Torque Distribution Research Articles

Driving Control Strategy and Specification Optimization for All-Wheel-Drive Electric Vehicle System with a Two-Speed Transmission

Equipping electric vehicles with a two-speed gearbox allows for achieving high torque and maximum speed through appropriate gear ratio adjustments. Additionally, tuning motor operating points to efficient zones, considering energy efficiency, significantly enhances the vehicle’s overall performance. This paper presents an AWD system configuration method, integrating a two-speed transmission to improve energy efficiency and driving performance through front and rear motor torque distribution and powertrain specification optimization. Based on vehicle simulations conducted using MATLAB/Simulink, a strategy for torque distribution between the front/rear axles was established using fuzzy logic, considering energy efficiency and driving stability. Furthermore, a multi-objective optimization was performed using a surrogate model trained through MATLAB parallel simulations. When the optimization results were applied to various vehicle specifications, it was observed that energy efficiency was improved, and acceleration performance was increased compared to a baseline vehicle without optimization.

Automatic determination of directional stability parameters of an electric vehicle with a two-motor scheme as part of the torque distribution controller

In case if the front and rear axle of the electric vehicle are not mechanically linked, the presence of automatic torque distribution to the axles or wheels becomes not only an addition to increase the level of consumer properties, but also a necessity. A method for determining the directional stability condition of an electric four-wheel drive vehicle is developed as part of the research by comparing the target and measured yaw rate, and is based on the formulated conditions of drift, skid, and counter steer registration. A method for detecting slipping of the driving wheels of an electric vehicle with a dual-motor scheme is developed, which is based on comparing the target and measured velocity differences of the front and rear axle and includes an auto oscillation detection function. A method for determining the target front and rear axle speed difference in a corner is described. Based on the tests performed, it is concluded that the proposed methods are applicable to the active torque distribution function between the axles of an all-wheel drive electric vehicle being developed by the authors of the paper, which provides improved directional stability and controllability, and counteracts slipping of the drive wheels.

Stability coordinated control strategy of autonomous unmanned 4WID-4WIS vehicle based on APD-LQR and AFSMC

To improve the four-wheel independent driving and four-wheel independent steering (4WID-4WIS) autonomous unmanned vehicles’ active safety performance at their maximum operating capacity, the control of path following, four-wheel steering (4WS) and lateral stability should be coordinated. This paper introduces a hierarchical coordinated control framework, in which several independent controllers collaborate to enhance the overall performance of the vehicle system. Initially, in the upper controller, an adaptive preview distance linear quadratic regulator (APD-LQR) path following algorithm is proposed, considering the dynamic characteristics of the tire. It aimed at making the following error converge and obtaining the optimal front wheel steering angle. Meanwhile, an adaptive fuzzy sliding mode control (AFSMC) algorithm is implemented for obtaining additional yaw moment. It aimed at coordinating and improving effectively path following performance and lateral stability. Using the phase plane approach, the sliding surface is dynamically modified. Subsequently, in the lower controller, a rear wheel angle controller based on vehicle speed is proposed. It aimed at further enhancing vehicle’s maneuverability and stability by fully utilizing its steering redundancy features. Moreover, a torque distribution controller establishes a comprehensive cost function and then the NSGA-III algorithm is employed to optimize the torque distribution coefficients. Finally, simulation and Hardware-in-Loop (HIL) test results demonstrates that the proposed coordination algorithm can fully utilize the redundancy features of the 4WID-4WIS vehicle, and significantly enhances the vehicle’s path following accuracy and lateral stability, especially under extreme driving conditions.

Lateral-Stability-Oriented Path-Tracking Control Design for Four-Wheel Independent Drive Autonomous Vehicles with Tire Dynamic Characteristics under Extreme Conditions

This paper proposes a lateral-stability-oriented path-tracking controller for four-wheel independent drive (4WID) autonomous vehicles. The proposed controller aims to maintain vehicle stability under extreme conditions while minimizing lateral deviation. Firstly, a tiered control framework comprising upper-level and lower-level controllers is introduced. The upper-level controller is a lateral stability path-tracking controller that incorporates tire dynamic characteristics, developed using model predictive control (MPC) theory. This controller dynamically updates the tire lateral force constraints in real time to account for variations in tire dynamics under extreme conditions. Additionally, it enhances lateral stability and reduces path-tracking errors by applying additional yaw torque based on minimum tire utilization. The lower-level controllers execute the required steering angles and yaw moments through the appropriate component equipment and torque distribution. The joint simulation results from CarSim and MATLAB/Simulink show that, compared to the traditional MPC controller with unstable sideslip, this controller can maintain vehicle lateral stability under extreme conditions. Compared to the MPC controller, which only considers lateral force constraints, this controller can significantly reduce lateral tracking errors, with an average yaw rate reduction of 31.62% and an average sideslip angle reduction of 40.21%.

