Model predictive torque vectoring control with active trail-braking for electric vehicles

In this work we present the development of a torque vectoring controller for electric vehicles. The proposed controller distributes drive/brake torque between the four wheels to achieve the desired handling response and, in addition, intervenes in the longitudinal dynamics in cases where the turning radius demand is infeasible at the speed at which the vehicle is traveling. The proposed controller is designed in both the Linear and Nonlinear Model Predictive Control framework, which have shown great promise for real time implementation the last decades. Hence, we compare both controllers and observe their ability to behave under critical nonlinearities of the vehicle dynamics in limit handling conditions and constraints from the actuators and tyre-road interaction. We implement the controllers in a realistic, high fidelity simulation environment to demonstrate their performance using CarMaker and Simulink

On pre-emptive vehicle stability control

Future vehicle localisation technologies enable major enhancements of vehicle dynamics control. This study proposes a novel vehicle stability control paradigm, based on pre-emptive control that considers the curvature profile of the expected path ahead in the computation of the reference direct yaw moment and braking control action. The additional information allows pre-emptive trail braking control, which slows down the vehicle if the predicted speed profile based on the current torque demand is deemed incompatible with the reference trajectory ahead. Nonlinear model predictive control is used to implement the approach, in which also the steering angle and reference yaw rate provided to the internal model are varied along the prediction horizon, to account for the expected vehicle path. Two pre-emptive stability control configurations with different levels of complexity are proposed and compared with the passive vehicle, and two state-of-the-art nonlinear model predictive stability controllers, one with and one without non-pre-emptive trail braking control. The performance is assessed along obstacle avoidance tests, simulated with a high-fidelity model of an electric vehicle with in-wheel motors. Results show that the pre-emptive controllers achieve higher maximum entry speeds – up to ∼34% and ∼60% in high and low tyre-road friction conditions – than the formulations without preview.This work was supported in part by the Horizon 2020 Framework Programme of the European Commission under grant agreements no. 769944 (STEVE project) and no. 824311 (ACHILES project)

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

Optimal Direct Yaw Moment Control of a 4WD Electric Vehicle

This thesis is concerned with electronic stability of an all-wheel drive electric vehicle with independent motors mounted in each wheel. The additional controllability and speed permitted using independent motors can be exploited to improve the handling and stability of electric vehicles. In this thesis, these improvements arise from employing a direct yaw moment control (DYC) system that seeks to adapt the understeer gradient of the vehicle and achieve neutral steer by employing a supervisory controller and simultaneously tracking an ideal yaw rate and ideal sideslip angle. DYC enhances vehicle stability by generating a corrective yaw moment realized by a torque vectoring controller which generates an optimal torque distribution among the four wheels. The torque allocation at each instant is computed by finding a solution to an optimization problem using gradient descent, a well-known algorithm that seeks the minimum cost employing the gradient of the cost function. A cost function seeking to minimize excessive wheel slip is proposed as the basis of the optimization problem, while the constraints come from the physical limitations of the motors and friction limits between the tires and road. The DYC system requires information about the tire forces in real-time, so this study presents a framework for estimating the tire force in all three coordinate directions. The sideslip angle is also a crucial quantity that must be measured or estimated but is outside the scope of this study. A comparative analysis of three different formulations of sliding mode control used for computation of the corrective yaw moment and an evaluation of how successfully they achieve neutral steer is presented. IPG Automotive’s CarMaker software, a high-fidelity vehicle simulator, was used as the plant model. A custom electric powertrain model was developed to enable any CarMaker vehicle to be reconfigured for independent control of the motors. This custom powertrain, called TVC_OpenXWD uses the torque/speed map of a Protean Pd18 implemented with lookup tables for each of the four motors. The TVC_OpenXWD powertrain model and controller were designed in MATLAB and Simulink and exported as C code to run them as plug-ins in CarMaker. Simulations of some common maneuvers, including the J-turn, sinusoidal steer, skid pad, and mu-split, indicate that employing DYC can achieve neutral steer. Additionally, it simultaneously tracks the ideal yaw rate and sideslip angle, while maximizing the traction on each tire[CB1] . The control system performance is evaluated based on its ability to achieve neutral steer by means of tracking the reference yaw rate, stabilizing the vehicle by means of reducing the sideslip angle, and to reduce chattering. A comparative analysis of sliding mode control employing a conventional switching function (CSMC), modified switching function (MSMC), and PID control (HSMC) demonstrates that the MSMC outperforms the other two methods in addition to the open loop system

Optimal handling characteristics for electric vehicles with torque vectoring.

