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Torque vectoring (TV) is a commonly used method for four in-wheel motor electric vehicles (4-IWM EVs). Several existing studies based on model predictive control (MPC) focus on improving system stability and energy efficiency by minimizing or maximizing a performance function, defined as the time integral of the weighted sum of two cost functions. However, this approach must address the challenge of balancing these two objectives. Furthermore, the MPC framework lacks sufficient robustness against model uncertainties and external disturbances. This study proposes a two-layer TV controller for a 4-IWM EV, designed to enhance both robustness and energy efficiency, as specified in the Autonomous Driving Control Benchmark Challenge of IEEE CDC 2023. The first layer includes a direct yaw moment control module and a longitudinal force control module based on first-order sliding mode control, integrated with nonlinear disturbance observers (NDOBs) to estimate disturbance amplitudes from rough roads and reduce chattering. The second layer employs MPC to allocate torque among the wheels to minimize total energy consumption. Simulations, performed using a full 4-IWM EV simulator developed in Modelica, focused on the ISO double lane change on a rough road, as required by the benchmark challenge. The results demonstrate that the proposed control system significantly improves the vehicle’s robustness and energy efficiency in this scenario. [ABSTRACT FROM AUTHOR]

This paper proposes a vehicle motion control method to enhance ride comfort at the passenger’s position, aiming to provide optimal ride comfort to passengers during Advanced Driver Assistance System(ADAS)/Autonomous Driving(AD) driving. The control logic is designed to prevent collisions with the preceding vehicle and maintain the road curvature, as in conventional ADAS/AD systems, while also minimizing the longitudinal and lateral accelerations, as well as the lateral velocity at the passenger’s position. The proposed control logic consists of a target vehicle motion module and a controller module. In the target vehicle motion module, the target longitudinal velocity, target lateral velocity, and target yaw rate at the vehicle’s center of gravity are determined. The target longitudinal velocity is determined to prevent collisions with the preceding vehicle and minimize both longitudinal and lateral accelerations, while the target lateral velocity is determined to minimize the lateral velocity at the passenger’s position. The target yaw rate is determined to track the road’s curvature. To track the determined target motions, the controller calculates control inputs for the drive motor, hydraulic braking, front-wheel steering, and torque vectoring. The controller consists of a longitudinal control module and a lateral control module. The longitudinal control module determines the control inputs for the drive motor and hydraulic braking needed to track the target longitudinal velocity, while the lateral control module determines the control inputs for front-wheel steering and torque vectoring needed to track the target lateral velocity and target yaw rate. The proposed control logic was validated in a simulation environment using MATLAB/Simulink and CarSim. The simulation results confirmed that the proposed approach improves the ride comfort at the passenger’s location compared to the conventional ADAS/AD systems.

The following article presents a high-level overview of how Model Predictive Control (MPC) is leveraged in passenger vehicles and their subsystems for improved performance. This overview presents the fundamental concepts of MPC algorithms and their common variants. After building some understanding of MPC methods, the paper discusses state-of-the-art examples of how MPC methods are leveraged to perform low- to high-level tasks within a typical passenger vehicle. This review also aims to provide the reader with intuition in formulating MPC systems based on the strengths and weaknesses of the different formulations of MPC. The paper also highlights active areas of research and development. [ABSTRACT FROM AUTHOR]

This work presents a predictive torque vectoring controller that optimally monitors the vehicle limits of handling using active torque distribution in the rear axle of a fully electric vehicle. It works in combination with a feedforward controller designed to improve the vehicle's agility. The overall torque vectoring strategy is described together with the vehicle lateral dynamics, sideslip angle estimator, and torque allocation method. Numerical simulations for various scenarios and road profiles show the benefits of predicting the vehicle's handling limits and the enhancement of vehicle stability in terms of reduced vehicle sideslip angle and driver effort. The proposed optimal control method for predicting vehicle handling limit violations does not require a dedicated solver, making it a promising candidate for real-time applications. The case study is a vehicle equipped with two rear in-wheel motors in the framework of , an ECSEL Joint Undertaking (JU) European research project. Hardware-in-the-loop (HiL) tests were performed on a dedicated e-axle test bench to integrate the torque vectoring controller with the real e-motors and a dual inverter. The results of the HiL testing demonstrate that the torque-vectoring requirements are satisfied by the hardware configuration in use. [ABSTRACT FROM AUTHOR]

