Direct Yaw Moment Control Research Articles

Stability Study of Distributed Drive Vehicles Based on Estimation of Road Adhesion Coefficient and Multi-Parameter Control

In order to improve the driving stability of distributed-drive intelligent electric vehicles under different roadway attachment conditions, this paper proposes a multi-parameter control algorithm based on the estimation of road adhesion coefficients. First, a seven-degree-of-freedom (7-DOF) vehicle dynamics model is established and optimized with a layered control strategy. The upper-level control module calculates the desired yaw rate and sideslip angle using the two-degree-of-freedom (2-DOF) vehicle model and estimates the road adhesion coefficient by using the singular-value optimized cubature Kalman filtering (CKF) algorithm; the middle-level utilizes the second-order sliding mode controller (SOSMC) as a direct yaw moment controller in order to track the desired yaw rate and sideslip angle while also employing a joint distribution algorithm to control the torque distribution based on vehicle stability parameters, thereby enhancing system robustness; and the lower-level controller performs optimal torque allocation based on the optimal tire loading rate as the objective. A Speedgoat-CarSim hardware-in-the-loop simulation platform was established, and typical driving scenarios were simulated to assess the stability and accuracy of the proposed control algorithm. The results demonstrate that the proposed algorithm significantly enhances vehicle-handling stability across both high- and low-adhesion road conditions.

Cooperative Control of Distributed Drive Electric Vehicles for Handling, Stability, and Energy Efficiency, via ARS and DYC

Distributed drive electric vehicles (DDEV), characterized by their independently drivable wheels, offer significant advantages in terms of vehicle handling, stability, and energy efficiency. These attributes collectively contribute to enhancing driving safety and extending the all-electric range for sustainable transportation. Nonetheless, the challenge persists in designing a control strategy that effectively coordinates the objectives of handling, stability, and energy efficiency under both lateral and longitudinal driving conditions. To this end, this paper proposes a cooperative control strategy for DDEVs, incorporating active rear steering (ARS) and direct yaw moment control (DYC) to enhance handling capabilities, stability, and energy efficiency. A stability boundary is delineated using an analytical expression that correlates with the front wheel steering angle, and an adjustment factor is introduced to quantify vehicle stability based on this input parameter. This factor aids in establishing a coordinated control reference for handling and stability. At the upper-level motion control layer, a model predictive control method is developed to track this reference and implement ARS and DYC for superior performance. Specifically, the rear lateral force serves as the control command for ARS, which is converted into a rear wheel steering angle using a tire inverse model. Meanwhile, the front lateral force is modeled as linear-time-varying to simplify calculations. At the lower-level torque allocation layer, the adjustment factor is utilized to balance tire workload rate and in-wheel motors’ (IWM) energy consumption, enabling efficient switching between energy consumption and driving stability targets, and the torque allocation is conducted to acquire the expected IWMs’ command. Both the upper and lower-level optimization problems are formulated as convex problems, ensuring efficient and effective solutions. Simulations verify the effectiveness of this strategy in improving handling, stability, and energy economy under DLC cases, while maintaining high computational efficiency.

Lateral stability control for distributed drive autonomous vehicle with extreme path tracking

To enhance the path-tracking accuracy and lateral stability of autonomous vehicles under extreme conditions, this paper proposes a coordinated control strategy based on an Active Front Steering (AFS) system and Direct Yaw Moment Control (DYC). First, a path-tracking controller based on Model Predictive Control (MPC) is designed, which includes a Kalman filter to correct lateral stiffness in real-time and calculates the front wheel steering angle output based on path-tracking errors and current direct yaw moment. Next, we formulated the Direct Yaw Moment Control objective as a linear combination of stability and maneuverability objectives, and used a fuzzy controller to dynamically coordinate the weights of stability and maneuverability objectives. This process not only improves the adaptability of the control strategy but also enhances vehicle performance under various road conditions. Furthermore, a Sliding Mode Control (SMC) is employed to calculate the required direct yaw moment. This approach ensures vehicle stability during high-speed driving or changes in road surface adhesion. To optimize torque distribution, we employed a constrained quadratic programming method to minimize tire load rates, thereby improving vehicle energy efficiency and handling. Finally, through Hardware-in-the-Loop (HIL) testing, we validated that the proposed control strategy achieves excellent tracking accuracy, real-time performance, and lateral stability under different road adhesion conditions and vehicle speeds. The control strategy developed in this study not only exhibits theoretical innovation but also demonstrates significant effectiveness in practical applications, providing valuable insights for path-tracking and lateral dynamic control strategies of autonomous vehicles under extreme conditions.

