Dynamic Coordinated Shifting Control of Automated Mechanical Transmissions without a Clutch in a Plug-In Hybrid Electric Vehicle

On the basis of the shifting process of automated mechanical transmissions (AMTs) for traditional hybrid electric vehicles (HEVs), and by combining the features of electric machines with fast response speed, the dynamic model of the hybrid electric AMT vehicle powertrain is built up, the dynamic characteristics of each phase of shifting process are analyzed, and a control strategy in which torque and speed of the engine and electric machine are coordinatively controlled to achieve AMT shifting control for a plug-in hybrid electric vehicle (PHEV) without clutch is proposed. In the shifting process, the engine and electric machine are well controlled, and the shift jerk and power interruption and restoration time are reduced. Simulation and real car test results show that the proposed control strategy can more efficiently improve the shift quality for PHEVs equipped with AMTs.


Introduction
Compared with traditional hybrid electric vehicles (HEVs), plug-in hybrid electric vehicles (PHEVs) have larger capacity energy storage device which can be charged from the grid, increasing the pure OPEN ACCESS electric driving distances, and greatly decreasing fuel consumption and exhaust emissions [1][2][3].PHEVs, which have been listed in the development plans for new generation automobiles by many countries, will be one of the important technical ways to achieve vehicle energy savings and emission reductions.
In vehicles equipped with an automated mechanical transmission (AMT) which has a fixed transmission ratio, there exists the problem of shift jerk and inevitable power interruptions due to its structure.By using the auxiliary dynamic action of the motor, the power source can be quickly controlled in the shifting process, and the shift quality can be improved for a hybrid electric vehicle equipped with AMT.To improve the shift quality and reduce the power interruption time and synchronize torque during the shifting process, Baraszu et al. [4] used the motor to drive the vehicle directly for shifting in parallel hybrid electric vehicles equipped with an AMT, which reduced the power interruption time during the AMT shifting process.Jo et al. [5] proposed a control strategy to reduce the synchronous speed difference of the synchronizer and synchronization time by controlling the engine and motor.Liao and Zhang [6] studied the shifting process of an HEV system in which the motor was installed at the back of the clutch, and introduced a control strategy to reduce the synchronizing torque of the synchronizer and synchronization time by controlling the torque and speed of the engine and motor.
However, in the AMT shifting process, the transmission ratio will change.Input speed and output speed of the clutch are different due to the ratio change and jerk occurs.Generally, the method for reducing shift jerk is to extend the friction time of the clutch for traditional AMT vehicles, but this can increase the power restoration time and decrease the service life of the clutch.Therefore, in order to extend the service life of the clutch and shift without releasing the clutch, Petterson et al. [7] proposed a shifting method without the use of clutch in which the engine torque was controlled to achieve gear shifting automatically.The Eaton company designed a AutoShift transmission [8] for shifting without releasing the clutch in which a braking device (the eddy current brake) installed in the transmission and the engine were controlled to achieve engine speed regulation, which can achieve the synchronization of shifting driving and driven parts to complete the shifting action.
This paper studies the single driveshaft parallel hybrid electric vehicle in which the motor is installed in front of the AMT.The role of the inertia brake installed in the AutoShift transmission can be achieved by controlling the motor torque.In the shifting process, torque and speed of the engine and motor are well controlled to reduce the shift jerk and power restoration time.On the basis of analysis of the shifting process, a vehicle dynamic model is built up, the dynamic characteristics of each phase of shifting process are analyzed, and a control strategy in which torque and speed of the engine and electric machine are coordinatively controlled to achieve AMT shifting control for PHEVs without clutches is proposed.The simulation platform of a parallel HEV with AMT is built up in Matlab/Simulink software, and a real car test is completed simultaneously.The test results show that the proposed control strategy can more efficiently reduce the shift jerk and power interruption and restoration time, and improve the shifting quality.
(2) The Shift Jerk The shift jerk is the rate of change of vehicle longitudinal acceleration, which is the important parameter for evaluating the shifting quality.The equation of shift jerk is as follows: where a(t) is the vehicle longitudinal acceleration, and v(t) is the vehicle longitudinal velocity.

