Optimization of Shift Strategy Based on Vehicle Mass and Road Gradient Estimation

Abstract

For electrically driven commercial vehicles equipped with three-speed automatic mechanical transmission (AMT), the transmission control unit (TCU) without vehicle mass and road gradient estimation function will lead to frequent shifting and insufficient power during vehicle full-load or grade climbing. Therefore, it is necessary to estimate the mass and road gradient for the electrically driven commercial vehicles equipped with the three-speed AMT, and to adjust the shift rule according to the estimation results. Given the above problems, this paper focuses on the control and development of the electrically driven three-speed AMT and takes the shift controller with the vehicle mass and road gradient estimation as the research goal. The mathematical model and simulation model of vehicle dynamics are established to verify the shift function of TCU. The least squares method and calibration techniques are applied to estimate the vehicle mass and road gradient. According to the estimation results, the existing shift strategy is optimized, and the software-in-the-loop simulation of the transmission controller is carried out to verify the function of the control algorithm software. The hardware-in-the-loop test model is established to verify the shift strategy’s optimization effect, which shortens the controller’s forward development cycle. According to the estimation results of mass and gradient, the error result of the proposed method is controlled within 4.5% for mass and 8.6% for gradient. The experiment verifies that the optimized shift strategy can effectively improve the dynamic performance of the vehicle. The HIL experimental results show that the vehicle can maintain low gear while climbing the hill, and the vehicle speed does not decrease significantly.

1. Introduction

Purely electrically driven commercial vehicles have the characteristic of a large difference in vehicle mass depending on whether they are loaded or unloaded, facing complex road conditions, etc. [1,2]. It is found that the application of a shift strategy without the estimation of the vehicle mass and road gradient will result in the problems of insufficient power and frequent shifting of commercial vehicles in the process of full loading or grade climbing [3,4,5]. To solve this problem and make the driving motor work in high-efficiency regimes, this paper estimates the vehicle mass and road gradient of commercial vehicles and optimizes the shift strategy based on the estimated results.

For commercial vehicles equipped with a three-speed automatic transmission (AMT), production cost is one of the key indicators that manufacturers are focused on [6]. However, adding sensors to estimate the vehicle mass and road gradient would seriously increase the cost. Therefore, most scholars are focusing on mass and gradient estimation without sensors currently.

Mahyuddin et al. [7] estimated road gradient and vehicle mass by using vehicle speed and driving torque only and proposed a sliding-mode observer-based parameter estimation method for the gradient and mass estimates. They proposed an error estimation method based on an adaptive observer without measuring the acceleration, and effectively suppressed interference through sliding mode control. Finally, they compared the estimated results with the existing recursive least squares (RLS) to verify the accuracy of the algorithm.

Mangan et al. [8] proposed a sensorless gradient estimation method by using vehicle data through a controller area network (CAN). They explored the relationship between vehicle-related data and road gradient in depth, completed online estimation of a gradient estimation algorithm under different driving conditions, and compared the accuracy of road gradient estimations based on an inclination sensor and acceleration error correction algorithm. The accuracy of the sensorless road gradient estimation algorithm has been verified, providing an economical and reliable method for road gradient estimation problems.

Hao Shengqiang et al. [9] used an accelerometer to estimate the dynamic mass of the vehicle, and then used a steady-state Kalman filter road gradient estimation model to estimate the road gradient. The joint simulation results of Simulink and Carsim showed that the steady-state Kalman filter and standard Kalman filter estimation results were consistent.

After estimating the loading mass of the vehicle and the road gradient, Guang xia [10] divided the vehicle mass and road gradient into different levels, and then adopted the hierarchical shift management strategy to implement different shift strategies for different levels of vehicle mass and road gradient. In the upper management system, according to the relevant national standards of automobiles, the gradient is divided into three grades: gentle gradient, medium gradient, and steep gradient. The vehicle mass is divided into three grades: no load, medium load, and heavy load. The nine kinds of road condition information estimated by the upper management system are transmitted to the lower-level shift strategy system. Then, it determines the most appropriate shift rule after judging the results of the upper management system, and shifts. It can effectively solve the phenomenon of frequent shift when the vehicle is grade climbing and of unexpected upshift when it is downgrade, reduce the wear of brake components, extend the service life of transmission components, and improve the power and comfort of the vehicle.

