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Launch Coordination Control Based on Twin-Clutch Torque Distribution for DCT Vehicle
5th IFAC Conference on 5th IFAC Conference on Engine Powertrain Simulation and Modeling 5th IFACand Conference onControl, Engine and Powertrain Control, Simulation and online Modeling Available at www.sciencedirect.com Changchun, China, September 2018 and Modeling Engine Powertrain Simulation 5th IFACand Conference onControl,20-22, Changchun, China, September 20-22, 2018 Changchun, China, September 2018 and Modeling Engine and Powertrain Control,20-22, Simulation Changchun, China, September 20-22, 2018
ScienceDirect
IFAC PapersOnLine 51-31 (2018) 904–909
Launch Coordination Control Based on Launch Launch Coordination Coordination Control Control Based Based on on Twin-Clutch Torque Distribution for DCT Launch Coordination Control Based on Twin-Clutch Torque Distribution for DCT Twin-Clutch Torque Distribution for DCT Vehicle Twin-Clutch Torque Distribution for DCT Vehicle Vehicle Vehicle ∗∗ ∗∗ ∗,∗∗ Zijiao Jiang ∗,∗∗ ∗,∗∗ ∗,∗∗ Qifang Liu ∗∗ ∗∗ Shiying Dong ∗∗ ∗∗ Hong Chen ∗,∗∗ ∗,∗∗
Zijiao Jiang ∗,∗∗ Qifang Liu ∗∗ Shiying Dong ∗∗ Hong Chen ∗,∗∗ Zijiao Jiang Qifang Liu Shiying Dong Hong Chen ∗∗ ∗,∗∗ ∗ Zijiao Jiang ∗,∗∗ Qifang Liu Shiying Dong ∗∗and Hong Chen Automotive Simulation Control, Jilin ∗ ∗ State Key Laboratory of of Automotive Simulation and Control, Jilin State Key Laboratory ∗ StateUniversity, Key Laboratory Automotive Simulation and Control, Jilin P. R. of China (e-mail:[email protected], (e-mail:[email protected], ∗ P. China StateUniversity, Key Laboratory Automotive Simulation and Control, Jilin University, P. R. R. of China (e-mail:[email protected], [email protected]) [email protected]) ∗∗ University, P. R. China (e-mail:[email protected], [email protected]) Department of Control Science and Engineering, ∗∗ ∗∗ Department of Control Science and Engineering, Jilin Jilin University, University, ∗∗ Department of [email protected]) Science and Engineering, Jilin University, P. R. China (e-mail:[email protected], [email protected]) ∗∗ P. R. China (e-mail:[email protected], [email protected]) Department Control Science and Engineering, Jilin University, P. R. China of (e-mail:[email protected], [email protected]) P. R. China (e-mail:[email protected], [email protected]) Abstract: launch control Abstract: For For Dual Dual Clutch Clutch Transmission Transmission (DCT) (DCT) vehicle, vehicle, this this study study provides provides aa launch control Abstract: For Dual Clutch Transmission (DCT) vehicle, this study The provides a launch control method that coordinates the transmission torque of twin clutches. launching process is method that coordinates the transmission torque of twin clutches. The launching process is Abstract: Dual Clutch (DCT) vehicle, this study by provides a launch control method into thatFor coordinates theTransmission transmission torque of twin clutches. The launching process is divided 2 stages. For the first stage, the total torque is obtained using Model Predictive divided into 2 stages. For the first stage, the total torque is obtained by using Model Predictive method into that the first transmission of twin clutches. The launching process is divided 2 coordinates stages. For the stage, thetorque total torque is to obtained by using Model Predictive Control (MPC) method, and total torque is distributed two clutches based on principle Control (MPC) method, andfirst total torque is distributed two clutches based onPredictive principle divided into 2 stages. For For the stage, the total torque is to obtained by using Model Control (MPC) method, andthe total torque is distributed to two clutches based on principle of equal slipping work. second stage, a torque distribution rule is given to allow of equal slippingmethod, work. For second stage, a torque to distribution rulebased is given to allow Control andthe total torque is distributed two clutches on controller principle of equal (MPC) slipping work. For the second stage, a torque distribution rule of is MPC given to allow launching clutch engaged and separating clutch disengaged. Then, stability launching clutch engaged and separating clutch disengaged. Then, stability of MPC controller of equal slipping work. with For the second stage, a PID torque distribution rule of is MPC given to allow launching clutch engaged and single separating clutch disengaged. Then, the stability controller is discussed. Compared clutch launch controller, simulation results show is discussed. Compared with clutchclutch launch PID controller, the simulation results show launching clutch engaged and single separating disengaged. Then, stability of MPC controller is discussed. Compared with single clutch could launch PID controller, the simulation results show that the proposed MPC launch controller greatly shorten the time of launching process, that the proposed MPC launch controller could greatly shorten the time of launching process, is discussed. Compared with single clutch launch PIDand controller, the simulation results show that the proposed MPCavoid launch controller could greatly shorten the time of launching process, decrease slipping work, possible power coupling power cycling. decrease slipping work, possible power coupling and powerthe cycling. that the proposed MPCavoid launch controller could greatly shorten time of launching process, decrease slipping work, avoid possible power coupling and power cycling. © 2018, IFAC (International Federation of Automatic Control) Hosting Elsevier Ltd. All rights reserved. decrease slipping work, avoid possible power coupling and powerbycycling. Keywords: Keywords: Twin-clutch Twin-clutch launch launch control, control, Torque Torque distribution, distribution, Model Model predictive predictive control control (MPC), (MPC), Keywords: Twin-clutch launch control, Torque distribution, Model predictive control (MPC), Dual clutch transmission (DCT). Dual clutch transmission (DCT). Keywords: control, Torque distribution, Model predictive control (MPC), Dual clutchTwin-clutch transmissionlaunch (DCT). Dual clutch transmission (DCT). 1. identified 1. INTRODUCTION INTRODUCTION identified by by Yan Yan (2014) (2014) to to launch launch with with twin twin clutches clutches based based 1. INTRODUCTION identified by Yanalgorithm. (2014) to launch with twin clutches based on self-adaptive A fuzzy control method is on self-adaptive algorithm. A fuzzy control method is dede1. INTRODUCTION identified by Yan (2014) to launch with twincritical clutches based on self-adaptive algorithm. A fuzzy control method is developed with fully consideration of clutch thermal Nowadays, the vehicles equipped with Dual Clutch Transwith fully consideration of clutch critical thermal Nowadays, the vehicles equipped with Dual Clutch Trans- veloped self-adaptive algorithm. A fuzzy control method is developed with by fully consideration of clutch critical thermal Nowadays, the vehicles equipped with Dual Clutch energy value comparing the between launching mission (DCT) play a increasingly significant role Transin au- on energy value by comparing the results results between launching mission (DCT) play a increasingly significant role in auveloped with fully consideration of clutch critical thermal Nowadays, the vehicles equipped with Dual Clutch Transenergy value by comparing the results between launching mission increasingly significant role in ausingle clutch and twin clutches in Zhang (2012). Liu tomotive(DCT) market.play So athere is a consistently-increasing de- with with single and twin clutches in Zhang (2012). Liu tomotive market. So is consistently-increasing devalueclutch by comparing results launching missionfor(DCT) play athere increasingly significant role in auwith single clutch twin the clutches in between Zhang (2012). Liu tomotive market. So launching there is a a experience, consistently-increasing de- energy (2012) considered aaand method of launching with clutchmand improving simultaneously (2012) considered method of launching with twin twin clutchexperience, simultaneously mand for improving launching with single clutch and twin clutches in Zhang (2012). Liu tomotive market. So there is a experience, consistently-increasing de- (2012) considered a method launching with Rules twin clutchmand for improving launching simultaneously es based on constant engineof speed control. about launch control is one of main issue in controlling vehilaunch control is one of mainexperience, issue in controlling vehi- es based on constant engine speed control. Rules about (2012) considered a method of launching with twin clutchmand for improving launching simultaneously es based on constant engine speed control. Rules about launch is one of main issue experience in controlling vehi- torque distribution of clutches were set cle withcontrol DCT. launching is torque distribution of twin twin clutches were set by by Sun Sun (2012), (2012), DCT. Improving Improving launching is widely widely cle with es based ontorque constant engine speed control. about launch is one of main issue experience in controlling vehi- who torque distribution twin clutches were set byRules Sun (2012), cle withcontrol DCT. Improving launching experience made of one clutch in proportion to torque concerned. Usually, traditional launching process isforwidely DCT who made torque of one clutch in proportion to torque concerned. Usually, traditional launching process for DCT torque distribution twin clutches set by work. Sun cle with DCT. Improving experience isforwidely who made torquetoofdistribute one clutch inwere proportion to (2012), torque concerned. Usually, traditional launching processcontrol DCT of another clutch equal slipping Kong uses single clutch which islaunching similar to launch of another clutch toofdistribute equal slipping work. Kong launch control of of uses single clutch is to made torque one clutch in proportion to torque concerned. traditional launching process for DCT of another clutch to distribute equal slipping work. Kong uses single Usually, clutch which which is similar similar to(AMT), launch control of who (2014) gave a sliding mode controller which controlled Automatic Mechanical Transmission some con(2014) gave a sliding mode controller which controlled Automatic Mechanical Transmission (AMT), some conto clutches distribute equal slipping work. Kong uses algorithms single Mechanical clutch is similar toto(AMT), launch control of of (2014) gaveclutch sliding mode to controller whichvehicle controlled Automatic conoil another pressure ofa both launch DCT with trol hadwhich beenTransmission proposed solve thissome problem, oil pressure of both clutches to launch DCT vehicle with trol algorithms had been proposed to solve this problem, (2014) gave a sliding mode controller which controlled Automatic Mechanical Transmission (AMT), some conoil pressure of both clutches to launch DCT vehicle with trol algorithms had been proposed to solve this problem, twin clutches. Zhao (2017) designed a high-order slidingsuch as Model Predictive Control (MPC) in Mario (2015), twin clutches. Zhao (2017) designed a high-order slidingsuch as Model Predictive Control (MPC) in Mario (2015), oil pressure of Zhao both