The direct yaw-moment control based on adaptive fuzzy LQR for distributed drive electric vehicles

This paper introduced a hierarchical control strategy for direct yaw moment (DYC) to enhance the handling and stability of distributed drive electric vehicles (DDEVs) at medium to high speeds. The upper controller entailed a speed-following PI controller and an adaptive fuzzy linear quadratic regulator (AFLQR) controller, with the control objectives centered on reducing the absolute value of the sideslip angle and tracking the desired yaw rate. The proposed approach utilizes a fuzzy logic-based AFLQR controller, which could dynamically adjust the weighting parameters for sideslip angle and yaw rate in response to the vehicle speed and sideslip angle, offering better adaptability to varying driving conditions. At the lower control level, a tire-dynamic-load-based torque distribution method was applied. The control strategy’s efficacy was demonstrated through co-simulation involving CarSim and Simulink. This evaluation compared AFLQR control against non-yaw control, conventional LQR control and sliding mode control (SMC), focusing on handling and stability during sinusoidal steering wheel input test and double lane change maneuver. Results highlight that AFLQR reduces the sideslip angle by 7.88% and the yaw rate error by 84.29% compared to LQR, enhancing vehicle handling and stability. Lastly, a hardware-in-the-loop (HIL) experiment verified the control strategy’s validity.

Integration of in-wheel motor sensorless systems and hierarchical direct yaw moment control for distributed drive electric vehicles

Ensuring robust and reliable control of distributed vehicles powered by in-wheel motor systems poses a significant challenge due to the harsh operating environments and high costs of such motor systems. Poor motor control, parameter variations, and sensor malfunction under these conditions can compromise the vehicle yaw stability. Integrating permanent magnet synchronous motor (PMSM) sensorless systems with vehicle yaw moment control offers a cost-effective solution for this issue without wheel angular speed sensors while enhancing yaw stability. In this paper, a composite nonlinear feedback sliding mode controller that can enhance the PMSM speed response is proposed. The proposed scheme exhibits a rotor speed overshoot and transient time of only 0.64% and 0.07s, respectively, which are smaller and shorter compared with other methods under motor parameter changes. Subsequently, the key states and tire-road friction coefficients required for vehicle control were estimated using sensorless rotor speeds and unscented Kalman filters, enabling the integration of the PMSM sensorless system with the vehicle yaw moment control. Additionally, a fuzzy adaptive hybrid sliding mode method is presented for yaw moment control enhancement. This method maintained the smallest sideslip angle root mean square error during double lane changes (0.4192 deg) compared with other methods. Analysis results show that different motor controllers and parameter changes significantly affect the vehicle dynamics performance. The proposed integrated scheme is feasible and effectively enhances the yaw moment control via high-performance sensorless PMSM systems.

Integrated Control of Intelligent Vehicle Driving Stability Using Three-Dimensional Phase Space

<div>To enhance vehicle dynamic stability during driving, we developed a three-dimensional phase space model that incorporates the sideslip angle of center of mass, yaw rate, and lateral load transfer rate. This model enabled real-time evaluation and active control of vehicle stability. First, longitudinal and lateral controllers were implemented to ensure precise vehicle trajectory. Second, a hierarchical control strategy was designed to actively manage the desired sideslip angle, yaw rate, and roll angle based on the vehicle’s destabilizing conditions, thereby maintaining the vehicle within a stable state space. We simulated and tested the stability analysis methods and integrated control strategies for both cars and trucks under DLC (double lane change) and CDC (circular driving condition) scenarios using joint simulations with CarSim/TruckSim and Simulink. The proposed integrated stability control strategy, which combined MPC-based trajectory tracking with direct yaw moment control and active suspension control, enhanced the vehicle’s directional and roll stability. This approach effectively mitigated vehicle instability under extreme conditions. Compared to the MPC lateral tracking control system, the performance of the integrated control system was significantly improved. In the DLC scenario, the maximum values of the sedan’s lateral deviation, sideslip angle, yaw rate, and vehicle roll angle decreased by 22.6%, 33.9%, 5.5%, and 1.2%, respectively. In the CDC scenario, the truck’s lateral acceleration, sideslip angle, yaw rate, and vehicle roll angle decreased by 7.5%, 46.8%, 8.2%, and 80%, respectively. Additionally, open-loop simulation tests were conducted under fishhook steering conditions for both passenger cars and trucks. The results further validated the effectiveness of the integrated control strategy, demonstrating its ability to significantly improve yaw rate and roll response, thereby enhancing overall vehicle stability under challenging driving conditions.</div>

