# Dynamic Shift Coordinated Control Based on Motor Active Speed Synchronization with the New Hybrid System

Authors: Ting Yan; Lin Yang; Bin Yan; Wei Zhou; Liang Chen; Wei Zhou
Journal: Shock and Vibration
 (2017)

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## Abstract

Considering the inherent disadvantages that severely affect driving comfortability during the shift process in HEVs, a dynamic shift coordinated control based on motor active speed synchronization is proposed to improve shift quality by reduction of shift vibration. The whole control scheme is comprised of three phases, preparatory phase, speed regulation phase, and synchronization phase, which are implemented consecutively in order. The key to inhibiting impact and jerk depends on the speed regulation phase, where motor active speed synchronization is utilized to reach the minimum speed difference between the two ends of synchronizer. A new hybrid system with superior performances is applied to present the validity of the adopted control algorithm during upshift or downshift, which can represent planetary gear system and conventional AMT shift procedure, respectively. Bench test, simulation, and road test results show that, compared with other methods, the proposed dynamic coordinated control can achieve shifting control in real time to effectively improve gear-shift comfort and shorten power interruption transients, with robustness in both conventional AMT and planetary gear train.


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## Body

## 1. Introduction

Hybrid electric vehicle (HEV) is emerging as an important substitution for traditional transportation due to its fuel economy improvement and emission reduction. Its powertrain can be classified as conventional AMT type and planetary gear train type based on coupled manner. A new type of hybrid system is proposed in this paper, whose structure combines both of the two mainstream types together, with superiority in dynamic performance and fuel economy as well [1–3]. However, since they have complicated powertrain structure and various operational modes, power interruption and torque fluctuation during mode transformation, especially in the shift synchronization period, can easily result in driving vibrations and jerks, which greatly influences driving comfortability. Alleviating and damping driving vibrations during gear-shift become one of the key issues in vehicle dynamic switching control [4].Many approaches have been proposed to find better solutions to overcome the shortcomings in gear-shifting process of HEV. Glielmo et al. raised a hierarchical method based on cascaded and decoupled speed and torque control loops [5]. Shin et al. developed a combined gear-shifting method assisted by motor speed feedback control [6]. Baraszu and Cikanek demonstrated that during the gear-shifting process a motor should provide torque directly to reduce the power interruption time [7]. A combination of Dynamic Programming (DP) and Pontryagin’s Minimum Principle (PMP) was utilized in a model predictive controller framework to realize a predictive controller in a receding horizon mode for a PHEV equipped with an AMT [8]. The computational burden and assumption that velocity profile is available ahead limit its application in real-time control. Control strategies used in clutchless gear-change drivelines in hybrid electric vehicles are discussed in [9–11]. This limits the usage of the proposed methods in these literatures to the gear-shifting process related to clutch engagement and the drivability performances cannot be guaranteed. The strategy in electric vehicles equipped with hydraulic combined clutch transmissions in [12] is presented to improve the shift quality. Nevertheless, the complexity of the shift hydraulic circuit and its nonlinear feature bring in challenges to predict the oil pressure acting on the brake piston. A synthesis algorithm to realize accurate engine speed control and shift motor position control without disengaging the clutch using engine active control was presented by Zhong et al. [13], which has not significantly improved the conditions on account of the slow response of engine. So motor active speed control was proposed to achieve shifting synchronization during gear-shifting process on account of the rapid response of motor characteristics [14, 15]. However, their powertrain structures are simple, which are both single motor in single axle without clutch, and the algorithms raised cannot be applied to complex powertrains with clutch or dual motors, not to mention with planetary gear system. As a consequence, a new motor active speed synchronization with clutch coordinated control is introduced to achieve a fast and smooth gear-shift in the new hybrid system.Due to the tremendous structural difference between the two gears of the new hybrid system, the speed difference between the two ends of synchronizer is large as it is ready to shift. Upshift or downshift directly will lead to strong vibrations and severe wear of the synchronizer. As a result, motor speed adjustment is required before the synchronization begins in order to minimize shift time and power interruption period and decrease the impact force and improve shift quality. Meanwhile, to acquire a fast and smooth gear-shift, the engine, motor, clutch, and actuator of the gearbox are controlled precisely and coordinately. Before switching to neural gear, the transmitted torque to the output shaft must be reduced to close to zero; otherwise attempting to disengage or engage the gears which are transmitting large torques can bring about torsional vibration, teeth surface damage of the gears, and synchronization difficulty. So unloading the power sources as well as disengaging the clutch completely is necessary prior to switching to neutral gear. Clutch remains disengaged throughout and motors are unloaded again before the synchronization begins due to the same reason. The coordinated control raised above can ensure the rapidity and smoothness of the gear-shift process as validated by on-board tests.The dynamic shift coordinated control scheme based on motor active speed regulation can be divided into three phases: unload and switch to neural gear, speed regulation, and mechanical speed synchronization by the synchronizer. The second phase is the core part. The new type of HEV system is employed to assess the feasibility of the control scheme. The reason to select this new hybrid system as the research object depends on two points. Firstly, the new hybrid system has huge advantages in fuel economy and dynamic performances. The rate of fuel saving can reach 17%~28% in different driving cycles in comparison with conventional parallel hybrid vehicles, which can attain up to nearly 40% when compared with traditional diesels [1, 3]. On the other hand, the maximum output torque before the final drive of the new system is over 3600 Nm, which can meet power demands in assorted situations. Secondly, it contains two representative powertrains in two gears and the structural difference between the two gears results in inevitable speed regulation during shift process. By presenting upshift and downshift control scheme, the regulation process in conventional AMT and planetary gear train can both be revealed in the new hybrid system, as shown in Section 3.2. In Section 2, the structure and operating principle of the new HEV system is presented. In Section 3, dynamic coordinated control and active speed synchronization are elaborated, respectively. Bench test and on-board test results showing the effectiveness of the proposed approach are presented in Section 4. Conclusions that summarize the results of the paper are obtained in Section 5.


## 2. The New HEV System

The simplified structural diagram of the HEV system adopted in this paper is shown in Figure1. It is mainly composed of a diesel engine, two permanent magnetic motors, and a planetary gear coupling system. MG2 is linked to the sun gear directly, while MG1 is connected to the ring gear and separated from engine by an electronic control clutch. Compared with the traditional hybrid system, the new system can adjust the speed range of engine operating point flexibly through the CVT coupling system, which ensures that engine is working in high-efficiency area and improves vehicle fuel economy. Meanwhile engine can collaborate with generator to drive the vehicle or charge the battery to meet vehicle dynamic and duration requirements.Figure 1
Simplified structural diagram of new HEV system (S: shift synchronizer, MG1: generator, MG2: motor, andK1/K2: gear ratio).While the shift synchronizer is placed at the right end, gear number is 1. And the motor output torque is amplified a few times via a conventional gear train to the output shaft to meet the working condition requirement as the demanded torque is high, such as vehicle launching process. As mentioned previously, this relationship can be written as follows:(1)Tf=TMG2×K1×K2,(2)ωf1=ωMG2K1×K2,where Tf and TMG2 denote the output shaft torque and MG2 torque, respectively, ωf1 and ωMG2 denote the output shaft speed at the first gear and MG2 speed, and K1 and K2 denote the gear ratios of the gear train.While the shift synchronizer is placed at the left end, gear number is 2. The sun gear (MG2) and the ring gear (MG1 and engine) are coupled and transfer torque to the planetary gear ultimately. With the known features of the planetary gear train, the relationship in the steady state is described as follows:(3)Tr=TMG2×α,(4)Tf=Tr+TMG2=TMG2×1+α,(5)Tr=TMG1+θ×TICE,(6)ωf2=α×ωMG1+ωMG21+α,where(7)θ=1,clutch  is  engaged0,clutch  is  disengaged0~1,clutch  is  slipping.α denotes the coefficient of planetary gear, Tr, TMG1, and TICE denote the ring gear torque, MG1 torque, and engine torque, respectively, and ωMG1, ωICE, and ωf2 denote MG1 speed, engine speed, and output shaft speed at the second gear.When the clutch is engaged,(8)ωMG1=ωICE.Engine is linked to the powertrain completely in the meantime. From (6) and (8), we can conclude that by adjusting MG2 speed the engine can work in its high-efficiency speed range, leading to vehicle fuel economy improvement, as shown in Figure 2.Figure 2
Adjusting MG2 speed to regulate engine operating point.While the shift synchronizer is placed in the middle, the powertrain is interrupted. No power can be transferred to the output shaft due to the interruption. It is at the neutral position at this moment.The operating state of the new HEV system can be divided into four modes. The selection criteria depend on vehicle speed, power requirement, and battery SOC. The four modes are tabulated in Table1.Table 1
The four operation modes of new HEV system.
Mode
Gear number
Clutch status
Description
Single-motor pure electric mode
1
Engaged
Only MG2 drives the vehicle
Series mode
1
Engaged
MG2 drives vehicle; MG1 and engine collaborate to generate electricity
Dual-motor pure electric mode
2
Disengaged
MG1 and MG2 drive the vehicle together
Series-parallel mode
2
Engaged
MG1, MG2, and engine drive the vehicle together


## 3. Dynamic Coordinated Control

Coordinated control with other components is indispensable during shift process. It is needed to guarantee the smoothness of synchronization after speed regulation. The whole dynamic coordinated control scheme is composed of three phases, which are shown in Figure3 and described in detail as follows. Every step in each phase should be confirmed from the feedback of the controlled components before taking on to the next step, which ensures the reliability of the whole procedure.Figure 3
The control scheme of the dynamic coordinated control.