clutches to launch DCT vehicle with trol algorithms had beeninControl proposed to solve thiscontrol problem, twin clutches. (2017) designed a high-order slidingsuch as Modelalgorithm Predictive (MPC) in Mario (2015), mode observer to estimate transmission torque based on optimization Gao (2016), fuzzy in observer Zhao to estimate transmission torque based on optimization algorithm in Gao (2016), fuzzy control in mode clutches. (2017) designed a high-order slidingsuch as Model Predictive (MPC) in Mario (2015), mode observer to estimate transmission torque based on optimization algorithm inControl Gaoand (2016), fuzzy control in twin estimation of vehicle drag torque, which could cooperate Minh (2012) and Zhang (2010) so on. However, launch estimation of vehicle drag torque, which could cooperate Minh (2012) and Zhang (2010) and so on. However, launch observer to estimate transmission torque basedwith on optimization algorithm in Gaoand (2016), fuzzy control in mode estimation of vehicle dragtotorque, which could cooperate Minh (2012) and Zhang (2010) so on. However, with optimum controller launch the DCT vehicle control strategy with single-clutch can easily lead tolaunch some with optimum controller totorque, launch which the DCT vehicle with control strategy with single-clutch can easily lead to some estimation of vehicle drag could cooperate Minh (2012) and Zhang (2010) and so on. However, launch with optimum controller to launch the DCT vehicle with control strategy with single-clutch can easily lead to some twin clutches. Most of control researches were rule-based, problems such as excessive wear, launching failure, etc. In twin clutches. Most of control researches were rule-based, problems such excessive wear, launching failure, etc. In optimum controller to launch the DCT vehicle with controlyears, strategy with single-clutch can easily leadtotolaunch some twin clutches. Most of control researches were rule-based, problems sucha as as excessive wear, launching failure, etc. In with only part of concerned model based methodrecent new idea of using twin clutches only small small partMost of them them concerned modelwere based methodrecent years, a new idea of using twin clutches to launch clutches. of control researches rule-based, problems suchaisas excessive wear, launching failure, etc. In twin only small part of control them concerned model based methodrecent years, new idea ofwhere usingthe twin clutches to control launch s. The rule-based is simple to implement whose DCT vehicle proposed, coordination DCT vehicle is new proposed, where the coordination control s. The rule-based is simple to implement whose small part of control themBut concerned based methodrecent years, ais idea ofwhere using twin clutches to control launch s. The rule-based control isrule-based simplemodel to control implement whose DCT vehicle proposed, coordination computation is small. often does of torque distribution is the mostthe difficult problem. Some only computation is small. But rule-based control often does of torque distribution is the most difficult problem. Some s. The rule-based control is simple to implement whose DCT vehicle is proposed, where the coordination control computation is small. But rule-based control often does of torque distribution is the most difficult problem. Some not give an optimal control for all conditions, so there is researches have been done up till now. For example, Zhao not give an optimal control for all conditions, so there is researches have been done up till now. For example, Zhao is small. But rule-based control often does of torque distribution is theupvehicle most difficult Some not giveneed an optimal control for allcontrol conditions, so there is researches have beena done till now. For problem. example, Zhao computation strong for algorithm-based to address this (2009) established DCT model and proposed strong need for algorithm-based control to address this (2009) established a DCT vehicle model and proposed not giveneed an optimal control for allcontrol conditions, so there is researches have beento upvehicle till now. For example, Zhao strong for algorithm-based to address this (2009) established a done DCT model and proposed current situation. a control strategy determine how to disengaged the situation. a(2009) control strategy to determine how to disengaged the current strong need for algorithm-based control to address this established a DCT vehicle model and proposed current situation. aseparating control strategy to determine howrate. to disengaged clutch based on the slip Qin (2010) the inthis paper, in order to improve the launching perforseparating clutch based on slip Qin incurrent situation. a control strategy to determine howrate. tois disengaged the separating clutch based on the the rate. Qin (2010) (2010) in- In In this paper, in order to the launching perforvestigated the strategy that one slip clutch based on fuzzy In this paper, in order to improve improve the performance of DCT, the dynamics during the launching process vestigated the strategy that one clutch is based on fuzzy separating clutch based on the slip rate. Qin (2010) in- mance of DCT, the dynamics during the launching process vestigated the strategy that one clutch isdifferent based on fuzzy control, and another clutch is based on drivers’ In this paper, in order to improve the performance of DCT, the dynamics during the launching process control, and another clutch is based on different drivers’ with twin clutches are analysed. The simulation model vestigated strategy that one clutch based fuzzy with twin clutches are analysed. The model control, and another clutch is based on isdifferent drivers’ purposes tothe get different constant engaging speed.on Vehicle mance of vehicle DCT, the dynamics during the simulation launching process with twin clutches are analysed. The simulation model of DCT is established in simulink environment. purposes to get different constant engaging speed. Vehicle control, and another clutch is based on different drivers’ of DCT vehicle is established in simulink environment. purposes to get different constant speed. Vehicle speed, slope angle, traction of road,engaging driver’s intension were with twinvehicle clutches are analysed. The simulation model of DCT is established in simulink environment. Moreover, to avoid power coupling and power cycling, speed, slope angle, traction of road, driver’s intension were purposes to get different constant speed. Vehicle to avoid power coupling and power cycling, speed, slope angle, traction of road,engaging driver’s intension were Moreover, of DCT vehicle is established in simulink environment. Moreover, to avoid power coupling and power cycling, different control laws are designed for the two stages of ⋆ speed, slope angle, traction of road, driver’s intension were Corresponding author: Q F. Liu ([email protected]). The work is different control laws are for the two stages of ⋆ Corresponding author: Q F. Liu ([email protected]). The work is Moreover, to avoid power coupling cycling, different laws are designed designed forand thepower twounder stages of launchingcontrol process. Besides, the control system dif⋆ supported by theauthor: National Nature Science Foundation China Corresponding Q F. Liu ([email protected]). Theofwork is launching process. Besides, the control system under difsupported by the National Nature Science Foundation of China different control laws are designed for the two stages of launching process. Besides, the control system under dif⋆ ferent working conditions is verified, and the evaluation (No.61520106008No. 6179560010)and ProgramFoundation for JLU The Science and supported by theauthor: National Nature Science ofwork China Corresponding Q F. Liu ([email protected]). is ferent working conditions verified, the evaluation (No.61520106008No. 6179560010)and Program for JLU Science and launching process. Besides,is controland system under different working conditions isthe verified, and the evaluation Technologyby Innovative Research Team. (No.61520106008No. 6179560010)and ProgramFoundation for JLU Science and supported the National Nature Science of China Technology Innovative Research Team. ferent working conditions is verified, and the evaluation Technology Innovative Research Team.Program for JLU Science and (No.61520106008No. 6179560010)and Technology Team.Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © ©Innovative 2018, IFAC IFACResearch (International Copyright 2018 948 Copyright © under 2018 IFAC 948 Control. Peer review responsibility of International Federation of Automatic Copyright © 2018 IFAC 948 10.1016/j.ifacol.2018.10.086 Copyright © 2018 IFAC 948
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indexes are investigated including the tracking result of rotation speed and torque, slipping work and jerk. The rest of the paper is organised as follows. In Section 2, the launching dynamics of DCT are given. In Section 3, MPC controller for the first stage and rule-based controller for the second stage are presented. Then stability of the controller is analysed. In Section 4, simulation model of vehicle equipped with DCT is established in simulink environment. Comparing results under two working conditions are presented. Finally, giving the conclusions and future works in Section 5. 2. MODELING AND CONTROL PROBLEM STATEMENT 2.1 DCT system model The simplified DCT model is shown in Fig. 1, which is mainly composed of 2 dry clutches, 2 gears, 2 input shafts, 2 intermediate shafts and 1 output shafts. The power from engine is devided into 2 parts and flowed into 2 input shafts. External dampers are used to simulate the stiffness and torsion of shafts. The power flows through 2 clutches, different gears, collects together and flows into the final drive and then drives the wheel. In this way of power flow, vehicles equipped with DCT completes launching. The
The block diagram of launch controller is shown in Fig. 2. At each sampling time, the controller receives vehicle states, controller outputs Tc1 and Tc2 into the system after calculation.
launching process, and extending service life of clutches. Of course, launching with twin clutches have many problems need to be faced. Firstly, there are several contradictory performance indexes must be met. For example, slipping work per unit should be less than 0.4 J/mm2 , jerk should be as small as possible, launching time should be less than 2 s, engine should not flame out and so on. Secondly, power coupling and power cycling of two clutches may occur during launching process, it means that reasonable distribution strategy of the torque transmitted by the two clutches is worth considering. Hence, in this paper, a control scheme based on MPC is proposed to obtain total transmitted torque, and the torque distribution strategy based on the clutch slip state is designed in two stages. When the slip speed of the clutch is large (the first stage), both clutches are in slipping, total torque is equally distributed to launching clutch and separating clutch for sharing the sliding friction. When speed of launching clutch equals to engine speed (the second stage), the torque transmitted by the separation clutch must be reduced to prevent power cycling.
