Optimal Design of Power-On Downshift Control of Series-Parallel Hybrid Transmission Based on Motor Active Speed Regulation

Abstract

Multi-speed transmission is the main development direction of hybrid transmission, which has brought higher shift quality requirements than traditional fuel vehicle transmission. However, there is less research on the shifting control of hybrid transmission, especially for the shifting control of dedicated hybrid transmission (DHT), which uses the wet clutch as a shift element. This paper studies the power-on downshift process of a two-speed series-parallel hybrid transmission, proposes a shifting control strategy based on motor active speed regulation, and deeply analyzes the causes of maximum impact during the shifting process. The results show that the reverse torque produced in the process of eliminating the remaining slip is the root cause of the maximum impact. On this basis, two optimization strategies are proposed to reduce the shift impact and improve the shift quality. The simulation results show that the proposed optimization strategies can effectively suppress the shift impact. In the meanwhile, for any control pressure of the OG (off-going) clutch in the speed phase within the range of (2.44–2.53 bar), a high shift quality in which the maximum impact is controlled lower than 10 m/s³ can be achieved, which has high engineering value and practical significance.

1. Introduction

In recent years, the proportion of new energy vehicle sales in the total vehicle sales in China has increased year by year, and the electrification of the vehicle has become an irreversible development trend, which means the transformation and upgrading of the automotive industry. As an important part of new energy vehicles, hybrid electric vehicles (HEVs), which are defined as the best transition solution from traditional fuel vehicles to pure electric vehicles, will dominate the auto market in the coming decades. Therefore, the related technologies of hybrid systems, such as configuration synthesis [1,2], structural parameter optimization [3,4], mode switching [5,6,7,8,9], and energy management [10,11,12], have been widely studied and applied.

The series-parallel hybrid system takes into account the characteristics of both series and parallel hybrid systems and can adapt to more complex driving conditions. It has become a mainstream hybrid system scheme in the current market, especially in the domestic market. Some scholars have systematically compared and analyzed the series-parallel and series hybrid systems in different vehicle types and driving cycles, which have different design parameters and have been unified into the same dimension. The results show that the series-parallel hybrid system has economic and dynamic advantages over the series hybrid system. This advantage becomes increasingly significant as vehicle weights and power demands increase [13].

Multi-speed transmission is the main development direction of hybrid transmission, and it is the inevitable demand to optimize the working area of power components and improve the power performance and fuel consumption of the vehicle. Studies have shown that the structural scheme with multiple gears can optimize the working point distribution area of the power source and improve the power performance and fuel economy to varying degrees [14]. Domestic hybrid systems that have been released in recent years, such as Geely’s Thor, GWM’s Lemon, GAC’s GMC2.0, and Chery’s CHERY POWER, are multi-speed series-parallel hybrid systems. Well-known international enterprises, such as Toyota [15] and General Motors [16], have also launched multi-speed hybrid systems, which are carried on their respective high-end models, improving the dynamic performance greatly.

The development of multi-speed hybrid transmission will inevitably bring the shifting control requirements. Especially in the era of automotive electrification, higher requirements for shift quality are put forward. The shifting control of the hybrid transmission inherits some technical features from the traditional fuel vehicle transmission [17,18] and produces new technical requirements at the same time. Among them, the most typical requirement is that, with multiple power sources, the speed matching and torque coordination control between them need to be more considered during the shifting process. This situation not only brings greater challenges but also provides a new idea for the shifting control—that is, letting the motor participate in the shifting process actively, which can make full use of the characteristics of rapid response and accurate control of motor torque to improve the shift quality. However, there is less research on the shifting control of hybrid transmission, especially for the shifting control of dedicated hybrid transmission (DHT), which uses the wet clutch as a shift element. On the one hand, the relevant research objects are primarily focused on AMT-based hybrid systems [19,20,21,22]. On the other hand, the relevant research on clutch control mainly focuses on engine starting process control [23,24,25,26,27,28,29] and torque coordination control during mode switching [30,31,32,33,34,35,36], most of which only involve a single clutch control. This paper studies the power-on downshift process of a two-speed series-parallel hybrid transmission, proposes a shifting control strategy based on motor active speed regulation, and deeply analyzes the causes of maximum impact during the shifting process. On this basis, two optimization strategies are proposed to reduce the shift impact and improve the shift quality. The simulation results show that the proposed optimization strategies can effectively suppress the shift impact, which has high engineering value and practical significance.