### 3.1. Preparatory Phase (Unload and Switch to Neutral Gear)

The aim of this phase is to make preparations for the motor active speed regulation. The main task includes unloading power sources, disengaging clutch, and putting into neutral gear. Motors and engine are in no-load condition after being unloaded, which makes it convenient to disengage the clutch later. No torque transmitted to the powertrain helps to switch to neutral gear smoothly to avoid jerks and noise.The preparatory phase period should not last too long. Otherwise, the driver would perceive the lack of power due to no power output during the phase. On the other hand, the descending slope of the command torque sent to DMCM should be considered not too large, which will induce the feeling of abruption. The flow chart is shown in Figure4.Figure 4
The preparatory phase’s flow chart.


### 3.2. Speed Regulation Phase

Speed regulation during shifting process is indispensable, which is aimed at adjusting the input shaft to a desired speed without overshoot and oscillation. It is found by experiments that only when the speed difference is less than an acceptable reference valueξ can the synchronization start. Moreover, it is easier to put into the target gear when the speed of the active speed-adjusting end is slightly higher than the passive end of the synchronizer, which is in consistence with the principle in conventional buses. So (9) must be satisfied before the synchronization begins:(9)δ≤ωsT-ωs≤ξ,where ωsT is the target speed of output shaft linked to the synchronizer in the speed regulation phase, ωs is actual speed of output shaft, and δ and ξ are speed calibrations determined by the speed difference calibration experiment in the bench test.The output shaft speed is closely associated with the vehicle speed, as shown in the following equation:(10)ωs=Vss×igr×602π,where Vss denotes vehicle speed, ig denotes final gear ratio, and r denotes the wheel’s radius.Due to short speed-adjusting time, large vehicle rotational inertia, and no power output during the neutral position period, vehicle speed can be assumed to be approximately constant. Thenωs can be presumed as nearly invariant as well from (10). Equation (11) can be obtained from (2) and (6):(11)ωsT=ωMG2TK1×K2downshiftωMG2T+α×ωMG1T1+αupshift,where ωMG1T and ωMG2T denote MG1 target speed and MG2 target speed.The speed regulation processes of upshift and downshift are discussed, respectively, due to the complicated structure of the new HEV system.


#### 3.2.1. The First Upshift Speed Regulation (Single-Motor Mode to Dual-Motor Mode)

In single-motor mode, Only MG2 propels the vehicle, while engine and MG1 are in idle state and do not output power at all:(12)ωMG1=ωICE=0.In dual-motor mode, MG1 and MG2 propel the vehicle together. One motor must be in speed control mode and the other in torque control mode to keep the system stable due to the features of planetary gear system. MG2 is chosen as the speed controlled motor because of its excellent speed adjustment performance. Then MG1 is in torque control mode as its torque regulation performance is good. The optimal combination of MG2 and MG1 speed of highest system efficiency (ωMG2∗,ωMG1∗) can be acquired based on two motors’ efficiency characteristic curves under different vehicle speed and vehicle demanded torque conditions. The calculation procedure is as follows.(1)
Set a combination of vehicle speed and demanded torque(Vss,TDmnd) as known quantities; then(13)TMG1=TDmnd×α1+α,(14)TMG2=TDmnd1+α.(2)
Given a series of MG1 speed (ωMG11,ωMG12,…,ωMG1n), the corresponding MG2 speed under Vss can be conducted (ωMG21,ωMG22,…,ωMG2n) from the relationship in (6):(15)ωMG2k=60Vss1+αig2πr-αωMG1kk=1,2,3,…,n.(3)
MG1 efficiencyηMG1k and MG2 efficiency ηMG2k are gained by making use of the obtained combination (ωMG1k,TMG1) and (ωMG2k,TMG2) to look up to MG1 and MG2 efficiency curves.(4)
If there is a combination(ωMG1i,TMG1,ηMG1i) or (ωMG2i,TMG2,ηMG2i), which meets the equation(16)ωMG1i×TMG1ηMG1i+ωMG2i×TMG2ηMG2i=min⁡ωMG1k×TMG1ηMG1k+ωMG2k×TMG2ηMG2k,i,k=1,2,…,n,then(ωMG1i,ωMG2i) is the speed optimal combination (ωMG1∗,ωMG2∗) under (Vss,TDmnd) conditions.(5)
Repeat the steps above to get all the optimal speed combination(ωMG1∗,ωMG2∗) under different vehicle speed and vehicle demanded torque conditions.After switching to neutral gear, set MG1 operating in torque controlled mode. Assume that MG1 command torque isTMG1T; the time from current speed to the target speed ωMG1raw is t1. MG1 unloads torque and prepares to put into the target gear when reaching the target speed. But MG1 speed will keep on rising up during the unload process because of its response delay until achieving the peak speed. Then it begins to drop slowly. Set the peak speed as ωMG1p and the period from ωMG1raw to ωMG1p as t2. Since MG1 has outstanding torque regulation performance, MG1 actual torque can be considered as achieving the command torque quickly by following a constant slope, as shown in Figure 5.Figure 5
Variables changing curves in upshift speed regulation 1.As MG1 reaches the peak speed, MG1 actual torque is close to zero and the speed change is gentle, which makes it the ideal optimal point.Set(17)ωMG1p=ωMG1∗.And the total MG1 speed regulation time istMG1: (18)tMG1=t1+t2.The speed regulation can be divided into two stages:0~t1 and t1~tMG1. Equation (19) can be obtained in each stage:(19)T-Tloss22k+Tt1-Tk-Tlosst1=JωMG1raw,T2-Tloss22k-TlossT-Tlossk=JωMG1p-ωMG1raw,t2=T-Tlossk.ThentMG1 is attained by solving the above equations: (20)tMG1=T-Tlossk+Tloss2-2TTloss-2JkωMG1p2kTloss-T,where T and Tloss denote MG1 command torque and friction torque; k is MG1 torque response slope.   J is MG1 equivalent rotational inertia.The assignment ofT should consider that if T is too large, even though t1 is short, the unloading process is long and speed increment is large. If T is too small, even though unloading time t2 is short, t1 will be long due to the small angular acceleration. tMG1 will be relatively long in either case. T∗ is presumed to be the optimal value of T, which meets the following equation: (21)fT∗,ωMG1p=min⁡tMG1.Take the partial derivative ofT in (20) and T∗ is obtained as follows:(22)∂tMG1∂T=Tloss2-2TTloss-2JkωMG1p2kTloss-T2-TkTloss-T=0,(23)T∗=Tloss+Tloss22+JkωMG1p.MG2 is set to operate in speed control mode on account of its fast response and regulation precision. By adjusting MG2 target speedωMG2T quickly, the output shaft speed can be coupled to ωsT exactly at the end of speed regulation.MG2 target speedωMG2T is(24)ωMG1T=ωMG2∗t≤tMG11+αωsT-αωMG1t>tMG1;namely, MG2 speed is regulated to optimum value ωMG2∗ prior to MG1 finishing torque regulation, which meets (9) as MG1 rises to the peak speed ωMG1∗. If (9) cannot be met during the whole MG1 speed regulation process, then MG2 target speed is modified to satisfy the coupling relationship as MG1 is free falling. The process is close to the shift speed regulation process in planetary gear systems with dual motors.


