An optimal torque distribution control strategy for four-independent wheel drive electric vehicles

In this paper, an optimal torque distribution approach is proposed for electric vehicle equipped with four independent wheel motors to improve vehicle handling and stability performance. A novel objective function is formulated which works in a multifunctional way by considering the interference among different performance indices: forces and moment errors at the centre of gravity of the vehicle, actuator control efforts and tyre workload usage. To adapt different driving conditions, a weighting factors tuning scheme is designed to adjust the relative weight of each performance in the objective function. The effectiveness of the proposed optimal torque distribution is evaluated by simulations with CarSim and Matlab/Simulink. The simulation results under different driving scenarios indicate that the proposed control strategy can effectively improve the vehicle handling and stability even in slippery road conditions.     

Unified decision-making and control for highway collision avoidance using active front steer and individual wheel torque control

ABSTRACT

Collision avoidance is a crucial function for all ground vehicles, and using integrated chassis systems to support the driver presents a growing opportunity in active safety. With actuators such as in-wheel electric motors, active front steer and individual wheel brake control, there is an opportunity to develop integrated chassis systems that fully support the driver in safety critical situations. Here we consider the scenario of an impending frontal collision with a stationary or slower moving vehicle in the same driving lane. Traditionally, researchers have approached the required collision avoidance manoeuver as a hierarchical scheme, which separates the decision-making, path planning and path tracking. In this context, a key decision is whether to perform straight-line braking, or steer to change lanes, or indeed perform combined braking and steering. This paper approaches the collision avoidance directly from the perspective of constrained dynamic optimisation, using a single optimisation procedure to cover these aspects within a single online optimisation scheme of model predictive control (MPC). While the new approach is demonstrated in the context of a fully autonomous safety system, it is expected that the same approach can incorporate driver inputs as additional constraints, yielding a flexible and coherent driver assistance system.     

Real-time model predictive control of connected electric vehicles

ABSTRACT

Electric Vehicles (EVs) motors develop high torque at low speeds, resulting in a high rate of acceleration with the added advantage of being fitted with smaller gearboxes. However, a rapid rise of torque in EVs fitted with central drive powertrains can create undesired torsional oscillations, which are influenced by wheel slip and flexibility in the halfshaft. These torsional oscillations in the halfshaft lead to longitudinal oscillations in the vehicle, thus creating problems with regard to comfort and drivability. The significance of using wheel slip in addition to halfshaft torsion for design of anti-jerk controllers for EVs has already been highlighted in our previous research. In this research, we have designed a look-ahead model predictive controller (LA-MPC) that calculates the required motor torque demand to meet the dual objectives of increased traction and anti-jerk control. The designed LA-MPC will improve drivability and energy consumption in connected EVs. The real-time capability of the LA-MPC has been demonstrated through hardware-in-the-loop experiments. The performance of the LA-MPC has been compared to other controllers presented in the literature. A validated high-fidelity longitudinal-dynamics model of the Rav4EV, which is the test vehicle of our research has been used to evaluate the controller.     

Effect of handling characteristics on minimum time cornering with torque vectoring

In this paper, the effect of both passive and actively-modified vehicle handling characteristics on minimum time manoeuvring for vehicles with 4-wheel torque vectoring (TV) capability is studied. First, a baseline optimal TV strategy is sought, independent of any causal control law. An optimal control problem (OCP) is initially formulated considering 4 independent wheel torque inputs, together with the steering angle rate, as the control variables. Using this formulation, the performance benefit using TV against an electric drive train with a fixed torque distribution, is demonstrated. The sensitivity of TV-controlled manoeuvre time to the passive understeer gradient of the vehicle is then studied. A second formulation of the OCP is introduced where a closed-loop TV controller is incorporated into the system dynamics of the OCP. This formulation allows the effect of actively modifying a vehicle's handling characteristic via TV on its minimum time cornering performance of the vehicle to be assessed. In particular, the effect of the target understeer gradient as the key tuning parameter of the literature-standard steady-state linear single-track model yaw rate reference is analysed.     

Wheel slip control with torque blending using linear and nonlinear model predictive control

Modern hybrid electric vehicles employ electric braking to recuperate energy during deceleration. However, currently anti-lock braking system (ABS) functionality is delivered solely by friction brakes. Hence regenerative braking is typically deactivated at a low deceleration threshold in case high slip develops at the wheels and ABS activation is required. If blending of friction and electric braking can be achieved during ABS events, there would be no need to impose conservative thresholds for deactivation of regenerative braking and the recuperation capacity of the vehicle would increase significantly. In addition, electric actuators are typically significantly faster responding and would deliver better control of wheel slip than friction brakes. In this work we present a control strategy for ABS on a fully electric vehicle with each wheel independently driven by an electric machine and friction brake independently applied at each wheel. In particular we develop linear and nonlinear model predictive control strategies for optimal performance and enforcement of critical control and state constraints. The capability for real-time implementation of these controllers is assessed and their performance is validated in high fidelity simulation.     