Optimal powertrain system design and V2V and V2I based hierarchical control strategy of FRIDEV under vehicle-following scenarios

In this paper, the front- and rear-independent-drive electric vehicle (FRIDEV) is selected as the target vehicle for its good dynamic and economy performance. Based on the analysis of the cost, efficiency, and loss characteristics of different motors, the interior permanent magnet synchronous motor (IPMSM) and induction motor (IM) are applied in the target powertrain system. Then, the proposed powertrain system is optimized based on the analysis of driving cycles. The optimal control strategy for the target powertrain system is developed, which consists of the driving mode switching algorithm and the driving torque distribution based on adaptive particle swarm optimization (APSO). Furthermore, in order to achieve the efficient autonomous driving of the target vehicle under the vehicle-following scenarios, a hierarchical control strategy is proposed with the combination of upper-level control of the speed planning strategy and the lower-level control of powertrain system control strategy. The upper-level control of speed planning strategy is designed, which can determine and track the target vehicle speed based on the information from vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications. Finally, simulation analysis in MATLAB/Simulink and virtual driving experiments are conducted to verify the superiority of the proposed powertrain system and hierarchical control strategy.

A learning‐based hierarchical energy management control strategy for hybrid electric vehicles

AbstractIn this work, a novel energy management control framework is developed for hybrid electric vehicles (HEVs) driving in car‐following scenarios. In order to enhance the energy efficiency while maintaining the driving safety, a hierarchical control approach consisting of an upper level speed tracking control scheme and a lower level energy management control strategy is proposed. For the upper level tracking control system, an iterative learning model predictive control (ILMPC) scheme is developed to guarantee the tracking performance and the driving safety simultaneously. Additionally, a model predictive control (MPC) algorithm is adopted at the lower level to optimize the torque distribution in real‐time based on the driving cycles generated by the upper level control system. With the proposed hierarchical control framework, HEVs are able to improve the energy efficiency significantly by taking the advantages of the operational repeatability. The convergence of the proposed control strategy is analyzed rigorously, and its effectiveness is illustrated through numerical simulations.

Torque distribution of distributed drive electric vehicle based on efficiency map of drive system

Abstract In order to optimize the system efficiency of distributed drive electric vehicles, based on the MAP of the efficiency of the drive motor system, the objective function of the optimal efficiency is established, and the problem of the no-load loss of the drive motor is considered. A torque distribution control strategy method considering the no-load loss of the motor is proposed. Then, AVL CRUISE and Simulink are used to establish a joint simulation platform, and a comparative simulation test analysis is carried out under ECE conditions. The simulation results show that the torque distribution strategy considering the loss makes the distributed drive motor work in a relatively high efficiency range. Compared with the torque distribution strategy without considering the loss, the power consumption is reduced by 3.4%, which effectively improves the vehicle economy. The research results can provide a reference for system efficiency optimization of distributed drive electric vehicles.

Braking Torque Distribution Reconfiguration Strategy of Vehicle With Faults of In-Wheel Motor Drive System

Braking Torque Distribution Reconfiguration Strategy of Vehicle With Faults of In-Wheel Motor Drive System

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.

