Improvement of an existing Integrated Vehicle Dynamics Control System influencing an urban electric car

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IN

DEGREE PROJECT VEHICLE ENGINEERING, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2020,

Improvement of an existing Integrated Vehicle Dynamics Control System influencing an urban electric car

ARIHANT SUREKA

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES

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Improvement of an existing Integrated Vehicle Dynamics Control System influencing an

urban electric car

Arihant Sureka

Master Thesis

Aeronautical and Vehicle Engineering

KTH Royal Institute of Technology

TRITA -SCI-GRU 2020:023

Postal Address Visiting Address Telephone Telefax Internet KTH Royal Institute of Technology Teknikringen 8 +46 8 790 6000 +46 8 790 9290 www.kth.se

Vehicle Dynamics Stockholm

SE-100 44 Stockholm Sweden

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Abstract

The Integrated Vehicle Dynamics Control (IVDC) concept can influence the vehicle behaviour both longitudinally and laterally with just one upper level control concept and further lower level controllers. This demands for state estimation of the vehicle which also includes estimating parameters of interest for the vehicle dynamicist.

The approach to this research is firstly in developing a robust unscented Kalman filter (UKF) estimator for the vehicle side slip tracking and also for cornering stiffness estimation which is then fed to the existing model predictive control allocation (MPCA) controller to enhance the lateral stability of the vehicle for the different manoeuvres studied. Based on these developments, two types of filters are created. One with adaption of distance between center of gravity (COG) and roll center height and another without adaption. The key factor in the estimator development is the time adaptive process covariance matrix for the cornering stiffnesses, with which only the initial values have to be parameterised.

Post the filter development, the parameters are identified based on the real-time vehicle usage factors like trailer towing, tyre pressure, etc. A statistical analysis of variance (ANOVA) is performed to know the influential factors amongst the group. A parametric optimisation is performed to improve the estimation quality.

Combining this research encompasses effective and adaptive method for a better quality of estimation with a kinematic vehicle model which behaves like a real world vehicle, at least virtually.

This study is carried out with the understanding of various optimal estimators, parametric sensitivity analysis and statistical inferences, facilitating a base for robust estimation.

Keywords: kalametric, state estimation, design matrix, aliasing, kalman filter, projection algorithm, resolution

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Sammanfattning

Konceptet Integrated Vehicle Dynamics Control (IVDC) kan påverka fordonets beteende både longitudinellt och lateralt med bara ett reglerkoncept i ett övre lager och ytterligare regulatorer på lägre nivåer. Detta kräver tillståndsuppskattning av fordonet som också inkluderar uppskattning av parametrar av intresse för en fordonsdynamiker.

Tillvägagångssättet för denna studie är för det första att utveckla en robust tillståndsestimering med hjälp av ett Unscented Kalman Filter (UKF) för att uppskatta ett fordons avdriftsvinkel och även för uppskattning av ett däcks sidkraftskoefficient, vilket sedan används i den befintliga modell-prediktiva regleralgoritmen (MPCA) för att förbättra lateralstabiliteten hos fordonet för de olika studerade manövrarna. Baserat på denna utveckling skapades två typer av filter, ett med anpassning av avståndet mellan tyngdpunkten (COG) och krängcentrumhöjden och ett annat utan anpassning. Nyckelfaktorn i estimeringsutvecklingen är den tidsberoende adaptiva inställningen av processkovariansmatrisen för sidkraftskoefficienterna, med vilken endast de initiala värdena behöver parametriseras.

Efter filterutvecklingen identifieras parametrar baserade på en förväntad kundanvändning och en statistisk variansanalys (ANOVA) utförs för att bestämma de mest inflytelserika faktorerna i gruppen. En parameteroptimering utförs för att förbättra uppskattningskvaliteten.

Kombinationen av detta arbete omfattar en effektiv och anpassningsbar metod för en bättre uppskattningskvalitet med en kinematisk fordonsmodell som har en fordonsrespons som ett verkligt fordon, åtminstone praktiskt taget. Denna studie har genomförts med förståelse för olika optimala estimatorer, parametrisk känslighetsanalys och statistiska slutsatser, vilket underlättar en bas för robust uppskattning.