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Fig. 2. The block diagram of controller
Fig. 1. Simplified dynamic model of DCT simplified 2-degree-of-freedom (DOF) dynamic equation is shown as: (1a) Ie ω˙ e = Te − Tc1 − Tc2 − ce ωe , (1b) Is ω˙ s = Tc1 Kc1 + Tc2 Kc2 − Tr − cs ωs . The above two equations represent the dynamic modeling of the engine to two clutches and the dynamic modeling of the clutch-to-wheel power flow, respectively. In above equations, Ie and ce are the equivalent moment and rotational viscous damping coefficient of engine, and Is and cs are the equivalent moment and rotational viscous damping coefficient of vehicle. Te , Tc1 and Tc2 are transmitting torque of engine, clutch C1 and C2 respectively, Tr is driving resistance. ωe and ωs are speed of engine and vehicle. Kc1 and Kc2 are the ratios of torque transmitted from clutches to corresponding output shafts, that is Kc1 = i1 if , Kc2 = i2 if , where i1 , i2 and if are the ratios of the first gear, the second gear and final drive. After the slipping stage, launching process is completed, which is stable working condition. 2.2 Control problem statement Launching with twin clutches have the advantage of averaging slipping work of each clutch, decreasing jerk during 949
3. CONTROLLER DESIGN 3.1 Launch controller design In the objective function, to quantitatively express the control performance index, the equation (1b) is differentiated and the system becomes: ¨ s = i1 if T˙c1 + i2 if T˙c2 − cs ω˙ s + d, (2) Is ω
here d represents model error and model uncertainty. Because driving resistance changes very little during launching process, this item usually can be ignored when designing controller. In this paper, the first gear is selected to launch the DCT vehicle. According to equation (2), state variables are selected as: [ ] [ ] x1 ωs x= = , (3) x2 ω˙ s to describe performance evaluation indexes explicitly, derivation of torques is selected as control input: (4) u = i1 if T˙c1 + i2 if T˙c2 ,
choose control output: y c = ωs ,
(5)
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the system dynamics can be rewritten as: { x˙ 1 = x2 , x˙ 2 = I1s (u − cs x2 ).
(6)
As Chen (2013) proposed, the corresponding linear state space equation is: x˙ = Ac x + Bcu u, (7) y = Cc x, where, ] [ 0 1 A c = 0 − cs , [ ]Is (8) 0 Bcu = 1 , Cc = [ 1 0 ] . Is
The discrete time { model is: x(k + 1) = Ax(k) + Bu u(k), (9) yc (k) = Cc x(k), where A = eAc Ts , ∫T (10) Bu = 0 s eAc τ dτ · Bcu , C = eC c T s . Here define Np is the number of prediction horizon steps, Nm is the number of control horizon steps, where satisfies Nm ≤ Np . Defining the predicted output sequence and control input sequence at time k as: yc (k + 1|k) def yc (k + 2|k) , Yp (k + 1|k) = (11) .. .
def U (k) =
yc (k + p|k) u(k) u(k + 1) .. .
r(k + p)
.
Ep (k + 1|k) = R(k + 1) − Sx x(k), (20) here first command of control sequence is used to input to the system, so control law is: u = [ Inu ×nu 0 · · · 0 ]1×m · )−1 ( (21) T T (Γy Su ) Γy Ep . (Γy Su ) Γy Su + ΓTu Γu
3.2 Control laws for 2 stages
When the system launch with 1st gear, torque, speed of engine and clutches are shown in Fig. 3, where t0 means vehicle start to launch, td means speed of engine is the same as speed of C1 and tf means torque of engine equals to torque of C1 . The launching process is mainly divided into 2 parts, td indicates the end of stage 1 and tf indicates the end of stage 2.
(12)
u(k)
2
J = ∥Γy (yc − R)∥ + ∥Γu u∥ . (17) where R is the desired engaging speed, i.e. R = ωe /i1 /if , 2 the first item J1 = ∥Γy (yc − R)∥ aims to make sure the 950
Fig. 3. Calculation chart of launching process The engine speed ωe is always greater than the speed of off-going disc, which belongs to clutch C1 during launching process, so there is no power cycling. Before the separating clutch divides, rule-based method is chosen to ensure slipping work of both clutch equally. The slipping work of two clutches is: ∫ td ∫ td (22) Tc2 (ωe − ωc2 )dt. Tc1 (ωe − ωc1 )dt = t0
2
p×1
Define:
p×1
u(k + m − 1) m×1 And the predicted outputs of Np steps could be calculated as below: Yp (k + 1|k) = Sx x(k) + Su u(k), (13) among equation (13), [ ]T Sx = Cc A Cc A2 . . . Cc Ap 1×p , 0 ... 0 C c Bu C c Bu ... 0 Cc ABu .. .. .. .. . . . . Su = . Cc Bu Cc Am−1 Bu Cc Am−2 Bu · · · .. .. .. .. . . . . p−1 p−2 p−m Cc A Bu Cc A Bu . . . Cc A Bu p×m (14) In launch control, one of the most important evaluation indexes during launching process is jerk, which could be express below: ) rdω˙ s r ( ˙ da r = = jerk = i1 Tc1 + i2 T˙c2 = u. (15) dt dt Is I s if The objective function is described as: (16) min J(y(k), U (k), Nm , Np ), where
on-coming and off-going discs of launching clutch engage 2 together. The second item J2 = ∥Γu u∥ aims to minimum jerk. The form of Γy and Γu are Γy = diag(Γy,1 , Γy,2 , · · · , Γy,p ), (18) Γu = diag(Γu,1 , Γu,2 , · · · , Γu,m ). Choose tracking inputs as below: r(k + 1) r(k + 2) . (19) R(k + 1) = .. .
t0
Integrating equation (4), total output torque of the two clutches can be ∫obtained: udt = i1 if Tc1 + i2 if Tc2 .
(23)
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Define ε as slip ratio: ωe − ωc2 ε= . (24) ωe − ωc1 The torques Tc1 and Tc2 transmitted by two clutches before the separating clutch starts to disengage are obtained by equations (22) and (23) separately: ∫ T = ε udt c1 εK∫c1 +Kc2 , t ≤ t < t (25) 0 d udt Tc2 = εKc1 +Kc2
The system turns into the next stage after td comes. In the 2nd stage, instead of MPC controller, rule-based controller is proposed to distribute torque. The changing rate of Tc2 is Kd : T˙c2 = Kd . (26) The control law of Tc2 could be obtained through integrate equation (26). When Tc2 decline to zero, it keeps zero. td td When t = td , Tc1 is the value of Tc1 and Tc2 is the value of Tc2 . At each sampling time, the increment of Tc1 is add of increment of Te and increment of Tc2 . But when Tc1 equals to Te , Tc1 stays equal to Te . So the rules are shown as below: { td + ∆Te + ∆Tc2 Tc1 = Tc1 (27) 2 , td ≤ t ≤ tf td Tc2 = Tc2 − 12 K˙ d (t − td ) Stage 2 ends up at tf when Tc1 equals to Te . Then the vehicle runs at 1st gear stably when the launching clutch fully engages and separating clutch does not transmit torque.