Modelling and model predictive control for a bicycle-rider system

This study proposes a bicycle-rider control model based on model predictive control (MPC). First, a bicycle-rider model with leaning motion of the rider’s upper body is developed. The initial simulation data of the bicycle rider are then used to identify the linear model of the system in state-space form for MPC design. Control characteristics of the proposed controller are assessed by simulating the roll-angle tracking control. In this riding task, the MPC uses steering and leaning torques as the control inputs to control the bicycle along a reference roll angle. The simulation results in different cases have demonstrated the applicability and performance of the MPC for bicycle-rider modelling.     

A novel direct yaw moment controller for in-wheel motor electric vehicles

A novel direct yaw moment controller is developed in this paper. A hierarchical control architecture is adopted in the controller design. In the upper controller, a driver model and a vehicle model are used to obtain the driver's intention and the vehicle states, respectively. The upper controller determines the desired yaw moment by means of sliding mode control. The lower controller distributes differential longitudinal forces according to the desired yaw moment. A nonlinear tyre model, ‘UniTire’, is utilised to develop the novel distribution strategy and the control boundary.     

A nonlinear model predictive control formulation for obstacle avoidance in high-speed autonomous ground vehicles in unstructured environments

This paper presents a nonlinear model predictive control (MPC) formulation for obstacle avoidance in high-speed, large-size autono-mous ground vehicles (AGVs) with high centre of gravity (CoG) that operate in unstructured environments, such as military vehicles. The term ‘unstructured’ in this context denotes that there are no lanes or traffic rules to follow. Existing MPC formulations for passenger vehicles in structured environments do not readily apply to this context. Thus, a new nonlinear MPC formulation is developed to navigate an AGV from its initial position to a target position at high-speed safely. First, a new cost function formulation is used that aims to find the shortest path to the target position, since no reference trajectory exists in unstructured environments. Second, a region partitioning approach is used in conjunction with a multi-phase optimal control formulation to accommodate the complicated forms the obstacle-free region can assume due to the presence of multiple obstacles in the prediction horizon in an unstructured environment. Third, the no-wheel-lift-off condition, which is the major dynamical safety concern for high-speed, high-CoG AGVs, is ensured by limiting the steering angle within a range obtained offline using a 14 degrees-of-freedom vehicle dynamics model. Thus, a safe, high-speed navigation is enabled in an unstructured environment. Simulations of an AGV approaching multiple obstacles are provided to demonstrate the effectiveness of the algorithm.     

Model predictive control with constraints for a nonlinear adaptive cruise control vehicle model in transition manoeuvres

A vehicle following control law, based on the model predictive control method, to perform transition manoeuvres (TMs) for a nonlinear adaptive cruise control (ACC) vehicle is presented in this paper. The TM controller ultimately establishes a steady-state following distance behind a preceding vehicle to avoid collision, keeping account of acceleration limits, safe distance, and state constraints. The vehicle dynamics model is for continuous-time domain and captures the real dynamics of the sub-vehicle models for steady-state and transient operations. The ACC vehicle can execute the TM successfully and achieves a steady-state in the presence of complex dynamics within the constraint boundaries.     

A model of driver steering control incorporating the driver's sensing of steering torque

Steering feel, or steering torque feedback, is widely regarded as an important aspect of the handling quality of a vehicle. Despite this, there is little theoretical understanding of its role. This paper describes an initial attempt to model the role of steering torque feedback arising from lateral tyre forces. The path-following control of a nonlinear vehicle model is implemented using a time-varying model predictive controller. A series of Kalman filters are used to represent the driver's ability to generate estimates of the system states from noisy sensory measurements, including the steering torque. It is found that under constant road friction conditions, the steering torque feedback reduces path-following errors provided the friction is sufficiently high to prevent frequent saturation of the tyres. When the driver model is extended to allow identification of, and adaptation to, a varying friction condition, it is found that the steering torque assists in the accurate identification of the friction condition. The simulation results give insight into the role of steering torque feedback arising from lateral tyre forces. The paper concludes with recommendations for further work.     

A study on model fidelity for model predictive control-based obstacle avoidance in high-speed autonomous ground vehicles

This paper investigates the level of model fidelity needed in order for a model predictive control (MPC)-based obstacle avoidance algorithm to be able to safely and quickly avoid obstacles even when the vehicle is close to its dynamic limits. The context of this work is large autonomous ground vehicles that manoeuvre at high speed within unknown, unstructured, flat environments and have significant vehicle dynamics-related constraints. Five different representations of vehicle dynamics models are considered: four variations of the two degrees-of-freedom (DoF) representation as lower fidelity models and a fourteen DoF representation with combined-slip Magic Formula tyre model as a higher fidelity model. It is concluded that the two DoF representation that accounts for tyre nonlinearities and longitudinal load transfer is necessary for the MPC-based obstacle avoidance algorithm in order to operate the vehicle at its limits within an environment that includes large obstacles. For less challenging environments, however, the two DoF representation with linear tyre model and constant axle loads is sufficient.     