Nyckelord: kalametric, tillståndsestimering, designmatris, vikningsdistorsion, kalmanfilter, projection algorithm, upplösning

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Acknowledgement

गु गोिवन्द दोऊ खड़े, काके लागूं पांय । ब लहारी गु अपने गोिवन्द िदयो बताय ।।

“I face both God and my guru. Whom should I bow first? I first bow to my guru because he’s the one who showed me the path to God.”

-Saint Kabir Das

With this thought, I bow to Lars Drugge, who has taught me to interpret the world of Vehicle Dynamics, and expressing it in terms of mathematical models. The insignia of KTH, ”Vetenskap och Konst”, meaning ”Science and Art”, has been bestowed upon me from the day I got introduced to the art of enhancing the driver feel with scientific methods through Lars. I would be indebted to him till my last breath. During the research, his precious guidance served to be quite useful in the evaluation of the IVDC structure.

A sincere gratitude is also expressed towards Alexander Fridrich, without whose supervision, implementing of new ideas and concepts would not have been possible. Even during times, when the research was in dark, he motivated me to perform the best through inspirations and observations. I would like to thank him for trusting my capabilities to perform the thesis at IVK, which is of great honour in itself. The work on the IVDC was an experience of a life-time.

My mother and father are the motivation behind my work, as they advocate in doing the maximum and best, you can do to live a day. My sisters who acted just as mother and without them the degree wouldn’t have been possible. Finally I want to thank my friends, who are the part of my extended family away from home and standing by my side everyday.

The KTH student mobility programme, which assisted me further to focus on my research without the financial stress is also greatly appreciated.

This work is dedicated to my maternal and paternal grandfathers, who are no more, but I can feel their support even from the heaven.

Arihant Sureka February, 2019 Stockholm / Stuttgart

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Author

Arihant Sureka

Department of Aeronautical and Vehicle Engineering KTH Royal Institute of Technology

Stockholm, Sweden

Place of Project

Forschungsinstitut für Kraftfahrwesen und Fahrzeugmotoren Stuttgart (FKFS) Stuttgart, Germany

Examiner

Lars Drugge

Department of Aeronautical and Vehicle Engineering KTH Royal Institute of Technology

Stockholm, Sweden

Supervisor

Alexander Fridrich, M.Sc.

Institut für Verbrennungsmotoren und Kraftfahrwesen (IVK) Stuttgart, Germany

Cover: 9 DOF Vehicle Driving Simulator at FKFS, Stuttgart

TRITA -SCI-GRU 2020:023

©ARIHANT SUREKA, 2020 Stockholm, Sweden

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List of Figures

1.1 Moving Base 9 DOF Driving Simulator at FKFS, Stuttgart . . . . 2

1.2 Operating Regions of different yaw moment control strategies. Conceptually developed from the understanding provided in [1]. . . . 2

1.3 Integrated Vehicle Dynamics Control . . . . 3

1.4 Parameter and state estimation with existing IVDC estimator. . . . 5

2.1 The IVDC structure. . . . 7

2.2 The 5MM. [5] . . . . 7

2.3 The 5MM structure. . . . 8

2.4 Reference Dynamics Generation based on manoeuvre selection and pedal mode. . 9

2.5 The Feed forward dynamics. . . . 9

2.6 Model predictive control allocation. . . . 10

2.7 Open and closed loop manoeuvre definition.[7] . . . . 10

3.1 a) Deterministic System, b) The observed output from the system is noisy and does not fit the model properly, and c) Explicit modelling the process with the error included in the Random Process as Process and Measurement Noise respectively. 13 3.2 Unscented mean and covariance propagation. a) Actual, b) First-order linearisation (EKF), c) Unscented (UT) [16] . . . . 18