Two Adaptive Sliding Mode Control Algorithms for Vehicle Stability Enhancement

This paper discusses two adaptive sliding mode control (ASMC) algorithms for enhancing vehicle stability through direct yaw moment control (DYC). DYC is based on a logic process derived from the understeering and oversteering behavior of a cornering vehicle. Furthermore, to achieve DYC in a four-wheeled passenger vehicle, the reference yaw moment computed by the proposed algorihms is converted into a braking pressure that is to be applied to the four wheels. The objective is to minimize the yaw rate error and constrain the sideslip angle to an acceptable range. According to Lyapunov theory, complete stability analysis guarantees the closed-loop stability and robustness of a control system. Simulation results were used to compare the two ASMC algorithms, and both algorithms showed high performance even under critical operating conditions.

Coordinated Control of Differential Drive-Assist Steering and Direct Yaw Moment Control for Distributed-Drive Electric Vehicles

Direct yaw moment control (DYC) and differential drive-assist steering (DDAS) for distributed-drive vehicles are both realized by allocating the in-wheel motor torque. To address the interference caused by overlapping control objectives, this paper proposes a multilayer control strategy that integrates DYC and DDAS, consisting of an upper controller, a coordinated decision layer, and a torque distribution layer. The upper controller, designed based on the vehicle’s dynamic characteristics, incorporates an adaptive fuzzy control DYC system and a dual PID control DDAS system. The coordinated decision layer is developed utilizing a phase-plane dynamic weighting method, delineating region boundaries by applying the double-line and limit cycle methods. The torque distribution strategy is formulated considering motor peak torque and road adhesion conditions. Multi-condition joint simulation experiments indicate that the proposed multilayer control strategy, integrating the advantages of DYC and DDAS, reduces peak steering wheel torque by approximately 10%, peak yaw rate by around 25%, peak sideslip angle by roughly 29%, and peak sideslip angle rate by about 19%, significantly improving driving stability and maneuvering flexibility.

Vehicle Stability Control Based on Vehicle Motion State and Tire Force Estimation

The direct yaw moment control system is able to greatly enhance the vehicle stability when driving on challenging road surfaces. This paper introduces a direct control approach for managing the vehicle yaw moment, utilizing terminal sliding mode control and a Square Root Cubature Kalman Filter (SRCKF). Initially, the longitudinal and lateral forces acting on the vehicle's tires are estimated through a sliding mode observer. Subsequently, the SRCKF algorithm and the four-wheel tire force are employed to accurately estimate the yaw rate and sideslip angle. Based on these estimations, additional yaw moments are determined using the terminal sliding mode control algorithm, and a combined control of yaw rate and sideslip angle is achieved through a threshold method. A rule-based braking force distribution strategy is then implemented to ensure vehicle stability control. Simulation results demonstrate that the tire force estimations from the sliding mode observer and the vehicle yaw rate and sideslip angle estimations from the SRCKF algorithm closely align with the output results from Carsim, with an error margin of less than 15%. The braking force distribution strategy, based on the direct yaw moment control using the terminal sliding mode algorithm, effectively tracks the desired yaw rate and sideslip angle.

Coordination control strategy of motion stability and tire slip for electric vehicle driven by in-wheel-motors

The Direct Yaw Moment Control (DYC) is a widely utilized technique for electric vehicles equipped with In-Wheel Motors (IWMs) to ensure yaw stability. However, most existing DYC studies calculate the additional control yaw moment solely based on the torque differences among the four IWMs, disregarding the nonlinear tire characteristics and wheel rotational movements. When road conditions are poor or torque changes are intense, the tire may slip, preventing it from generating the required longitudinal tire force for the desired direct yaw moment. To address this challenge, this study introduces a coordination control strategy for motion stability and tire slip in electric vehicles (EV) driven by IWMs. To enhance control performance, the nonlinear tire characteristics and wheel rotational movements are integrated into the modeling process when calculating tire forces. Additionally, a state and parameter coupling estimation algorithm is utilized to obtain feedback on tire parameters and vehicle motion states. Using these estimation results as a foundation, a coordination strategy is developed to achieve reference motion state tracking and tire slip ratio control. The Model Predictive Control (MPC) algorithm is employed to solve the control problem with constraints on both control inputs and outputs, and the estimation results are utilized to update the control model as well as provide states feedback. Simulations and experiments are conducted to validate the feasibility and effectiveness of the proposed control strategy. The results demonstrate that our proposed control strategy effectively improves vehicle stability by coordinating vehicle motion and tire slip control.