With a shift in the automotive industry's focus towards sustainability and energy efficiency, optimizing vehicle handling dynamics has been put on a secondary level. Moreover, there is a growing trend towards comfort-oriented design, conversely to the vehicle-handling one. Nevertheless, recent advancements such as the integration of multiple independently controlled electric motors on a vehicle is enabling torque vectoring, which offers a promising opportunity for reconciling these conflicting objectives. This paper proposes a novel approach for jointly improving vehicle handling and energy efficiency performance. Indeed, through advanced simulation techniques, the effects of various suspension configurations are explored to strike a balance between cornering performance and energy consumption. Then, a torque vectoring controller is designed in combination with a meticulous tuning of the suspension setup. This innovative approach of considering the active control design together with the suspensions' setup allows to obtain superior performances. Indeed, the desired vehicle cornering capabilities can be achieved while also guaranteeing a significantly more efficient vehicle in straight-line running, which covers most of the usual road driving time. [ABSTRACT FROM AUTHOR]

This paper describes control methods to improve electric vehicle performance in terms of handling, stability and cornering by adjusting the weight distribution and implementing control systems (e.g., wheel slip control, and yaw rate control). The vehicle is first simulated using the bicycle model to capture the dynamics. Then, a study on the effect of weight distribution on the driving behavior is conducted. The study is performed for three different weight configurations. Moreover, a yaw rate controller and a wheel slip controller are designed and implemented to improve the vehicle's performance for cornering and longitudinal motion under the different loading conditions. The simulation through the bicycle model is compared to the experiments conducted on a rear-wheel driven radio-controlled (RC) electric vehicle. The paper shows how the wheel slip controller contributes to the stabilization of the vehicle, how the yaw rate controller reduces understeering, and how the location of the center of gravity (CoG) affects steering behavior. Lastly, an analysis of the combination of control systems for each weight transfer is conducted to determine the configuration with the highest performance regarding acceleration time, braking distance, and steering behavior. [ABSTRACT FROM AUTHOR]

The approaches of foreign specialists to improving electronic control systems for the dynamic state of vehicles (traction, directional stability, and rollover resistance) to improve their safe operation are analyzed. The three main components of the active driveline torque-management (ADTM) system (the center clutch, the electronic limited slip differential (eLSD), and the torque vectoring system) are considered. The possibilities and limitations of using active torque control systems to ensure vehicle safety are shown. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The following article presents a high-level overview of how Model Predictive Control (MPC) is leveraged in passenger vehicles and their subsystems for improved performance. This overview presents the fundamental concepts of MPC algorithms and their common variants. After building some understanding of MPC methods, the paper discusses state-of-the-art examples of how MPC methods are leveraged to perform low- to high-level tasks within a typical passenger vehicle. This review also aims to provide the reader with intuition in formulating MPC systems based on the strengths and weaknesses of the different formulations of MPC. The paper also highlights active areas of research and development.

This paper presents a novel differential with lateral torque vectoring activated by an auxiliary motor, called motor-modulated lateral torque vectoring differential, or briefly, MLTD. Its architecture and kinematic characteristics are described, and the optimal cornering performance due to torque vectoring is evaluated using a steady-state vehicle dynamic model. Then, a conceptual design case of MLTD installed in a front-wheel-drive electric vehicle is conducted to assess its feasibility in terms of cornering, driving performances, and energy efficiency performance. The calculations show that an optimal distribution ratio between left and right torques for maximum lateral acceleration can be obtained for a specific cornering condition, further used for DM sizing in the preliminary stage. The simulations for energy consumption at constant-speed turning reveal that energy efficiencies of MLTD are lower than those of conventional differentials with evenly distributed torques. However, this deficiency may be paid off by moderately cutting down the rolling resistance of tire while the superior cornering performances brought by torque vectoring is still preserved. Accordingly, the newly proposed MLTD possesses greater flexibility to improve energy efficiency and driving range of electric vehicles without trading off against its desirable cornering performance and safe handling, and is thus worthy of further development. [ABSTRACT FROM AUTHOR]