#### 3.2.2. The Second Upshift Speed Regulation (Single-Motor Mode/Series Mode to Series-Parallel Mode)

In series-parallel mode, engine participates in propelling the vehicle. Taking the output shaft speedωs, vehicle demanded torque TDmnd, and engine power PICE as the known quantity, a three-dimensional function table is made. The object of the function is to acquire the highest combined efficiency of the engine and electrical system and meet the vehicle power requirement and reach SOC control target. The optimal combination (ωMG2∗,ωMG1∗) is gained by following the procedure below.(1) Set the combination(ωs,TDmnd,PICE) as the known quantity. Vehicle demanded power PDmnd=TDmnd×ωs.(2) Given a series of MG1 speed(ωMG11,ωMG12,…,ωMG1n), the corresponding MG2 speed can be obtained as (ωMG21,ωMG22,…,ωMG2n) under vehicle speed Vss condition by the following relationship:(25)ωMG2k=ωs×1+α-α×ωMG1kk=1,2,3,…,n.Engine speed is equal to MG1 speed.(3) Engine torque is given as follows:(26)TICE1,TICE2,TICE3,…,TICEn=PICEωMG11,PICEωMG12,PICEωMG13,…,PICEωMG1n.MG1 command torque is given as follows:(27)TMG11,TMG12,…,TMG1n=TDmnd×α1+α-TICE1,TDmnd×α1+α-TICE2,…,TDmnd×α1+α-TICEn.MG2 torque is given as follows:TMG2=TDmnd/(1+α).(4) MG1 efficiencyηMG1k, MG2 efficiency ηMG2k, and engine efficiency ηICEk are gained by making use of the obtained combinations (ωMG1k,TMG1),(ωMG2k,TMG2), and (ωICEk,TICE) to look up to MG1, MG2, and engine efficiency curves.(5) If there are combinations(ωMG1i,TMG1,ηMG1i), (ωMG2i,TMG2,ηMG1i), and (ωICEi,TICE,ηICEi) which meet the equation(28)ωMG1i×TMG1ηMG1i+ωMG2i×TMG2ηMG2i+γ×PICEηICEi=min⁡ωMG1k×TMG1ηMG1k+ωMG2k×TMG2ηMG2k+γ×PICEηICEki,k=1,2,…,n,where γ is the equivalent conversion factor from engine power to electric power, then (ωMG1i,ωMG2i) is the speed optimal combination (ωMG1∗,ωMG2∗) under (Vss,TDmnd) conditions.(6) Repeat the steps above to get all the optimal speed combination(ωMG1∗,ωMG2∗) under different vehicle speed, vehicle demanded torque, and engine power conditions.When entering series-parallel mode, clutch has to be engaged as soon as possible. Hence the speed difference between MG1 and engine should not be too big; otherwise engaging directly will result in severe abrasion and jerk. Moreover, readjusting MG1 speed will delay MG1 torque recovery time. To avoid the problems appearing after upshift process, engine speed is always commanded to the optimum speedωMG1∗ during the shift process, which is also the target speed of MG1:(29)ωICE∗=ωMG1T=ωMG1∗.MG2 speed regulation target is the same as (24). MG1 command torque in single-motor mode to series-parallel mode is identical to (23). The derivation of T∗in series mode to series-parallel mode is similar to (19) and (22):(30)T∗=Tloss+Tloss22+JkωMG1p-ωMG1sωMG1p>ωMG1sTloss-Tloss22+JkωMG1s-ωMG1pωMG1p<ωMG1s,where ωMG1s is MG1 speed in series mode. Unlike the single-motor mode to series-parallel mode, T∗ in series mode to series-parallel mode may be positive or negative depending on whether ωMG1s is less than ωMG1p or not. The situation when T∗>0 is similar to Figure 4, while T∗<0 is shown in Figure 6.Figure 6
Variables changing curves in upshift speed regulation 2.


#### 3.2.3. Downshift Speed Regulation

Only MG2 connects to the powertrain after downshift no matter in single-motor mode or in series mode. MG2 target speed can be obtained in (31), which is similar to conventional AMT:(31)ωMG1T=ωsT×K1×K2.MG1 speed does not need to be regulated during downshift process. MG1 only needs to make preparations to unload and put into target gear. In summary, the flow chart of shift speed regulation process is as shown in Figure7.Figure 7
The speed regulation phase’s flow chart.


### 3.3. Synchronization Phase

Mechanical speed synchronization is executed by the synchronizer to put into the target gear from neutral gear in this phase, during which shift motor drives the synchronizer to reach the stroke range of the target gear. Hybrid control unit (HCU) adjusts the pulse duty ratio of 24 V voltage to control the power of shift motor in order to overcome the different situations. Moreover, PID control of position and velocity closed loop is utilized to solve the nonlinear and parameter uncertainty situation in mechanical synchronization. If the synchronization time exceeds normal default value, it means that motor stalling appears due to speed regulation failure or shift motor faults. Shift motor has to be stopped immediately at this moment. The shift process interrupts and enters fault mode, where the target gear is revised to neutral gear due to the fact that the resistance to neural gear is relatively small and no contact exists between synchronizer and powertrain in neural gear so as to protect the shift mechanism and check fault reason in park condition. After returning to neutral gear, the shift synchronizer can try to put into the target gear again up to three times. If three attempts all end in failure, then fault lamp is lightened and the gear fixes in neural gear. The flow chart of synchronization phase is shown in Figure8.Figure 8
The synchronization phase’s flow chart.


## 3.1. Preparatory Phase (Unload and Switch to Neutral Gear)

The aim of this phase is to make preparations for the motor active speed regulation. The main task includes unloading power sources, disengaging clutch, and putting into neutral gear. Motors and engine are in no-load condition after being unloaded, which makes it convenient to disengage the clutch later. No torque transmitted to the powertrain helps to switch to neutral gear smoothly to avoid jerks and noise.The preparatory phase period should not last too long. Otherwise, the driver would perceive the lack of power due to no power output during the phase. On the other hand, the descending slope of the command torque sent to DMCM should be considered not too large, which will induce the feeling of abruption. The flow chart is shown in Figure4.Figure 4
The preparatory phase’s flow chart.


## 3.2. Speed Regulation Phase

Speed regulation during shifting process is indispensable, which is aimed at adjusting the input shaft to a desired speed without overshoot and oscillation. It is found by experiments that only when the speed difference is less than an acceptable reference valueξ can the synchronization start. Moreover, it is easier to put into the target gear when the speed of the active speed-adjusting end is slightly higher than the passive end of the synchronizer, which is in consistence with the principle in conventional buses. So (9) must be satisfied before the synchronization begins:(9)δ≤ωsT-ωs≤ξ,where ωsT is the target speed of output shaft linked to the synchronizer in the speed regulation phase, ωs is actual speed of output shaft, and δ and ξ are speed calibrations determined by the speed difference calibration experiment in the bench test.The output shaft speed is closely associated with the vehicle speed, as shown in the following equation:(10)ωs=Vss×igr×602π,where Vss denotes vehicle speed, ig denotes final gear ratio, and r denotes the wheel’s radius.Due to short speed-adjusting time, large vehicle rotational inertia, and no power output during the neutral position period, vehicle speed can be assumed to be approximately constant. Thenωs can be presumed as nearly invariant as well from (10). Equation (11) can be obtained from (2) and (6):(11)ωsT=ωMG2TK1×K2downshiftωMG2T+α×ωMG1T1+αupshift,where ωMG1T and ωMG2T denote MG1 target speed and MG2 target speed.The speed regulation processes of upshift and downshift are discussed, respectively, due to the complicated structure of the new HEV system.