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equations is built in MATLAB environment, which is described in details in Zhao (2017): Ie ω˙ e = Te − Tc1 − Tc2 − ce ωe , Ic1 ω˙ c1 = Tc1 − Tm1c1 − Tg5c1 − Tg3c1 − cc1 ωc1 , I ˙ g5 = Tg5c1 i5 η − cg5 ωg5 , g5 ω I ω˙ = T g3 g3 g3c1 i3 η − cg3 ωg3 , Ic2 ω˙ c2 = Tc2 − Tm1c2 − Tg4c2 − Tg6c2 − cc2 ωc2 , Ig4 ω˙ g4 = Tg4c2 i4 η − cg4 ωg4 , I ˙ g6 = Tg6c2 i6 η − cg6 ωg6 , g6 ω (Im1 + Ig1 + Ig2 )ω˙ m1 = Tm1c1 i1 η +Tm1c2 i2 η − Tsm1 − (cm1 + cg1 + cg2 )ωm1 , I s ω˙ s = Tsm1 ia η − Tsm2 ia /η − Tr − cs ωs , Im2 ω˙ m2 = Tsm2 − cm2 ωm2 . (32) The relationships among input shafts, intermediate shafts and output shafts are shown below: { ωc1 = ωm1 i1 = ωg5 i5 = ωg3 i3 , ωm1 = ωm2 = ωs ia , (33) ωc2 = ωm1 i2 = ωg4 i4 = ωg6 i6 . All the parameters in the simulation model is listed in Table 1. In this model, the engine torque Te can be acquired through engine MAP as shown in Fig. 4 which is used to describe the engine torque characteristics. When launching Engine MAP
200 150 Te Nm
3.3 Analysis of stability Because of uncertainty of the vehicle resistance and varying vehicle parameters, considering the uncertainties of the system, it is necessary to analyse the stability of proposed MPC controller. The controlled system is described as below: x(k + 1) = Ax(k) + Bu u(k), (28) Firstly define: Kmpc = [ Inu ×nu 0 · · · 0 ]1×m )−1 ( (29) T T · (Γy Su ) Γy Su + ΓTu Γu (Γy Su ) Γy ,
and
u(k) = Kmpc · Ep (k + 1|k), (30) Substitute equations (20), (29) and (30) into equation (28) to obtain the closed loop control system x(k + 1) = (A − Bu Kmpc Sx )x(k) (31) +B u Kmpc R(k + 1). All the eigenvalues of matrix A − Bu Kmpc Sx are in the unit cycle, where Nm and Np are taken at regular intervals from 10 steps to 100 steps. The scope of eigenvalues’ real part is from 0.9151 to 0.9950, the scope of imaginary parts’ absolute value is from 0 to 0.0677. Closed loop system is nominal asymptotically stable. 4. RESULTS AND ANALYSIS To testify the effectiveness of the proposed controller, a equivalent DCT vehicle model based on 8-DOF dynamics 951
100 50
0 10000
1
5000 we rev/min
0.5 0 0
acc
Fig. 4. Engine MAP with first gear, the system runs under two working conditions, one is light load (vehicle mass is 1420 kg) called working condition 1, another one is heavy load (vehicle mass is 1680 kg) called working condition 2. The simulation results with MPC controller are shown in Fig. 5(a) and Fig. 6(a). In order to testify the superiority of the proposed method, a PID controller which only launches with clutch C1 , rather than coordination control of twin clutches is also established to compare the simulation results with MPC controller under same working conditions. The simulation results are shown in Fig. 5(b) and Fig. 6(b). Quantified comparisons between the simulation results of PID launch controller and MPC launch controller are also shown in Table 2 and Table 3. To launch vehicle in limited time, the system increases throttle opening from 0.1 in working condition 1 to 0.2 in working condition 2, where both of the throttle opening is consistent. Under working condition 1, it can be seen the on-coming and off-going discs of launching clutch are fully engaged in 1.605 s which launches with single clutch under PID controller. Compared with the results above, the MPC controller gives a better performance which
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Table 1. Parameters in the simulation model Parameters Te , Tc1 , Tc2 Tg5c1 , Tg3c1 , Tg4c2 , Tg6c2 Tm1c1 , Tm1c2 Tsm1 , Tsm2 Ie , Ic1 , Ic2 Ig1 , Ig2 , Ig3 , Ig4 , Ig5 , Ig6 Im1 , Im2 , Is i1 , i2 , i3 , i4 , i5 , i6 , ia ce , cc1 , cc2 cg1 , cg2 , cg3 , cg4 , cg5 , cg6 cm1 , cm2 , cs ωe , ωc1 , ωc2 ωg 1, ωg 2, ωg 3, ωg 4, ωg 5, ωg 6, ωa ωm1 , ωm2 , ωs η
Meaning T denotes torque, e denotes engine, c denotes clutches T denotes reaction torque, g denotes gear, c denotes clutches T denotes reaction torque, m denotes intermediate shaft, c denotes clutches T denotes reaction torque, s denotes output shaft, m denotes intermediate shaft I denotes inertia, e denotes engine, c denotes clutches I denotes inertia, g denotes gears I denotes inertia, m denotes intermediate shafts, s denotes vehicle i denotes transmission ratio, number denotes gear, a denotes final drive c denotes viscous friction coefficient, e denotes engine, c denotes clutches c denotes viscous friction coefficient, g denotes gears c denotes viscous friction coefficient, m denotes intermediate shaft, s denotes vehicle ω denotes rotating speed, e denotes engine, c denotes clutches ω denotes rotating speed, g denotes gear, a denotes final drive ω denotes rotating speed, m denotes intermediate shaft, s denotes vehicle Efficiency
could help the vehicle launch in just 0.644 s with twin clutches. In working condition 2, vehicle finishes launching in 1.660 s under PID controller and in 0.789 s under MPC controller. It can be seen that MPC launch controller can decreases the launching time up to 52%. Both the slipping work of twin clutches in two working conditions under MPC launch controller are all less than 0.4 J/mm2 . When compared with PID launch controller, MPC launch controller gives a 60% reduction of engaging time and a 63% reduction of sliding time. When launching with twin clutches, the torque results show that the separating clutch transmits torque for more than 0.5 s, also averages torque and slipping friction during launching process, decrease engaging speed, in which way could lengthen service life of launching clutch. And the torque of both clutches changes smoothly, which ensures the comfortable driving experience for passengers. The smooth increase of vehicle speed means launching success of DCT vehicle under MPC launch controller. The analysis above shows that vehicle launches successfully with satisfying all the evaluation indexes, including torque should change smoothly, slipping work should be less than 0.4 J/mm2 and engine should not flame out. The results under two working conditions also indicate that the proposed controller has better robust stability. Table 2. Comparison of simulation results under working condition 1 Parameters Engaging time(s) Sliding time(s) Engaging speed(r/ min) Slipping work(J/mm2 )
C1 1.605 1.751 2143 0.1735
C1 &C2 0.644 0.990 1607 0.0926&0.0935
Change -60% -43% -25% -47%
Table 3. Comparison of simulation results under working condition 2 Parameters Engaging time(s) Sliding time(s) Engaging speed(r/ min) Slipping work(J/mm2 )
C1 1.660 2.987 3082 0.3303
C1 &C2 0.789 1.095 2538 0.1902&0.1914
Change -52% -63% -18% -42%
5. CONCLUSION This paper focus on design of control method for launching process of DCT vehicle. Controller in the framework of 952
MPC is designed to launch vehicle with twin clutches. Control strategy is organised to launch vehicle, decrease jerk and average slipping work of twin clutches which are expressed in objective function and control rules. An accurate DCT vehicle model is established in simulink environment to testify the effectiveness of proposed launch controller. A comparison of launching process between PID launch controller with single clutch and MPC twin clutches controller shows that the proposed strategy could greatly improve driving experience. In the future work, simulating launching with second gear and hardware-inloop experiment will be considered to further demonstrate the effectiveness of the method. The dynamics of clutches actuators will be also introduced because torque of clutches can not be implemented directly. REFERENCES Mario P, Maurizio C, Adolfo S. Multiple Constrained MPC Design for Automotive Dry Clutch Engagement. IEEE/ASME Transactions on Mechatronics, 20,1:469– 480,2015. Gao B Z, Hong J L, Qu T, et al. Linear-quadratic output regulator for systems with disturbance: application to vehicle launch control. The 31st Youth Academic Annual Conference of Chinese Association of Automation, 135– 140,2016. Minh V T, Rashid A A. Automatic control of clutches and simulations for parallel hybrid vehicles. International Journal of Automotive Technology, 13,4:645–651,2012. Zhang J L, Ma B, Zheng C S. Improved Fuzzy Control of Dual Clutch Transmission during Launch Process. International Conference on Mechatronics and Automation, 676–681,2010. Zhao Z Q, Zhou Y S, Cao C L. Driveline system modeling and starting control strategy of DCT. Modern Manufacturing Engineering, 7:120–124,2009. Qin D T, Liu Y G, Hu J J, et al. Control and Simulation of Launch with Two Clutches for Dual Clutch Transmissions. Journal of Mechanical Engineering, 46,18:121– 127,2010. Yan Y Q, Song J, Li L, et al. Self-adaption initial acceleration control strategies of a dry dual clutch transmission. Journal of Tsinghua University(Science and Technology), 54,6:734–737,2014. Zhang J L, Guo J, Gui L. Study on launch control strategies of dual clutch transmission. International
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(a) the proposed MPC controller
(a) the proposed MPC controller
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(b) a well tuned PID controller
(b) a well tuned PID controller
Fig. 6. Simulation results under working conditions 2.
Fig. 5. Simulation results under working conditions 1. Conference on Mechatronics and Automation, 1142– 1147,2012. Liu Z J, Ren C B, Wang L. Simulation Analysis on Control Strategy of Launch with two Clutches for Dry DCT. Advanced Materials Research, 932–936,2012. Sun W, Yang Y L, Ma J. Study on Torque Transfer Control Strategy of DCT Launching with Two Clutches. Agricultural Equipment & Vehicle Engineering, 50,4:11– 13,2012. Kong H F, Zhou D, Zhao W, et al. Research of Starting Control of DCT Vehicle Dual Clutch based on Sliding Mode Variable Structure. Journal of Mechanical Transmission, 38,6:14–18,2014. Zhao Z G, Li X Y,He L, et al. Estimation of Torques Transmitted by Twin-Clutch of Dry Dual-Clutch Transmission During Vehicle’s Launching Process. IEEE Trans953
actions on Vehicular Technology, 66,6:4727–4741,2017. Chen H. Model Predictive Control. Science Press, 2013. Zhao Z G, Gu J D,He L. Estimation of Torques Transited by Twin-Clutch during Shifting Process for Dry Dual Clutch Transmission. Journal of Mechanical Engineering, 53,14:77–87,2017.
