Design of an anti-lock brake algorithm based on wheel load measurements B. Hazen s i s e h T e c n e i c S f o r e t s a M Delft Center for Systems and Control Design of an anti-lock brake algorithm based on wheel load measurements Master of Science Thesis For the degree of Master of Science in Systems and Control at Delft University of Technology B. Hazen September 5, 2016 Faculty of Mechanical, Maritime and Materials Engineering (3mE) · Delft University of Technology Copyright © Delft Centre for Systems and Control (DCSC) All rights reserved. Abstract Anti-lock Brake System (ABS) is an active safety system nowadays implemented in every new car and could prevent the wheels from locking during heavy braking. Steering becomes ineffective and the brake distance longer than necessary when the wheels are locked. ABS has reduced the amount of non-fatal crashes significantly, but there are still situations in which it can control worse than driver would himself. For example, when driving on low-friction roads. The aim in this thesis is to develop a new ABS algorithm using potentially available infor- mation about wheel forces. Data of wheel forces is currently not measured in consumer cars, but SKF is developing load sensing bearings which could be feasible for such cars. The sensor output provides more directly relevant information than wheel deceleration data does. The latter is used in current ABS technology. A novel ABS algorithm that uses both force and wheel slip measurements for control is designed. The algorithm is validated on a Simulink model consisting of Delft-Tyre, simplified actuator dynamics, (optional) sensor noise, and a quarter car model. An Extended Kalman Filter (EKF) based on the Burckhardt model acts as reference for the controlalgorithm. TheBurckhardtmodelisacomputationallylightweightformulaandallows the EKF to be used on-line against relatively little computational cost. Friction estimation is essential in the designed ABS algorithm, as it is dependant on the road surface which is not known a priori. The designed algorithm is first assessed in a Simulink model on different road surfaces. Field tests are performed as well. They show that the combination of force and slip measurements is indeed promising. On-line estimates using the EKF are found sufficiently accurate to be used as main reference for the controller. Master of Science Thesis B. Hazen ii B. Hazen Master of Science Thesis Table of Contents Acknowledgements xi 1 Introduction 1 1-1 Road safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1-2 Challenges in ABS control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1-3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1-4 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Modelling 7 2-1 Vehicle and road . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2-1-1 Tyre-road contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2-1-2 Equations of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2-1-3 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2-1-4 Tyre relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2-1-5 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2-2 Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2-3 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2-4 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2-5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3 Controller design 19 3-1 Control variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3-1-1 Slip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3-1-2 Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3-1-3 Combining force and slip . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3-2 Control methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3-2-1 PID control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3-2-2 Multiple-phase control . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Master of Science Thesis B. Hazen iv Table of Contents 3-3 Control algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3-3-1 A basis for force-based control . . . . . . . . . . . . . . . . . . . . . . . 24 3-3-2 Proposed controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3-4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3-5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4 Friction estimation 33 4-1 Friction models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4-1-1 Burckhardt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4-1-2 Simplified friction model . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4-2 The Extended Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4-3 Implementation in the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4-4 EKF validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4-4-1 Model comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4-4-2 Model performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4-5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5 Controller assessment in simulation 47 5-1 The perfect brake manoeuvre . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5-2 Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5-3 Control algorithm tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5-4 Influences of tyre-road characteristics . . . . . . . . . . . . . . . . . . . . . . . . 50 5-4-1 Wheel slip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5-4-2 Friction coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5-4-3 Assessment using performance indicators . . . . . . . . . . . . . . . . . . 53 5-4-4 Changing road surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5-5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6 Controller validation in field tests 61 6-1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6-2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6-3 Slip-based braking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6-3-1 Friction estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6-3-2 Slip and friction-based triggering . . . . . . . . . . . . . . . . . . . . . . 66 6-4 Combined force and slip-based braking . . . . . . . . . . . . . . . . . . . . . . . 68 6-5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 7 Conclusions 71 Appendices 75 A EKF fundamentals 77 B. Hazen Master of Science Thesis Table of Contents v B EKF using a buffer 79 C Calculation of performance indicators 83 D Simulation results 85 E Adaptability of the EKF 89 E-1 Case 1: µ∗ remains 1.12, λ∗ changes from 0.08 to 0.15 . . . . . . . . . . . . . . 89 x E-2 Case 2: µ∗ remains 1.12, λ∗ changes from 0.15 to 0.08 . . . . . . . . . . . . . . 91 x E-3 Case 3: µ∗ changes from 1.12 to 0.85, λ∗ remains 0.08 . . . . . . . . . . . . . . 92 x E-4 Case 4: µ∗ changes from 0.85 to 1.12, λ∗ remains 0.08 . . . . . . . . . . . . . . 93 x Bibliography 95 Glossary 99 List of Acronyms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Index 101 Master of Science Thesis B. Hazen vi Table of Contents B. Hazen Master of Science Thesis