### 3.2.1. The First Upshift Speed Regulation (Single-Motor Mode to Dual-Motor Mode)

In single-motor mode, Only MG2 propels the vehicle, while engine and MG1 are in idle state and do not output power at all:(12)ωMG1=ωICE=0.In dual-motor mode, MG1 and MG2 propel the vehicle together. One motor must be in speed control mode and the other in torque control mode to keep the system stable due to the features of planetary gear system. MG2 is chosen as the speed controlled motor because of its excellent speed adjustment performance. Then MG1 is in torque control mode as its torque regulation performance is good. The optimal combination of MG2 and MG1 speed of highest system efficiency (ωMG2∗,ωMG1∗) can be acquired based on two motors’ efficiency characteristic curves under different vehicle speed and vehicle demanded torque conditions. The calculation procedure is as follows.(1)
Set a combination of vehicle speed and demanded torque(Vss,TDmnd) as known quantities; then(13)TMG1=TDmnd×α1+α,(14)TMG2=TDmnd1+α.(2)
Given a series of MG1 speed (ωMG11,ωMG12,…,ωMG1n), the corresponding MG2 speed under Vss can be conducted (ωMG21,ωMG22,…,ωMG2n) from the relationship in (6):(15)ωMG2k=60Vss1+αig2πr-αωMG1kk=1,2,3,…,n.(3)
MG1 efficiencyηMG1k and MG2 efficiency ηMG2k are gained by making use of the obtained combination (ωMG1k,TMG1) and (ωMG2k,TMG2) to look up to MG1 and MG2 efficiency curves.(4)
If there is a combination(ωMG1i,TMG1,ηMG1i) or (ωMG2i,TMG2,ηMG2i), which meets the equation(16)ωMG1i×TMG1ηMG1i+ωMG2i×TMG2ηMG2i=min⁡ωMG1k×TMG1ηMG1k+ωMG2k×TMG2ηMG2k,i,k=1,2,…,n,then(ωMG1i,ωMG2i) is the speed optimal combination (ωMG1∗,ωMG2∗) under (Vss,TDmnd) conditions.(5)
Repeat the steps above to get all the optimal speed combination(ωMG1∗,ωMG2∗) under different vehicle speed and vehicle demanded torque conditions.After switching to neutral gear, set MG1 operating in torque controlled mode. Assume that MG1 command torque isTMG1T; the time from current speed to the target speed ωMG1raw is t1. MG1 unloads torque and prepares to put into the target gear when reaching the target speed. But MG1 speed will keep on rising up during the unload process because of its response delay until achieving the peak speed. Then it begins to drop slowly. Set the peak speed as ωMG1p and the period from ωMG1raw to ωMG1p as t2. Since MG1 has outstanding torque regulation performance, MG1 actual torque can be considered as achieving the command torque quickly by following a constant slope, as shown in Figure 5.Figure 5
Variables changing curves in upshift speed regulation 1.As MG1 reaches the peak speed, MG1 actual torque is close to zero and the speed change is gentle, which makes it the ideal optimal point.Set(17)ωMG1p=ωMG1∗.And the total MG1 speed regulation time istMG1: (18)tMG1=t1+t2.The speed regulation can be divided into two stages:0~t1 and t1~tMG1. Equation (19) can be obtained in each stage:(19)T-Tloss22k+Tt1-Tk-Tlosst1=JωMG1raw,T2-Tloss22k-TlossT-Tlossk=JωMG1p-ωMG1raw,t2=T-Tlossk.ThentMG1 is attained by solving the above equations: (20)tMG1=T-Tlossk+Tloss2-2TTloss-2JkωMG1p2kTloss-T,where T and Tloss denote MG1 command torque and friction torque; k is MG1 torque response slope.   J is MG1 equivalent rotational inertia.The assignment ofT should consider that if T is too large, even though t1 is short, the unloading process is long and speed increment is large. If T is too small, even though unloading time t2 is short, t1 will be long due to the small angular acceleration. tMG1 will be relatively long in either case. T∗ is presumed to be the optimal value of T, which meets the following equation: (21)fT∗,ωMG1p=min⁡tMG1.Take the partial derivative ofT in (20) and T∗ is obtained as follows:(22)∂tMG1∂T=Tloss2-2TTloss-2JkωMG1p2kTloss-T2-TkTloss-T=0,(23)T∗=Tloss+Tloss22+JkωMG1p.MG2 is set to operate in speed control mode on account of its fast response and regulation precision. By adjusting MG2 target speedωMG2T quickly, the output shaft speed can be coupled to ωsT exactly at the end of speed regulation.MG2 target speedωMG2T is(24)ωMG1T=ωMG2∗t≤tMG11+αωsT-αωMG1t>tMG1;namely, MG2 speed is regulated to optimum value ωMG2∗ prior to MG1 finishing torque regulation, which meets (9) as MG1 rises to the peak speed ωMG1∗. If (9) cannot be met during the whole MG1 speed regulation process, then MG2 target speed is modified to satisfy the coupling relationship as MG1 is free falling. The process is close to the shift speed regulation process in planetary gear systems with dual motors.


### 3.2.2. The Second Upshift Speed Regulation (Single-Motor Mode/Series Mode to Series-Parallel Mode)

In series-parallel mode, engine participates in propelling the vehicle. Taking the output shaft speedωs, vehicle demanded torque TDmnd, and engine power PICE as the known quantity, a three-dimensional function table is made. The object of the function is to acquire the highest combined efficiency of the engine and electrical system and meet the vehicle power requirement and reach SOC control target. The optimal combination (ωMG2∗,ωMG1∗) is gained by following the procedure below.(1) Set the combination(ωs,TDmnd,PICE) as the known quantity. Vehicle demanded power PDmnd=TDmnd×ωs.(2) Given a series of MG1 speed(ωMG11,ωMG12,…,ωMG1n), the corresponding MG2 speed can be obtained as (ωMG21,ωMG22,…,ωMG2n) under vehicle speed Vss condition by the following relationship:(25)ωMG2k=ωs×1+α-α×ωMG1kk=1,2,3,…,n.Engine speed is equal to MG1 speed.(3) Engine torque is given as follows:(26)TICE1,TICE2,TICE3,…,TICEn=PICEωMG11,PICEωMG12,PICEωMG13,…,PICEωMG1n.MG1 command torque is given as follows:(27)TMG11,TMG12,…,TMG1n=TDmnd×α1+α-TICE1,TDmnd×α1+α-TICE2,…,TDmnd×α1+α-TICEn.MG2 torque is given as follows:TMG2=TDmnd/(1+α).(4) MG1 efficiencyηMG1k, MG2 efficiency ηMG2k, and engine efficiency ηICEk are gained by making use of the obtained combinations (ωMG1k,TMG1),(ωMG2k,TMG2), and (ωICEk,TICE) to look up to MG1, MG2, and engine efficiency curves.(5) If there are combinations(ωMG1i,TMG1,ηMG1i), (ωMG2i,TMG2,ηMG1i), and (ωICEi,TICE,ηICEi) which meet the equation(28)ωMG1i×TMG1ηMG1i+ωMG2i×TMG2ηMG2i+γ×PICEηICEi=min⁡ωMG1k×TMG1ηMG1k+ωMG2k×TMG2ηMG2k+γ×PICEηICEki,k=1,2,…,n,where γ is the equivalent conversion factor from engine power to electric power, then (ωMG1i,ωMG2i) is the speed optimal combination (ωMG1∗,ωMG2∗) under (Vss,TDmnd) conditions.(6) Repeat the steps above to get all the optimal speed combination(ωMG1∗,ωMG2∗) under different vehicle speed, vehicle demanded torque, and engine power conditions.When entering series-parallel mode, clutch has to be engaged as soon as possible. Hence the speed difference between MG1 and engine should not be too big; otherwise engaging directly will result in severe abrasion and jerk. Moreover, readjusting MG1 speed will delay MG1 torque recovery time. To avoid the problems appearing after upshift process, engine speed is always commanded to the optimum speedωMG1∗ during the shift process, which is also the target speed of MG1:(29)ωICE∗=ωMG1T=ωMG1∗.MG2 speed regulation target is the same as (24). MG1 command torque in single-motor mode to series-parallel mode is identical to (23). The derivation of T∗in series mode to series-parallel mode is similar to (19) and (22):(30)T∗=Tloss+Tloss22+JkωMG1p-ωMG1sωMG1p>ωMG1sTloss-Tloss22+JkωMG1s-ωMG1pωMG1p<ωMG1s,where ωMG1s is MG1 speed in series mode. Unlike the single-motor mode to series-parallel mode, T∗ in series mode to series-parallel mode may be positive or negative depending on whether ωMG1s is less than ωMG1p or not. The situation when T∗>0 is similar to Figure 4, while T∗<0 is shown in Figure 6.Figure 6
Variables changing curves in upshift speed regulation 2.


### 3.2.3. Downshift Speed Regulation

Only MG2 connects to the powertrain after downshift no matter in single-motor mode or in series mode. MG2 target speed can be obtained in (31), which is similar to conventional AMT:(31)ωMG1T=ωsT×K1×K2.MG1 speed does not need to be regulated during downshift process. MG1 only needs to make preparations to unload and put into target gear. In summary, the flow chart of shift speed regulation process is as shown in Figure7.Figure 7
The speed regulation phase’s flow chart.