The organization of this paper is as follows: In Section 2, the structure of the hybrid system is analyzed, and the dynamic model related to the shifting process is built. In Section 3, a shifting control strategy based on motor active speed regulation is proposed, which is needed to determine the motor control torque and clutch control pressure at different stages of the shifting process. The influence of the key parameter on the shifting results is also analyzed. In Section 4, the proposed strategy is simulated with Simulink, and the mechanism of impact during the shifting process is analyzed in detail. On this basis, two optimal control strategies to suppress the impact are proposed and simulated and verified with the same software. In Section 5, the conclusions of the shifting control strategies are presented.

2. Structure and Dynamic Model of Hybrid System

The research object of this paper is a two-speed series-parallel hybrid system, as shown in Figure 1, including an engine, clutch HC, motor MG1, motor MG2, and a two-speed transmission formed by a planetary row, clutch C, and brake B. The planetary row takes ring gear as the input and a carrier as the output, and the hybrid transmission takes the shaft of gear Z4 as the output shaft, which is connected with the driving axle by gears Z6Z7. The engine is connected with the ring gear by HC, MG1 is connected with the ring gear by gears Z1Z2, the carrier is connected with the output shaft by gears Z3Z4, and MG2 is connected with the output shaft by gears Z5Z4.

Figure 2 shows the drivetrain model of the two-speed series-parallel hybrid system. In this model, the engine is simplified to a spring–damper system, and the motor MG1 and MG2 are expressed as certain rotating inertia under the action of the control torque. In the two-speed transmission model, each element is simplified to certain rotating inertia and connects with the planetary row model, which only represents the kinematic relationship among the planetary elements. Since this study is focused on the shifting process, which will be little affected by the resistance of the tire and vehicle, the tire and vehicle are modeled as certain rotating inertia, and the output torque of the hybrid system T_out acts on the tire and vehicle through the spring–damper system.

2.1. Two-Speed Transmission

When the clutch HC is closed, the following equations can be obtained:

$${\omega }_R={\omega }_{eng}=\frac{{\omega }_{MG1}}{i_{12}}$$

(1)

$$T_{in}=T_{eng}+T_{MG1}{i}_{12}$$

(2)

where ${\omega }_R$, ${\omega }_{eng},$ and ${\omega }_{MG1}$ are the ring gear speed, engine speed, and MG1 speed, respectively, $T_{in}$ is the input torque of the planetary row, $T_{eng}$ and $T_{MG1}$ are the output torque of the engine and MG1, respectively, and $i_{12}$ is the gear ratio of Z1Z2.

According to the kinematic and dynamic equations of the planetary row, as the following equations show:

$${\omega }_R+K{\omega }_S-\left(1+K\right){\omega }_C=0$$

(3)

$$T_C:T_S:T_R=-\left(1+K\right):K:1$$

(4)

where $K$ is ratio of teeth number between the sun gear and ring gear; ${\omega }_S$ and ${\omega }_C$ are the sun gear speed and carrier speed, respectively; and $T_C$, $T_S,$ and $T_R$ are the internal torque of the carrier, sun gear, and ring gear, respectively.

When the vehicle is in first gear, the brake B is locked and clutch C is opened, which brings ${\omega }_S=0$, and then, the following equation can be obtained according to Equation (3):

$${\omega }_R=\left(1+K\right){\omega }_C$$

(5)

If the towing torque is not considered when the clutch is opened, the transmission torque of these two clutches can be calculated by:

$$\left\{\begin{array}{c}{T}_{C1}=0 \\ T_B=K{T}_{in}\end{array}\right.$$

(6)

where $T_{C1}$ and $T_B$ are the transmission torque of clutch C and brake B, respectively.

