Key Takeaways & Executive Findings
- •• A T-S fuzzy-based vehicle dynamics model effectively captures time-varying tire cornering stiffness and vehicle speeds, representing uncertain parameters via norm-bounded uncertainties. • A robust model predictive control (MPC) strategy, solved via linear matrix inequalities (LMIs), guarantees vehicle handling stability under nonlinear conditions. • The proposed method was validated on a Carsim/Simulink joint platform, demonstrating superior lateral stability compared to conventional approaches. • The approach addresses the challenge of nonlinearities in distributed drive electric vehicles, enhancing direct yaw-moment control performance.
Abstract
Distributed drive electric vehicles (DDEVs) endow the ability to improve vehicle stability performance through direct yaw-moment control (DYC). However, the nonlinear characteristics pose a great challenge to vehicle dynamics control. For this purpose, this paper studies the DYC through the Takagi-Sugeno (T-S) fuzzy-based model predictive control to deal with the nonlinear challenge. First, a T-S fuzzy-based vehicle dynamics model is established to describe the time-varying tire cornering stiffness and vehicle speeds, and thus the uncertain parameters can be represented by the norm-bounded uncertainties. Then, a robust model predictive control (MPC) is developed to guarantee vehicle handling stability. A feasible solution can be obtained through a set of linear matrix inequalities (LMIs). Finally, the tests are conducted by the Carsim/Simulink joint platform to verify the proposed method. The comparative results show that the proposed strategy can effectively guarantee the vehicle’s lateral stability while handling the nonlinear challenge.
1. Introduction
Thanks to the advantages of being pollution-free and energy-saving, electric vehicles (EVs) are drawing more attention and are also treated as an important form of transport in the near future [1–3]. In recent years, the studies of distributed drive electric vehicles (DDEVs) have increased in the industry and academia. Due to the modular powertrain layout and short transmission chain, the DDEVs can control the vehicle through four quick-response and accurately executed in-wheel motors. It provides a flexible control mode for the DYC system to improve the vehicle lateral stability [4–6]. Compared with the traditional electronic stability control (ESC) to realize the DYC separately using the braking forces, DDEVs can adopt the differential driving/braking forces. DYC can be widely used to enhance vehicle handling performance and lateral stability [7, 8] by tracking the desired yaw rate and reducing the sideslip angle. However, under some extreme driving conditions [9], such as a double-lane-change maneuver at a high speed, the vehicle presents the inherent nonlinearities, in which the tire enters into the saturation state. The linear vehicle model cannot represent the vehicle dynamics responses accurately [10]. This proposes great challenges to the DYC design.
To describe the nonlinear characteristics, some nonlinear tire model expressions are presented based on the experimental results, including the Magic formula [11], Brush model [12], Fiala tire model, and UniTire model [13]. Combining these tire formulas with the dynamics model can accurately present the vehicle nonlinear characteristics, based on which some controllers are developed to guarantee the vehicle performance. A longitudinal-lateral motion combined magic formula is used in Ref. [14] to calculate the tire forces. Then a nonlinear model predictive control is developed to guarantee the vehicle dynamics responses for the steady and transient states. The longitudinal and lateral slip loss described by the tire model is also considered in the objective functions to reduce energy consumption. The tire forces are represented by the UniTire model in Ref. [15] to obtain the reserve capacity, based on which a linear time-varying control is proposed to coordinate the active front steering system and electronic stability control system. The distribution rule for the longitudinal and lateral forces is to maintain the same reserve capacity while guaranteeing the handling performance. Moreover, to speed up the calculation and facilitate the application, a nonlinear model control incorporated with a fast solution algorithm is presented in Ref. [16] to enhance vehicle stability on low friction-coefficient surfaces. The Fiala tire model is used to obtain the tire lateral forces in real-time. Then the optimization process is transformed into a two-point boundary value problem. It should be noted that these studies can be effective in representing the vehicle dynamics characteristics. Due to the real-time calculation of tire forces, the comput
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Faan Wang, Xinqi Liu, Guodong Yin, Liwei Xu, Jinhao Liang, Yanbo Lu (2025). T-S Fuzzy Based Model Predictive Control Method for the Direct Yaw Moment Control System Design. Chinese Journal of Mechanical Engineering. https://doi.org/10.1186/s10033-025-01292-w
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Frequently Asked Questions
What is the main contribution of this paper?
The paper proposes a T-S fuzzy-based model predictive control method for direct yaw moment control in distributed drive electric vehicles, addressing nonlinear challenges and enhancing lateral stability.
How does the T-S fuzzy model handle nonlinearities?
The T-S fuzzy model represents time-varying tire cornering stiffness and vehicle speeds using norm-bounded uncertainties, effectively capturing nonlinear vehicle dynamics.
What method is used to solve the control problem?
A robust model predictive control (MPC) is developed, and a feasible solution is obtained through a set of linear matrix inequalities (LMIs).
How was the proposed method validated?
The method was validated using a Carsim/Simulink joint platform, and comparative results showed it effectively guarantees vehicle lateral stability under nonlinear conditions.
What are the practical implications of this research?
The proposed control strategy can improve the safety and stability of distributed drive electric vehicles, especially in extreme driving conditions, contributing to the advancement of electric vehicle control systems.
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