## 3.2.1. The First Upshift Speed Regulation (Single-Motor Mode to Dual-Motor Mode)

In single-motor mode, Only MG2 propels the vehicle, while engine and MG1 are in idle state and do not output power at all:(12)ωMG1=ωICE=0.In dual-motor mode, MG1 and MG2 propel the vehicle together. One motor must be in speed control mode and the other in torque control mode to keep the system stable due to the features of planetary gear system. MG2 is chosen as the speed controlled motor because of its excellent speed adjustment performance. Then MG1 is in torque control mode as its torque regulation performance is good. The optimal combination of MG2 and MG1 speed of highest system efficiency (ωMG2∗,ωMG1∗) can be acquired based on two motors’ efficiency characteristic curves under different vehicle speed and vehicle demanded torque conditions. The calculation procedure is as follows.(1)
Set a combination of vehicle speed and demanded torque(Vss,TDmnd) as known quantities; then(13)TMG1=TDmnd×α1+α,(14)TMG2=TDmnd1+α.(2)
Given a series of MG1 speed (ωMG11,ωMG12,…,ωMG1n), the corresponding MG2 speed under Vss can be conducted (ωMG21,ωMG22,…,ωMG2n) from the relationship in (6):(15)ωMG2k=60Vss1+αig2πr-αωMG1kk=1,2,3,…,n.(3)
MG1 efficiencyηMG1k and MG2 efficiency ηMG2k are gained by making use of the obtained combination (ωMG1k,TMG1) and (ωMG2k,TMG2) to look up to MG1 and MG2 efficiency curves.(4)
If there is a combination(ωMG1i,TMG1,ηMG1i) or (ωMG2i,TMG2,ηMG2i), which meets the equation(16)ωMG1i×TMG1ηMG1i+ωMG2i×TMG2ηMG2i=min⁡ωMG1k×TMG1ηMG1k+ωMG2k×TMG2ηMG2k,i,k=1,2,…,n,then(ωMG1i,ωMG2i) is the speed optimal combination (ωMG1∗,ωMG2∗) under (Vss,TDmnd) conditions.(5)
Repeat the steps above to get all the optimal speed combination(ωMG1∗,ωMG2∗) under different vehicle speed and vehicle demanded torque conditions.After switching to neutral gear, set MG1 operating in torque controlled mode. Assume that MG1 command torque isTMG1T; the time from current speed to the target speed ωMG1raw is t1. MG1 unloads torque and prepares to put into the target gear when reaching the target speed. But MG1 speed will keep on rising up during the unload process because of its response delay until achieving the peak speed. Then it begins to drop slowly. Set the peak speed as ωMG1p and the period from ωMG1raw to ωMG1p as t2. Since MG1 has outstanding torque regulation performance, MG1 actual torque can be considered as achieving the command torque quickly by following a constant slope, as shown in Figure 5.Figure 5
Variables changing curves in upshift speed regulation 1.As MG1 reaches the peak speed, MG1 actual torque is close to zero and the speed change is gentle, which makes it the ideal optimal point.Set(17)ωMG1p=ωMG1∗.And the total MG1 speed regulation time istMG1: (18)tMG1=t1+t2.The speed regulation can be divided into two stages:0~t1 and t1~tMG1. Equation (19) can be obtained in each stage:(19)T-Tloss22k+Tt1-Tk-Tlosst1=JωMG1raw,T2-Tloss22k-TlossT-Tlossk=JωMG1p-ωMG1raw,t2=T-Tlossk.ThentMG1 is attained by solving the above equations: (20)tMG1=T-Tlossk+Tloss2-2TTloss-2JkωMG1p2kTloss-T,where T and Tloss denote MG1 command torque and friction torque; k is MG1 torque response slope.   J is MG1 equivalent rotational inertia.The assignment ofT should consider that if T is too large, even though t1 is short, the unloading process is long and speed increment is large. If T is too small, even though unloading time t2 is short, t1 will be long due to the small angular acceleration. tMG1 will be relatively long in either case. T∗ is presumed to be the optimal value of T, which meets the following equation: (21)fT∗,ωMG1p=min⁡tMG1.Take the partial derivative ofT in (20) and T∗ is obtained as follows:(22)∂tMG1∂T=Tloss2-2TTloss-2JkωMG1p2kTloss-T2-TkTloss-T=0,(23)T∗=Tloss+Tloss22+JkωMG1p.MG2 is set to operate in speed control mode on account of its fast response and regulation precision. By adjusting MG2 target speedωMG2T quickly, the output shaft speed can be coupled to ωsT exactly at the end of speed regulation.MG2 target speedωMG2T is(24)ωMG1T=ωMG2∗t≤tMG11+αωsT-αωMG1t>tMG1;namely, MG2 speed is regulated to optimum value ωMG2∗ prior to MG1 finishing torque regulation, which meets (9) as MG1 rises to the peak speed ωMG1∗. If (9) cannot be met during the whole MG1 speed regulation process, then MG2 target speed is modified to satisfy the coupling relationship as MG1 is free falling. The process is close to the shift speed regulation process in planetary gear systems with dual motors.


## 3.2.2. The Second Upshift Speed Regulation (Single-Motor Mode/Series Mode to Series-Parallel Mode)

In series-parallel mode, engine participates in propelling the vehicle. Taking the output shaft speedωs, vehicle demanded torque TDmnd, and engine power PICE as the known quantity, a three-dimensional function table is made. The object of the function is to acquire the highest combined efficiency of the engine and electrical system and meet the vehicle power requirement and reach SOC control target. The optimal combination (ωMG2∗,ωMG1∗) is gained by following the procedure below.(1) Set the combination(ωs,TDmnd,PICE) as the known quantity. Vehicle demanded power PDmnd=TDmnd×ωs.(2) Given a series of MG1 speed(ωMG11,ωMG12,…,ωMG1n), the corresponding MG2 speed can be obtained as (ωMG21,ωMG22,…,ωMG2n) under vehicle speed Vss condition by the following relationship:(25)ωMG2k=ωs×1+α-α×ωMG1kk=1,2,3,…,n.Engine speed is equal to MG1 speed.(3) Engine torque is given as follows:(26)TICE1,TICE2,TICE3,…,TICEn=PICEωMG11,PICEωMG12,PICEωMG13,…,PICEωMG1n.MG1 command torque is given as follows:(27)TMG11,TMG12,…,TMG1n=TDmnd×α1+α-TICE1,TDmnd×α1+α-TICE2,…,TDmnd×α1+α-TICEn.MG2 torque is given as follows:TMG2=TDmnd/(1+α).(4) MG1 efficiencyηMG1k, MG2 efficiency ηMG2k, and engine efficiency ηICEk are gained by making use of the obtained combinations (ωMG1k,TMG1),(ωMG2k,TMG2), and (ωICEk,TICE) to look up to MG1, MG2, and engine efficiency curves.(5) If there are combinations(ωMG1i,TMG1,ηMG1i), (ωMG2i,TMG2,ηMG1i), and (ωICEi,TICE,ηICEi) which meet the equation(28)ωMG1i×TMG1ηMG1i+ωMG2i×TMG2ηMG2i+γ×PICEηICEi=min⁡ωMG1k×TMG1ηMG1k+ωMG2k×TMG2ηMG2k+γ×PICEηICEki,k=1,2,…,n,where γ is the equivalent conversion factor from engine power to electric power, then (ωMG1i,ωMG2i) is the speed optimal combination (ωMG1∗,ωMG2∗) under (Vss,TDmnd) conditions.(6) Repeat the steps above to get all the optimal speed combination(ωMG1∗,ωMG2∗) under different vehicle speed, vehicle demanded torque, and engine power conditions.When entering series-parallel mode, clutch has to be engaged as soon as possible. Hence the speed difference between MG1 and engine should not be too big; otherwise engaging directly will result in severe abrasion and jerk. Moreover, readjusting MG1 speed will delay MG1 torque recovery time. To avoid the problems appearing after upshift process, engine speed is always commanded to the optimum speedωMG1∗ during the shift process, which is also the target speed of MG1:(29)ωICE∗=ωMG1T=ωMG1∗.MG2 speed regulation target is the same as (24). MG1 command torque in single-motor mode to series-parallel mode is identical to (23). The derivation of T∗in series mode to series-parallel mode is similar to (19) and (22):(30)T∗=Tloss+Tloss22+JkωMG1p-ωMG1sωMG1p>ωMG1sTloss-Tloss22+JkωMG1s-ωMG1pωMG1p<ωMG1s,where ωMG1s is MG1 speed in series mode. Unlike the single-motor mode to series-parallel mode, T∗ in series mode to series-parallel mode may be positive or negative depending on whether ωMG1s is less than ωMG1p or not. The situation when T∗>0 is similar to Figure 4, while T∗<0 is shown in Figure 6.Figure 6
Variables changing curves in upshift speed regulation 2.


## 3.2.3. Downshift Speed Regulation

Only MG2 connects to the powertrain after downshift no matter in single-motor mode or in series mode. MG2 target speed can be obtained in (31), which is similar to conventional AMT:(31)ωMG1T=ωsT×K1×K2.MG1 speed does not need to be regulated during downshift process. MG1 only needs to make preparations to unload and put into target gear. In summary, the flow chart of shift speed regulation process is as shown in Figure7.Figure 7
The speed regulation phase’s flow chart.