When the vehicle is in second gear, the clutch C is locked and brake B is opened, which brings ${\omega }_R={\omega }_S$, and then, Equation (3) is changed to:

$${\omega }_R={\omega }_S={\omega }_C$$

(7)

The transmission torque of these two clutches can be calculated by:

$$\left\{\begin{array}{c}{T}_{C1}=\frac{K}{K+1}{T}_{in}\\ T_B=0 \end{array}\right.$$

(8)

The lever diagram of the downshift process is shown in Figure 3.

According to the above analysis, it can be seen that, during the downshift, clutch C is the OG (off-going) clutch, which is defined as the clutch that changes from a closed state to an open state during the shifting process, and brake B is the OC (oncoming) clutch, which is defined as the clutch that changes from an opened state to a closed state during the shifting process.

2.2. Motor Speed Regulation Control

During the shifting process, the motor MG1 is controlled by the PI controller, according to the slip of target gear $\Delta \omega$, which can be calculated by:

$$\Delta \omega ={\omega }_{in}-\frac{{\omega }_{out}}{i_{tgt}}$$

(9)

where ${\omega }_{in}$ is the input speed of the hybrid transmission, ${\omega }_{out}$ is the output speed of the driving axle, and $i_{tgt}$ is the transmission ratio of the target gear.

The control torque of the PI controller is:

$$T_{MG1\_PI}=P·\left|\Delta \omega \right|+I·\int \left|\Delta \omega \right|dt$$

(10)

where P and I are the proportional and integral factors of the PI controller, respectively.

Figure 4 shows the comparison between the $\Delta \omega$ and OC clutch slip. As shown in Figure 4, $\Delta \omega$ can reflect the changing trend of the OC clutch slip, but the value is not equal. When upshifting, $\Delta \omega >0$; when downshifting,$\Delta \omega <0$; when there is no shift command, $\Delta \omega =0$. In this paper, $\Delta \omega$ is adopted to be the input variable of the PI controller but not the OC clutch slip, which is because the clutch slip is difficult to measure directly in practice.

According to Equation (10), after $\Delta \omega$ becomes zero during the shifting process, the integrator should stop working and output a constant value. That is not suitable for the actual shift control requirements. When the speed regulation is completed, the control torque of the motor needs to be 0. Therefore, the following setting is made: at the end of the speed regulation, when $\Delta \omega <50 \mathrm{rpm}$, stop the integrator and set the integrator output to 0.

By performing a series of filtering and amplification processing on $T_{MG1\_PI}$, the control torque of motor MG1 $T_{MG1\_req}$ can be gotten. Due to the physical characteristics of the motor, there will be a certain delay between the real torque and control torque. The comparison among these three torque values is presented in Figure 5.

In addition, according to the shifting control requirements, the PI controller is only worked in the speed phase stage and turned off in other stages of the shifting process. That will help to improve the stability of the shifting process.

2.3. Clutch Control

The transmission torque of the clutch in the slipping state can be calculated by:

$$T_{CL}=\mu N{R}_m·\max \left[\left(P_{act}-P_{KP}\right),0\right]$$

(11)

$$R_m=\frac{2\left(R_0^3-R_i^3\right)}{3\left(R_0^2-R_i^2\right)}$$

(12)

where $\mu$ is the friction coefficient, $N$ is the number of friction surfaces, $R_m$ is the equivalent radius of the friction surface, $R_0$ and $R_i$ are the outer and inner radius of the friction surface, respectively, $P_{act}$ is the real pressure of the clutch, $P_{KP}$ is the kiss point pressure of the clutch. In this paper, $P_{KP}=1.5 \mathrm{bar}$.