Zhang Lijie et al. [11] applied the long short-term memory (LSTM) neural network to the estimation of road gradient, acquired the road gradient information in real time, integrated the estimated road gradient information with shift rule, and designed a gear decision system based on vehicle mass and road gradient estimation, which effectively solved problems such as frequent shifting during grade climbing. However, the estimation method based on neural network needs to collect a large amount of experimental data. It is not conducive to reducing the development cycle of the controller.

This paper focuses on the forward development of the transmission control unit (TCU) and develops a TCU based on the vehicle mass and driving road gradient estimation without production cost increasing. This paper models the longitudinal dynamics model of the vehicle and adds the vehicle mass and road gradient estimation in TCU. After verifying the accuracy of the model, the shift strategy has been optimized to meet different driving conditions of commercial vehicles based on the TCU estimated results.

Therefore, in Section 2, the dynamic theory of the relevant vehicle model is introduced, the vehicle model is built, and the correctness of the traditional shifting strategy is verified based on the built model. On the premise of ensuring the correct traditional shifting strategy, Section 3 begins to estimate the vehicle mass and road gradient by using the least square method and calibration technology, and Simulink simulates the estimated results. Section 4 makes fuzzy rules, and according to the estimation results of mass and road gradient, the fuzzy control system outputs the offset compensation amount of the traditional shifting strategy and realizes the optimization of the traditional shifting strategy. Finally, the HIL experiment system is set up in Section 5, and the optimization effect of shifting strategy is verified by HIL experiment.

2. Verification of TCU Shift Function Based on Vehicle Model of Simulink

The longitudinal dynamics modeling of the vehicle is mainly based on the vehicle driving dynamics balance equation [12]. Functions such as calculating the vehicle speed and gear shifting can be achieved by modeling the dynamics of each component mathematically.

During vehicle driving, the speed is $V_e$ (m/s). The acceleration is $acc$ (m/s²). The gradient angle is $\alpha$ (rad). The force on the vehicle includes the driving force of the vehicle $F_t$ and the rolling resistance $F_r$ generated by the rolling resistance couple when the wheels contact the ground. The vehicle is considered as an entirety. The air resistance $F_a$ is generated by forward driving. When driving on a gradient, the gradient resistance $F_g$ is generated due to the vehicle’s gravity $G=mg$. Therefore, the balance equation during driving can be expressed as Equation (1):

$${\displaystyle \frac{T_m i_g{i}_0{\eta }_T}{r_w}}=mgf\mathit{cos}\alpha +{\displaystyle \frac{1}{2}}{C}_{D}A\rho V_e^2+mg\mathit{sin}\alpha +m \ast acc$$

(1)

In Equation (1), $T_m$ is the torque of the driving motor; $i_g$ is the transmission ratio of the transmission, whose value is 55.75, 32.7, 13.68; $i_0$ is the main reduction ratio, whose value is 1; ${\eta }_T$ is the transmission efficiency; $r_w$ is the wheel radius; $m$ is the vehicle mass; $g$ is gravitational acceleration; $f$ is the rolling resistance coefficient; $A$ is the windward area of the vehicle; $\rho$ is the air density; and $C_D$ is the drag coefficient.

The parameters of the commercial vehicle in this paper are shown in

Table 1. Vehicle parameters.

Parameter	Value
Rated torque of drive motor (Nm)	350
Drive motor peak torque (Nm)	580
First gear ratio	55.75
Second gear ratio	32.7
Third gear ratio	13.68
Main reduction ratio	1
Vehicle unloaded mass (kg)	6800
Vehicle full-loaded mass (kg)	22,000
Wheel radius (m)	0.512
Windward area (${\mathrm{m}}^2$)	7.92
Windward resistance coefficient	0.56
Air density ($\mathrm{kg}/{\mathrm{m}}^3$)	1.225
Maximum braking force (Nm)	36,000
Rolling resistance coefficient	0.0041

:

To verify the shifting function of the TCU, model-in-the-loop simulation was conducted in Matlab/Simulink based on the vehicle dynamics model. The structure of the model-in-the-loop simulation is shown in Figure 1. All vehicle data are input into the TCU software by simulating the driver input. Then, the TCU software shifts according to the vehicle status, achieving shifting and solenoid valve control.