Dynamic Model for AMT Shifting
The process of AMT shifting without a clutch can be divided into five phases  where C is the mode clutch, which is connected in hybrid driving mode and disconnected in motor driving mode; S is the synchronizer, J e is the equivalent moment of inertia of the engine and the driving parts of the clutch, J m is the moment of inertia of the motor, J c is the equivalent moment of inertia of the driven parts of the clutch and the transmission input shaft, J t_o is the equivalent moment of inertia of the transmission output shaft, T e is the engine torque, ω e is the engine speed, T m is the torque transmitted by the motor, T c is the torque transmitted by the clutch, ω c is the speed of the driven parts of the clutch, T t_r is the external resistance torque of the transmission output shaft, ω t_o is the speed of the transmission output shaft, i g(n) is the transmission ratio of the n gear (n = 1st, 2nd, …, 5th), T t_io is the torque transmitted from the input shaft to the output shaft, T t_oi is the torque transmitted from the output shaft to the input shaft.The relationship between T t_oi and T t_io is as follows: (3) where η T is the transmission efficiency.

Dynamic Analysis of AMT Shifting without Clutch
Taking the upshift from 1st to 2nd gear as an example, the dynamic characteristics of the shifting process are analyzed [11][12][13].In the normal driving and shifting process without clutch, there is . When the vehicle is driving on the 1st gear, the i g(n) is i 1 , and the dynamic equations can be expressed as follows: where i 0 is the main reducer ratio, r is the wheel radius.The equation of shift jerk is as follows: Due to the short shift time, the external resistance is assumed to be constant when the shifting action is performed on flat road, i.e.: So Equation ( 5) can be simplified as follows: From the Equation ( 7) we can know that the shift jerk value is related to the change of the synthetic torque of the engine and motor.According to the reference value of the shift jerk, the equation of value range for the synthetic torque of the engine and motor can be obtained as follows: where j ref is reference value of the shift jerk.The recommended values are 10 m/s 3 and 17.64 m/s 3 respectively in Germany and China.

Dynamic Analysis of Pre-Shifting
The dynamic characteristics of this phase are the same as that of normal driving.When the transmission input torque becomes zero, the transmission can shift off to the neutral gear.Otherwise, the engine speed will increase sharply due to the abrupt decrease of the load.Additionally, when the _ _ ( ) meshing gears are loaded, shifting off can lead to excessive wear of the gear faces.Shifting off can be easily achieved without excessive wear of the gear faces when zero torque is transmitted to the driving shaft of the synchronizer.

Dynamic Analysis after Shifting off
The power is interrupted after shifting off.In this phase, the transmission does not transmit the torque, i.e., T t_io = 0.The equations of kinematics and dynamic relationship are as follows:

Dynamic Analysis of Synchronization
Because the speed regulating performance of the motor is better than the engine, the motor is used to adjust the speed of the driving parts for the synchronizer.
(1) The active synchronization of the motor In this phase, the dynamic equations of the input parts of the transmission are as follows:   where ω 1 is the input speed of the transmission before synchronization, ω 2 is the input speed of the transmission after synchronization.
In the synchronizing process, the engine and motor torque do not change, so Equation ( 10) can be simplified as follows: where ω t_o1 is the output speed of the transmission before synchronization, ω t_o2 is the output speed of the transmission after synchronization.
In the shifting process, the change of vehicle speed is very small, so we can consider ω t_o1 is approximately equal to ω t_o2 , so the equations of the input speed relationship are as follows: The synchronizing process includes two phases: the active synchronization of the motor and the synchronization of the synchronizer.The equations of speed difference of the driving and driven parts for the synchronizer are as follows: where ∆ω t_o1 is the speed difference removed by the motor, ∆ω t_o2 is the speed difference removed by the synchronizer.
Thus, using Equations ( 11) and ( 13), the active synchronization time of the motor is: (2) The synchronization of the synchronizer In this phase, the dynamic equations of the input parts of the transmission are as follows: The equation of the synchronizing torque is as follows: where T syn is the synchronizing torque in the synchronizer cone, F a is the shifting force applied to the synchronizer, R is the average effective radius, f is the friction coefficient between the friction surfaces of the ring and the ring gear, and α is the cone angle of the ring.Using the Equations ( 15) and ( 16), we can obtain that: The synchronization time of the synchronizer is: The total synchronization time of the synchronizing process is: In traditional vehicles, the only way of reducing the synchronization time is to increase the synchronizing torque in the synchronizer or the shifting force applied to the synchronizer.As shown in Equation ( 19), for HEVs, the motor can output a large synchronizing torque to remove the larger speed differences of the synchronization process.