According to Equation (11), the critical control pressure $P_{cri}$, which is the minimum pressure to ensure the clutch keeps a closed state, can be calculated by:

$$P_{cri}=\frac{T_{CL}}{\mu N{R}_m}+P_{KP}$$

(13)

In addition, the slipping work produced by the clutch is an important index to evaluate the shift quality, which can be calculated by:

$$W_{CL}={{\displaystyle \int }}_{t_0}^{t_1}{T}_{CL}\Delta {\omega }_{CL}dt$$

(14)

where $t_0$ and $t_1$ are the start time and end time of the shifting process, respectively, and $\Delta {\omega }_{CL}$ is the slip of the clutch.

3. Control Strategy Based on Motor Active Speed Regulation

The core of the shifting control strategy based on motor active speed regulation is to realize the fast and accurate matching of clutch speed through the motor active speed regulation control, so as to realize the fast and stable shifting process. The shifting process is divided into the following four stages: filling phase (FL), speed phase (SP), torque phase (TQ), and locking phase (LC). The control strategies in different stages are as follows:

Filling phase: At the beginning, set the OC clutch pressure to fast filling pressure $P_{FL}$ and reduce it to $P_{KP}$ a moment later (about 50~80 ms), so as to eliminate the empty travel of the piston. At the same time, rapidly reduce the OG clutch pressure to a certain value $P_1$, which is slightly higher than $P_{cri}$ of the OG clutch, so that the torque capacity of the OG clutch is closed to the current transmission torque.

Speed phase: Hold the OC clutch pressure at $P_{KP}$ and reduce the OG clutch pressure to $P_2$, which is slightly lower than $P_{cri}$. According to the absolute value of $\Delta \omega$, motor MG1 is controlled to accelerate the ring gear by the PI controller, so as to eliminate the OC clutch slip quickly. When $\left|\Delta \omega \right|$ is lower than the set value, which is defined as the threshold of entering the torque phase, the speed phase ends and the torque phase starts. In addition, in order to protect the clutch from excessive friction and improve the service life, the maximum allowable sliding time is set. When the sliding time exceeds the set value, it is forced to enter the torque phase.

Torque phase: Reduce the OG clutch pressure to $P_3$ and increase the OC clutch pressure to $P_4$, so as to complete the torque exchange between clutches, where $P_3$ is slightly lower than $P_{KP}$, and $P_4$ is slightly higher than $P_{cri}$ of the OC clutch.

Locking phase: Rapidly increase the OC clutch pressure to the locking pressure while rapidly decreasing the OG clutch pressure to zero.

The change of the clutch control pressure at different shifting stages is shown in Figure 6.

During the shifting process, the key control parameter is the OG clutch control pressure $P_2$ in the speed phase. Calculate the OG clutch transmission torque $T_{CL}$ at this moment according to Equations (2) and (8), and then, the critical control pressure $P_{cri}$ can be calculated according to Equation (13).

Taking $P_{cri}$ as the benchmark, if $P_2$ is too high, on the one hand, it will increase the resistance of the motor speed regulation and increase the slipping work in the shifting process. On the other hand, it will also increase the speed regulation time, thus extending the duration of the shifting process. Moreover, if $P_2$ is higher, it is easy to cause the remaining slip to not be eliminated by the motor in the late stage of the speed regulation, which will lead to a series of problems. If $P_2$ is too low, the slipping work will be reduced; however, it is easy to cause slip overshoot, which will lead to a large shift impact.

Figure 7 shows the shifting phenomenon with abnormal $P_2$. When $P_2$ is too high, as shown in Figure 7a, the remaining slip cannot be eliminated continuously, as it decreases to a certain value (higher than the threshold for entering the torque phase), resulting in the slip delay phenomenon. If the slip delay time is too long, it will lead to the phenomenon that the motor output torque increases again under the action of the integrator in the PI controller, which will lead to the sliding time exceeding the maximum allowable value. Therefore, it is forced to enter the torque phase, and the remaining slip will cause a large shift impact under the action of the OC clutch.

