An Acceleration Slip Regulation Strategy for Four-Wheel Drive Electric Vehicles Based on Sliding Mode Control
<p>The four-wheel drive (4WD) electric vehicle acceleration slip regulation (ASR) system layout.</p> "> Figure 2
<p>Comparison of two methods for tyre slip rate calculation: (<b>a</b>) Simulation results of Equation (6); (<b>b</b>) Simulation results of Equation (7).</p> "> Figure 3
<p>The modified tyre slip rate at a low vehicle velocity.</p> "> Figure 4
<p>The acceleration slip regulation strategy.</p> "> Figure 5
<p>Simulation results of average distribution of inter-axle torque on good roads: (<b>a</b>) The front and rear axle tyre slip rate; (<b>b</b>) Vehicle acceleration.</p> "> Figure 6
<p>Simulation results of torque distribution by axle load on good roads: (<b>a</b>) The front and rear axle tyre slip rate; (<b>b</b>) Vehicle acceleration.</p> "> Figure 7
<p>Simulation of stepping on the pedal lightly to accelerate on a mid-adhesion road: (<b>a</b>) Optimal torque of inter-axle distribution control; (<b>b</b>) Average torque distribution control; (<b>c</b>) Acceleration under optimal torque of the inter-axle distribution control; (<b>d</b>) Acceleration under the average torque distribution control.</p> "> Figure 8
<p>The change of sliding mode surface and controlled variables in the sliding mode control process: (<b>a</b>) Convergence process of the front and rear axle speed deviation; (<b>b</b>) Output torque of the front and rear axle motor under sliding mode control.</p> "> Figure 9
<p>Simulation results of stepping on the pedal heavily on snowy roads: (<b>a</b>) Independent control of the optimal slip rate; (<b>b</b>) Optimal distribution of inter-axle control; (<b>c</b>) Acceleration under independent control of optimal slip rate control; (<b>d</b>) Acceleration under optimal distribution of inter-axle torque control.</p> "> Figure 10
<p>Front and rear axle input torque under different control modes: (<b>a</b>) Front axle slip rate control deviation; (<b>b</b>) Rear axle slip rate control deviation; (<b>c</b>) Output torque under independent control of the optimal slip rate mode.</p> "> Figure 11
<p>Simulation results of torque distribution on changing roads: (<b>a</b>) Changes of slip rate with light pedal; (<b>b</b>) Changes of slip rate with heavy pedal; (<b>c</b>) Control mode switching; (<b>d</b>) Control mode switching; (<b>e</b>) Vehicle performance under light pedal; (<b>f</b>) Vehicle performance under heavy pedal.</p> "> Figure 12
<p>Simulation results under the same road with the changing driver accelerator pedal: (<b>a</b>) Driver accelerator pedal signal; (<b>b</b>) The change of control mode under inter-axle torque distribution control strategy; (<b>c</b>) Change of slip rate; (<b>d</b>) Vehicle acceleration.</p> ">
Abstract
:1. Introduction
2. System Model
2.1. Vehicle Dynamics Model
2.2. Tyre Model
No. | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|
bi | 1.02316 | 21.80968 | 526.2336 | 0.09624 | 250.33146 | 0.00906 |
No. | 6 | 7 | 8 | 9 | 10 | – |
bi | −0.00255 | 0.03726 | 0.87693 | −0.00009 | −0.00033 | – |
2.3. Motor Model
2.4. Slip Rate Calculation Model
3. Control Strategies
- (1)
- Td ≤ 2 × Tmax ≤ Troad, generally corresponds to a condition of high road adhesion. In this case, the drive wheel slip will not happen over the entire range of the accelerator pedal, and it’s not necessary to perform a complex torque distribution for the front and rear axles, just let αf = αr = αpedal. Although the slip rates of the front and rear axles will be different with the same drive torque due to the different vertical loads of front and rear axles, the vehicle dynamic performance and driving stability will not be influenced.
- (2)
- Td ≤ Troad ≤ 2 × Tmax, generally corresponds to the condition of middle road adhesion. In this case, although the driver-desired torque Td is smaller than Troad, the slip phenomenon may happen on the driving shaft with a smaller axle load due to the bad road conditions. So a reasonable allocation of the drive torque of the front and rear axles is required to ensure Tf + Tr = Td, thereby avoiding slipping under the condition of avoiding vehicle dynamics loss.
- (3)
- 2 × Tmax ≥ Td ≥ Troad, generally corresponds to the condition of low road adhesion. In this case, the driver-desired torque Td is bigger than Troad, and the inter-axle torque distribution will cause an unavoidable slip phenomenon. In order to make full use of the road adhesion, the independent control for front and rear axles is the best control plan, thus the slip rates of the front and rear axles can be controlled to be equal to the optimal rate slip. In this way Tf + Tr = Troad, and the vehicle can acquire the biggest power at this moment.
3.1. Mode 1: Average Distribution of Inter-Axle Torque
3.2. Mode 2: Optimal Distribution of Inter-Axle Torque
3.3. Mode 3: Independent Control of Optimal Slip Rate
4. Simulation Results and Analysis
Parameters | Values | Parameters | Values |
---|---|---|---|
co | 500 | kri | 80 |
cfi | 50 | m | 5000 kg |
cri | 500 | nN | 4000 |
Cs | 1.81 kg·m2 | rw | 0.447 m |
Cx | 1.65 kg·m2 | ulow | 1.83 m/s |
Iw | 2.035 kg·m2 | τm | 200 |
ko | −100 | σx | 0.91 |
kfi | −200 | – | – |
4.1. Simulation on Average Distribution of Inter-Axle Torque
4.2. Simulation of Optimal Distribution of Inter-Axle Torque
4.3. Simulation of Independent Control of Optimal Slip Rate
4.4. Comprehensive Simulation and Analysis of the Acceleration Slip Regulation Control Strategy
5. Conclusions
- (1)
- Aiming at the 4WD electric vehicle, which was driven by front and rear independent motors, a model of the ASR system was established.
- (2)
- Compared with the conventional method of slip rate calculation, using the state equation of slip rate can be more accurate to describe the tyre slip process in a low vehicle velocity situation.
- (3)
- An ASR control strategy which contains three torque distribution mode was designed, namely average distribution of inter-axle torque for high road adhesion, optimal distribution of inter-axle torque for middle road adhesion and independent control of optimal slip rate for low road adhesion. Several simulations were carried out with MATLAB/Simulink, and the simulation results with some comparisons show that, the proposed strategy could realize the transformation among different control modes, thus fully use the road adhesion conditions, make the vehicle’s dynamic performance to follow the driver’s wishes. As a result, the vehicle longitudinal drive stability and dynamic performance are ensured.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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He, H.; Peng, J.; Xiong, R.; Fan, H. An Acceleration Slip Regulation Strategy for Four-Wheel Drive Electric Vehicles Based on Sliding Mode Control. Energies 2014, 7, 3748-3763. https://doi.org/10.3390/en7063748
He H, Peng J, Xiong R, Fan H. An Acceleration Slip Regulation Strategy for Four-Wheel Drive Electric Vehicles Based on Sliding Mode Control. Energies. 2014; 7(6):3748-3763. https://doi.org/10.3390/en7063748
Chicago/Turabian StyleHe, Hongwen, Jiankun Peng, Rui Xiong, and Hao Fan. 2014. "An Acceleration Slip Regulation Strategy for Four-Wheel Drive Electric Vehicles Based on Sliding Mode Control" Energies 7, no. 6: 3748-3763. https://doi.org/10.3390/en7063748