The model-in-the-loop simulation was conducted on the TCU control model to verify the traditional dual-parameter economic shift rule based on the vehicle dynamics model. While the input throttle pedal opening increased from 0% to 100% gradually and the gear lever remained in the D-gear, the TCU completed the shifting control, and the motor speed and vehicle speed simulation results are shown in Figure 2. The gear increases from 1 to 2 at 30 s. In this process, the transmission ratio is reduced, the motor is speed-controlled, and the motor speed is reduced and adjusted to the target speed. At the same time, due to the power interruption in the AMT shift process, the vehicle speed fluctuates around 30 s. Similarly, when the gear rises from 2 to 3 at 52 s, the speed ratio is further reduced, the motor is speed-controlled, the speed is adjusted to the target speed, and the vehicle speed also fluctuates. After releasing the accelerator pedal, the motor speed and vehicle speed begin to decline at 92 s and 100 s, respectively, to downshift; at these two times when the transmission ratio increases, the motor speed will rise to the target speed. Due to the deceleration process, the vehicle speed in these two processes did not change significantly.

The research object of this paper is a three-speed AMT, whose gear selection and shifting mechanism adopt an I-shaped design scheme. The gear selection mechanism and shifting mechanism work together to push the dog tooth clutch. When shifting from first gear to second gear, the shift lever is first disengaged by the push solenoid valve, and then the shift lever is shifted from 10 mm to 0 mm. Then, the shift lever is selected by the shift solenoid valve, and the shift lever is moved from 0 mm to 11.5 mm. Finally, the shift lever is pushed to −10 mm through the push solenoid valve and shifted to second gear. When shifting from second gear to third gear, there is no need to select a gear. Thus, the gear lever is moved from −10 mm to 10 mm through the push solenoid valve. The opposite operation is performed when downshifting from third gear to second gear and downshifting from second gear to first gear. The result of the model-in-the-loop simulation is shown in Figure 3a. The switch control of the solenoid valve throughout the process is shown in Figure 3b, with a working current of 625 mA. The simulation result shows that the TCU controls the solenoid valve and gear selection mechanism correctly.

To verify the correctness of the shift control strategy of the TCU, the target gear and current gear were collected separately, as shown in Figure 4a. When the target gear and current gear are inconsistent, the TCU controls the transmission to enter the shift phase, as shown in Figure 4b. The simulation result shows that the shift control strategy is correct.

Through the model-in-the-loop simulation of TCU, not only the correctness of the vehicle dynamics model was verified, but also the shifting function of TCU, laying the foundation for adding vehicle mass and road gradient estimation algorithms and optimizing shifting strategies in the future.

3. Estimation Algorithm for Vehicle Mass and Road Gradient

For purely electrically driven commercial vehicles equipped with a three-speed AMT, there is a significant difference in vehicle mass between unloaded and fully loaded condition, and the working road condition is complex, which can affect the dynamic characteristics of the vehicle and be clearly reflected in driving data [13,14,15,16,17,18].

Therefore, the key in this paper is to study the correlation between vehicle dynamics, vehicle mass, and road gradient, and to deeply analyze the impact mechanism of them. By extracting vehicle dynamic driving data from a controller area network (CAN), the vehicle mass and road gradient are estimated.

3.1. Vehicle Mass Based on the Least Squares Method

For an electrically driven commercial vehicle, the change in vehicle mass mainly happens at loading and unloading when the vehicle is static. The vehicle mass can be considered not to change during the driving process, so the estimation of the vehicle mass has no highly real-time requirement. At the same time, to eliminate the error caused by interference, this paper selects the least squares method with variable forgetting factor to estimate the vehicle mass [19]. The least squares method with variable forgetting factor model is Equation (2):

$$\left\{\begin{array}{c}\widehat{m}\left(k\right)=\widehat{m}\left(k-1\right)+K\left(k-1\right)\left[y\left(k\right)-E\left(k\right)\widehat{m}\left(k-1\right)\right]\\ K\left(k\right)={\displaystyle \frac{P\left(k-1\right)E\left(k\right)}{\lambda +E\left(k\right)P\left(k-1\right)E\left(k\right)}}\\ P\left(k\right)={\displaystyle \frac{1}{\lambda }}\left(I-K\left(k\right)E\left(k\right)\right)P\left(k-1\right)\end{array}\right.$$

(2)

In Equation (2), $\widehat{m}\left(k\right)$ is the parameter vector being evaluated at the current time, $\widehat{m}\left(k-1\right)$ is the evaluated parameter vector at the previous time, $K\left(k-1\right)$ is the gain vector of the previous time, $y\left(k\right)$ is the output vector at the current time, $E\left(k\right)$ is the input vector at the current time, $P\left(k\right)$ is the covariance matrix at the current time, and $\lambda$ is the weighted forgetting factor.