3.3 UKF Kalman Filter schematics without zwadaption. . . . 26

3.4 UKF Kalman Filter schematics with zwadaption. . . . 27

3.5 Distance between the COG height and the roll center denoted by zw. . . . 27

3.6 Parameter Projection Region[34] . . . . 28

3.7 βestimation with and without zwadaptation. . . . 30

3.8 Cvand Chestimation with and without zwadaptation. . . . 31

3.9 ψ˙estimationestimation with and without zwadaptation. . . . 32

3.10 Filter with Adaption of zwin the manoeuvre and filter with constant value of zw. . 32

3.11 Filter with Adaption of zwin the manoeuvre and filter with constant value of zw. . 33

3.12 Adaptive covariance value of Q for Cvand Chfor Chirp Steer Manoeuvre upto 2 and 5 Hz frequency. . . . 33

4.1 The DOE parameters were based on the above physical understandings and thus chosen. . . . 34

4.2 Roof box simulation in the model inspiring the settings for incremental and decremental COG with increasing mass. [35] . . . . 35

4.3 βerrordepicting the error variation on varying the vehicle body mass, with fixed zw. 36 4.4 βerrordepicting the error variation on increasing body mass and decreasing COG Height, signifying the increase of cabin load and external load on the deck. For example, skis, cycles, etc. The plot is with fixed zw. . . . 36

4.5 βerrordepicting the error variation on varying the body roll (XX) inertia. The plot is with fixed zw. . . . 37

4.6 βerrordepicting the error variation on varying the body yaw (ZZ) inertia. The plot is with fixed zw. . . . 37

4.7 βerrordepicting the error variation on varying the front left tyre radius. The plot is with fixed zw. . . . 38

4.8 βerrordepicting the error variation on varying the rear left tyre radius. The plot is with fixed zw. . . . 38

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4.9 βerror depicting the error variation on front biasing of the COG longitudinal distance. The plot is with fixed zw. . . . 38 4.10 βerror depicting the error variation on rear biasing of the COG longitudinal

distance. The plot is with fixed zw. . . . 39 4.11 Affect on estimated average front and rear cornering stiffnesses on variation of

body and overall vehicle mass with fixed zw. . . 40 4.12 Affect on estimated average front and rear cornering stiffnesses on variation of

body mass and COG height with fixed zw. . . 40 4.13 Affect on estimated average front and rear cornering stiffnesses on variation of

roll-yaw inertia and front-rear left tyre radius with fixed zw. . . . 41 4.14 Affect on estimated average front and rear cornering stiffnesses on front and rear

COG biasing with fixed zw. . . . 42 4.15 Fractional Factorial Design Map and the opted strategies.[38] . . . . 45 4.16 Pareto Chart for Sine Steer Manoeuvre at 0.5 Hz frequency for 2⁶_IV⁻² fractional

factorial design. . . . 47 4.17 Pareto Chart for Sine Steer Manoeuvre at 0.5 Hz frequency for 2⁶_V⁻¹ fractional

factorial design. . . . 48 4.18 Pareto Chart for Sine Steer Manoeuvre at 1 Hz frequency for 2⁶_V⁻¹ fractional

factorial design. . . . 49 4.19 Pareto Chart for Sine Steer Manoeuvre at 2.5 Hz frequency for 2⁶_V⁻¹ fractional

factorial design. . . . 50 4.20 Pareto Chart for Sine with Dwell Manoeuvre for 2⁶_V⁻¹fractional factorial design. . 51 4.21 The F distribution . . . . 54 4.22 F statistic and Probability (p-value) for 2⁶_IV⁻² factorial design for Sine Steer at

frequency 0.5 Hz . . . . 58 4.23 F statistic and Probability (p-value) for 2⁶_V⁻¹ factorial design for Sine Steer at

frequency 0.5 Hz . . . . 58 4.24 F statistic and Probability (p-value) for 2⁶_IV⁻² factorial design for Sine Steer at

frequency 1 Hz . . . 60 4.25 F statistic and Probability (p-value) for 2⁶_V⁻¹ factorial design for Sine Steer at

frequency 1 Hz . . . . 61 4.26 F statistic and Probability (p-value) for 2⁶_IV⁻²factorial design for Chirp Steer upto