As shown in Figure 7b, when $P_2$ is too low, the pressure acting on the OG clutch is not enough to match the input torque. When the OC clutch slip reduces to 0—that is, the sun gear speed reduces to 0—there is still a positive torque (assuming that the current speed direction of the sun gear is positive) applying on the sun gear, making the sun gear speed continue to accelerate in reverse and resulting in the overshoot of the clutch slip. According to the above description of the shift control strategy the torque phase has entered, the reverse slip will gradually disappear with the increase of the OC clutch pressure. If the overshoot is serious, a large impact will occur at the moment when the slip becomes 0.

4. Simulation and Optimization of Shift Control Strategy

4.1. Simulation Results and Discussion

According to the shift control strategy mentioned above, the downshift process is simulated by Simulink. At the beginning of the shifting process, the input torque $T_{in}$ is 107.5 nm, and the corresponding critical control pressure $P_{cri}$ of the OG clutch is 2.528 bar. Therefore, the set $P_2$ is 2.51 bar, and the threshold of entering the torque phase is 15 rpm. The simulation results are presented in Figure 8.

As shown in Figure 8, at the moment of 30.06 s, $\left|\Delta \omega \right|$ is 15 rpm, which meets the conditions for entering the torque phase, so that finishes the speed phase and starts the torque phase. At this moment, the OC clutch remaining slip is 28.2 rpm, which needs to be eliminated during the torque exchange process in the torque phase, and the MG1 real torque has not been reduced to 0. In this process, the maximum jerk occurs, and the value is 36.6 m/s³, which exceeds the shift impact requirement (≤10 m/s³).

Further analyze the large impact caused by the remaining slip. As shown in Figure 9, after entering the torque phase, the elimination of the remaining slip can be divided into two stages: in stage I, the OC clutch control pressure rises, and the OG clutch control pressure decreases. Due to the hysteresis of the clutch pressure response, the real pressure and transmission torque of the clutches have not changed, so the remaining slip is still reduced only by MG1. However, as the output torque of MG1 gradually decreases, the elimination rate of the remaining slip is also slower and slower. There is even a trend of slip recovery when the MG1 torque is close to 0. In this stage, the wheel output torque $T_{\mathrm{wheel}}$ does not change significantly, and no obvious impact occurs. In stage II, the real pressure of the clutches begins to change, and the torque starts to exchange. With the increase of the torque transmitted by the OC clutch, the elimination rate of the remaining slip begins to increase gradually until the slip is 0. It can be seen that the OG clutch torque reduces gradually with the decrease in real pressure, but the OC clutch torque increases in reverse first with the increase in real pressure until the slip is 0 and then rises rapidly. As a result, the $T_{\mathrm{wheel}}$ fluctuated significantly, which leads to a large impact. The above analysis shows that, when the OC clutch transmits torque with the remaining slip, it can be seen from the kinematics theorem that the transmission torque before the slip disappears is a reverse torque. That is the main reason for the large shift impact.

Based on the above analysis, two optimization strategies are proposed to reduce the vehicle impact and improve the shift quality.

Strategy 1: Reduce the OG clutch control pressure $P_2$, which can reduce the speed regulation resistance in stage I to reduce or even eliminate the remaining slip when entering stage II and achieve a reduction of the shift impact.

Strategy 2: At the end of the speed phase, increase the OC clutch pressure in advance, which means increasing the resistance of the OC clutch during the process of eliminating the remaining slip, because the OG clutch pressure has not been reduced. It can reduce the reverse torque of the OC clutch to reduce the shift impact.

4.2. Optimization Results and Discussion

4.2.1. Strategy 1: Reducing OG Clutch Control Pressure $P_2$

In range (2.42 bar–2.53 bar), set the OG clutch control pressure $P_2$ at an interval of 0.01 bar, respectively. Simulate the strategy, and record the maximum jerk, shift time, and slipping work in

Table 1. Shift evaluating the indexes under different $P_2$.