The dynamic equation of the vehicle has been introduced in Section 2. When estimating the vehicle mass, the windward area, wind resistance coefficient, air mass density, rolling resistance coefficient, vehicle speed, and other information can be obtained by CAN signals. Therefore, the parameters such as the vehicle mass are substituted into the dynamic balance equation:

$${\displaystyle \frac{T_m i_g{i}_0{\eta }_T}{r_w}}-{\displaystyle \frac{1}{2}}{C}_{D}A\rho V_e^2=mgf\mathit{cos}\alpha +mg\mathit{sin}\alpha +m \ast acc$$

(3)

Let $y\left(k\right)={\displaystyle \frac{T_m{i}_g{i}_0{\eta }_T}{r_w}}-{\displaystyle \frac{1}{2}}{C}_{D}A\rho V_e^2$, which represents the output of the system. Let $E\left(k\right)=gf\mathit{cos}\alpha +g\mathit{sin}\alpha +acc$, which represents the observation of the system. $m$ is the parameter to be estimated.

3.2. Road Gradient Estimation Based on Vehicle Dynamics

Compared with the vehicle mass, the road gradient is a real-time variable, and the change of the road gradient will also cause vehicle acceleration change. According to the introduction of vehicle dynamics in Section 2, Equation (1) is transformed to Equations (4) and (5).

$$m_0 \ast {acc}_0=F_t-m_{0}gf-F_a-F_b$$

(4)

$$m \ast acc=F_t-mgf\mathit{cos}\alpha -F_a-mg\mathit{sin}\alpha -F_b$$

(5)

In the equation, ${acc}_0$ is the theoretical acceleration with the vehicle unloaded, $acc$ is the actual acceleration, the unloaded vehicle mass is $m_0$, and the real mass is $m$. Equation (4) is the dynamic balance equation of the vehicle when the vehicle is unloaded and running on a horizontal road, and Equation (5) is the dynamic balance equation of the vehicle when the vehicle is loaded and running on the actual road. By analyzing the correlation between the acceleration and the vehicle mass and road gradient through Equations (4) and (5), it can be concluded that the difference between the theoretical acceleration when the vehicle is unloaded and running on a flat road and the actual acceleration when the vehicle is loaded and running on the actual road is caused by the change of the vehicle mass and road gradient. Therefore, the vehicle mass and road gradient can be estimated by calibrating the difference between theoretical and actual acceleration in engineering.

Combined with the fact that the vehicle does not have time-varying characteristics, and the road gradient has time-varying characteristics, it can be concluded that in vehicle driving, the difference between the loaded vehicle acceleration and unloaded vehicle acceleration is a constant value, and the acceleration change caused by road gradient change is related to the gradient value. Therefore, the collected acceleration value can be compensated by the previous estimation results of the vehicle mass, which is the unloaded acceleration value. Then, the road gradient can be estimated by calibrating the acceleration difference in engineering.

Through Equations (4) and (5), the difference between the unloaded vehicle acceleration running on the horizontal road and the actual acceleration calculated by the speed sensor can be calculated. The theoretical unloaded vehicle acceleration running on the horizontal road can be converted according to Equation (5):

$${acc}_0={\displaystyle \frac{F_t-m_{0}gf-F_a}{m_0}}$$

(6)

Convert the output shaft speed to vehicle speed, and then calculate the acceleration:

$$v_e={\displaystyle \frac{0.377n{r}_w}{i_0}}$$

(7)

The actual acceleration difference is:

$$acc=\Delta \delta {\displaystyle \frac{0.377r_w}{i_0}}$$

(8)

In Equation (8), $\Delta \delta$ is the output shaft acceleration calculated from the output shaft speed collected by the sensor.