The yaw acceleration required for circuit driving is determined by the time variation of the yaw rate due to two factors: corner radius and velocity at the center of gravity. Torque vectoring systems have the advantage where the yaw moment can be changed only by the longitudinal force without changing the lateral force of the tires, which greatly affects lateral acceleration. This is expected to improve the both the spinning performance and the orbital performance, which are usually in a trade-off relationship. In this study, we proposed a yaw moment control technology that actively utilized a power unit with a brake system, which was easy to implement in a system, and compared the performance of vehicles equipped with and without the proposed system using the Milliken Research Associates moment method for quasi-steady-state analysis. The performances of lateral acceleration and yaw moment were verified using the same method, and a variable corner radius simulation for circuit driving was used to compare time and performance. The results showed the effectiveness of the proposed system.

This paper considers the problem of stabilizing and energy-efficient torque vectoring for electric vehicles with four independent in-wheel motors. In electric vehicles with four in-wheel motors, four electric motors are separately attached to the four wheels without an extra drive shaft. The mechanical and structural nature enables reduction of energy loss during power transmission and securing extra interior space. In addition, independent control of wheel torques can provide better yaw motion stability and improved energy efficiency. This paper proposes two model predictive control (MPC) methods for stability-constrained energy-efficient torque vectoring of four in-wheel motor electric vehicles. For the adaptive weighting factors of multiple objective functions of reference tracking and energy saving, we use exponential functions that vary with the lateral motion and steering input. Depending on the optimal control problem formulation with different dynamical system equations and constraints, the associated predictive controller can be represented as either a linear parameter-varying MPC (LPV-MPC) or nonlinear MPC (NMPC). For LPV-MPC, longitudinal and lateral motions are decoupled, whereas the coupled dynamics of the two-track model are exploited in NMPC. For comparisons and demonstrations of LPV-MPC and NMPC in the MPC of torque vectoring, three driving scenarios are simulated with a high-fidelity vehicle simulation solution, CarMaker (IPG Automotive). In comparison with the built-in IPG driver implemented in CarMaker, we demonstrate fuel efficiency improvements of over 2–3% on average with guaranteed yaw stability.

This paper deals with the torque vectoring control problem for uncertain in-wheel motor vehicles. The main objective of this study is to enhance the cornering performance of vehicles at high speed driving and this is done by generating possibly different motor torques applied to wheels. The proposed controller consists of a model predictive control based outer-loop controller and a disturbance observer based inner-loop controller. The outer-loop controller finds the optimal longitudinal tire force considering state and input constraints. The inner-loop controller estimates the difference between the nominal tire model that is used by the outer-loop controller and the unmodeled disturbance, and compensates the disturbance so that the actual vehicle follows the nominal model. The proposed controller is validated via numerical experiments for circular driving, double lane change, and skidpad scenarios and it is shown that the state tracking performance is improved by using the proposed controller.

Featured Application: The methodology presented in this paper can be applied to the design and evaluation of torque vectoring systems in hybrid electric vehicles. Comparison of different controllers is helpful in making design choices in these applications. In today's automotive industry, electrification is a major trend. In-wheel electric motors are among the most promising technologies yet to be fully developed. Indeed, the presence of multiple in-wheel motors acting as independent actuators allows for the implementation of innovative active systems and control strategies. This paper analyzes different design possibilities for a torque vectoring system applied to an originally compact front-wheel drive hybrid electric vehicle with one internal combustion engine for the front axle and two added electric motors integrated in the wheels of the rear axle. A 14 degrees of freedom vehicle model is present o accurately reproduce the nonlinearities of vehicle dynamic phenomena and exploited to obtain high-fidelity numerical simulation results. Different control methods are compared, a PID, an LQR, and four different sliding mode control strategies. All controllers achieve sufficiently good results in terms of lateral dynamics compared with the basic hybrid version. The various aspects and features of the different strategies are analyzed and discussed. Chattering reduction strategies are developed to improve the performance of sliding mode controllers. For a complete overview, control systems are compared using a performance factor that weighs control accuracy and effort in different driving maneuvers, i.e., ramp and step steering maneuvers performed under quite different conditions ranging up to the limits. [ABSTRACT FROM AUTHOR]