Shift on
After the synchronization, the speed difference of the driving and driven parts of synchronizer is zero.The shift on action can be performed soon after the output torques of the engine and motor are zero.Shifting on can be easily achieved when zero torque is transmitted to the driving shaft of the synchronizer.

Restoring the Engine and Motor Torque
After shifting, the engine and motor torque should be restored to the commanded level at an appropriate rate to avoid affecting the shift quality.

Coordinated Torque Control of the Engine and Motor
To meet the needs of the shifting control, the engine and motor output torques are coordinately controlled to the target torques.As shown in Figure 3, the target output torque for the engine is determined by the engine map data in the current state.By calculating the throttle opening in the current state and the actual limited throttle opening after a change, the actual engine output torque can be estimated [13,14].
(1) The target throttle opening θ e_tar According to the vehicle demand torque, the vehicle controller calculates the corresponding target engine output torque in the current state.In the steady condition, through the accurate bench calibration, the engine output torque is determined by the engine speed and the target throttle opening, i.e.: (2) The engine output torque on the limited throttle opening state According to the engine output torque in the current state and the target throttle opening θ e_tar , the variable quantity ∆θ of the throttle opening needs to be limited.According to the limited throttle opening θ e_act , the actual output torque for the engine can be calculated: Energies 20 (3) The a The vehi according to output torqu

Shifting
Based on speed of the proposed as ncludes the off, the spee shifting on, t  (3) As the throttle opening is kept constant, the engine output torque can be obtained from the curve of steady output torque and speed acquired from the engine controller.(4) Based on the above engine output torque, the total output torque of the engine and the motor is controlled to be zero by controlling the motor output torque.( 5) The shifting off action can be performed soon after the total output torque of the engine and the motor becomes zero.

The Speed Synchronization Control
After shifting off, the input speed of the transmission can be adjusted to the target speed by regulating the motor speed.The synchronization process is completed when the speed difference of the driving and driven parts for synchronizer is zero.

The Coordinated Control of the Engine and Motor Torque before Shifting on
To improve the shift quality and reduce the shift jerk, the shifting on action can be performed only when the input torque of the transmission is zero.So the following actions will be performed: (1) After the speed synchronization, the operating mode of the electric machine switches from the motor to the generator.(2) The throttle opening is kept on the threshold value α min , the engine output torque can be obtained from the curve of steady output torque and speed acquired from the engine controller.(3) Based on the above engine output torque, the total output torque of the engine and the motor is controlled to be zero by controlling the motor output torque.(4) The shifting on action can be performed soon after the total output torque of the engine and the motor becomes zero.

The Engine and Motor Torque Restoration after Shifting
After shifting, the engine and motor torque should be restored to the commanded level at an appropriate rate to avoid affecting the quality of the shift.

Simulation Analysis
Based on the Matlab/Simulink software, a PHEV simulation model is built up to analyze the above discussed shifting control strategy [15].The vehicle and powertrain parameters are shown in Table 1.The diagram of the PHEV simulation model, which includes the driver model, the control system model, the engine model, the motor model, the transmission model, the battery model and the vehicle dynamic model, is shown in Figure 5. ulation resul in Figure 6 ease to the t et to zero to n is in the u etween driv When the sh the motor, uration is a ompleted, w ion.
Figure structu [10]: (1) decreasing the engine and motor torque; (2) shift off; (3) adjusting engine and motor speed; (4) shift on; (5) restoring the engine and motor torque.To analyze the dynamic characteristics of each phase of the shifting process, a dynamic model for AMT shifting without a clutch is built up as shown in Figure 2.

Figure 2 .
Figure 2. Dynamic model for AMT shifting without a clutch.

Figure 4 .
Figure 4. Flow chart of AMT shifting control without clutch.

Table 1 .
The vehicle and powertrain parameters.