Therefore, the difference of acceleration $∆a$ is expressed as:

$$∆a={acc}_0-acc$$

(9)

In this paper, the road gradient is estimated by calibrating the difference between theoretical and actual acceleration $∆a$. Through the simulation, the compensation value of the acceleration difference is first calibrated and combined with the estimation results of the vehicle mass. This process requires the simulation of different vehicle mass, and the two-dimensional table of the acceleration difference compensation is calibrated according to different vehicle mass. Secondly, according to the simulation results of the compensated acceleration difference, the mapping relationship between the acceleration difference and the road gradient of $∆a$ is preliminarily calibrated to form a two-dimensional data table. It should be emphasized that the simulation calibration result is only applicable to the simulation stage. Hardware-in-the-loop (HIL) and the real vehicle test still need to calibrate according to the experimental environment.

3.3. Validation of Vehicle Mass and Road Gradient Estimation

In this paper, for the engineering problems of TCU forward development, the estimation function is added in the development process of TCU. In Section 1, the basic shift function of the current TCU was introduced and verified. Based on the development of TCU function in Section 1, the estimation function of the vehicle mass and road gradient is added. Therefore, the least squares method with variable forgetting factor is built in Matlab/Simulink. The calibration and estimation model of the road gradient is built. In the software-in-the-loop simulation, a given section of the road with gradient is simulated. The variation range of road gradient (i) is 0–10°, and the variation range of vehicle mass is 6800–22,000 kg. Figure 5 shows the simulated road gradient. The simulated actual road gradient gradually increases from 5 s to the maximum road gradient at 20 s, at which time sin alpha equals 0.1744, corresponding to the road gradient (i) of 10°; after maintaining the maximum road gradient of 10° for 10 s, the road gradient value decreases, and sin alpha decreases to 0.0872 at 40 s, corresponding to the road gradient of 5°. The road gradient value then stays the same until the end.

In order to verify the effectiveness of the function, the simulation is carried out on the basis of the vehicle dynamics model introduced in Section 1. According to the given road gradient, the vehicle mass is set to simulate three kinds of working condition: unloaded with gradient (vehicle mass is 6800 kg; the road gradient is shown in Figure 5), loaded with gradient (vehicle mass is 14,400 kg; the road gradient is shown in Figure 5), and loaded without gradient (vehicle mass is 22,000 kg; the road gradient is 0°). The estimation of the vehicle mass and road gradient is simulated and verified. The simulation results are shown in Figure 6, Figure 7 and Figure 8.

By analyzing the simulation results, it can be concluded that in the estimation of the vehicle mass, the vehicle mass will converge to the true value regardless of the influence of road gradient. The simulation of unloaded with gradient (vehicle mass is 6800 kg; the road gradient is shown in Figure 5) is analyzed in Figure 6. The estimated mass converges at about 1 s and then remains stable. After stabilization, the error of the estimated mass is small, within ±200 kg, and the estimated mass is accurate. The error of gradient estimate in the whole simulation process is within ±0.015 sin alpha, which is acceptable. The simulation results of loaded with gradient (vehicle mass is 14,400 kg; the road gradient is shown in Figure 5) are analyzed in Figure 7. The estimated mass converges around 1 s, and the subsequent estimated result fluctuates around the true value, with the maximum error within ±1000 kg. For commercial vehicles with a large mass variation range, this error range is acceptable. The simulation results of loaded without gradient (vehicle mass is 22,000 kg; the road gradient is 0°) are analyzed in Figure 8. The estimated mass converges at about 1 s and remains stable after convergence. The error of mass estimation after stabilization is small, within ±400 kg. The stable error is within ±0.015 sin alpha. In short, the results of three kinds of working conditions show that the error result of the proposed method is controlled within 4.5% for mass and 8.6% for gradient. There is a certain deviation in the estimation result, but for heavy commercial vehicles, the error range is acceptable. In the road gradient estimation, the estimated value is basically consistent with the actual value, and the error range is acceptable. The reason for this phenomenon is that the accuracy of the road gradient estimation is related to the estimation of the vehicle mass and the calibration parameters of the acceleration correction. The accuracy of the vehicle mass estimation directly affects the estimation results of the road gradient.

4. Shift Strategy Optimization Based on Mass and Gradient Estimation Result

In order to solve the problem of insufficient power and frequent shifting caused by the traditional dual-parameter shift strategy in the process of fully loaded or grade climbing, it is necessary to optimize the traditional dual-parameter shift rule after estimating the vehicle mass and road gradient, so as to make the vehicle have more power and comfort when grade climbing or fully loaded. In Section 3, we introduced the estimation algorithm of the vehicle mass and road gradient added to TCU software. According to the estimation results of the vehicle mass and road gradient by TCU software, we can obtain the current vehicle mass and road gradient information in real time. We can manage the estimation result of vehicle mass and road gradient by TCU through hierarchical management [20] to better realize the optimization effect of shift strategy.