Electric vehicles (EVs) enable the integration of powertrains with multiple motors, allowing for the adjustment of torque delivered to each wheel. This approach permits the implementation of torque vectoring techniques (TV) to enhance the vehicle's stability and cornering response, providing better control of yaw moments. This study utilizes comprehensive telemetry data and an advanced simulator model to assess the influence of torque vectoring (TV) on a Formula SAE (Society of Automotive Engineers) competition vehicle. The telemetry data were collected from a fully instrumented 2WD car, which was then employed to calibrate the simulation model. The calibrated model was subsequently utilized to predict the performance enhancements that could be achieved by implementing a 4WD system. The methodology proved to be a valuable contribution to vehicle design development. This approach also helps evaluate the potential advantages of torque vectoring for drivers with limited experience. [ABSTRACT FROM AUTHOR]

The yaw acceleration required for circuit driving is determined by the time variation of the yaw rate due to two factors: corner radius and velocity at the center of gravity. Torque vectoring systems have the advantage where the yaw moment can be changed only by the longitudinal force without changing the lateral force of the tires, which greatly affects lateral acceleration. This is expected to improve the both the spinning performance and the orbital performance, which are usually in a trade-off relationship. In this study, we proposed a yaw moment control technology that actively utilized a power unit with a brake system, which was easy to implement in a system, and compared the performance of vehicles equipped with and without the proposed system using the Milliken Research Associates moment method for quasi-steady-state analysis. The performances of lateral acceleration and yaw moment were verified using the same method, and a variable corner radius simulation for circuit driving was used to compare time and performance. The results showed the effectiveness of the proposed system. [ABSTRACT FROM AUTHOR]

This study concerns the comparative investigation of two advanced lateral stability automotive controllers with respect to a commercial solution. The research aims to improve the stability performances achieved by a combined tracking of yaw rate and side-slip angle through the application of optimal efforts. The proposed solutions are based on Linear Quadratic Regulation and Sliding Mode Control, respectively. Both rely on the same approach for the control objective definition but differ from the action perspective. This solution involves the adoption of a differential braking actuation technique to deliver a desired yaw moment to the car body to track controlled states. Indeed, a sliding controller can also traction torques of hub-motor configurations as well as steering corrections, achieving vehicle stability and a driving response in accordance with the pilot's intentions. Calibration and validation of the controllers are performed through a Hardware-in-the-Loop simulation rig, along with a real-time static simulator, performing different close-loop maneuvers to assess achievements in terms of lateral stability. Results show that both solutions ensure higher handling performances if compared to Non-controlled or Commercial-controlled vehicle scenarios. [ABSTRACT FROM AUTHOR]

Electric vehicles (EVs) offer benefits in terms of reducing emissions and saving energy over other conventional vehicles. There have been various studies on EVs for energy efficiency and driving performance improvement. As an area of EV systems, dual-motor systems with planetary gear trains have been studied for fuel efficiency improvement, but they have limitations for torque vectoring and maximum torque compared to other typical systems. To overcome these limitations, a novel dual-motor EV system with a planetary gear train has been suggested for eco and dynamic driving modes. The system achieves variable motor operating points for energy efficiency improvement by using dual motors with a planetary gear train. Multiple driving modes are implemented by a synchronizer for torque vectoring and motor maximum torque driving. The suggested system was analyzed by comparison with a typical left-and-right-wheel independent drive dual-motor system with representative EPA test cycles. The novel dual-motor system shows not only the possibility of eco driving by improving fuel efficiency compared to typical dual-motor systems but also performance driving with torque vectoring functionality, which is not available for previous dual-motor systems with planetary gear trains.

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.

Improved mathematical and simulation modes of the active differential mechanism (DM) with controllable torque redistribution would better contribute to developing intelligent vehicle transmissions. The issue is caused by actualizing the precise steerability control using advanced automated transmissions, allowing torque vectoring for all-wheel-drive vehicles and ensuring an option for correcting the vehicle trajectory. This paper presents an alternative mathematical method for obtaining differential equations for modeling vehicle transmission components and its implementation for simulating the Audi sport DM. First, the steerability issues of sport DM technology are discussed, and the sport DM design is described in detail. Then, a mathematical approach is proposed that includes three types of equation systems: generalized dynamics equations, kinematic constraint equations, and gearing condition equations. The approach also considers the flexibility of the clutch’s frictional pack, friction torque, lockup condition, and piston dynamics. Finally, a Simulink model that reflects the DM operation and calculation procedures is developed. A series of simulations of the sport DM operation with forcible torque distribution is carried out. The results show that the proposed mathematical model is universal, efficient, and accurate.