${\mathit{P}}_2 \left(\mathbf{bar}\right)$	Maximum Jerk (m/s3)	Shift Time (s)	Slipping Work (kJ)
2.42	15.6	0.96	0.350
2.43	19.0	0.97	0.360
2.44	4.3	0.98	0.371
2.45	8.1	0.99	0.397
2.46	6.9	1.00	0.402
2.47	10.7	1.01	0.423
2.48	22.4	1.03	0.449
2.49	26.7	1.04	0.462
2.50	33.8	1.05	0.474
2.51	36.6	1.06	0.488
2.52	63.4	1.62	1.164
2.53	72.9	1.64	1.168

. The variation of the indexes under different $P_2$ is presented in Figure 10.

As shown in Figure 10, take the simulation results under the control pressure of 2.51 bar as a reference; when $P_2>2.51 \mathrm{bar}$, all the indexes are significantly increased with the increase of $P_2$, and the shift quality is significantly reduced; when $2.44 \mathrm{bar}\le P_2\le 2.51 \mathrm{bar}$, all the indexes are reduced gradually with the decrease of $P_2$, which means the shift quality is improved. when $P_2<2.44 \mathrm{bar}$, the slipping work and shift time further reduced, and the shift impact increases. The reason was mentioned in Section 3, which is the slip overshoot caused by low OG clutch pressure.

The variation of the OC clutch slip under different $P_2$ is presented in Figure 11. It can be seen that, when $P_2<2.47 \mathrm{bar}$, the slip overshoot begins to appear due to the low sliding friction. When $2.47 \mathrm{bar}\le P_2\le 2.51 \mathrm{bar}$, there is no slip overshoot, but the slip delay phenomenon begins to appear, and the higher the pressure is, the longer the delay time is, and the higher the remaining slip speed is when entering stage II. When $P_2>2.51 \mathrm{bar}$, a serious slip delay occurs, which reduces the shift quality.

According to the above analysis, it can be seen that the best range of $P_2$ is (2.44–2.46 bar). In this range, the maximum jerk is controlled within 10 m/s³. Further analyze the variation of the OG clutch torque and wheel output torque when the range of $P_2$ is (2.44–2.47 bar), as shown in Figure 12. When $2.44 \mathrm{bar}\le P_2\le 2.46 \mathrm{bar}$, there is a slip overshoot, which means that the slip will be reduced to 0 twice. When it reduces to 0 for the first time, the clutch transmission torque is slightly pulsed, and for the second time, torque fluctuation occurs. Both of these two changes of clutch transmission torque can cause the fluctuation of the wheel output torque and result in an impact, and the second impact amplitude is higher than the first, and it is the maximum jerk during the shifting process. In this range of $P_2$, it can be seen that the maximum jerk is less than 10 m/s³. When $P_2$ is set to 2.43 bar or lower, the clutch torque pulse increases significantly when the first slip changes to 0, making the impact here become the maximum impact of the shifting process. When $P_2$ is set to 2.47 bar or higher, the slip overshoot disappears (in fact, there is a slight overshoot, but the overshoot amplitude and time are very small and short, so that can be ignored). In the process of the slip being reduced to 0, the reverse torque of the clutch is generated, which leads to fluctuation of the wheel output torque and shift impact. In essence, the reverse torque produced at 2.47 bar is the same phenomenon as the second torque fluctuation at (2.44–2.46 bar), but the former is a forward slip, which produces a reverse torque in the opposite direction to the wheel output torque, so the impact is larger; and the latter is a reverse slip formed by overshoot, which produces a forward torque in the same direction as the wheel output torque, so the impact is smaller.

