Research on the Trajectory Tracking of Adaptive Second-Order Sliding Mode Control Based on Super-Twisting
Abstract
:1. Introduction
2. Construction of the Vehicle Dynamics Model
3. Adaptive Preview Model
3.1. Optimum Curvature Single Point Preview
3.2. Adaptive Preview Time
4. Design of a Second Order Sliding Mode Controller
4.1. Design of Low-Pass Filters
4.2. Design of the Super-Twisting Controller
4.3. Phase Diagram Analysis of the Vehicle Dynamic Stability
4.4. Low-Pass Filter Validation
5. Design of the MPC Controller
5.1. MPC Output Function Derivation
5.2. MPC Algorithm Objective Function Design
5.3. MPC Algorithm Constraint Design
5.4. MPC Simulation Verification
6. Design of the Conventional Sliding Mode Control (CSMC) Controller
7. Control System Simulation Verification
7.1. Construction of a Joint Simulation Platform
7.2. ST Controller Simulation without Considering the Uncertainty of the Parameters
7.3. Comparison Tests of ST Controller and MPC Controller
7.4. Comparison Tests of ST Controller and CSMC Controller
7.5. Simulation with Considering the Uncertainty of the Parameters
8. Conclusions
- This article designs a second-order sliding mode controller based on the ST algorithm, which combines an adaptive preview controller with the second-order sliding mode algorithm. The adaptive preview can take into account the trajectory deviation, road boundary, and overall vehicle motion response characteristics to solve for a suitable preview time and set a matching preview distance to make the controller more in line with the driver’s habits so that it can sense the road ahead in advance to make the corresponding control strategy. Finally, the Lyapunov function and phase plane analysis methods are used to prove its convergence and stability respectively;
- In designing the ST second-order sliding mode control algorithm, the chattering is also further reduced by combining a low-pass filter with the ST algorithm. This paper also proposes a method based on the standard deviation of the gradient to calculate the smoothness of the curve, using this parameter to evaluate the chattering of the curve, the standard deviation of the gradient was used to evaluate smoothness, and the smoothness after filtering is one-seventeenth of that before filtering;
- The ideal yaw rate can be obtained by adaptive preview control. The difference between the ideal yaw rate and the actual yaw rate is fed into the designed ST second-order sliding mode controller to solve the required steering wheel angle as the target for tracking control. To demonstrate the effectiveness of this controller, an MPC algorithm was designed for comparison experiments. Compared to the MPC controller, the tracking accuracy of the ST controller has improved to 64.42% and 51.02% at 36 and 54 km/h, respectively. At the same time, it was also compared with conventional sliding mode control and the results showed that the tracking accuracy of the ST controller has improved to 41.78%, and the smoothness of the ST controller is one-nineteenth that of the CSMC. This means the ST controller can produce inputs with weaker chattering; and
- Simulations are carried out on parameter uncertainties in this article, where parameter uncertainties include system parameter uptake and external disturbances, and Gaussian white noise is used to replace these uncertainties. With simulation at 36 and 54 km/h, the simulation results show that despite the effect of Gaussian white noise, the trajectory of the ST controller still fits the ideal trajectory and the tracking error does not exceed 0.3 m. Although there are slight fluctuations in the steering wheel angle and transverse angular velocity, they are still within the acceptable range and the actuator still works properly.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameters | Values | Comments |
---|---|---|
T | 0.5 | Time associated with vehicle steering response characteristics |
λ | 60 | Parameter of ST algorithm |
k1 | 0.2 | Parameter of ST algorithm |
k2 | 0.1 | Parameter of ST algorithm |
ξ | 6 | The cut-off frequency of a low-pass filter |
a | 1.016 | Distance from center of mass to front wheel |
b | 1.562 | Distance from center of mass to rear wheel |
Cf | 108,861 | Lateral stiffness of front wheel |
Cr | 108,861 | Lateral stiffness of rear wheel |
Iz | 1523 | Yaw inertia |
isw | 19.562 | Angular velocity ratio |
Parameters | Values | Comments |
---|---|---|
Np | 30 | Predicted step size |
Nc | 60 | Control step |
Row | 10 | Relaxation factor weight |
Parameters | Input/Output Channels | Comments |
---|---|---|
Lead distance to driver preview point 1 | IMP_LX_SEN_1 | m |
Steering wheel angle | IMP_STEER_SW | deg |
Lateral distance to target point 2 | L_Drv_2 | m |
Longitudinal speed | Vx_SM | km/h |
Yaw rate | AV_Y | deg/s |
Slip angle | Beta | deg |
Lateral distance to target point 2 | L_Drv_1 | s |
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Bei, S.; Hu, H.; Li, B.; Tian, J.; Tang, H.; Quan, Z.; Zhu, Y. Research on the Trajectory Tracking of Adaptive Second-Order Sliding Mode Control Based on Super-Twisting. World Electr. Veh. J. 2022, 13, 141. https://doi.org/10.3390/wevj13080141
Bei S, Hu H, Li B, Tian J, Tang H, Quan Z, Zhu Y. Research on the Trajectory Tracking of Adaptive Second-Order Sliding Mode Control Based on Super-Twisting. World Electric Vehicle Journal. 2022; 13(8):141. https://doi.org/10.3390/wevj13080141
Chicago/Turabian StyleBei, Shaoyi, Hongzhen Hu, Bo Li, Jing Tian, Haoran Tang, Zhenqiang Quan, and Yunhai Zhu. 2022. "Research on the Trajectory Tracking of Adaptive Second-Order Sliding Mode Control Based on Super-Twisting" World Electric Vehicle Journal 13, no. 8: 141. https://doi.org/10.3390/wevj13080141