This paper presents a novel differential with lateral torque vectoring activated by an auxiliary motor, called motor-modulated lateral torque vectoring differential, or briefly, MLTD. Its architecture and kinematic characteristics are described, and the optimal cornering performance due to torque vectoring is evaluated using a steady-state vehicle dynamic model. Then, a conceptual design case of MLTD installed in a front-wheel-drive electric vehicle is conducted to assess its feasibility in terms of cornering, driving performances, and energy efficiency performance. The calculations show that an optimal distribution ratio between left and right torques for maximum lateral acceleration can be obtained for a specific cornering condition, further used for DM sizing in the preliminary stage. The simulations for energy consumption at constant-speed turning reveal that energy efficiencies of MLTD are lower than those of conventional differentials with evenly distributed torques. However, this deficiency may be paid off by moderately cutting down the rolling resistance of tire while the superior cornering performances brought by torque vectoring is still preserved. Accordingly, the newly proposed MLTD possesses greater flexibility to improve energy efficiency and driving range of electric vehicles without trading off against its desirable cornering performance and safe handling, and is thus worthy of further development.

In today’s automotive industry, electrification is a major trend. In-wheel electric motors are among the most promising technologies yet to be fully developed. Indeed, the presence of multiple in-wheel motors acting as independent actuators allows for the implementation of innovative active systems and control strategies. This paper analyzes different design possibilities for a torque vectoring system applied to an originally compact front-wheel drive hybrid electric vehicle with one internal combustion engine for the front axle and two added electric motors integrated in the wheels of the rear axle. A 14 degrees of freedom vehicle model is present o accurately reproduce the nonlinearities of vehicle dynamic phenomena and exploited to obtain high-fidelity numerical simulation results. Different control methods are compared, a PID, an LQR, and four different sliding mode control strategies. All controllers achieve sufficiently good results in terms of lateral dynamics compared with the basic hybrid version. The various aspects and features of the different strategies are analyzed and discussed. Chattering reduction strategies are developed to improve the performance of sliding mode controllers. For a complete overview, control systems are compared using a performance factor that weighs control accuracy and effort in different driving maneuvers, i.e., ramp and step steering maneuvers performed under quite different conditions ranging up to the limits.

Electric vehicles (EVs) enable the integration of powertrains with multiple motors, allowing for the adjustment of torque delivered to each wheel. This approach permits the implementation of torque vectoring techniques (TV) to enhance the vehicle’s stability and cornering response, providing better control of yaw moments. This study utilizes comprehensive telemetry data and an advanced simulator model to assess the influence of torque vectoring (TV) on a Formula SAE (Society of Automotive Engineers) competition vehicle. The telemetry data were collected from a fully instrumented 2WD car, which was then employed to calibrate the simulation model. The calibrated model was subsequently utilized to predict the performance enhancements that could be achieved by implementing a 4WD system. The methodology proved to be a valuable contribution to vehicle design development. This approach also helps evaluate the potential advantages of torque vectoring for drivers with limited experience.

Automobiles are becoming more and more complex as multiple control systems are integrated into the vehicle platform. This paper investigates the coordination of active rear steering (RWS) and torque vectoring (TV) – which is enabled by independent electric motors at the rear axle – in controlling vehicle lateral dynamics. The proposed controller aims at enhancing vehicle handling performance and stability while cornering. The coordination of the two actuators is achieved by weighting their contribution based on their impact on vehicle dynamics according to the working condition. The impact of each control system is assessed by means of phase portraits. These plots are a very powerful tool for analysing vehicle nonlinear dynamics as they readily display vehicle stability properties and map equilibrium point locations and movement to changing parameters and control inputs. Based on phase portrait analysis, a performance index is thus proposed, which weights more the control action (TV or RWS) capable of leading the vehicle at the nearest equilibrium point with the fastest rate. The controller performance is assessed through numerical simulations carried out using a nonlinear 14 dofs vehicle model. Results are compared with ones of the two controllers alone (RWS and TV) in different manoeuvers and adherence conditions. [ABSTRACT FROM AUTHOR]