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Cranfield University CRANFIELD UNIVERSITY KONSTANTINOS ZARKADIS MODEL PREDICTIVE TORQUE VECTORING CONTROL WITH ACTIVE TRAIL-BRAKING FOR ELECTRIC VEHICLES SCHOOL OF AEROSPACE, TRANSPORT AND MANUFACTURING Transport Systems MSc by Research Academic Year: 2016–2017 Supervisor: Dr E. Velenis and Dr S. Longo February 2018 CRANFIELD UNIVERSITY SCHOOL OF AEROSPACE, TRANSPORT AND MANUFACTURING Transport Systems MSc by Research Academic Year: 2016–2017 KONSTANTINOS ZARKADIS Model Predictive Torque Vectoring Control with Active Trail-Braking for Electric Vehicles Supervisor: Dr E. Velenis and Dr S. Longo February 2018 This thesis is submitted in partial fulfilment of the requirements for the degree of MSc by Research. © Cranfield University 2018. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright owner. Abstract In this work we present the development of a torque vectoring controller for electric ve- hicles. 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 Nonlin- ear 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. Keywords torque vectoring; MPC; nonlinear predictive control; FEV. v vi ABSTRACT Contents Abstract v Table of Contents vii List of Figures ix List of Tables xi List of Abbreviations xiii Acknowledgements xv 1 Introduction 1 1.1 Motivation . .1 1.2 Literature Review . .5 1.2.1 Active Chassis Control . .6 1.2.2 Electric Motor as Control Actuator . .8 1.2.3 Model Predictive Control in Chassis Control . 12 1.3 Gap in knowledge . 15 1.4 Objectives and Methodology . 16 2 Vehicle Modelling 19 2.1 Vehicle Dynamics . 19 2.2 Tyre Forces . 22 2.3 Powertrain . 25 3 Model Predictive Control Fundamentals 29 3.1 Cost Function . 32 3.2 State Constraints . 33 3.3 Input Constraints . 34 4 Linear Torque Vectoring Control Development 37 4.1 Simulation Results . 39 vii viii CONTENTS 4.1.1 Step Steer . 39 4.1.1.1 Importance of velocity constraint . 39 4.1.1.2 Understeer gradient tuning performance . 44 4.1.2 Double Lane Change . 44 4.1.2.1 Double Lane Change m = 0:5.............. 45 4.1.2.2 Double Lane Change m = 0:7.............. 47 4.1.2.3 Double Lane Change m = 0:9.............. 50 4.2 Computational Performance . 52 4.3 Discussion . 54 5 Nonlinear Torque Vectoring Control Development 57 5.1 Nonlinear MPC formulation . 57 5.2 Simulation Results . 58 5.2.1 Step Steer . 58 5.2.2 Double Lane Change . 61 5.2.2.1 Double Lane Change m = 0:5.............. 61 5.2.2.2 Double Lane Change m = 0:7.............. 65 5.2.2.3 Double Lane Change m = 0:9.............. 67 5.3 Torque rate expansion . 70 5.3.1 Step Steer Results . 70 5.3.2 Double Lane Change Results . 72 5.4 Computational Performance . 78 5.5 Discussion . 80 6 Conclusions and Further Research 83 6.1 Concluding Remarks . 83 6.2 Future Work . 85 A Tuning Parameters 87 List of Figures 1.1 Understeer gradient characteristic . .3 1.2 Torque Vectoring technique . .5 2.1 Vehicle coordinate system . 20 2.2 Four wheel vehicle model. 22 2.3 Lateral road coefficient approximation; (a) mmax = 0:9, (b) mmax = 0:7, (c) mmax = 0:5.................................. 26 2.4 Static torque map of YASA-750 motor. [60] . 27 3.1 Receding Horizon Control policy. 30 3.2 Wheel torque limit calculation block. 34 3.3 Torque demand limit calculation block. 35 4.1 Velocity, step-steer at Tdmd = 1000Nm and Vin = 40kph.......... 40 4.2 Yaw rate, step-steer at Tdmd = 1000Nm and Vin = 40kph.......... 41 4.3 Position, step-steer at Tdmd = 1000Nm and Vin = 40kph.......... 42 4.4 Wheel torques, step-steer at Tdmd = 1000Nm and Vin = 40kph....... 43 4.5 Total torque, step-steer at Vin = 40kph with a variation of Tdmd....... 43 4.6 Position responses of different Kund, step-steer at Tdmd = 1000Nm and Vin = 40kph.................................. 44 4.7 Lateral dynamics CarMaker driver parameters. 