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IFAC PapersOnLine 51-31 (2018) 904–909
Launch Coordination Control Based on Launch Launch Coordination Coordination Control Control Based Based on on Twin-Clutch Torque Distribution for DCT Launch Coordination Control Based on Twin-Clutch Torque Distribution for DCT Twin-Clutch Torque Distribution for DCT Vehicle Twin-Clutch Torque Distribution for DCT Vehicle Vehicle Vehicle ∗∗ ∗∗ ∗,∗∗ Zijiao Jiang ∗,∗∗ ∗,∗∗ ∗,∗∗ Qifang Liu ∗∗ ∗∗ Shiying Dong ∗∗ ∗∗ Hong Chen ∗,∗∗ ∗,∗∗
Zijiao Jiang ∗,∗∗ Qifang Liu ∗∗ Shiying Dong ∗∗ Hong Chen ∗,∗∗ Zijiao Jiang Qifang Liu Shiying Dong Hong Chen ∗∗ ∗,∗∗ ∗ Zijiao Jiang ∗,∗∗ Qifang Liu Shiying Dong ∗∗and Hong Chen Automotive Simulation Control, Jilin ∗ ∗ State Key Laboratory of of Automotive Simulation and Control, Jilin State Key Laboratory ∗ StateUniversity, Key Laboratory Automotive Simulation and Control, Jilin P. R. of China (e-mail:[email protected], (e-mail:[email protected], ∗ P. China StateUniversity, Key Laboratory Automotive Simulation and Control, Jilin University, P. R. R. of China (e-mail:[email protected], [email protected]) [email protected]) ∗∗ University, P. R. China (e-mail:[email protected], [email protected]) Department of Control Science and Engineering, ∗∗ ∗∗ Department of Control Science and Engineering, Jilin Jilin University, University, ∗∗ Department of [email protected]) Science and Engineering, Jilin University, P. R. China (e-mail:[email protected], [email protected]) ∗∗ P. R. China (e-mail:[email protected], [email protected]) Department Control Science and Engineering, Jilin University, P. R. China of (e-mail:[email protected], [email protected]) P. R. China (e-mail:[email protected], [email protected]) Abstract: launch control Abstract: For For Dual Dual Clutch Clutch Transmission Transmission (DCT) (DCT) vehicle, vehicle, this this study study provides provides aa launch control Abstract: For Dual Clutch Transmission (DCT) vehicle, this study The provides a launch control method that coordinates the transmission torque of twin clutches. launching process is method that coordinates the transmission torque of twin clutches. The launching process is Abstract: Dual Clutch (DCT) vehicle, this study by provides a launch control method into thatFor coordinates theTransmission transmission torque of twin clutches. The launching process is divided 2 stages. For the first stage, the total torque is obtained using Model Predictive divided into 2 stages. For the first stage, the total torque is obtained by using Model Predictive method into that the first transmission of twin clutches. The launching process is divided 2 coordinates stages. For the stage, thetorque total torque is to obtained by using Model Predictive Control (MPC) method, and total torque is distributed two clutches based on principle Control (MPC) method, andfirst total torque is distributed two clutches based onPredictive principle divided into 2 stages. For For the stage, the total torque is to obtained by using Model Control (MPC) method, andthe total torque is distributed to two clutches based on principle of equal slipping work. second stage, a torque distribution rule is given to allow of equal slippingmethod, work. For second stage, a torque to distribution rulebased is given to allow Control andthe total torque is distributed two clutches on controller principle of equal (MPC) slipping work. For the second stage, a torque distribution rule of is MPC given to allow launching clutch engaged and separating clutch disengaged. Then, stability launching clutch engaged and separating clutch disengaged. Then, stability of MPC controller of equal slipping work. with For the second stage, a PID torque distribution rule of is MPC given to allow launching clutch engaged and single separating clutch disengaged. Then, the stability controller is discussed. Compared clutch launch controller, simulation results show is discussed. Compared with clutchclutch launch PID controller, the simulation results show launching clutch engaged and single separating disengaged. Then, stability of MPC controller is discussed. Compared with single clutch could launch PID controller, the simulation results show that the proposed MPC launch controller greatly shorten the time of launching process, that the proposed MPC launch controller could greatly shorten the time of launching process, is discussed. Compared with single clutch launch PIDand controller, the simulation results show that the proposed MPCavoid launch controller could greatly shorten the time of launching process, decrease slipping work, possible power coupling power cycling. decrease slipping work, possible power coupling and powerthe cycling. that the proposed MPCavoid launch controller could greatly shorten time of launching process, decrease slipping work, avoid possible power coupling and power cycling. © 2018, IFAC (International Federation of Automatic Control) Hosting Elsevier Ltd. All rights reserved. decrease slipping work, avoid possible power coupling and powerbycycling. Keywords: Keywords: Twin-clutch Twin-clutch launch launch control, control, Torque Torque distribution, distribution, Model Model predictive predictive control control (MPC), (MPC), Keywords: Twin-clutch launch control, Torque distribution, Model predictive control (MPC), Dual clutch transmission (DCT). Dual clutch transmission (DCT). Keywords: control, Torque distribution, Model predictive control (MPC), Dual clutchTwin-clutch transmissionlaunch (DCT). Dual clutch transmission (DCT). 1. identified 1. INTRODUCTION INTRODUCTION identified by by Yan Yan (2014) (2014) to to launch launch with with twin twin clutches clutches based based 1. INTRODUCTION identified by Yanalgorithm. (2014) to launch with twin clutches based on self-adaptive A fuzzy control method is on self-adaptive algorithm. A fuzzy control method is dede1. INTRODUCTION identified by Yan (2014) to launch with twincritical clutches based on self-adaptive algorithm. A fuzzy control method is developed with fully consideration of clutch thermal Nowadays, the vehicles equipped with Dual Clutch Transwith fully consideration of clutch critical thermal Nowadays, the vehicles equipped with Dual Clutch Trans- veloped self-adaptive algorithm. A fuzzy control method is developed with by fully consideration of clutch critical thermal Nowadays, the vehicles equipped with Dual Clutch energy value comparing the between launching mission (DCT) play a increasingly significant role Transin au- on energy value by comparing the results results between launching mission (DCT) play a increasingly significant role in auveloped with fully consideration of clutch critical thermal Nowadays, the vehicles equipped with Dual Clutch Transenergy value by comparing the results between launching mission increasingly significant role in ausingle clutch and twin clutches in Zhang (2012). Liu tomotive(DCT) market.play So athere is a consistently-increasing de- with with single and twin clutches in Zhang (2012). Liu tomotive market. So is consistently-increasing devalueclutch by comparing results launching missionfor(DCT) play athere increasingly significant role in auwith single clutch twin the clutches in between Zhang (2012). Liu tomotive market. So launching there is a a experience, consistently-increasing de- energy (2012) considered aaand method of launching with clutchmand improving simultaneously (2012) considered method of launching with twin twin clutchexperience, simultaneously mand for improving launching with single clutch and twin clutches in Zhang (2012). Liu tomotive market. So there is a experience, consistently-increasing de- (2012) considered a method launching with Rules twin clutchmand for improving launching simultaneously es based on constant engineof speed control. about launch control is one of main issue in controlling vehilaunch control is one of mainexperience, issue in controlling vehi- es based on constant engine speed control. Rules about (2012) considered a method of launching with twin clutchmand for improving launching simultaneously es based on constant engine speed control. Rules about launch is one of main issue experience in controlling vehi- torque distribution of clutches were set cle withcontrol DCT. launching is torque distribution of twin twin clutches were set by by Sun Sun (2012), (2012), DCT. Improving Improving launching is widely widely cle with es based ontorque constant engine speed control. about launch is one of main issue experience in controlling vehi- who torque distribution twin clutches were set byRules Sun (2012), cle withcontrol DCT. Improving launching experience made of one clutch in proportion to torque concerned. Usually, traditional launching process isforwidely DCT who made torque of one clutch in proportion to torque concerned. Usually, traditional launching process for DCT torque distribution twin clutches set by work. Sun cle with DCT. Improving experience isforwidely who made torquetoofdistribute one clutch inwere proportion to (2012), torque concerned. Usually, traditional launching processcontrol DCT of another clutch equal slipping Kong uses single clutch which islaunching similar to launch of another clutch toofdistribute equal slipping work. Kong launch control of of uses single clutch is to made torque one clutch in proportion to torque concerned. traditional launching process for DCT of another clutch to distribute equal slipping work. Kong uses single Usually, clutch which which is similar similar to(AMT), launch control of who (2014) gave a sliding mode controller which controlled Automatic Mechanical Transmission some con(2014) gave a sliding mode controller which controlled Automatic Mechanical Transmission (AMT), some conto clutches distribute equal slipping work. Kong uses algorithms single Mechanical clutch is similar toto(AMT), launch control of of (2014) gaveclutch sliding mode to controller whichvehicle controlled Automatic conoil another pressure ofa both launch DCT with trol hadwhich beenTransmission proposed solve thissome problem, oil pressure of both clutches to launch DCT vehicle with trol algorithms had been proposed to solve this problem, (2014) gave a sliding mode controller which controlled Automatic Mechanical Transmission (AMT), some conoil pressure of both clutches to launch DCT vehicle with trol algorithms had been proposed to solve this problem, twin clutches. Zhao (2017) designed a high-order slidingsuch as Model Predictive Control (MPC) in Mario (2015), twin clutches. Zhao (2017) designed a high-order slidingsuch as Model Predictive Control (MPC) in Mario (2015), oil pressure of Zhao both clutches to launch DCT vehicle with trol algorithms had beeninControl proposed to solve thiscontrol problem, twin clutches. (2017) designed a high-order slidingsuch as Modelalgorithm Predictive (MPC) in Mario (2015), mode observer to estimate transmission torque based on optimization Gao (2016), fuzzy in