The estimation results of TCU on vehicle mass can be divided into three levels, namely, light load (6800–11,866 kg), medium load (11,866–16,933 kg), and heavy load (16,933–22,000 kg). The estimation results of TCU on the road gradient can be divided into three levels: small gradient (0–0.067 sin alpha), medium gradient (0.067–0.134 sin alpha), and large gradient (0.134–0.2 sin alpha).

In this paper, fuzzy control [21] is used to realize the compensation effect of different levels of estimation results on the shift strategy. Firstly, the input variable universe is determined. Since the estimated value includes two parameters, the vehicle mass and the road gradient, they are taken as inputs. According to the provisions of hierarchical management, the universe of the vehicle mass is specified as [6800, 22,000], and the universe of the road gradient is specified as [0, 0.2]. The shift rule will be compensated to varying degrees under different vehicle mass and road gradient.

The fuzzy subset of the input parameter vehicle mass is defined as {Light load (S), Medium load (M), Heavy load (B)}. The fuzzy subset of the input parameter road gradient is defined as {Small gradient (S), Medium gradient (M), Large gradient (B)}. The fuzzy subset of the output parameter shift point is defined as {Very short (VS), Short (S), Medium (M), Long (B), Very long (VB)}.

Considering that the vehicle mass and road gradient parameters jointly affect the vehicle performance, and the effects of the two parameters on the vehicle performance are similar, this paper selects the triangular membership function, namely trimf function, whose fuzzy subset membership function of the vehicle mass and road gradient is shown in Figure 9 and Figure 10. The fuzzy subset membership function shift point is shown in Figure 11.

Considering the fuzzy control logic of the vehicle mass and road gradient on the shift strategy, different mass and gradient changes lead to the output of different shift point offsets, to realize the shift strategy of the traditional economic mode when unloaded and flat road and meet the economic requirements. When the vehicle is loaded or there is a gradient, the shift is delayed in meeting the power and comfort requirements of the vehicle. Therefore, it is concluded that the greater the vehicle mass and road gradient, the more delay offsets to the shift point there will be. The smaller the vehicle mass and road gradient, the fewer the delay offsets to the shift point. These results are presented below in the fuzzy rule table shown as

Table 2. Fuzzy rule.

Mass	S	M	B
Gradient
S	VS	S	M
M	S	M	B
B	M	B	VB

.

According to the fuzzy rule table, the shift strategy is formulated and optimized. Based on the TCU software introduced in Section 1, the shift strategy is optimized. The economic shift point is combined with the shift point offset obtained by fuzzy control, which is jointly output as the final shift point. The work of optimizing the shift strategy is completed according to the estimated results of the vehicle mass and the road gradient.

5. Verification of Optimized Shift Strategy

5.1. Design of HIL

The hardware-in-the-loop (HIL) test system is an indispensable test in the V-type development process [22]. To save time in the vehicle test, the controller must be HIL-tested before the vehicle test. The HIL test is a semi-physical and semi-virtual test technology. The equipment selected in this paper is the dSPACE platform. The physical controlled object added in the HIL test is a TCU controller and the shift pneumatic valve used in the shift process, and the virtual controlled object is a vehicle dynamics model. The overall design structure of the system is shown in Figure 12.

According to the system shown in Figure 12, the IO interface has been established, and CAN communication has been tested. The plant model for the HIL test is established based on the vehicle transmission system model, the original mathematical model of the shift execution system, as well as the signal flow mathematical model of each module built in Matlab/Simulink. The completed construction of an HIL test environment is shown in Figure 13.

5.2. Result of HIL

After building the HIL model of the vehicle, generating the object code and writing it to the controller and completing the hardware and software configuration of the dSPACE platform, the HIL simulation for TCU forward development is carried out. On the one hand, it can verify the shift function of TCU software. On the other hand, it can verify the optimization effect of the shift strategy according to the vehicle mass and road gradient estimation results.