frequency 2.5 Hz . . . . 62 4.27 F statistic and Probability (p-value) for 2⁶_V⁻¹factorial design for Chirp Steer upto

frequency 2.5 Hz . . . . 62 5.1 UKF estimated β for Sine Steer Manoeuvre at 0.5 and 2.5 Hz frequency for each

setting of Roll Damping. . . . 64 5.2 UKF estimated β for Sine Steer Manoeuvre at 0.5 and 2.5 Hz frequency for each

setting of Roll Stiffness. . . . 65 5.3 UKF estimated β for Chirp Steer Manoeuvre upto 2 Hz frequency for each setting

of Roll Damping and Stiffness. . . . 65 5.4 Vehicle Side Slip error (βerror), between the True Side Slip and the UKF estimated

Side Slip for each setting of distance between COG height and roll centre for Sine Steer at 0.5 Hz frequency. . . . . 66 5.5 Frequency distribution of βerror deviation across each setting of the distance

between COG height and roll centre for Sine Steer Manoeuvre at 0.5 Hz frequency. 66

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5.6 Frequency distribution of βerror deviation across each setting of the distance between COG height and roll centre for Sine Steer Manoeuvre at 2.5 Hz frequency. 67 5.7 Frequency distribution of βerror deviation across each setting of the distance

between COG height and roll centre for Chirp Steer Manoeuvre upto 3 Hz frequency. 67 5.8 Average βerrorfor Sine Steer at frequency of 0.5 Hz for different zw, with error bar

depiction . . . . 69 5.9 Average βerrorfor Chirp Steer upto frequency of 2 Hz for different zw, with error

bar depiction . . . . 69 5.10 Average βerror for Sine with Dwell manoeuvre for different zw, with error bar

depiction . . . . 69 5.11 zwvalidation for Active chassis depicting the avg. βerrorfor virtual Fy, for all the

three manoeuvres. . . . 70 5.12 zwvalidation for Active chassis depicting the avg. βerrorfor real Fy, for all the three

manoeuvres. . . . 71 6.1 Estimated Side Slip angle to Steering angle bode plot response diagram for Step

Steer Manoeuvre for β estimation through different filters. . . . . 73 A.1 βerrordepicting the error variation on varying the front axle mass and COG Height

for Sine Steer at frequency of 1 Hz. . . . . 78 A.2 βerrordepicting the error variation on varying the rear axle, vehicle LHS and RHS

for Sine Steer at frequency of 1 Hz. . . . . 79 A.3 βerrordepicting the error variation on varying the front and rear wheel track for

Sine Steer frequency at 1 Hz. . . 80 A.4 βerrordepicting the error variation on varying the pitch (YY) inertia. . . 80 A.5 Affect on estimated average front and rear cornering stiffnesses on varying COG

height, each axle mass, LHS-RHS mass, front-rear wheel track and pitch inertia. . 81 A.6 Pareto Chart for Sine Steer Manoeuvre at frequency 1 and 2.5 Hz for 2⁶_V⁻²

fractional factorial design. . . . 82 A.7 F statistic and Probability (p-value) for 2⁶_IV⁻² factorial design for Sine Steer at

frequency 2.5 Hz . . . . 84 A.8 F statistic and Probability (p-value) for 2⁶_V⁻¹ factorial design for Sine Steer at

frequency 2.5 Hz . . . . 84

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List of Tables

3.1 EKF Time Update Algorithm [15] . . . . 17

3.2 EKF Measurement Update Algorithm [15] . . . . 17

3.3 UKF Time Update Algorithm [15] . . . 20

3.4 UKF Measurement Update Algorithm [15] . . . . 20

3.5 Sampling Importance Resampling (SIR) Algorithm [19] . . . . 21

4.1 Design of Experiment - Physical parameters studied to observe the changes in the state estimation of the Kalman filter . . . . 35