## 3.3. Synchronization Phase

Mechanical speed synchronization is executed by the synchronizer to put into the target gear from neutral gear in this phase, during which shift motor drives the synchronizer to reach the stroke range of the target gear. Hybrid control unit (HCU) adjusts the pulse duty ratio of 24 V voltage to control the power of shift motor in order to overcome the different situations. Moreover, PID control of position and velocity closed loop is utilized to solve the nonlinear and parameter uncertainty situation in mechanical synchronization. If the synchronization time exceeds normal default value, it means that motor stalling appears due to speed regulation failure or shift motor faults. Shift motor has to be stopped immediately at this moment. The shift process interrupts and enters fault mode, where the target gear is revised to neutral gear due to the fact that the resistance to neural gear is relatively small and no contact exists between synchronizer and powertrain in neural gear so as to protect the shift mechanism and check fault reason in park condition. After returning to neutral gear, the shift synchronizer can try to put into the target gear again up to three times. If three attempts all end in failure, then fault lamp is lightened and the gear fixes in neural gear. The flow chart of synchronization phase is shown in Figure8.Figure 8
The synchronization phase’s flow chart.


## 4. Experiments Validation

In order to prepare for the on-board road test, a hybrid electric system bench test-bed was built to debug and validate the basic characteristics of motors and vehicle function implementation, as shown in Figure9. It consists of coupling system (including two motors and transmission), DMCMs, dynamometer, battery, engine, and accessories.Figure 9
Bench test-bed for new hybrid electric system.


### 4.1. Motor Dynamic Characteristic Test on Bench Test-Beds

It can be concluded from (23) and (30) that parameters J, k, and Tloss must be confirmed to attain the optimal command torque T∗. As a series of MG1 free-fall curves under different initial speed conditions shown in Figure 10, in the initial period of time, all the MG1 speed curves are approximated to a straight line of the same slope in the shift speed range. The kinetic equation is shown as follows:(32)Tloss=JΔωΔt.Figure 10
MG1 free-fall speed curves.T
l
o
s
s can be obtained by MG1 torque in its stable speed control mode state. As verified by experiment, in MG1 speed range during shift process, Tloss is about 15 Nm. The slope of MG1 free-fall curves is around 19.4rad/s2 from Figure 10.J is 0.77kg∗m2 from (32). It is far more than the normal rotational inertia of rotors in permanent magnet motors. That is because MG1 transmission shaft is always linked to the ring gear in planetary gear system. Besides, planet gear and carrier are also rotating when MG1 rotates alone. Hence J is actually the sum of MG1 rotational inertia and planetary gear system equivalent rotational inertia. k is 2500 as motor torque response rate is 100 Nm/40 ms according to the motor control requirement. By calculating on the basis of the optimization algorithm mentioned above, ωMG1∗is 1200 rpm. ωMG1s is 1300 rpm during series mode to series-parallel mode.T
∗ is 509 Nm obtained from (23) in the first upshift speed regulation. To verify the validity of the torque value T∗, the relationships of total regulation time tMG1 and speed difference ΔωMG1 with unload speed ωMG1raw under different command torque conditions are recorded by experiments. The results are displayed in Figures 11 and 12.Figure 11
The curves ofωMG1raw and tMG1 under different TMG1T.Figure 12
The curves ofωMG1raw and ΔωMG1 under different TMG1T.It can be concluded thattMG1 and ΔωMG1 are interrestricted with each other from Figures 11 and 12. Short tMG1 requires TMG1T to be large enough, which will result in large ΔωMG1. On the contrary, small TMG1T signifies small ΔωMG1, but speed regulation process will be prolonged and the whole shift process will be postponed accordingly. By comparing the results of several sets of data, T∗ around 500 Nm can be regarded as the selected command torque comprehensively considering its fast speed regulation and acceptable increase of speed, which is also consistent with the calculation results from (23). As T∗ goes on increasing, the time contraction effect is not obvious, whereas ΔωMG1 increases significantly.In the second upshift speed regulation,T∗ is 158 Nm as calculated from (30). Reducing ΔωMG1 is considered as the main target at the moment due to the fact that the speed regulation time is relatively small.ω
M
G
1
r
a
w can be obtained from (33) after TMG1_T and ωMG1p are confirmed:(33)ωMG1raw=ωMG1p-Tloss-TMG1T22JMG1k.In practical engineering application,ωMG1raw can be determined by calibration tests directly. Given TMG1T=T∗ as the condition, ωMG1p can be recorded by unloading from a set of different ωMG1raw. A one-dimensional map was made on basis of the data. ωMG1raw can be gained by the known ωMG1p looking up the map backwards. Taking the first upshift mode as an example, T∗=509Nm; the map is shown in Figure 13.Figure 13
The peak speedωMG1p with unload speed ωMG1raw.Meanwhile, speed control test for MG2 speed characteristics was carried out to make sure that MG2 speed response is fast and accurate. A series of MG2 speed regulation tests were implemented throughout the speed range of shift process. The test results suggest that most of MG2 speed regulation ends in 0.5 s with high accuracy and regulating requirements are satisfied.The shift success rate was highest whenδ and ξ were determined to be 10 rpm and 40 rpm by carrying on the tests about output shaft speed difference in (9). The vibration and noise are also in acceptable level.


### 4.2. Simulation Test

To prove the effectiveness of the proposed method, a simulation test was operated based on AMESim (Advanced Modeling Environment for performing Simulations of engineering systems). Since the maximum impact degree during the shift process mainly relies on the speed regulation phase and synchronization phase, the upshift procedure from single-motor mode to dual-motor mode was chosen as the simulation object. The simulation architecture diagram of the proposed method was built based on the powertrain transmission solution demo of AMESim, as shown in Figure14.Figure 14
The simulation architecture diagram of the proposed method.The normal force applied on the sleeve of the synchronizer was obtained by the PID method to track an optimal sleeve displacement curve. Meanwhile a normal method without speed regulation phase was simulated to compare the effects, whose structure is shown in Figure15.Figure 15
The simulation architecture diagram of the normal method without speed regulation.The simulation results of both methods are listed in Figures16–18. The 0.3 s ahead in proposed method was occupied by speed regulation and the synchronization times in both methods are 0.3 s. Due to the fact that the synchronization time is constant (based on the displacement curve), the impact degree can reflect the drivability performance. It denotes the variation rate of vehicle longitudinal acceleration and embodies driver’s feeling about the impact load directly and quantitatively, as shown in the following equation:(34)J=dadt=d2vdt2.Figure 16
The simulation results of the normal method without speed regulation.Figure 17
The simulation architecture diagram of the proposed method.Figure 18
The impact degree curves of the proposed method and normal method with an optimal displacement curve.On the other hand, another simulation based on a constant force exerted on the sleeve of the synchronizer was operated. The results are shown in Figure19. The synchronization times of the proposed method and normal method are 0.354 s and 0.544 s, respectively. And the maximum impact degrees are 4.08 m/s3 and 20.7 m/s3, respectively.Figure 19
The results of the proposed method and normal method with a constant force.The two simulation results can verify that the speed regulation phase influences the drivability performance significantly and the proposed method can restrain the impact degree and accelerate the synchronization process remarkably.


### 4.3. Road Test

The vehicle carrying the new hybrid electric system is shown in Figure20.Figure 20
The vehicle carrying the new hybrid electric system.


#### 4.3.1. Upshift Test

Clutch states and gear states definitions are listed in Table2.Table 2
Definitions of clutch and gear states.
Clutch states
Definitions
Gear states
Definitions
1
Clutch is disengaged
1
At gear 1
2
Clutch is slipping
2
At gear 2
3
Clutch is engaged
0
At gear 0
3
In shift processConsidering the space limit, single-motor mode to dual-motor mode is chosen as the research object of upshift process. Clutch state and gear state are displayed in Figure21. The control commands are in strict accordance with the shifting process execution. The variation curves of speed and torque of two motors are shown in Figure 22. Engine is ignored, since it is in condition of rest.Figure 21
Clutch state and gear state in upshift process.Figure 22
The variation curves of speed and torque of two motors.It can be obtained that, after clutch disengages actually, the command gear turns to neutral gear and the shift mechanism begins to move towards the neutral gear. Then motor speed regulation begins in the neutral gear. MG1 command torque is 500 Nm, which is cleared to zero after MG1 actual speed reaches 969 rpm. The actual torque of MG1 decreases to zero when MG1 speed attains 1182 rpm. MG2 speed is 2952 rpm as the gear position just turns to the neutral gear. MG2 command speed is 0 rpm at the beginning. Then MG2 command speed direction changes from 0 to 1 when its speed is below 200 rpm. MG2 speed reverses as the speed direction is 1. The value of MG2 command speed is calculated by (24). It is first based on MG1 peak speed and its command speed changes as MG1 speed starts to free fall. After MG1 and MG2 speed regulation finishes, the relationship in (9) is satisfied. Then motor torque is cleared and mechanical synchronization begins. The shift mechanism starts to migrate into the target gear.The total shift process costs 1.08 s in the road test results. MG1 speed is 1170 rpm and MG2 speed is −321 rpm after speed regulation process finishes. The coupling speedωsT is 714 rpm and output shaft speed ωs is 690 rpm at this time. The speed difference is 24 rpm, which meets the requirement of (9).The degree of jerk during the shift process is recorded as well. The test results in Figure22 indicate that the maximum degree of jerk is 8.42 m/s3, which is smaller than Chinese standard (J<17.64m/s3). So the comfort requirements are met during the upshift process.