45 4.8 Yaw rate, double lane change at m = 0:5, Tdmd = 700Nm and Vin = 8kph. 46 4.9 Position, double lane change at m = 0:5, Tdmd = 700Nm and Vin = 8kph.. 46 4.10 Velocity, double lane change at m = 0:5, Tdmd = 700Nm and Vin = 8kph.. 47 4.11 Yaw rate, double lane change at m = 0:7, Tdmd = 950Nm and Vin = 8kph. 48 4.12 Position, double lane change at m = 0:7, Tdmd = 950Nm and Vin = 8kph.. 48 4.13 Velocity, double lane change at m = 0:7 and Vin = 8kph.......... 49 4.14 Total torque, double lane change at m = 0:7, Tdmd = 950Nm and Vin = 8kph. 50 4.15 Yaw rate, double lane change at m = 0:9, Tdmd = 1150Nm and Vin = 8kph. 51 4.16 Position, double lane change at m = 0:9, Tdmd = 1150Nm and Vin = 8kph. 51 4.17 Velocity, double lane change at m = 0:9 and Vin = 8kph.......... 52 4.18 Total torque, double lane change at m = 0:9, Tdmd = 1150Nm and Vin = 8kph..................................... 52 ix x LIST OF FIGURES 4.19 LMPC performance, step-teer at Tdmd = 1000Nm and Vin = 40kph..... 53 4.20 LMPC performance, double lane change; top - m = 0:5, Tdmd = 700Nm; middle - m = 0:7, Tdmd = 950Nm; bottom - m = 0:9, Tdmd = 1150Nm... 54 5.1 Velocity, step-steer at Tdmd = 1200Nm and Vin = 40kph.......... 59 5.2 Yaw rate, step-steer at Tdmd = 1200Nm and Vin = 40kph.......... 59 5.3 Position, step-steer at Tdmd = 1200Nm and Vin = 40kph.......... 60 5.4 Total torque, step-steer at Tdmd = 1200Nm and Vin = 40kph........ 60 5.5 Velocity, double lane change at m = 0:5, Tdmd = 700Nm and Vin = 8kph.. 62 5.6 Yaw rate, double lane change at m = 0:5, Tdmd = 700Nm and Vin = 8kph. 62 5.7 Position, double lane change at m = 0:5, Tdmd = 700Nm and Vin = 8kph.. 63 5.8 Total torque, double lane change at m = 0:5, Tdmd = 700Nm and Vin = 8kph. 64 5.9 Velocity, double lane change at m = 0:7, Tdmd = 950Nm and Vin = 8kph.. 65 5.10 Yaw rate, double lane change at m = 0:7, Tdmd = 950Nm and Vin = 8kph. 66 5.11 Position, double lane change at m = 0:7, Tdmd = 950Nm and Vin = 8kph.. 66 5.12 Total torque, double lane change at m = 0:7, Tdmd = 950Nm and Vin = 8kph. 67 5.13 Velocity, double lane change at m = 0:9, Tdmd = 1150Nm and Vin = 8kph. 68 5.14 Yaw rate, double lane change at m = 0:9, Tdmd = 1150Nm and Vin = 8kph. 68 5.15 Position, double lane change at m = 0:9, Tdmd = 1150Nm and Vin = 8kph. 69 5.16 Total torque, double lane change at m = 0:9, Tdmd = 1150Nm and Vin = 8kph..................................... 69 5.17 Velocity, step-steer at Tdmd = 1000Nm and Vin = 40kph.......... 70 5.18 Yaw rate, step-steer at Tdmd = 1000Nm and Vin = 40kph.......... 71 5.19 Position, step-steer at Tdmd = 1000Nm and Vin = 40kph.......... 71 5.20 Total torque, step-steer at Tdmd = 1000Nm and Vin = 40kph........ 72 5.21 Velocity, double lane change; top - m = 0:5, Tdmd = 700Nm; middle - m = 0:7, Tdmd = 950Nm; bottom - m = 0:9, Tdmd = 1150Nm........ 73 5.22 Yaw rate, double lane change; top - m = 0:5, Tdmd = 700Nm; middle - m = 0:7, Tdmd = 950Nm; bottom - m = 0:9, Tdmd = 1150Nm........ 75 5.23 Position, double lane change; top - m = 0:5, Tdmd = 700Nm; middle - m = 0:7, Tdmd = 950Nm; bottom - m = 0:9, Tdmd = 1150Nm........ 76 5.24 Total torque, double lane change; top - m = 0:5, Tdmd = 700Nm; middle - m = 0:7, Tdmd = 950Nm; bottom - m = 0:9, Tdmd = 1150Nm........ 77 5.25 NMPC performance, step-steer at Tdmd = 1000Nm and Vin = 40kph; Left images - torque rates NMPC; Right images - wheel torques NMPC. 78 5.26 NMPC performance, double lane change; top - m = 0:5, Tdmd = 700Nm; middle - m = 0:7, Tdmd = 950Nm; bottom - m = 0:9, Tdmd = 1150Nm... 79 5.27 NMPC dT performance, double lane change; top - m = 0:5, Tdmd = 700Nm; middle - m = 0:7, Tdmd = 950Nm; bottom - m = 0:9, Tdmd = 1150Nm... 80 List of Tables 2.1 Vehicle properties. 22 3.1 Motor specs in simulation. [1] . 36 xi xii LIST OF TABLES List of Abbreviations 4WS Four Wheel Steering ABS Anti-lock Braking System AFS Active Front Steering ATTS Active Torque Transfer System AWD All-Wheel Drive AYC Active Yaw Control CC Cruise Control CM Centre of Mass DoF Degrees of Freedom DYC Direct Yaw Control EM Electric Motor EoM Equations of Motion ESP Electronic Stability Program EV Electric Vehicle FWD Front-Wheel Drive HEV Hybrid Electric Vehicle ICE Internal Combustion Engine LTV Linear Time Varying LQG Linear Quadratic Gaussian xiii xiv LIST OF ABBREVIATIONS LQR Linear Quadratic Regulation MF Magic Formula MPC Model Predictive Control NMPC Nonlinear Model Predictive Control PDIP Primal-Dual Interior Point PID Proportional Integral Derivative QP Quadratic Program RHC Receding Horizon Control RWD Rear-Wheel Drive SATM School of Aerospace, Transport and Manufacturing SH-AWD Super Handling All-Wheel Drive SMC Sliding Mode Control SUV Sport Utility Vehicle TCS Traction Control System UKF Unscented Kalman Filter Acknowledgements I would first like to thank my supervisors Drs.
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