Cooperative energy optimal control involving optimization of longitudinal motion, powertrain, and air conditioning systems

This paper is concerned with the optimal control strategies for the longitudinal control, powertrain, and air conditioning (A/C) system of connected four-wheel hub-drive electric vehicles (EVs). A hierarchical control framework is developed to enhance the energy economy of the vehicle. Real-time connected information is utilized in the upper layer to determine the travel mode. Then, a multi-objective motion planning system (MOMPS) is proposed to plan the optimal acceleration trajectory. In the lower layer, an offline global optimization approach is employed to find the torque combinations that minimize the total power loss. The proposed A/C controller operates based on the bi-level model predictive control (Bi-level MPC) algorithm. A novel prediction model is developed to enable the A/C system to decrease energy consumption by leveraging the speed of the vehicle. The performance of the MOMPS is evaluated using urban test road data, demonstrating that the MOMPS can balance multiple objectives compared to global dynamic programing (Global DP) and the intelligent driver model (IDM). In addition, the proposed torque distribution strategy results in a 4.98% energy-savings rate through comparison with the even torque distribution strategy. Moreover, the A/C controller proposed in this paper can optimize energy consumption by 13.57% compared to a baseline strategy that maintains a constant setting.

Torsion of end-bearing pile foundations in layered anisotropic geomaterials

ABSTRACT An analysis for the torsional dynamic response of end-bearing pile foundations embedded in a layered transversely isotropic geomaterial (soil/rock) is presented. The deformation of the transversely isotropic soil or rock is described by the method of separation of variables. The elasticity theory for a viscoelastic medium with frequency independent hysteretic material damping, and the Extended Hamilton’s Principle are utilised to derive the differential equations describing pile and soil motions. The differential equations are solved analytically in an iterative algorithm. The accuracy of the analysis is verified with existing studies reported in the literature for pile foundations embedded in a homogeneous and layered soil deposit. The effect of the degree of anisotropy on the pile-soil response – dynamic pile-head stiffness, distribution of pile rotation and torque with depth, dimensionless soil displacement function for various values of pile slenderness and pile-soil stiffness ratios in a homogenous soil deposit is investigated. Design charts of static pile-head stiffness in a homogeneous soil deposit for a wide range of pile-soil stiffness and pile slenderness ratios, and degree of anisotropy are also reported. The effect of soil layering for a pile embedded in a two-layered soil deposit is also studied.

Improved Lateral Dynamics through Optimized Torque Distribution

Improved Lateral Dynamics through Optimized Torque Distribution

Design and research of face gear central limited slip differential and analysis of its influence on vehicle performance

In this paper, a new design scheme of face gear central limited-slip differential (F-LSD) is proposed, which aims to unveil the technical veil of central limited-slip differential and fill the research blank of face gear application in the field of central limited-slip differential. Through the analysis of structural principle and motion characteristics, the dynamic equilibrium equation and locking coefficient model of F-LSD are established. The Simulink simulation model based on F-LSD dynamics and the torque distribution model of the whole transmission system are established. A 7-DOF vehicle dynamics model was established, and the performance of F-LSD vehicle in four conditions of acceleration, climbing, chassis twist sine wave and double line change was studied by using simulation software. At the same time, four groups of four-wheel drive vehicles with different central differential speeds were set as the control test group. The simulation results show that F-LSD system can effectively improve the vehicle's dynamic performance and extrication performance, and will not reduce the vehicle's handling stability, which provides a reference for the practical application of the face gear central limited slip differential.

Research on a Chassis Stability Control Method for High-Ground-Clearance Self-Propelled Electric Sprayers

In response to the complex working conditions and poor driving stability of high-clearance self-propelled sprayers, a nonlinear model of the chassis power system was established based on the independently controllable torque of each wheel of the developed electric sprayer. A layered-architecture chassis drive control strategy was formulated, and a stability control framework comprising an instability judgment module, an upper controller, and a lower controller was constructed based on the analysis of the impact of the centroid slip angle, the yaw rate, and the wheel slip rate on driving stability. An ideal reference model was established based on the seven-degree-of-freedom model of the sprayer, and the current state of the sprayer body was determined using the instability judgment module. A drive anti-slip controller and a yaw moment controller based on fuzzy PID theory and sliding mode control theory were designed. Additionally, an optimal torque distribution algorithm was developed based on tire characteristics to rationally allocate drive torque to each wheel, ensuring the stability of the sprayer during operation. Simulation tests were conducted using MATLAB/Simulink to evaluate the sprayer under four different driving conditions during transport and field operations. The test results showed that the “SMC + optimal distribution” control method in the chassis stability control strategy reduced the maximum deviations of the yaw rate and centroid slip angle by an average of 89.5% and 13.6%, respectively, compared to no control. The wheel slip rate during straight driving was well maintained at around 15%, enhancing the driving stability of the sprayer.