#### 4.3.2. Downshift Test

The downshift process mainly refers to MG2 speed regulation. MG1 and engine are at idle state. MG2 speed regulation process is shown in Figure23.Figure 23
The parameters curves during downshift process.MG2 speed direction is changed from reverse to forward in the neutral gear. The target speed is regulated according to (31). MG2 control mode is tuned from speed control to torque control after speed regulation. Then MG2 starts to unload by clearing MG2 torque to zero. When the actual torque reaches zero, mechanical synchronization starts.The total downshift time is 0.919 s. At the end of speed regulation, MG2 speedωMG2T is 2107 rpm. ωsT is 469 rpm by calculation in (2). Output shaft actual speed ωs is 457 rpm, which is 12 rpm less than ωsT. As a result, the speed regulation is effective and (9) can be met. Besides, the degree of jerk during downshift process also meets the smooth standard.Many methods are presented in other literatures about gear-shift process with different structures, such as the combined gear-shifting method assisted by motor speed feedback control [5], control strategy without disengaging clutch [16], and combined control algorithm based on feed-forward, bang-bang, and PID control [7]. The results are listed in Table 3. Compared with other approaches and structures, the new hybrid system’s structural change during gear-shift is more complex, but the jerk and power interruption time are less than others, which can validate that the proposed dynamic shift coordinated control can inhibit vehicle jerks and vibrations during short shift time intervals.Table 3
Upshift and downshift on-board experiments results.
Methods
Powertrain
Shift time (s)
Max jerk (m/s3)
Dynamic coordinated control
Conventional AMT & planetary gear train
Upshift 1.08
Upshift 8.42 m/s3
Downshift 0.92
Downshift 11.96 m/s3
Motor speed feedback control
AMT with dual clutch
Upshift 1.24
Upshift 13.2 rad/s3
Downshift 0.72–0.83
Downshift 82.5 rad/s3
Without disengaging clutch
Conventional AMT
1.35–1.41
9–12.3 m/s3
Combined algorithm
Conventional AMT
Upshift 1.20
—
Downshift 1.10


## 4.1. Motor Dynamic Characteristic Test on Bench Test-Beds

It can be concluded from (23) and (30) that parameters J, k, and Tloss must be confirmed to attain the optimal command torque T∗. As a series of MG1 free-fall curves under different initial speed conditions shown in Figure 10, in the initial period of time, all the MG1 speed curves are approximated to a straight line of the same slope in the shift speed range. The kinetic equation is shown as follows:(32)Tloss=JΔωΔt.Figure 10
MG1 free-fall speed curves.T
l
o
s
s can be obtained by MG1 torque in its stable speed control mode state. As verified by experiment, in MG1 speed range during shift process, Tloss is about 15 Nm. The slope of MG1 free-fall curves is around 19.4rad/s2 from Figure 10.J is 0.77kg∗m2 from (32). It is far more than the normal rotational inertia of rotors in permanent magnet motors. That is because MG1 transmission shaft is always linked to the ring gear in planetary gear system. Besides, planet gear and carrier are also rotating when MG1 rotates alone. Hence J is actually the sum of MG1 rotational inertia and planetary gear system equivalent rotational inertia. k is 2500 as motor torque response rate is 100 Nm/40 ms according to the motor control requirement. By calculating on the basis of the optimization algorithm mentioned above, ωMG1∗is 1200 rpm. ωMG1s is 1300 rpm during series mode to series-parallel mode.T
∗ is 509 Nm obtained from (23) in the first upshift speed regulation. To verify the validity of the torque value T∗, the relationships of total regulation time tMG1 and speed difference ΔωMG1 with unload speed ωMG1raw under different command torque conditions are recorded by experiments. The results are displayed in Figures 11 and 12.Figure 11
The curves ofωMG1raw and tMG1 under different TMG1T.Figure 12
The curves ofωMG1raw and ΔωMG1 under different TMG1T.It can be concluded thattMG1 and ΔωMG1 are interrestricted with each other from Figures 11 and 12. Short tMG1 requires TMG1T to be large enough, which will result in large ΔωMG1. On the contrary, small TMG1T signifies small ΔωMG1, but speed regulation process will be prolonged and the whole shift process will be postponed accordingly. By comparing the results of several sets of data, T∗ around 500 Nm can be regarded as the selected command torque comprehensively considering its fast speed regulation and acceptable increase of speed, which is also consistent with the calculation results from (23). As T∗ goes on increasing, the time contraction effect is not obvious, whereas ΔωMG1 increases significantly.In the second upshift speed regulation,T∗ is 158 Nm as calculated from (30). Reducing ΔωMG1 is considered as the main target at the moment due to the fact that the speed regulation time is relatively small.ω
M
G
1
r
a
w can be obtained from (33) after TMG1_T and ωMG1p are confirmed:(33)ωMG1raw=ωMG1p-Tloss-TMG1T22JMG1k.In practical engineering application,ωMG1raw can be determined by calibration tests directly. Given TMG1T=T∗ as the condition, ωMG1p can be recorded by unloading from a set of different ωMG1raw. A one-dimensional map was made on basis of the data. ωMG1raw can be gained by the known ωMG1p looking up the map backwards. Taking the first upshift mode as an example, T∗=509Nm; the map is shown in Figure 13.Figure 13
The peak speedωMG1p with unload speed ωMG1raw.Meanwhile, speed control test for MG2 speed characteristics was carried out to make sure that MG2 speed response is fast and accurate. A series of MG2 speed regulation tests were implemented throughout the speed range of shift process. The test results suggest that most of MG2 speed regulation ends in 0.5 s with high accuracy and regulating requirements are satisfied.The shift success rate was highest whenδ and ξ were determined to be 10 rpm and 40 rpm by carrying on the tests about output shaft speed difference in (9). The vibration and noise are also in acceptable level.


## 4.2. Simulation Test

To prove the effectiveness of the proposed method, a simulation test was operated based on AMESim (Advanced Modeling Environment for performing Simulations of engineering systems). Since the maximum impact degree during the shift process mainly relies on the speed regulation phase and synchronization phase, the upshift procedure from single-motor mode to dual-motor mode was chosen as the simulation object. The simulation architecture diagram of the proposed method was built based on the powertrain transmission solution demo of AMESim, as shown in Figure14.Figure 14
The simulation architecture diagram of the proposed method.The normal force applied on the sleeve of the synchronizer was obtained by the PID method to track an optimal sleeve displacement curve. Meanwhile a normal method without speed regulation phase was simulated to compare the effects, whose structure is shown in Figure15.Figure 15
The simulation architecture diagram of the normal method without speed regulation.The simulation results of both methods are listed in Figures16–18. The 0.3 s ahead in proposed method was occupied by speed regulation and the synchronization times in both methods are 0.3 s. Due to the fact that the synchronization time is constant (based on the displacement curve), the impact degree can reflect the drivability performance. It denotes the variation rate of vehicle longitudinal acceleration and embodies driver’s feeling about the impact load directly and quantitatively, as shown in the following equation:(34)J=dadt=d2vdt2.Figure 16
The simulation results of the normal method without speed regulation.Figure 17
The simulation architecture diagram of the proposed method.Figure 18
The impact degree curves of the proposed method and normal method with an optimal displacement curve.On the other hand, another simulation based on a constant force exerted on the sleeve of the synchronizer was operated. The results are shown in Figure19. The synchronization times of the proposed method and normal method are 0.354 s and 0.544 s, respectively. And the maximum impact degrees are 4.08 m/s3 and 20.7 m/s3, respectively.Figure 19
The results of the proposed method and normal method with a constant force.The two simulation results can verify that the speed regulation phase influences the drivability performance significantly and the proposed method can restrain the impact degree and accelerate the synchronization process remarkably.


## 4.3. Road Test

The vehicle carrying the new hybrid electric system is shown in Figure20.Figure 20
The vehicle carrying the new hybrid electric system.


