University, Changchun, China, June 2011. 10. Fu, X.; Luo, Y.; Han, Y.; Jiang, F.; Li, K. Coordinated Control Strategy for the Electro-Hydraulic Braking System of Intelligent Hybrid Electric Vehicle. Automot. Eng. 2011, 33, 915–919. 11. Numasato, H.; Tomizuka, M. Settling Control and Performance of a Dual-Actuator. IEEE/ASME Trans. Mech. 2008, 8, 431–438. [CrossRef] 12. Wang, K.; He, R. Analysis on Coordination Control Technology of Electric-Mechanical Composite Braking System of Vehicle. Nat. Sci. 2014, 12, 10–17. 13. Yuan, L.; Hu, B.; Wei, K.; Chen, S. Control Principle of Modern PMSM and Matlab Simulation; Beijing University of Aeronautics and Astronautics Press: Beijing, China, 2016. 14. Jin, L.; Wang, X.; Li, W. Current Sliding Mode Control and Load Disturbance Compensation of PMSM for HEV. Automot. Eng. 2013, 35, 553–558. 15. Yang, Y.; Li, X.; Su, N.; Huang, J. Control Strategy for Mode-Switch of Full Hybrid Electric Vehicle. China J. Highw. Transp. 2014, 27, 109–119. 16. Gong, M.; Zhao, D.; Xu, M. Two-way Hydraulic Braking System Performance Simulation of Heavy Vehicles. J. Jilin Univ. Technol. 2010, 40, 725–728. 17. Wu, T. Study on the Dynamic Coordination Control Algorithm of Braking Force for EV. Master’s Thesis, Jilin University, Changchun, China, June 2013.

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).