4.2 The quantitative factors with the original level and the treatment levels. . . . 44

4.3 Number of Runs for a 2^kFull Factorial. . . . 44

4.4 The 2⁶_IV⁻², L 16 Orthogonal Fractional Factorial Design Matrix. . . . 45

4.5 The 2⁶_V⁻¹, L 32 Orthogonal Fractional Factorial Design Matrix. . . . 46

4.6 Types of statistical interference. . . . 52

4.7 Contingency table for hypothesis testing. . . . 53

4.8 Treatments with runs as observations. . . . 54

4.9 Parametric notation for the factors. . . . 57

4.10 The F Distribution table for the average βerrorfor Sine Steer at 0.5 Hz frequency for 2⁶_IV⁻²fractional design scheme. . . . 59

4.11 The F Distribution table for the average βerrorfor Sine Steer at 0.5 Hz frequency for 2⁶_V⁻¹fractional design scheme. . . . 59

4.12 The F Distribution table for the average Front Cornering Stiffness (Cv) for Sine Steer at 0.5 Hz frequency for 2⁶_IV⁻²fractional design scheme. . . . 59

4.13 The F Distribution table for the average Front Cornering Stiffness (Cv) for Sine Steer at 0.5 Hz frequency for 2⁶_V⁻¹fractional design scheme. . . . 59

4.14 The F Distribution table for the average Rear Cornering Stiffness (Ch) for Sine Steer at 0.5 Hz frequency for 2⁶_IV⁻²fractional design scheme. . . 60

4.15 The F Distribution table for the average Rear Cornering Stiffness (Ch) for Sine Steer at 0.5 Hz frequency for 2⁶_V⁻¹fractional design scheme. . . 60

5.1 Interval category schemes for zw. . . . 68

A.1 The generator and the confounding terms for 2⁶_IV⁻²fractional design scheme. . . . 83

A.2 The generator and the confounding terms for 2⁶_V⁻¹fractional design scheme. . . . 83

A.3 The F Distribution table for the average βerrorfor Sine Steer at 2.5 Hz frequency for 2⁶_V⁻¹fractional design scheme. . . . 85

A.4 The F Distribution table for the average Front Cornering Stiffness (Cv) for Sine Steer at 2.5 Hz frequency for 2⁶_V⁻¹fractional design scheme. . . . 85

A.5 The F Distribution table for the average Rear Cornering Stiffness (Ch) for Sine Steer at 2.5 Hz frequency for 2⁶_V⁻¹fractional design scheme. . . . 85

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List of Symbols

β Vehicle side slip

βest Estimated vehicle side slip

β_error Error between True and Estimated vehicle side slip Cv Front cornering stiffness

C_h Rear cornering stiffness

zw Distance between roll center height and COG αv Front axle slip angle

αh Rear axle slip angle δv Front tyre steering angle δh Rear tyre steering angle

lV Longitudinal distance between COG and front axle lH Longitudinal distance between COG and rear axle Vx Longitudinal vehicle velocity

ψ˙ Yaw rate

ψ¨ Yaw moment

ϕ˙ Roll rate

ϕ¨ Roll moment

ϕ Roll angle

m Vehicle mass

J_x Roll inertia Jz Yaw inertia

a_y_estimated Estimated lateral acceleration Fy_virt Virtual lateral force

M_z_virt Virtual yaw moment H0 Null hypothesis H_A Alternative hypothesis µk k possibilities

β_p Probability error Fcalculated Fisher value calculated F_α Confidence interval of F ϵij Error terms

τi Deviation from grand mean

µ Grand mean

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List of abbreviations

DNA Vehicle specific handling characteristics CAE Computer Aided Engineering

VDC Vehicle Dynamics Control TVC Torque vectoring control 5MM Five mass model

FWS Front wheel steering RWS Rear wheel steering COG Center of Gravity ANOVA Analysis of Variance

IVDC Integrated vehicle dynamics control MPC Model predicitve control

MPCA Model predicitve control allocation MF Magic formula

CI Confidence interval SS Sum of squares df Degree of fredom UKF Unscented Kalman Filter EKF Extended Kalman Filter SWA Steering wheel angle MIMO Multi input multi output

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Research questions

How can the states of an electric high-performance vehicle

with rear wheel steering be estimated robustly?