observer Zhao to estimate transmission torque based on optimization algorithm in Gao (2016), fuzzy control in mode clutches. (2017) designed a high-order slidingsuch as Model Predictive (MPC) in Mario (2015), mode observer to estimate transmission torque based on optimization algorithm inControl Gaoand (2016), fuzzy control in twin estimation of vehicle drag torque, which could cooperate Minh (2012) and Zhang (2010) so on. However, launch estimation of vehicle drag torque, which could cooperate Minh (2012) and Zhang (2010) and so on. However, launch observer to estimate transmission torque basedwith on optimization algorithm in Gaoand (2016), fuzzy control in mode estimation of vehicle dragtotorque, which could cooperate Minh (2012) and Zhang (2010) so on. However, with optimum controller launch the DCT vehicle control strategy with single-clutch can easily lead tolaunch some with optimum controller totorque, launch which the DCT vehicle with control strategy with single-clutch can easily lead to some estimation of vehicle drag could cooperate Minh (2012) and Zhang (2010) and so on. However, launch with optimum controller to launch the DCT vehicle with control strategy with single-clutch can easily lead to some twin clutches. Most of control researches were rule-based, problems such as excessive wear, launching failure, etc. In twin clutches. Most of control researches were rule-based, problems such excessive wear, launching failure, etc. In optimum controller to launch the DCT vehicle with controlyears, strategy with single-clutch can easily leadtotolaunch some twin clutches. Most of control researches were rule-based, problems sucha as as excessive wear, launching failure, etc. In with only part of concerned model based methodrecent new idea of using twin clutches only small small partMost of them them concerned modelwere based methodrecent years, a new idea of using twin clutches to launch clutches. of control researches rule-based, problems suchaisas excessive wear, launching failure, etc. In twin only small part of control them concerned model based methodrecent years, new idea ofwhere usingthe twin clutches to control launch s. The rule-based is simple to implement whose DCT vehicle proposed, coordination DCT vehicle is new proposed, where the coordination control s. The rule-based is simple to implement whose small part of control themBut concerned based methodrecent years, ais idea ofwhere using twin clutches to control launch s. The rule-based control isrule-based simplemodel to control implement whose DCT vehicle proposed, coordination computation is small. often does of torque distribution is the mostthe difficult problem. Some only computation is small. But rule-based control often does of torque distribution is the most difficult problem. Some s. The rule-based control is simple to implement whose DCT vehicle is proposed, where the coordination control computation is small. But rule-based control often does of torque distribution is the most difficult problem. Some not give an optimal control for all conditions, so there is researches have been done up till now. For example, Zhao not give an optimal control for all conditions, so there is researches have been done up till now. For example, Zhao is small. But rule-based control often does of torque distribution is theupvehicle most difficult Some not giveneed an optimal control for allcontrol conditions, so there is researches have beena done till now. For problem. example, Zhao computation strong for algorithm-based to address this (2009) established DCT model and proposed strong need for algorithm-based control to address this (2009) established a DCT vehicle model and proposed not giveneed an optimal control for allcontrol conditions, so there is researches have beento upvehicle till now. For example, Zhao strong for algorithm-based to address this (2009) established a done DCT model and proposed current situation. a control strategy determine how to disengaged the situation. a(2009) control strategy to determine how to disengaged the current strong need for algorithm-based control to address this established a DCT vehicle model and proposed current situation. aseparating control strategy to determine howrate. to disengaged clutch based on the slip Qin (2010) the inthis paper, in order to improve the launching perforseparating clutch based on slip Qin incurrent situation. a control strategy to determine howrate. tois disengaged the separating clutch based on the the rate. Qin (2010) (2010) in- In In this paper, in order to the launching perforvestigated the strategy that one slip clutch based on fuzzy In this paper, in order to improve improve the performance of DCT, the dynamics during the launching process vestigated the strategy that one clutch is based on fuzzy separating clutch based on the slip rate. Qin (2010) in- mance of DCT, the dynamics during the launching process vestigated the strategy that one clutch isdifferent based on fuzzy control, and another clutch is based on drivers’ In this paper, in order to improve the performance of DCT, the dynamics during the launching process control, and another clutch is based on different drivers’ with twin clutches are analysed. The simulation model vestigated strategy that one clutch based fuzzy with twin clutches are analysed. The model control, and another clutch is based on isdifferent drivers’ purposes tothe get different constant engaging speed.on Vehicle mance of vehicle DCT, the dynamics during the simulation launching process with twin clutches are analysed. The simulation model of DCT is established in simulink environment. purposes to get different constant engaging speed. Vehicle control, and another clutch is based on different drivers’ of DCT vehicle is established in simulink environment. purposes to get different constant speed. Vehicle speed, slope angle, traction of road,engaging driver’s intension were with twinvehicle clutches are analysed. The simulation model of DCT is established in simulink environment. Moreover, to avoid power coupling and power cycling, speed, slope angle, traction of road, driver’s intension were purposes to get different constant speed. Vehicle to avoid power coupling and power cycling, speed, slope angle, traction of road,engaging driver’s intension were Moreover, of DCT vehicle is established in simulink environment. Moreover, to avoid power coupling and power cycling, different control laws are designed for the two stages of ⋆ speed, slope angle, traction of road, driver’s intension were Corresponding author: Q F. Liu ([email protected]). The work is different control laws are for the two stages of ⋆ Corresponding author: Q F. Liu ([email protected]). The work is Moreover, to avoid power coupling cycling, different laws are designed designed forand thepower twounder stages of launchingcontrol process. Besides, the control system dif⋆ supported by theauthor: National Nature Science Foundation China Corresponding Q F. Liu ([email protected]). Theofwork is launching process. Besides, the control system under difsupported by the National Nature Science Foundation of China different control laws are designed for the two stages of launching process. Besides, the control system under dif⋆ ferent working conditions is verified, and the evaluation (No.61520106008No. 6179560010)and ProgramFoundation for JLU The Science and supported by theauthor: National Nature Science ofwork China Corresponding Q F. Liu ([email protected]). is ferent working conditions verified, the evaluation (No.61520106008No. 6179560010)and Program for JLU Science and launching process. Besides,is controland system under different working conditions isthe verified, and the evaluation Technologyby Innovative Research Team. (No.61520106008No. 6179560010)and ProgramFoundation for JLU Science and supported the National Nature Science of China Technology Innovative Research Team. ferent working conditions is verified, and the evaluation Technology Innovative Research Team.Program for JLU Science and (No.61520106008No. 6179560010)and Technology Team.Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © ©Innovative 2018, IFAC IFACResearch (International Copyright 2018 948 Copyright © under 2018 IFAC 948 Control. Peer review responsibility of International Federation of Automatic Copyright © 2018 IFAC 948 10.1016/j.ifacol.2018.10.086 Copyright © 2018 IFAC 948
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indexes are investigated including the tracking result of rotation speed and torque, slipping work and jerk. The rest of the paper is organised as follows. In Section 2, the launching dynamics of DCT are given. In Section 3, MPC controller for the first stage and rule-based controller for the second stage are presented. Then stability of the controller is analysed. In Section 4, simulation model of vehicle equipped with DCT is established in simulink environment. Comparing results under two working conditions are presented. Finally, giving the conclusions and future works in Section 5. 2. MODELING AND CONTROL PROBLEM STATEMENT 2.1 DCT system model The simplified DCT model is shown in Fig. 1, which is mainly composed of 2 dry clutches, 2 gears, 2 input shafts, 2 intermediate shafts and 1 output shafts. The power from engine is devided into 2 parts and flowed into 2 input shafts. External dampers are used to simulate the stiffness and torsion of shafts. The power flows through 2 clutches, different gears, collects together and flows into the final drive and then drives the wheel. In this way of power flow, vehicles equipped with DCT completes launching. The
The block diagram of launch controller is shown in Fig. 2. At each sampling time, the controller receives vehicle states, controller outputs Tc1 and Tc2 into the system after calculation.
launching process, and extending service life of clutches. Of course, launching with twin clutches have many problems need to be faced. Firstly, there are several contradictory performance indexes must be met. For example, slipping work per unit should be less than 0.4 J/mm2 , jerk should be as small as possible, launching time should be less than 2 s, engine should not flame out and so on. Secondly, power coupling and power cycling of two clutches may occur during launching process, it means that reasonable distribution strategy of the torque transmitted by the two clutches is worth considering. Hence, in this paper, a control scheme based on MPC is proposed to obtain total transmitted torque, and the torque distribution strategy based on the clutch slip state is designed in two stages. When the slip speed of the clutch is large (the first stage), both clutches are in slipping, total torque is equally distributed to launching clutch and separating clutch for sharing the sliding friction. When speed of launching clutch equals to engine speed (the second stage), the torque transmitted by the separation clutch must be reduced to prevent power cycling.