Battery health-considered energy management strategy for a dual-motor two-speed battery electric vehicle based on a hybrid soft actor-critic algorithm with memory function

Energy management strategies (EMSs) ease mileage anxiety and improve the health performance of battery electric vehicles (BEVs). This study proposes a soft actor-critic (SAC)-based EMS for dual-motor two-speed BEV to minimize electrical energy consumption and battery capacity losses. In addition, two optimization tricks are employed to optimize the original SAC. The linear mapping trick is integrated into the actor-network of SAC to enable agents to search for optimal EMS in a discrete (driving mode)-continuous (torque distribution) hybrid action space. The SAC-based EMS is modeled as a partially observable Markov decision process (POMDP) to obtain more information about the real state of the environment. Based on this, another optimization trick, the long short-term memory (LSTM) network, is integrated into the actor and critic of SAC to make full use of both historical and current environmental information. Simulation results show that the proposed method learns the optimal EMS, its converged episodes are shortened to the 97th, the health performance of the battery is the closest to the dynamic programming (DP)-based EMS, and maintains battery operating at a range of 30–40°C. In addition, the proposed EMS has the best adaptability in test cycles, reaching 99.42% and 99.29% of DP-based EMS, respectively.

Research on Optimal Driving Torque Control Strategy for Multi-Axle Distributed Electric Drive Heavy-Duty Vehicles

Multi-axle distributed electric drive heavy-duty vehicles have the characteristics of high transmission efficiency, strong maneuverability, and good passability, making them widely used in large cargo transportation. However, the current driving torque control strategies of multi-axle distributed electric drive heavy-duty vehicles lack comprehensive consideration of their longitudinal and lateral dynamic characteristics, making it difficult to comprehensively optimize multiple performances such as power economy, comfort, and stability. In order to solve the above problems, This work focuses on a five-axle distributed electric drive heavy-duty vehicle. Firstly, given the differences in dynamics between two-axle vehicles and multi-axle vehicles, the dynamic model of the multi-axle distributed electric drive heavy-duty vehicle and its critical components is constructed. Then, by analyzing the characteristics of power economy, comfort, and stability of the multi-axle distributed electric drive heavy-duty vehicle, an optimal driving torque control strategy based on multiple performance coordination is proposed. Finally, on the hardware-in-the-loop (HiL) platform, the performance of the optimal driving torque control strategy proposed in this paper is verified by using the China Heavy-Duty Commercial Vehicle Test Cycle for Truck (CHTC-HT) and a straight-line acceleration driving condition on a split friction road. The simulation test results show that, compared with the traditional torque average distribution strategy, the proposed optimal driving torque control strategy can reduce the energy consumption rate by 3.45% in CHTC-HT. The strategy is attributed to the driving torque distribution based on the vehicle’s optimal instantaneous energy consumption, and vehicle comfort is also ensured by the driving mode switching frequency suppression. Subsequently, the vehicle’s stability on the split friction road is effectively improved by the torque coordination compensation strategy. This control strategy significantly improves the comprehensive performance of multi-axle distributed electric drive heavy-duty vehicles.

A multi-layer predictive energy management strategy for intelligent hybrid electric trucks collaborated with eco-driving control

Nowadays, hybrid electric trucks (HETs) are also urgently expected to further enhance energy efficiency with the development of intelligent driving system. A multi-layer predictive energy management strategy is designed for intelligent parallel HET to enhance fuel economy and computational efficiency. Depending on intelligently implementation of traffic prediction with navigation data, an online smart battery SOC generation is proposed to obtain an approximately global optimal SOC reference trajectory in the upper layer. In the bottom controller, a novel method, the tolerant sequential model predictive control (MPC) collaborated with sampling strategy, could achieve eco-driving in consideration of both driving comfort and safety with less computation time in autonomous driving scenario. Moreover, to simultaneously accomplish fuel economy and decrease computational burden, the integrated equivalent consumption minimization strategy with dynamic programming (ECMS-DP) solver for MPC scheme is presented to frozen SOC state and jointly control torque distribution and gear action. Numerical simulations demonstrate that the proposed multi-layer strategy has improved over 20 % fuel economy and decreased almost 50 % computational burden relative to traditional MPC benchmark strategy, which could exhibit great effectiveness and potential for practical implementation in real driving routes.