What impact does the variation of physical parameters

of the vehicle have on the robustness of the developed estimator?

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1 Introduction

“On a given day, a given circumstance, you think you have a limit. And you then go for this limit and you touch this limit, and you think, Okay, this is the limit.’ As soon as you touch this limit, something happens and you suddenly can go a little bit further. With your mind power, your determination, your instinct, and the experience as well, you can fly very high .”

-Ayrton Senna The mobility has evolved to a manifold in this decade with the rise of the autonomous vehicles in the scene. The propulsion has had a paradigm shift from the conventional internal combustion engines to hybrid and further on now to in-wheel individual electric drives. The electric propulsion depict the electrification of the vehicle on a large scale. Driver centric technologies to improve motion sickness, driver feel, driving modes and the intervention of driver assistance systems (though behaving differently in different modes), portray a vehicle’s character or to be specific it’s “DNA”. Still, even with the autonomous vehicles in the picture, preference to place the driver as the main interface in order to develop and fine tune the vehicle behaviour is taken care of. So, it’s clearly understandable that the passenger vehicle is not merely a machine mobilising people, but it must be felt and enjoyed at the same time.

This trend of technology specific evolution has also paved way for the virtual world of design and validation to an extent where, the driver can express the vehicle feel even before any physical prototyping is carried out. The vehicle behaviour can be studied first hand with complex models involving all the physical parameters with linearities and non-linearities easily with abundance of computational power available today. This when further explored led a way to the discovery of the driving simulators where actual software and hardware interfaces can be synchronised with various iterations and optimisation to create a mule of the vehicle in-development. Driving simulators can produce the results which can be satisfying to the experimenter to a large scale.

These Computer-Aided Engineering (CAE), such as hardware in loop, software in loop, virtual prototyping with physical hardware systems, are used to duplicate the vehicle motion based on numerous mathematical models, and the results obtained are credited to the complexity the system can handle. Although, with such great computations at our disposal, the weather or the climate specific validation is yet limited.

The work carried out in this thesis focuses on vehicle dynamics CAE methods with physical parameters such as kinematics which are deployed so as to replicate the vehicle virtually. The layout of the control system structure is explained in the following sections.

1.1 Vehicle Dynamics Control

Vehicle Dynamics Control (VDC) is an aid of extending the vehicle performance limitation from the mechanical limits as proposed in the design criteria. The driver assistance systems can be deployed to enhance vehicle safety, limit(s) of handling, cabin comfort, emergency avoidance scenarios and the driver feel. The sensors incorporated within the development may include audio, video, vibration sensors like accelerometers, infrared, temperature, etc and many more depending upon the vehicle segment and the driving attributes.

The driver assistance systems modify the vehicle response to reduce the driver burden. The software algorithms play a major role in providing the vehicle a particular character apart from

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IVDC 1. INTRODUCTION

Figure 1.1: Moving Base 9 DOF Driving Simulator at FKFS, Stuttgart

the passive tuning. The algorithms can be divided into active and passive [1]. The active algorithm is normally adaptive to the driver input and driver behaviour. The passive algorithm constraints the vehicle in a particular defined boundary which is responsive although there could be too much of intervention during the operation which make the driver annoying and the fun to drive factor is decreased or lost.

The software development with integrated chassis control system is challenging as compared to the systems focusing on individual functions. Global chassis control systems combines the conventional Anti-lock Braking System (ABS), Traction Control System (TCS), Electronic Stability Program (ESP), etc to an integrated control system rather than an individual function. Torque Vectoring operates in the whole region spanning from understeer to oversteer whereas ESP has a dead zone which is difficult to alter as depicted by the handling diagram in Fig. 1.2.

Figure 1.2: Operating Regions of different yaw moment control strategies. Conceptually developed from the understanding provided in [1].

There is a demand that, all the active systems should be synergised in a network and function with a parallel algorithm in order to provide the vehicle more agile, sporty and driver responsive characteristic. The system mutual dependency is reduced by introduction of controlling layers and

Master Thesis in Vehicle Engineering 2

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co-ordination levels. The better the integration of the function, the better system synchronisation is. This paves way to fewer stand alone systems which may be redundant.