Torque vectoring by virtue of independent electric motors is the focus of an increasing number of studies as electric vehicles gain prominence as the chosen direction for the automotive industry. Building on active yaw control systems developed over the past decades, torque vectoring benefits from the high-responsiveness and controllability of the electric motor actuator. Furthermore, and especially in the case of vehicles equipped with one independent motor per wheel, the overall performance envelope of the vehicle is significantly improved, as well as the ability to actively shape the vehicle handling. Much attention has been focussed on controller development and control allocation aspects of torque vectoring controllers, but little on the appropriate yaw rate reference. Optimal control studies have been successfully used to mimic the expert driver in both minimum-time circuit racing and high-sideslip rally driving, and can offer insight into how to optimally tune active chassis control systems, such as torque vectoring yaw control. The main aim of this thesis was to investigate the optimal handling characteristics of an electric vehicle with four independent electric motors at the limits of performance. A TV controller was first developed for a prototype sportscar with 4 independent motors, employing a model-based design process that encompassed real-time software in the loop testing. Real-world track testing demonstrated the controller was able to successfully modify the handling characteristic of the vehicle in both understeer and oversteer directions, achieving good controller performance in steady-state and transient manoeuvres. The limit performance of the TV-controlled vehicle was subsequently investigated in the simulation domain. Numerical techniques were used to solve optimal control problems for a single-track vehicle model with linear tyres and an external yaw moment term representing the overall yaw moment arising from the difference in torques at each wheel. For a U-turn manoeuvre, it was shown that torque vectoring significantly lowers manoeuvre time in comparison with the vehicle without TV active, and that modifying the passive understeer gradient does not affect manoeuvre time. The system dynamics were reformulated to include a feedback torque vectoring controller. The target yaw rate reference was varied and it was found that the manoeuvre time was highly sensitive to the yaw rate reference. For minimising laptime, the target understeer gradient should be set to the passive understeer gradient value. The methodology was repeated for a higher fidelity model including nonlinear tyres and lateral load transfer, and found that when the torque vectoring controller was included in the system dynamics, the manoeuvre time showed little sensitivity to the target understeer gradient. Following the contradictory results of the optimal control problems, the vehicle models were investigated next. Time optimal yaw rate gain surfaces were generated from further minimum-time optimal control problems. Open-loop manoeuvres investigating effects of tyre model, lateral load transfer and torque vectoring generation mechanism found that tyre modelling was the dominant differentiator and tyre nonlinearity is an essential modelling consideration. Optimal control techniques have been used for high sideslip manoeuvring for conventional vehicles but no studies have explored the effects of torque vectoring on agility. In the final chapter, an aggressive turn-around manoeuvre was simulated and it was found that torque vectoring can significantly increase agility and reduce the space taken for an aggressive turn-around manoeuvre. Reducing yaw inertia increased agility, as well as increasing longitudinal slips limits. A critique of agility metrics in this context was given.PhD in Transport System

Vehicle Dynamic and Control of Constrained Multi-Actuation Systems at the Limits of Handling