Combined Path Following and Direct Yaw-Moment Control for Unmanned Electric Vehicles Based on Event-Triggered T–S Fuzzy Method

Combined Path Following and Direct Yaw-Moment Control for Unmanned Electric Vehicles Based on Event-Triggered T–S Fuzzy Method

Output‐based enhanced closed‐loop model reference adaptive control and its application to direct yaw moment control

Output‐based enhanced closed‐loop model reference adaptive control and its application to direct yaw moment control

An NMPC-Based Integrated Longitudinal and Lateral Vehicle Stability Control Based on the Double-Layer Torque Distribution.

With the ongoing promotion and adoption of electric vehicles, intelligent and connected technologies have been continuously advancing. Electrical control systems implemented in electric vehicles have emerged as a critical research direction. Various drive-by-wire chassis systems, including drive-by-wire driving and braking systems and steer-by-wire systems, are extensively employed in vehicles. Concurrently, unavoidable issues such as conflicting control system objectives and execution system interference emerge, positioning integrated chassis control as an effective solution to these challenges. This paper proposes a model predictive control-based longitudinal dynamics integrated chassis control system for pure electric commercial vehicles equipped with electro-mechanical brake (EMB) systems, centralized drive, and distributed braking. This system integrates acceleration slip regulation (ASR), a braking force distribution system, an anti-lock braking system (ABS), and a direct yaw moment control system (DYC). This paper first analyzes and models the key components of the vehicle. Then, based on model predictive control (MPC), it develops a controller model for integrated stability with double-layer torque distribution. The required driving and braking torque for each wheel are calculated according to the actual and desired motion states of the vehicle and applied to the corresponding actuators. Finally, the effectiveness of this strategy is verified through simulation results from Matlab/Simulink. The simulation shows that the braking deceleration of the braking condition is increased by 32% on average, and the braking distance is reduced by 15%. The driving condition can enter the smooth driving faster, and the time is reduced by 1.5 s~5 s. The lateral stability parameters are also very much improved compared with the uncontrolled vehicles.

Improving Direct Yaw-Moment Control via Neural-Network-Based Non-Singular Fast Terminal Sliding Mode Control for Electric Vehicles.

Given the increased significance of electric vehicles in recent years, this study aimed to develop a novel form of direct yaw-moment control (DYC) to enhance the driving stability of four-wheel independent drive (4WID) electric vehicles. Specifically, this study developed an innovative non-singular fast terminal sliding mode control (NFTSMC) method that integrates NFTSM and a fast-reaching control law. Moreover, this study employed a radial basis function neural network (RBFNN) to approximate both the entire system model and uncertain components, thereby reducing the computational load associated with a complex system model and augmenting the overall control performance. Using the aforementioned factors, the optimal additional yaw moment to ensure the lateral stability of a vehicle is determined. To generate the additional yaw moment, we introduce a real-time optimal torque distribution method based on the vertical load ratio. The stability of the proposed approach is comprehensively verified using the Lyapunov theory. Lastly, the validity of the proposed DYC system is confirmed by simulation tests involving step and sinusoidal inputs conducted using Matlab/Simulink and CarSim software. Compared to conventional sliding mode control (SMC) and NFTSMC methods, the proposed approach showed improvements in yaw rate tracking accuracy for all scenarios, along with a significant reduction in the chattering phenomenon in control torques.

Adaptive fractional-order nonsingular terminal sliding mode control and sequential quadratic programming torque distribution for lateral stability of FWID-EVs with actuator constraints

This paper proposes a novel sliding mode control (SMC) algorithm for direct yaw moment control of four-wheel independent drive electric vehicles (FWID-EVs). The algorithm integrates adaptive law theory, fractional-order theory, and nonsingular terminal sliding mode reaching law theory to reduce chattering, handle uncertainty, and avoid singularities in the SMC system. A sequential quadratic programming (SQP) method is also proposed to optimize the yaw moment distribution under actuator constraints. The performance of the proposed algorithm is evaluated by a hardware-in-the-loop test with two driving maneuvers and compared with two existing SMC-based schemes together with the cases with the change of vehicle parameters and disturbances. The results demonstrate that the proposed algorithm can eliminate chattering and achieve the best lateral stability as compared with the existing schemes.

Distributed-Drive Vehicle Lateral-Stability Coordinated Control Based on Phase-Plane Stability Region

The lateral stability control of vehicles is one of the most crucial aspects of vehicle safety. This article introduces a coordinated-control strategy designed to enhance the handling stability of distributed-drive electric vehicles. The upper controller uses active front steering and direct yaw moment-control controllers designed based on sliding-mode control theory. The lower controller optimally allocates control inputs to the upper controller, considering factors such as load transfer and tire load rate. It divides the stability region by relying on the phase plane and develops a coordinated-control strategy based on the degree of deviation of the vehicle state from the stability region. The results of the simulation experiments demonstrate that the proposed control strategy effectively improves handling stability under extreme working conditions.