A combined-slip predictive control of vehicle stability with experimental verification

In this paper, a model predictive vehicle stability controller is designed based on a combined-slip LuGre tyre model. Variations in the lateral tyre forces due to changes in tyre slip ratios are considered in the prediction model of the controller. It is observed that the proposed combined-slip controller takes advantage of the more accurate tyre model and can adjust tyre slip ratios based on lateral forces of the front axle. This results in an interesting closed-loop response that challenges the notion of braking only the wheels on one side of the vehicle in differential braking. The performance of the proposed controller is evaluated in software simulations and is compared to a similar pure-slip controller. Furthermore, experimental tests are conducted on a rear-wheel drive electric Chevrolet Equinox equipped with differential brakes to evaluate the closed-loop response of the model predictive control controller.     

Velocity control with disturbance observer for pedal-assisted electric bikes

This paper proposes a velocity control approach for light electric bicycles with human power assistance. A disturbance observer mechanism is used to estimate the sum of the human torque and resistance torques. The resulting vehicle velocity control provides better battery energy efficiency by knowledge of the instantaneous human torque assistance and better speed control by knowledge of the instantaneous resistive torque. The disturbance observer is tuned in terms of the DC gain of a low-passed Q-filter for both open-loop and closed-loop schemes. Assuming that the slow varying nature of the disturbance has been properly estimated and compensated, the torque control law is designed via an optimal control approach to achieve multi-objective performances regarding the external disturbance input, control signal magnitude, and velocity tracking error. The three main parameters of the electric bike, including the moment of inertia, the radius of tyre and the vehicle weight are allowed to be variational. Specifically, the deviation of the inertia moment and deviation of the tyre radius are addressed during the controller design in terms of linear matrix inequalities. On the other hand, the effect of vehicle weight deviation on the system behaviour is evaluated when the vehicle is implemented with the constructed control law. Based on the parameters and specifications of the EL-168 electric bike produced by KENTFA Advanced Technology, Taiwan, the design results are verified through time–response simulations.     

Decoupling control in velocity-varying four-wheel steering vehicles with H∞ performance by longitudinal velocity and yaw rate feedback

In this paper, decoupling control with H_∞ performance for four-wheel steering (4WS) vehicles under varying longitudinal velocity is studied. A novel control scheme for a nonlinear model of three states, respectively, the longitudinal and lateral velocities, and yaw rate, is proposed to address this issue. The scheme is composed of two varying-parameter controllers designing problems for both longitudinal and lateral systems with coupling performance. Varying parameters of both these controllers depend only on longitudinal velocity. Controlled by these controllers, the longitudinal system is decoupled with lateral velocity and yaw rate, and the lateral system is input–output decoupling with H_∞ performance. In addition, feedback signals are the longitudinal velocity and yaw rate, hence observations or measurements of lateral velocity are not necessary. Simulations show that vehicles controlled by our scheme are input–output diagonal decoupling and execute very well while longitudinal velocity varies in a large range, coupling appears between longitudinal and lateral systems, and external disturbances do exist. In summary, this control scheme can improve handling characteristics, safety and comfort proved from theory to practice in this paper.     

A receding horizon sliding control approach for electric powertrains with backlash and flexible half-shafts

Active control of electric powertrains is challenging, due to the fact that backlash and structural flexibility in transmission components can cause severe performance degradation or even instability of the control system. Furthermore, high impact forces in transmissions reduce driving comfort and possibly lead to damage of the mechanical elements in contact. In this paper, a nonlinear electric powertrain is modelled as a piecewise affine (PWA) system. The novel receding horizon sliding control (RHSC) idea is extended to constrained PWA systems and utilised to systematically address the active control problem for electric powertrains. Simulations are conducted in Matlab/Simulink in conjunction with the high fidelity Carsim software. RHSC shows superior jerk suppression and target wheel speed tracking performance as well as reduced computational cost over classical model predictive control (MPC). This indicates the newly proposed RHSC is an effective method to address the active control problem for electric powertrains.     

A control strategy for parallel hybrid electric vehicles based on extremum seeking

An energy management control strategy for a parallel hybrid electric vehicle based on the extremum-seeking method for splitting torque between the internal combustion engine and electric motor is proposed in this paper. The control strategy has two levels of operation: the upper and lower levels. The upper level decision-making controller chooses the vehicle operation mode such as the simultaneous use of the internal combustion engine and electric motor, use of only the electric motor, use of only the internal combustion engine, or regenerative braking. In the simultaneous use of the internal combustion engine and electric motor, the optimum energy distribution between these two sources of energy is determined via the extremum-seeking algorithm that searches for maximum drivetrain efficiency. A dynamic programming solution is also obtained and used to form a benchmark for performance evaluation of the proposed method based on extremum seeking. Detailed simulations using a realistic model are presented to illustrate the effectiveness of the methodology.     