4.2.2. Strategy 2: Increasing OC Clutch Pressure in Advance

Simulation Results of Strategy 2

At the end of the speed phase, when $\left|\Delta \omega \right|$ is reduced to a certain value, which is higher than the threshold of entering the torque phase, increase the OC clutch pressure in advance to increase the resistance of the OG clutch in the torque exchange process, so as to reduce the reverse torque of the OC clutch. Set the slip threshold for starting to increase the OC clutch pressure to 90 rpm, and set the increased OC clutch pressure $P_{OC}$ to 1.65 bar. The simulation results are shown in Figure 13. At the time of 29.97 s, when $\left|\Delta \omega \right|$ is reduced to 85 m/s, the corresponding OC clutch slip is 149.6 m/s. At this moment, the OC clutch pressure begins to rise from 1.5 bar to 1.65 bar gradually and remains at 1.65 bar until the speed phase is finished. It can be seen that the maximum jerk of the shifting process is reduced to 9.7 m/s³.

The control effects of two shifting processes with and without strategy 2 under the same control pressure of the OC clutch are compared in Figure 14. It can be seen that, as the OC control pressure is increased in advance, the slip delay phenomenon disappears, the reverse torque that is generated in the process of eliminating the remaining slip is significantly suppressed, and the corresponding fluctuation of the wheel output torque is also significantly reduced, so that the impact here is reduced from 36.6 m/s³ to 9.7 m/s³, and the optimization effect of strategy 2 is obvious. In addition, the end time of the speed phase is also earlier than that without strategy 2, which means that the speed regulation time is shortened so that the shift time of the whole shifting process is shortened.

Comparison of Optimization Effects under Different $P_{OC}$

In range (1.52–1.72 bar), set $P_{OC}$ at an interval of 0.01 bar or 0.02 bar, respectively, to compare the optimization effects under different $P_{OC}$. The pressure setting and the corresponding shift evaluating indexes are shown in

Table 2. Shift evaluating indexes under different $P_{OC}$.

${\mathit{P}}_{\mathit{O}\mathit{C}} \left(\mathbf{bar}\right)$	Maximum Jerk (m/s3)	Shift Time (s)	Slipping Work (kJ)
1.52	30.4	1.06	0.487
1.54	23.1	1.05	0.473
1.56	16.9	1.05	0.473
1.58	12.3	1.05	0.473
1.60	9.6	1.05	0.473
1.61	8.1	1.05	0.473
1.62	7.9	1.05	0.473
163	8.2	1.05	0.473
1.64	9.3	1.05	0.473
1.65	9.7	1.05	0.473
1.66	10.1	1.05	0.473
1.68	12.4	1.05	0.473
1.70	13.6	1.05	0.473

, and the variation of the indexes under different control pressures is presented in Figure 15.

As shown in Figure 15, with the increase of $P_{OC}$ in the range (1.52–1.70 bar), the maximum jerk first decreases and then gradually increases, and the shift time and slipping work remain unchanged after decreasing to a certain value. It can be seen from the above analysis that, when $P_2$ is 2.51 bar and strategy 2 is adopted, the best $P_{OC}$ is 1.62 bar, which the maximum jerk can be optimized from 36.6 m/s³ to 7.9 m/s³. Moreover, when the OC clutch control pressure is within the range of (1.60–1.65 bar), the maximum jerk can be reduced to less than 10 m/s³.

Comparison of Optimization Effects under Different $P_2$

Adopting strategy 2 to optimize the shifting process under different $P_2$, the corresponding best $P_{OC}$ and the shift indexes are shown in

Table 3. The best $P_{OC}$ and the shift indexes under different $P_2$.

${\mathit{P}}_2 \left(\mathbf{bar}\right)$	$\mathbf{The} \mathbf{Best} {\mathit{P}}_{\mathit{O}\mathit{C}} \left(\mathbf{bar}\right)$	Maximum Jerk (m/s3)		Shift Time (s)		Slipping Work (kJ)
		W	W/O	W	W/O	W	W/O
2.47	1.53	6.5	10.7	1.01	1.01	0.423	0.423
2.48	1.57	8.2	22.4	1.02	1.03	0.435	0.449
2.49	1.60	8.5	26.7	1.03	1.04	0.448	0.462
2.50	1.60	7.8	33.8	1.04	1.05	0.460	0.474
2.51	1.62	7.9	36.6	1.05	1.06	0.473	0.488
2.52	1.67	8.3	63.4	1.07	1.62	0.500	1.164
2.53	1.64	6.8	72.9	1.08	1.64	0.510	1.170

Note: W is with strategy 2. W/O is without strategy 2.