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Fig. 2. The block diagram of controller
Fig. 1. Simplified dynamic model of DCT simplified 2-degree-of-freedom (DOF) dynamic equation is shown as: (1a) Ie ω˙ e = Te − Tc1 − Tc2 − ce ωe , (1b) Is ω˙ s = Tc1 Kc1 + Tc2 Kc2 − Tr − cs ωs . The above two equations represent the dynamic modeling of the engine to two clutches and the dynamic modeling of the clutch-to-wheel power flow, respectively. In above equations, Ie and ce are the equivalent moment and rotational viscous damping coefficient of engine, and Is and cs are the equivalent moment and rotational viscous damping coefficient of vehicle. Te , Tc1 and Tc2 are transmitting torque of engine, clutch C1 and C2 respectively, Tr is driving resistance. ωe and ωs are speed of engine and vehicle. Kc1 and Kc2 are the ratios of torque transmitted from clutches to corresponding output shafts, that is Kc1 = i1 if , Kc2 = i2 if , where i1 , i2 and if are the ratios of the first gear, the second gear and final drive. After the slipping stage, launching process is completed, which is stable working condition. 2.2 Control problem statement Launching with twin clutches have the advantage of averaging slipping work of each clutch, decreasing jerk during 949
3. CONTROLLER DESIGN 3.1 Launch controller design In the objective function, to quantitatively express the control performance index, the equation (1b) is differentiated and the system becomes: ¨ s = i1 if T˙c1 + i2 if T˙c2 − cs ω˙ s + d, (2) Is ω
here d represents model error and model uncertainty. Because driving resistance changes very little during launching process, this item usually can be ignored when designing controller. In this paper, the first gear is selected to launch the DCT vehicle. According to equation (2), state variables are selected as: [ ] [ ] x1 ωs x= = , (3) x2 ω˙ s to describe performance evaluation indexes explicitly, derivation of torques is selected as control input: (4) u = i1 if T˙c1 + i2 if T˙c2 ,
choose control output: y c = ωs ,
(5)
IFAC E-CoSM 2018 906 Changchun, China, September 20-22, 2018 Zijiao Jiang et al. / IFAC PapersOnLine 51-31 (2018) 904–909
the system dynamics can be rewritten as: { x˙ 1 = x2 , x˙ 2 = I1s (u − cs x2 ).
(6)
As Chen (2013) proposed, the corresponding linear state space equation is: x˙ = Ac x + Bcu u, (7) y = Cc x, where, ] [ 0 1 A c = 0 − cs , [ ]Is (8) 0 Bcu = 1 , Cc = [ 1 0 ] . Is
The discrete time { model is: x(k + 1) = Ax(k) + Bu u(k), (9) yc (k) = Cc x(k), where A = eAc Ts , ∫T (10) Bu = 0 s eAc τ dτ · Bcu , C = eC c T s . Here define Np is the number of prediction horizon steps, Nm is the number of control horizon steps, where satisfies Nm ≤ Np . Defining the predicted output sequence and control input sequence at time k as: yc (k + 1|k) def yc (k + 2|k) , Yp (k + 1|k) = (11) .. .
def U (k) =
yc (k + p|k) u(k) u(k + 1) .. .
r(k + p)
.
Ep (k + 1|k) = R(k + 1) − Sx x(k), (20) here first command of control sequence is used to input to the system, so control law is: u = [ Inu ×nu 0 · · · 0 ]1×m · )−1 ( (21) T T (Γy Su ) Γy Ep . (Γy Su ) Γy Su + ΓTu Γu
3.2 Control laws for 2 stages
When the system launch with 1st gear, torque, speed of engine and clutches are shown in Fig. 3, where t0 means vehicle start to launch, td means speed of engine is the same as speed of C1 and tf means torque of engine equals to torque of C1 . The launching process is mainly divided into 2 parts, td indicates the end of stage 1 and tf indicates the end of stage 2.
(12)
u(k)
2
J = ∥Γy (yc − R)∥ + ∥Γu u∥ . (17) where R is the desired engaging speed, i.e. R = ωe /i1 /if , 2 the first item J1 = ∥Γy (yc − R)∥ aims to make sure the 950
Fig. 3. Calculation chart of launching process The engine speed ωe is always greater than the speed of off-going disc, which belongs to clutch C1 during launching process, so there is no power cycling. Before the separating clutch divides, rule-based method is chosen to ensure slipping work of both clutch equally. The slipping work of two clutches is: ∫ td ∫ td (22) Tc2 (ωe − ωc2 )dt. Tc1 (ωe − ωc1 )dt = t0
2
p×1
Define:
p×1
u(k + m − 1) m×1 And the predicted outputs of Np steps could be calculated as below: Yp (k + 1|k) = Sx x(k) + Su u(k), (13) among equation (13), [ ]T Sx = Cc A Cc A2 . . . Cc Ap 1×p , 0 ... 0 C c Bu C c Bu ... 0 Cc ABu .. .. .. .. . . . . Su = . Cc Bu Cc Am−1 Bu Cc Am−2 Bu · · · .. .. .. .. . . . . p−1 p−2 p−m Cc A Bu Cc A Bu . . . Cc A Bu p×m (14) In launch control, one of the most important evaluation indexes during launching process is jerk, which could be express below: ) rdω˙ s r ( ˙ da r = = jerk = i1 Tc1 + i2 T˙c2 = u. (15) dt dt Is I s if The objective function is described as: (16) min J(y(k), U (k), Nm , Np ), where
on-coming and off-going discs of launching clutch engage 2 together. The second item J2 = ∥Γu u∥ aims to minimum jerk. The form of Γy and Γu are Γy = diag(Γy,1 , Γy,2 , · · · , Γy,p ), (18) Γu = diag(Γu,1 , Γu,2 , · · · , Γu,m ). Choose tracking inputs as below: r(k + 1) r(k + 2) . (19) R(k + 1) = .. .
t0
Integrating equation (4), total output torque of the two clutches can be ∫obtained: udt = i1 if Tc1 + i2 if Tc2 .
(23)
IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018 Zijiao Jiang et al. / IFAC PapersOnLine 51-31 (2018) 904–909
Define ε as slip ratio: ωe − ωc2 ε= . (24) ωe − ωc1 The torques Tc1 and Tc2 transmitted by two clutches before the separating clutch starts to disengage are obtained by equations (22) and (23) separately: ∫ T = ε udt c1 εK∫c1 +Kc2 , t ≤ t < t (25) 0 d udt Tc2 = εKc1 +Kc2
The system turns into the next stage after td comes. In the 2nd stage, instead of MPC controller, rule-based controller is proposed to distribute torque. The changing rate of Tc2 is Kd : T˙c2 = Kd . (26) The control law of Tc2 could be obtained through integrate equation (26). When Tc2 decline to zero, it keeps zero. td td When t = td , Tc1 is the value of Tc1 and Tc2 is the value of Tc2 . At each sampling time, the increment of Tc1 is add of increment of Te and increment of Tc2 . But when Tc1 equals to Te , Tc1 stays equal to Te . So the rules are shown as below: { td + ∆Te + ∆Tc2 Tc1 = Tc1 (27) 2 , td ≤ t ≤ tf td Tc2 = Tc2 − 12 K˙ d (t − td ) Stage 2 ends up at tf when Tc1 equals to Te . Then the vehicle runs at 1st gear stably when the launching clutch fully engages and separating clutch does not transmit torque.