### 4.3.1. Upshift Test

Clutch states and gear states definitions are listed in Table2.Table 2
Definitions of clutch and gear states.
Clutch states
Definitions
Gear states
Definitions
1
Clutch is disengaged
1
At gear 1
2
Clutch is slipping
2
At gear 2
3
Clutch is engaged
0
At gear 0
3
In shift processConsidering the space limit, single-motor mode to dual-motor mode is chosen as the research object of upshift process. Clutch state and gear state are displayed in Figure21. The control commands are in strict accordance with the shifting process execution. The variation curves of speed and torque of two motors are shown in Figure 22. Engine is ignored, since it is in condition of rest.Figure 21
Clutch state and gear state in upshift process.Figure 22
The variation curves of speed and torque of two motors.It can be obtained that, after clutch disengages actually, the command gear turns to neutral gear and the shift mechanism begins to move towards the neutral gear. Then motor speed regulation begins in the neutral gear. MG1 command torque is 500 Nm, which is cleared to zero after MG1 actual speed reaches 969 rpm. The actual torque of MG1 decreases to zero when MG1 speed attains 1182 rpm. MG2 speed is 2952 rpm as the gear position just turns to the neutral gear. MG2 command speed is 0 rpm at the beginning. Then MG2 command speed direction changes from 0 to 1 when its speed is below 200 rpm. MG2 speed reverses as the speed direction is 1. The value of MG2 command speed is calculated by (24). It is first based on MG1 peak speed and its command speed changes as MG1 speed starts to free fall. After MG1 and MG2 speed regulation finishes, the relationship in (9) is satisfied. Then motor torque is cleared and mechanical synchronization begins. The shift mechanism starts to migrate into the target gear.The total shift process costs 1.08 s in the road test results. MG1 speed is 1170 rpm and MG2 speed is −321 rpm after speed regulation process finishes. The coupling speedωsT is 714 rpm and output shaft speed ωs is 690 rpm at this time. The speed difference is 24 rpm, which meets the requirement of (9).The degree of jerk during the shift process is recorded as well. The test results in Figure22 indicate that the maximum degree of jerk is 8.42 m/s3, which is smaller than Chinese standard (J<17.64m/s3). So the comfort requirements are met during the upshift process.


### 4.3.2. Downshift Test

The downshift process mainly refers to MG2 speed regulation. MG1 and engine are at idle state. MG2 speed regulation process is shown in Figure23.Figure 23
The parameters curves during downshift process.MG2 speed direction is changed from reverse to forward in the neutral gear. The target speed is regulated according to (31). MG2 control mode is tuned from speed control to torque control after speed regulation. Then MG2 starts to unload by clearing MG2 torque to zero. When the actual torque reaches zero, mechanical synchronization starts.The total downshift time is 0.919 s. At the end of speed regulation, MG2 speedωMG2T is 2107 rpm. ωsT is 469 rpm by calculation in (2). Output shaft actual speed ωs is 457 rpm, which is 12 rpm less than ωsT. As a result, the speed regulation is effective and (9) can be met. Besides, the degree of jerk during downshift process also meets the smooth standard.Many methods are presented in other literatures about gear-shift process with different structures, such as the combined gear-shifting method assisted by motor speed feedback control [5], control strategy without disengaging clutch [16], and combined control algorithm based on feed-forward, bang-bang, and PID control [7]. The results are listed in Table 3. Compared with other approaches and structures, the new hybrid system’s structural change during gear-shift is more complex, but the jerk and power interruption time are less than others, which can validate that the proposed dynamic shift coordinated control can inhibit vehicle jerks and vibrations during short shift time intervals.Table 3
Upshift and downshift on-board experiments results.
Methods
Powertrain
Shift time (s)
Max jerk (m/s3)
Dynamic coordinated control
Conventional AMT & planetary gear train
Upshift 1.08
Upshift 8.42 m/s3
Downshift 0.92
Downshift 11.96 m/s3
Motor speed feedback control
AMT with dual clutch
Upshift 1.24
Upshift 13.2 rad/s3
Downshift 0.72–0.83
Downshift 82.5 rad/s3
Without disengaging clutch
Conventional AMT
1.35–1.41
9–12.3 m/s3
Combined algorithm
Conventional AMT
Upshift 1.20
—
Downshift 1.10


## 4.3.1. Upshift Test

Clutch states and gear states definitions are listed in Table2.Table 2
Definitions of clutch and gear states.
Clutch states
Definitions
Gear states
Definitions
1
Clutch is disengaged
1
At gear 1
2
Clutch is slipping
2
At gear 2
3
Clutch is engaged
0
At gear 0
3
In shift processConsidering the space limit, single-motor mode to dual-motor mode is chosen as the research object of upshift process. Clutch state and gear state are displayed in Figure21. The control commands are in strict accordance with the shifting process execution. The variation curves of speed and torque of two motors are shown in Figure 22. Engine is ignored, since it is in condition of rest.Figure 21
Clutch state and gear state in upshift process.Figure 22
The variation curves of speed and torque of two motors.It can be obtained that, after clutch disengages actually, the command gear turns to neutral gear and the shift mechanism begins to move towards the neutral gear. Then motor speed regulation begins in the neutral gear. MG1 command torque is 500 Nm, which is cleared to zero after MG1 actual speed reaches 969 rpm. The actual torque of MG1 decreases to zero when MG1 speed attains 1182 rpm. MG2 speed is 2952 rpm as the gear position just turns to the neutral gear. MG2 command speed is 0 rpm at the beginning. Then MG2 command speed direction changes from 0 to 1 when its speed is below 200 rpm. MG2 speed reverses as the speed direction is 1. The value of MG2 command speed is calculated by (24). It is first based on MG1 peak speed and its command speed changes as MG1 speed starts to free fall. After MG1 and MG2 speed regulation finishes, the relationship in (9) is satisfied. Then motor torque is cleared and mechanical synchronization begins. The shift mechanism starts to migrate into the target gear.The total shift process costs 1.08 s in the road test results. MG1 speed is 1170 rpm and MG2 speed is −321 rpm after speed regulation process finishes. The coupling speedωsT is 714 rpm and output shaft speed ωs is 690 rpm at this time. The speed difference is 24 rpm, which meets the requirement of (9).The degree of jerk during the shift process is recorded as well. The test results in Figure22 indicate that the maximum degree of jerk is 8.42 m/s3, which is smaller than Chinese standard (J<17.64m/s3). So the comfort requirements are met during the upshift process.


## 4.3.2. Downshift Test

The downshift process mainly refers to MG2 speed regulation. MG1 and engine are at idle state. MG2 speed regulation process is shown in Figure23.Figure 23
The parameters curves during downshift process.MG2 speed direction is changed from reverse to forward in the neutral gear. The target speed is regulated according to (31). MG2 control mode is tuned from speed control to torque control after speed regulation. Then MG2 starts to unload by clearing MG2 torque to zero. When the actual torque reaches zero, mechanical synchronization starts.The total downshift time is 0.919 s. At the end of speed regulation, MG2 speedωMG2T is 2107 rpm. ωsT is 469 rpm by calculation in (2). Output shaft actual speed ωs is 457 rpm, which is 12 rpm less than ωsT. As a result, the speed regulation is effective and (9) can be met. Besides, the degree of jerk during downshift process also meets the smooth standard.Many methods are presented in other literatures about gear-shift process with different structures, such as the combined gear-shifting method assisted by motor speed feedback control [5], control strategy without disengaging clutch [16], and combined control algorithm based on feed-forward, bang-bang, and PID control [7]. The results are listed in Table 3. Compared with other approaches and structures, the new hybrid system’s structural change during gear-shift is more complex, but the jerk and power interruption time are less than others, which can validate that the proposed dynamic shift coordinated control can inhibit vehicle jerks and vibrations during short shift time intervals.Table 3
Upshift and downshift on-board experiments results.
Methods
Powertrain
Shift time (s)
Max jerk (m/s3)
Dynamic coordinated control
Conventional AMT & planetary gear train
Upshift 1.08
Upshift 8.42 m/s3
Downshift 0.92
Downshift 11.96 m/s3
Motor speed feedback control
AMT with dual clutch
Upshift 1.24
Upshift 13.2 rad/s3
Downshift 0.72–0.83
Downshift 82.5 rad/s3
Without disengaging clutch
Conventional AMT
1.35–1.41
9–12.3 m/s3
Combined algorithm
Conventional AMT
Upshift 1.20
—
Downshift 1.10


## 5. Conclusion

A new type of hybrid electric system is utilized to conduct the experiments of shift control and verify the validity of the proposed dynamic shift coordinated control. Motor active speed regulation is required to keep the speed difference between two ends of synchronizer under acceptable level to meet the demand of vibrations and shift success rate. The simulation and road test results proved that, compared with other approaches, the degrees of jerks in both upshift and downshift processes were restrained more effectively, with the shift time interval being shorter as well. Besides, the robustness in conventional AMT and planetary gear train can be validated by tests results during downshift and upshift processes. So far, the situation where vehicle speed dramatically changes during shift process has not been taken into consideration, especially shift in ramp ways. This is also the research direction and focus in the future.



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*Source: 2716251-2017-07-11.xml*