.

As shown in Table 3, when $P_2$ is higher than its best range (2.44–2.46 bar), strategy 2 can be used to optimize the occurred slip delay, and different $P_2$ corresponds to different $P_{OC}$, which can realize the best optimization effect. It can be seen that each index has been optimized to varying degrees, and the more serious the slip delay is, the more obvious the optimization effect is. After being optimized by strategy 2, the maximum jerk is controlled within the range of (6.5–8.5 m/s³), while $P_2$ is in the above range. Moreover, the optimized shift time and sliding work still show an obvious positive correlation with $P_2$.

5. Conclusions

(1)

In this paper, a shifting control strategy based on motor active speed regulation is proposed, and the core is to realize the fast and accurate matching of the clutch speed through the motor active speed regulation control, so as to realize the fast and stable shifting process. The coordinated control of clutch pressure and motor torque in different stages of the shifting process is designed, and the influence of the key parameter on the shifting results is analyzed.

(2)

Based on the dynamic model, the critical control pressure $P_{cri}$ is calculated; then, the shifting process when $P_2$ is close to $P_{cri}$ is simulated and analyzed. The results show that, when entering the torque phase, there is a remaining slip of the clutch; in the process of eliminating the remaining slip, the reverse torque of the clutch is produced. It is the root cause of producing the maximum impact in the shifting process. On this basis, two optimization control strategies, which are reducing the OG clutch control pressure $P_2$ and increasing the OC clutch pressure in advance before entering the torque phase, are proposed to reduce the impact and improve the shift quality

(3)

For strategy 1, the following conclusions are drawn: (1) when $P_2$ is lower than $P_{cri}$, there is an optimal range of $P_2$, in which the shift impact can be controlled within 10 m/s³. In this paper, $P_{cri}$ is 2.582 bar, and the corresponding optimal control pressure range of $P_2$ is (2.44–2.46 bar). Moreover, in the above range, when $P_2=2.44 \mathrm{bar}$, the maximum jerk can be reduced to the lowest value of 4.3 m/s³. (2) When $P_2$ is in the optimal range, there is a slight slip overshoot in the torque phase. If $P_2$ is lower than this range, the slip overshoot will increase, thereby increasing the shift impact. If $P_2$ is higher than this range, the slip overshoot will disappear, and the slip delay will be produced, which will also increase the shift impact. (3) The shift time and sliding work show an obvious positive correlation with $P_2$. (4) The optimal range of $P_2$ is related to $P_{cri}$—that is, to the input torque of transmission. In practice, it is necessary to obtain the optimal range under different input torques through calibration tests.

(4)

For strategy 2, the following conclusions are drawn: (1) when adopting strategy 2, the slip delay phenomenon disappears, the reverse torque that is generated in the process of eliminating the remaining slip is significantly suppressed, and the corresponding fluctuation of the wheel output torque is also significantly reduced so that the impact is significantly reduced. (2) Strategy 2 can be used when $P_2$ is higher than the optimal range, and the slip delay occurs. Once it is adopted, each index will be optimized to varying degrees, and the more serious the slip delay is, the more obvious the optimization effect is. (3) For different $P_2$, the corresponding best $P_{OC}$ is also different.

(5)

The optimal range of strategy 1 is (2.44–2.46 bar), while the effective action range of strategy 2 is (2.47–2.53 bar). Therefore, strategy 2 can be seen as a supplement to strategy 1. For any $P_2$ within the range of (2.44–2.53 bar), a higher shift quality can be achieved.