Electric Vehicle Steering System Fuzzy Modeling and Controller Design

Electric vehicle (EV) steering control becomes much more important in many senses such as driving comfort and safety. Unlike the traditional internal combustion engine powered vehicles that possess only one control input related to the steering wheel, the so‐called direct yaw moment control is yet another control input in EVs thanks to the dispersedly located in‐wheel motors. In view of controller design crucially depending on a proper mathematical model, this paper first focuses on the modeling of EV steering system with uncertainty in the system considered for the latter robust controller design. Then a Takagi‐Sugeno (T‐S) fuzzy model is obtained based on the EV's model, which is capable of varying vehicle velocity in a range. Finally, a robust controller with inputs constraint is designed based on the model, and the effectiveness is verified by computer simulations. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Adaptive Nonsingular Fast Terminal Sliding Mode-Based Direct Yaw Moment Control for DDEV under Emergency Conditions

This paper presents an innovative three-level direct yaw moment control strategy for distributed drive electric vehicles (DDEV) under emergency conditions. The phase plane analysis is used at the supervisory level to design the stability boundary function taking into account the impact of the road adhesion coefficient. To guarantee the performance of finite-time convergence and singularity-free methods, the adaptive nonsingular fast terminal sliding mode control (ANFTSMC) is developed at the decision level to determine the extra yaw moment for tracking the intended side slip angle and yaw rate. Among this, the unstable domain in the phase plane is further separated into moderately and severely unstable according to the degree of vehicle instability, which is defined by the distance between the state phase point and the stability boundary. Meanwhile, the adaptive weight between the handling and stability is obtained. At the executive level, the quadratic programming algorithm is adopted to allocate four-wheel torque with the objective of optimal tire utilization rate. Finally, the co-simulation test is executed in both closed-loop and open-loop circumstances; according to the simulation results, the presented ANFTSMC method outperforms the SMC, and it can decrease the tracking error and improve the handling and stability.

Autonomous High-Speed Overtaking of Intelligent Chassis Using Fast Iterative Model Predictive Control

High-speed overtaking is one of the structured driving scenarios of autonomous vehicles (AVs), and safety and real-time control requirements must be fulfilled during this scenario. In this work, we develop an overtaking path-planning and tracking framework for AVs based on the improved artificial potential field (APF) and fast iterative model predictive control (MPC). The improved APF is used to plan a feasible, high-speed overtaking path by considering the constraints of vehicle dynamics and introducing the adjustment factor into the potential function to avoid local optimization and target unreachability problems. In addition, to reduce the computational burden and fulfill the real-time control requirements of trajectory tracking, a fast iterative MPC algorithm is proposed herein. This algorithm adds disturbances that possess the nonlinear characteristics of the real model by using a linearized model. In terms of vehicle configuration, we consider that the target vehicle has the four-wheel steer (4WS)-four-wheel drive (4WD) chassis configuration and the fast iterative MPC is also used to coordinate the conflict between 4WS and direct yaw moment control (DYC) to improve tracking accuracy and vehicle stability during overtaking. Simulink/Carsim co-simulation and hardware-in-the-loop (HIL) tests are conducted to verify the effectiveness of the proposed controller.

On Torque Vectoring Control: Review and Comparison of State-of-the-Art Approaches

Torque vectoring is a widely known technique to improve vehicle handling and to increase stability in limit conditions. With the advent of electric vehicles, this is becoming a key topic since it is possible to have distributed powertrains, i.e., multiple motors are adopted, in which each motor is controlled separately from the others. Moreover, electric motors deliver the torque required by the controller faster and more precisely than internal combustion engines, active differentials and conventional hydraulic brakes. The state of the art of Direct Yaw Moment Control (DYC) techniques, ranging from classical to modern control theories, are analyzed and discussed in this paper. The aim is to give an overview of the currently available approaches while identifying their drawbacks regarding performances and robustness when dealing with common issues like model uncertainties, external disturbances, friction limit and common state estimation problems. This contribution analyzes all the steps from the lateral dynamics reference generation to the desired control action computation and allocation to the available actuators. In addition, some of the presented control logic is evaluated in a simulation environment for a passenger car. Results of both open-loop and closed-loop maneuvers allow the comparison and clarification of each control strategy’s key advantages.