With recent advances in electric vehicles, having electric motors directly driving the wheels is gaining attraction. When a vehicle is equipped with four independent electric hub motors or independently controlled brakes in each of the four wheels, it gives the control designers the option of controlling each wheel independently in real-time. Independent torque distribution enables developing optimal torque distribution systems for various objective functions. A good example of the benefits of an independent torque distribution strategy is the ability to maximize the vehicle's lateral grip. When a vehicle is operated at the friction handling limits, optimizing the lateral grip will maximize the vehicle maneuverability resulting in reduced vehicle’s oversteer or understeer behavior. Vehicle dynamics at the limits of handling is highly nonlinear, and hence, detailed dynamic analysis is necessary to understand the behavior of the vehicle. In this dissertation, the equations of motion of a vehicle driven on a road with the bank and grade angles are derived. The effect of these angles on the nonlinear vehicle dynamic model is studied and compared with a high-fidelity CarSim model for evaluation. A comprehensive dynamic analysis, based on the phase portrait method, is performed to investigate the effect of axle torque distribution on the stability of the vehicle dynamics. Inspired by the dynamic square method, an optimal torque distribution method is studied with the objective of maximizing the vehicle's lateral grip while the vehicle remains at its friction handling limit is developed. An optimal torque distribution algorithm is then developed in the form of a feedforward controller for two different configurations, one for the axial torque distribution and one for the corner torque distribution. The controllers are evaluated through simulation and experimental studies and results show improvement in both maneuverability and stability when the vehicle is operated at the handling limits. The new optimal actuation strategy is extended to controller design for performance vehicles equipped with active aerodynamic systems. Active aerodynamic systems are one of the few actuators capable of increasing normal loads acting on the wheels. Increasing the wheels' normal loads would result into higher tire-ground forces, hence providing higher brake/drive torque inputs. A control platform consists of a feedforward controller and a constrained feedback model predictive controller (MPC) is developed for such performance vehicles equipped with a front and rear active aerodynamic system. The objective function of the feedback MPC is for the yaw tracking, while the objective of the feedforward controller is to maximize the vehicle lateral grip. This new controller will optimize the active aerodynamic actuation system to maximize vehicle performance and maneuverability. The controller provides the optimal angle of attack for each aero surface so that the yaw tracking error be minimized. The controller has been evaluated in the CarSim simulation environment. Subsequently, the optimal torque distribution and the active aerodynamic controller are integrated into the form of a constrained multi-actuation model predictive control structure. The actuators of this control system are the four in-wheel independent electric motors and the two active aerodynamic surfaces at the front and rear of the vehicle. The control structure has constraints on the vehicle states, input amplitudes, and the input increments. The objective of the controller is to stabilize the vehicle while minimizing the yaw tracking error. A constraint adjustment module is designed to observe the actuators' constraints. This module prevents any excessive actuation command by adjusting the input constraints. This will minimize the cost and energy and reduce the computational time of the optimization solver by deactivating unnecessary actuators. The proposed multi-actuation controller is simulated and verified on CarSim and the obtained results are presented with detailed explanations

Real-time path-tracking MPC for an over-actuated autonomous electric vehicle

This paper illustrates the development of a nonlinear constrained predictive path-tracking controller, including realistic vehicle dynamics and multiple actuator inputs and its implementation in real time on an experimental vehicle platform. The controller is formulated for a particular over-actuated vehicle equipped with Torque Vectoring (TV) as well as All-Wheel-Steering (AWS) functionalities, which allow for the enhanced control of vehicle dynamics. The proposed Nonlinear Model Predictive Controller (NMPC) takes into account the nonlinearities in vehicle dynamics across the range of operation up to the limits of handling as dictated by the adhesion limits of the tyres. In addition, crucial constraints regarding the actuators’ physical limits are included in the formulation. The performance of the controller is demonstrated in a high fidelity simulation environment, as well as in real-time on a test vehicle, during the execution of demanding driving scenarios

A Novel Learning Based Model Predictive Control Strategy for Plug-in Hybrid Electric Vehicle

The multi-source electromechanical coupling renders energy management of plug-in hybrid electric vehicles (PHEVs) highly nonlinear and complex. Furthermore, the complicated nonlinear management process highly depends on knowledge of driving conditions, and hinders the control strategies efficiently applied instantaneously, leading to massive challenges in energy saving improvement of PHEVs. To address these issues, a novel learning based model predictive control (LMPC) strategy is developed for a serial-parallel PHEV with the reinforced optimal control effect in real time application. Rather than employing the velocity-prediction based MPC methods favored in the literature, an original reference-tracking based MPC solution is proposed with strong instant application capacity. To guarantee the optimal control effect, an online learning process is implemented in MPC via the Gaussian process (GP) model to address the uncertainties during state estimation. The tracking reference in LMPC based control problem in PHEV is achieved by a microscopic traffic flow analysis (MTFA) method. The simulation results validate that the proposed method can optimally manage energy flow within vehicle power sources in real time, highlighting its anticipated preferable performance