To verify the optimization effect of the shift strategy, two groups of experiments were designed. The first experiment was to test the TCU without adding vehicle mass and road gradient estimation function. The vehicle mass would not change during the driving, so the simulated vehicle mass was 22,000 kg. Due to the road gradient changing in real time, the vehicle is simulated through a section of road with the changing road gradient. The simulated actual road gradient gradually increases from 5 s to the maximum road gradient at 20 s, at which time sin alpha equals 0.1744, corresponding to the road gradient (i) of 10°; after maintaining the maximum road gradient of 10° for 5 s, the road gradient value decreases, and sin alpha decreases to 0 at 40 s, this process is shown in Figure 14. Observe the vehicle speed, current gear, and other differences with the accelerator pedal opening changing. In Experiment 2, the TCU with vehicle mass and road gradient estimation function was simulated with the same road conditions. Same as before, change the accelerator pedal opening and observe the vehicle speed, current gear, and other differences. The optimization effect of the shift strategy is analyzed based on the comparison results of the two experiments, which are shown in Figure 15 and Figure 16.

The experiment results show that the TCU without the vehicle mass and road gradient estimation function in experiment 1 will cause the vehicle to shift frequently and lack power during driving. In Figure 15a, when driving at 11 s, the transmission upshifted to the second gear based on the traditional shift strategy. At this time, as the transmission ratio was greatly reduced, the wheel torque of the vehicle was insufficient. As shown in Figure 15b, the vehicle begins to slow down significantly at 20 s and reaches the downshift point at 26 s due to the vehicle speed reduction. The gear in Figure 15a is reduced back to first gear, while the vehicle speed is already very low, close to 5 km/h, which obviously lacks power. After that, due to the reduction of the road gradient, the vehicle re-accelerates and reaches the upshift point again, and the gear in Figure 15a rises from 1 to 2, which is an obvious phenomenon of frequent gear shifting. In Experiment 2, the TCU, with optimized shift strategy, can well offset the shift point. As can be seen from Figure 16a, the vehicle keeps running in first gear all the time, and only at about 38 s does the vehicle shift up when its vehicle speed reaches the upshift point after offset compensation. Due to the continuous increase of the road gradient, the vehicle also has the phenomenon of deceleration. The reason for this phenomenon is that the vehicle lacks driving torque in the grade climbing process. This problem can be solved by increasing the opening of the accelerator pedal. The shift strategy always controls the transmission to maintain the first gear and reduce the shift frequency.

In contrast to the existing research, the least square method is used in this study to estimate the vehicle mass. At the same time, calibration technology is innovatively used to estimate the road gradient. The estimation method using calibration technology can make the content of this study better match actual engineering projects and can also be used for the transfer of different engineering projects. At the same time, the HIL experiment provides us with rich experimental conditions. Road conditions with large gradients are not easy to obtain in practice, and the HIL system solves this problem well. However, the accuracy of the results of road gradient estimation using calibration technology depends on the level of calibration technology of engineers. The limitation of this method is that engineers are required to do experiments to modify the calibration parameters, which make for time-consuming work. In the future, we will try to summarize the internal law of each stage calibration and shorten the calibration time of each stage.

6. Conclusions

This paper develops a TCU which can automatically estimate vehicle mass and road gradient and optimize the shift strategy according to the estimation results. It can be used to meet the complex working conditions of electrically driven commercial vehicles.

(1) For the forward development of TCU, the software-in-the-loop simulation was conducted to verify the basic shift function of TCU based on the vehicle longitudinal dynamics model.

(2) Based on the vehicle dynamics equation, the estimation function of the vehicle mass and road gradient was added to the TCU software, and the correctness of the estimation was verified. The verification results show that the estimation of the vehicle mass is relatively accurate, while there are errors in the estimation of the road gradient. After the mass estimation value was stable, the gradient estimation result was modified to verify the correctness of the estimation result.

(3) According to the estimation results of the vehicle mass and road gradient, the traditional shift strategy was optimized. Through the fuzzy control method, the shift point was offset according to the vehicle mass and road gradient.

(4) The functionality of the optimized TCU was verified by building a hardware-in-the-loop system, applying code generation technology and the rapid prototype control platform of the dSPACE platform. The experimental results show that the TCU with the optimized shift strategy can effectively control the shift point offset, provide more wheel drive torque when the vehicle is loaded or grade climbing, improve the dynamic performance of the vehicle, reduce the shift times, and improve the comfort of the vehicle.