Optimal torque coordinating control of the launching with twin clutches simultaneously involved for dry dual-clutch transmission

As for the self-developed six-speed dry dual-clutch transmission (DCT), the optimal torque-coordinated control strategy between engine and dual clutches is proposed to resolve the problem of launching with twin clutches simultaneously involved based on the minimum value principle. Focusing on the sliding friction phase of the launching process, dynamics equations of dry DCT with two intermediate shafts are firstly established, and then the optimal transmitting torque variation rate and the driven plate's rotating speed of dual clutches are deduced by using the minimum value principle, in which the jerk intensity and friction work are taken as the performance indexes, and the terminal constraints of state variables are determined according to the driver's launching intention. Besides, the separating conditions of non-target gear clutch and the torque distributing relations of twin clutches are derived from the launching control targets that guarantee the approximately equal friction extent of two clutches and no power cycle. After the synchronisation of driving and driven plates of on-coming clutch, the output torque of engine is smoothly switched to the driver's demand level. Furthermore, launching the simulation model of the dry DCT vehicle is set up on the Matlab/Simulink platform. Simulation results indicate that the proposed launching control strategy not only can effectively reflect the driver's intention and extend the life span of twin clutches, but also obtain an excellent launching quality. Finally, the torque control laws of two clutches obtained through the simulation are transformed into clutch position control laws for the future realisation in the real car, and the closed-loop position controls of twin clutches in the launching process are conducted on the test bench with two sets of clutch actuator, obtaining preferable tracking effects.     

A novel vehicle dynamics stability control algorithm based on the hierarchical strategy with constrain of nonlinear tyre forces

Direct yaw moment control (DYC), which differentially brakes the wheels to produce a yaw moment for the vehicle stability in a steering process, is an important part of electric stability control system. In this field, most control methods utilise the active brake pressure with a feedback controller to adjust the braked wheel. However, the method might lead to a control delay or overshoot because of the lack of a quantitative project relationship between target values from the upper stability controller to the lower pressure controller. Meanwhile, the stability controller usually ignores the implementing ability of the tyre forces, which might be restrained by the combined-slip dynamics of the tyre. Therefore, a novel control algorithm of DYC based on the hierarchical control strategy is brought forward in this paper. As for the upper controller, a correctional linear quadratic regulator, which not only contains feedback control but also contains feed forward control, is introduced to deduce the object of the stability yaw moment in order to guarantee the yaw rate and side-slip angle stability. As for the medium and lower controller, the quantitative relationship between the vehicle stability object and the target tyre forces of controlled wheels is proposed to achieve smooth control performance based on a combined-slip tyre model. The simulations with the hardware-in-the-loop platform validate that the proposed algorithm can improve the stability of the vehicle effectively.     

Combined longitudinal and lateral control for automated vehicle guidance

This paper deals with the longitudinal and lateral control of an automotive vehicle within the framework of fully automated guidance. The automotive vehicle is a complex system characterised by highly nonlinear longitudinal and lateral coupled dynamics. Consequently, automated guidance must be simultaneously performed with longitudinal and lateral control. This work presents an automated steering strategy based on nonlinear model predictive control. A nonlinear longitudinal control strategy considering powertrain dynamics is also proposed to cope with the longitudinal speed tracking problem. Finally, a simultaneous longitudinal and lateral control strategy helps to improve the combined control performance. This whole control strategy is tested through simulations showing the effectiveness of the present approach.     

Integrated chassis control for a three-axle electric bus with distributed driving motors and active rear steering system

This paper describes an integrated chassis control framework for a novel three-axle electric bus with active rear steering (ARS) axle and four motors at the middle and rear wheels. The proposed integrated framework consists of four parts: (1) an active speed limiting controller is designed for anti-body slip control and rollover prevention; (2) an ARS controller is designed for coordinating the tyre wear between the driving wheels; (3) an inter-axle torque distribution controller is designed for optimal torque distribution between the axles, considering anti-wheel slip and battery power limitations and (4) a data acquisition and estimation module for collecting the measured and estimated vehicle states. To verify the performances, a simulation platform is established in Trucksim software combined with Simulink. Three test cases are particularly designed to show the performances. The proposed algorithm is compared with a simple even control algorithm. The test results show satisfactory lateral stability and rollover prevention performances under severe steering conditions. The desired tyre wear coordinating performance is also realised, and the wheel slip ratios are restricted within stable region during intensive driving and emergency braking with complicated road conditions.