A novel EMS design framework for SPHTs based on instantaneous layer, driving event layer, and driving cycle layer

To effectively harness the energy-saving potential of series–parallel hybrid transmissions (SPHTs) with multiple gears and modes and to enhance the driving cycle adaptability of the rule-based energy management strategy (RB EMS), this study establishes a novel EMS design framework for SPHTs at three levels: the instantaneous, the driving event, and the driving cycle layers. Firstly, an equivalent fuel factor based on the principles of energy conservation and calorific value measurements is constructed, the energy consumption of different working modes and torque combinations under different instantaneous power units is determined, and the decision conditions of working modes are determined. Secondly, the energy consumption of engine and motor torque combination under constant speed, acceleration and deceleration driving events is compared, and the torque distribution feature of multi-power sources is determined. Thirdly, a driving cycle distribution factor is introduced and calculated using vehicle navigation map information, which can adjust the gear switching condition of parallel driving mode online. Based on above, an RB EMS adjusted with driving cycles (ADC-RB EMS) is proposed. The effectiveness of the proposed strategy is then verified through real-world vehicle tests. The fuel consumption performance of this strategy falls between the RB EMS and the dynamic programming (DP) strategy. According to the fuel consumption results, the RB EMS consumes an additional 0.35 L/100 km of fuel, while the DP strategy saves only 3.66% more energy compared to this strategy. The application potential of driving cycle distribution factor in instantaneous optimal control is tested. Compared with ADC-RB and CD-CS, the fuel saving rate is 1.71% and 5.67% respectively, which proves the energy saving performance of A-ECMS. This study provides a development direction for improving the energy saving effect of the RB EMS.

Distributed Drive Electric Vehicle Handling Stability Coordination Control Framework Based on Adaptive Model Predictive Control.

Distributed drive electric vehicles improve steering response and enhance overall vehicle stability by independently controlling each motor. This paper introduces a control framework based on Adaptive Model Predictive Control (AMPC) for coordinating handling stability, consisting of three layers: the dynamic supervision layer, online optimization layer, and low-level control layer. The dynamic supervision layer considers the yaw rate and maneuverability limits when establishing the β-β˙ phase plane stability boundary and designs variable weight factors based on this stability boundary. The online optimization layer constructs the target weight-adaptive AMPC strategy, which can adjust the control weights for maneuverability and lateral stability in real time based on the variable weight factors provided by the dynamic supervision layer. The low-level control layer precisely allocates the driver's requested driving force and additional yaw moment by using torque distribution error and tire utilization as the cost function. Finally, experiments are conducted on a Simulink-CarSim co-simulation platform to assess the performance of AMPC. Simulation results show that, compared to the traditional MPC strategy, this control strategy not only enhances maneuverability under normal conditions but also improves lateral stability control under extreme conditions.

Fundamental properties of the gyroscope oscillation

Despite partial solutions by famous scientists during the early Industrial Revolution, gyroscope problems remained unsolvable until the beginning of the twentieth century when several fundamental physical laws were finally formulated to describe them. Today, the principles of classical mechanics enable the formulation and description of the physical processes involved in the rotation of any object. Gyroscopic devices are objects that rotate and exhibit oscillation, which has been a challenging problem in engineering mechanics. The oscillation of a gyroscope is caused by the interaction between external and inertial torques. This is different from other examples of oscillation, such as pendulums and springs, which have been well documented. The main difference in the physics of gyroscopic oscillation is that the spinning rotors of the gyroscopic devices are supported on one side, with their axes perpendicular to the axis of oscillation. The oscillation of gyroscopic devices is interrelated with the potential and kinetic energy of their components. However, the physics of oscillation of such objects has not been fully described in publications until recently. The theory of gyroscopic effects for rotating objects has now been published and provides a solution to this problem. According to this theory, gyroscopic inertial torques represent the potential energy of the external torque and kinetic energy of the spinning rotor. This paper demonstrates the distribution of inertial torques about the axes of Cartesian coordinates, which enables the computation of gyroscope motion and oscillation.