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equations is built in MATLAB environment, which is described in details in Zhao (2017): Ie ω˙ e = Te − Tc1 − Tc2 − ce ωe , Ic1 ω˙ c1 = Tc1 − Tm1c1 − Tg5c1 − Tg3c1 − cc1 ωc1 , I ˙ g5 = Tg5c1 i5 η − cg5 ωg5 , g5 ω I ω˙ = T g3 g3 g3c1 i3 η − cg3 ωg3 , Ic2 ω˙ c2 = Tc2 − Tm1c2 − Tg4c2 − Tg6c2 − cc2 ωc2 , Ig4 ω˙ g4 = Tg4c2 i4 η − cg4 ωg4 , I ˙ g6 = Tg6c2 i6 η − cg6 ωg6 , g6 ω (Im1 + Ig1 + Ig2 )ω˙ m1 = Tm1c1 i1 η +Tm1c2 i2 η − Tsm1 − (cm1 + cg1 + cg2 )ωm1 , I s ω˙ s = Tsm1 ia η − Tsm2 ia /η − Tr − cs ωs , Im2 ω˙ m2 = Tsm2 − cm2 ωm2 . (32) The relationships among input shafts, intermediate shafts and output shafts are shown below: { ωc1 = ωm1 i1 = ωg5 i5 = ωg3 i3 , ωm1 = ωm2 = ωs ia , (33) ωc2 = ωm1 i2 = ωg4 i4 = ωg6 i6 . All the parameters in the simulation model is listed in Table 1. In this model, the engine torque Te can be acquired through engine MAP as shown in Fig. 4 which is used to describe the engine torque characteristics. When launching Engine MAP
200 150 Te Nm
3.3 Analysis of stability Because of uncertainty of the vehicle resistance and varying vehicle parameters, considering the uncertainties of the system, it is necessary to analyse the stability of proposed MPC controller. The controlled system is described as below: x(k + 1) = Ax(k) + Bu u(k), (28) Firstly define: Kmpc = [ Inu ×nu 0 · · · 0 ]1×m )−1 ( (29) T T · (Γy Su ) Γy Su + ΓTu Γu (Γy Su ) Γy ,
and
u(k) = Kmpc · Ep (k + 1|k), (30) Substitute equations (20), (29) and (30) into equation (28) to obtain the closed loop control system x(k + 1) = (A − Bu Kmpc Sx )x(k) (31) +B u Kmpc R(k + 1). All the eigenvalues of matrix A − Bu Kmpc Sx are in the unit cycle, where Nm and Np are taken at regular intervals from 10 steps to 100 steps. The scope of eigenvalues’ real part is from 0.9151 to 0.9950, the scope of imaginary parts’ absolute value is from 0 to 0.0677. Closed loop system is nominal asymptotically stable. 4. RESULTS AND ANALYSIS To testify the effectiveness of the proposed controller, a equivalent DCT vehicle model based on 8-DOF dynamics 951
100 50
0 10000
1
5000 we rev/min
0.5 0 0
acc
Fig. 4. Engine MAP with first gear, the system runs under two working conditions, one is light load (vehicle mass is 1420 kg) called working condition 1, another one is heavy load (vehicle mass is 1680 kg) called working condition 2. The simulation results with MPC controller are shown in Fig. 5(a) and Fig. 6(a). In order to testify the superiority of the proposed method, a PID controller which only launches with clutch C1 , rather than coordination control of twin clutches is also established to compare the simulation results with MPC controller under same working conditions. The simulation results are shown in Fig. 5(b) and Fig. 6(b). Quantified comparisons between the simulation results of PID launch controller and MPC launch controller are also shown in Table 2 and Table 3. To launch vehicle in limited time, the system increases throttle opening from 0.1 in working condition 1 to 0.2 in working condition 2, where both of the throttle opening is consistent. Under working condition 1, it can be seen the on-coming and off-going discs of launching clutch are fully engaged in 1.605 s which launches with single clutch under PID controller. Compared with the results above, the MPC controller gives a better performance which
IFAC E-CoSM 2018 908 Changchun, China, September 20-22, 2018 Zijiao Jiang et al. / IFAC PapersOnLine 51-31 (2018) 904–909
Table 1. Parameters in the simulation model Parameters Te , Tc1 , Tc2 Tg5c1 , Tg3c1 , Tg4c2 , Tg6c2 Tm1c1 , Tm1c2 Tsm1 , Tsm2 Ie , Ic1 , Ic2 Ig1 , Ig2 , Ig3 , Ig4 , Ig5 , Ig6 Im1 , Im2 , Is i1 , i2 , i3 , i4 , i5 , i6 , ia ce , cc1 , cc2 cg1 , cg2 , cg3 , cg4 , cg5 , cg6 cm1 , cm2 , cs ωe , ωc1 , ωc2 ωg 1, ωg 2, ωg 3, ωg 4, ωg 5, ωg 6, ωa ωm1 , ωm2 , ωs η
Meaning T denotes torque, e denotes engine, c denotes clutches T denotes reaction torque, g denotes gear, c denotes clutches T denotes reaction torque, m denotes intermediate shaft, c denotes clutches T denotes reaction torque, s denotes output shaft, m denotes intermediate shaft I denotes inertia, e denotes engine, c denotes clutches I denotes inertia, g denotes gears I denotes inertia, m denotes intermediate shafts, s denotes vehicle i denotes transmission ratio, number denotes gear, a denotes final drive c denotes viscous friction coefficient, e denotes engine, c denotes clutches c denotes viscous friction coefficient, g denotes gears c denotes viscous friction coefficient, m denotes intermediate shaft, s denotes vehicle ω denotes rotating speed, e denotes engine, c denotes clutches ω denotes rotating speed, g denotes gear, a denotes final drive ω denotes rotating speed, m denotes intermediate shaft, s denotes vehicle Efficiency
could help the vehicle launch in just 0.644 s with twin clutches. In working condition 2, vehicle finishes launching in 1.660 s under PID controller and in 0.789 s under MPC controller. It can be seen that MPC launch controller can decreases the launching time up to 52%. Both the slipping work of twin clutches in two working conditions under MPC launch controller are all less than 0.4 J/mm2 . When compared with PID launch controller, MPC launch controller gives a 60% reduction of engaging time and a 63% reduction of sliding time. When launching with twin clutches, the torque results show that the separating clutch transmits torque for more than 0.5 s, also averages torque and slipping friction during launching process, decrease engaging speed, in which way could lengthen service life of launching clutch. And the torque of both clutches changes smoothly, which ensures the comfortable driving experience for passengers. The smooth increase of vehicle speed means launching success of DCT vehicle under MPC launch controller. The analysis above shows that vehicle launches successfully with satisfying all the evaluation indexes, including torque should change smoothly, slipping work should be less than 0.4 J/mm2 and engine should not flame out. The results under two working conditions also indicate that the proposed controller has better robust stability. Table 2. Comparison of simulation results under working condition 1 Parameters Engaging time(s) Sliding time(s) Engaging speed(r/ min) Slipping work(J/mm2 )
C1 1.605 1.751 2143 0.1735
C1 &C2 0.644 0.990 1607 0.0926&0.0935
Change -60% -43% -25% -47%
Table 3. Comparison of simulation results under working condition 2 Parameters Engaging time(s) Sliding time(s) Engaging speed(r/ min) Slipping work(J/mm2 )
C1 1.660 2.987 3082 0.3303
C1 &C2 0.789 1.095 2538 0.1902&0.1914
Change -52% -63% -18% -42%
5. CONCLUSION This paper focus on design of control method for launching process of DCT vehicle. Controller in the framework of 952
MPC is designed to launch vehicle with twin clutches. Control strategy is organised to launch vehicle, decrease jerk and average slipping work of twin clutches which are expressed in objective function and control rules. An accurate DCT vehicle model is established in simulink environment to testify the effectiveness of proposed launch controller. A comparison of launching process between PID launch controller with single clutch and MPC twin clutches controller shows that the proposed strategy could greatly improve driving experience. In the future work, simulating launching with second gear and hardware-inloop experiment will be considered to further demonstrate the effectiveness of the method. The dynamics of clutches actuators will be also introduced because torque of clutches can not be implemented directly. REFERENCES Mario P, Maurizio C, Adolfo S. Multiple Constrained MPC Design for Automotive Dry Clutch Engagement. IEEE/ASME Transactions on Mechatronics, 20,1:469– 480,2015. Gao B Z, Hong J L, Qu T, et al. Linear-quadratic output regulator for systems with disturbance: application to vehicle launch control. The 31st Youth Academic Annual Conference of Chinese Association of Automation, 135– 140,2016. Minh V T, Rashid A A. Automatic control of clutches and simulations for parallel hybrid vehicles. International Journal of Automotive Technology, 13,4:645–651,2012. Zhang J L, Ma B, Zheng C S. Improved Fuzzy Control of Dual Clutch Transmission during Launch Process. International Conference on Mechatronics and Automation, 676–681,2010. Zhao Z Q, Zhou Y S, Cao C L. Driveline system modeling and starting control strategy of DCT. Modern Manufacturing Engineering, 7:120–124,2009. Qin D T, Liu Y G, Hu J J, et al. Control and Simulation of Launch with Two Clutches for Dual Clutch Transmissions. Journal of Mechanical Engineering, 46,18:121– 127,2010. Yan Y Q, Song J, Li L, et al. Self-adaption initial acceleration control strategies of a dry dual clutch transmission. Journal of Tsinghua University(Science and Technology), 54,6:734–737,2014. Zhang J L, Guo J, Gui L. Study on launch control strategies of dual clutch transmission. International
IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018 Zijiao Jiang et al. / IFAC PapersOnLine 51-31 (2018) 904–909
(a) the proposed MPC controller
(a) the proposed MPC controller
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(b) a well tuned PID controller
(b) a well tuned PID controller
Fig. 6. Simulation results under working conditions 2.
Fig. 5. Simulation results under working conditions 1. Conference on Mechatronics and Automation, 1142– 1147,2012. Liu Z J, Ren C B, Wang L. Simulation Analysis on Control Strategy of Launch with two Clutches for Dry DCT. Advanced Materials Research, 932–936,2012. Sun W, Yang Y L, Ma J. Study on Torque Transfer Control Strategy of DCT Launching with Two Clutches. Agricultural Equipment & Vehicle Engineering, 50,4:11– 13,2012. Kong H F, Zhou D, Zhao W, et al. Research of Starting Control of DCT Vehicle Dual Clutch based on Sliding Mode Variable Structure. Journal of Mechanical Transmission, 38,6:14–18,2014. Zhao Z G, Li X Y,He L, et al. Estimation of Torques Transmitted by Twin-Clutch of Dry Dual-Clutch Transmission During Vehicle’s Launching Process. IEEE Trans953
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