1.2 Background: Integrated Vehicle Dynamics Control

The existing Integrated Vehicle Dynamics Control (IVDC), was initially developed on a non linear two-track model with actuator dynamics of four in-wheel individual electric motors, [2]. The vehicle model includes side wind disturbance compensation, rear wheel steering and additive dynamic steering. The architecture is based on Torque Vectoring control with ABS and TCS as lower level controllers. A Model Predictive Control (MPC) optimization problem was defined with a cost function implied with a CVXGEN [3] optimizer function.

The basic idea is based on the individual distribution of wheel moments such that an extra moment is created at the vehicle’s vertical axis (yaw moment), which influences the yaw dynamics of the vehicle, and in critical driving situations the vehicle is stabilised. Likewise, strong under or oversteer can be prevented and a more dynamic neutral steer be achieved.

The investigation and implementation of control concepts for torque vectoring with the focus on a class of nonlinear controllers such as ”sliding mode controller” is part of the existing IVDC system.

The work is subjected to algorithms for optimal conversion of virtual manipulated variables into real manipulated variables under consideration of the longitudinal and lateral dynamic requirements of the driver, as a whole to get an appealing driving experience. The overall concept is rounded off by an active rear axle steering based on a pilot control concept for the reduction of the slip angle. The advantages of the IVDC model are sketched in Fig. 1.3.

Figure 1.3: Integrated Vehicle Dynamics Control

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1.2.1 LEICHT Chassis and IVDC

The LEICHT chassis, which stands for Lightweight, Energy-efficient, Integrated Chassis with Hub-motor Technology, is developed by the German Aerospace agency, Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), [4]. The chassis is developed with respect to the future electric vehicles with a patented hub motor technology for powering the individual wheels independently.

The chassis features a new and innovative suspension technology for futuristic comfort and a possibility of achieving individual wheel control. This passive LEICHT chassis is combined with the existing IVDC, to enhance the vehicle stability and extend the physical boundaries of operation.

In this thesis, the specially adapted chassis unit LEICHT is examined with regard to vehicle dynamics control. The vehicle concept sees electrified single-wheel drives with an integrated transmission which offers completely new possibilities regarding the driving dynamics control and the associated increase in driving safety and energy efficiency through the targeted distribution of drive and recuperation torques.

1.3 Problem Statement

Manoeuvres with lower frequency excitations lead to poor estimation of vehicle side slip β, and improper control allocation through torque vectoring via lower level controllers. This leads to vehicle instability affecting vehicle performance. Negative cornering stiffnesses are estimated through Kalman filter which in turn creates a noisy β estimation. With negative cornering stiffness, the vehicle understeers, also with the IVDC controller, which is not desirable (Fig. 1.4). The large tracking error (considered for Sine Steer, Chirp Steer, Step Steer, etc. as explained in section 2.2) between true and estimated vehicle side slip drifts the control behaviour of the IVDC leading to the vehicle instability. This is a major issue with the controller with the coupling of feed forward dynamics.

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0 20 40 60 80 100

Maneuver Completion (%) -5

0 5 10

Side slip angle (rad)

10^-4

Estimated Vehicle

Off-tracking

(a) Sine with Dwell Manoeuvre

0 20 40 60 80 100

-1 0 1 2 3 4 5

Cornering Stiffness (N/rad)

10⁵

Front Cornering Stiffness Rear Cornering Stiffness

Phase Difference

Negative Front Cornering Stiffness would cause understeer

(b) Sine Steer at 0.5 Hz

0 20 40 60 80 100

-1 0 1 2 3 4 5 6

Cornering Stiffness (N/rad)

10⁵

Front Cornering Stiffness Rear Cornering Stiffness

Decreasing Cornering Stiffness at peak 2Hz excitation

(c) Chirp Steer upto 2 Hz

0 20 40 60 80 100

Maneuver Completion (%) 0

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Yaw Rate (rad/sec)

(d) Braking from Steady State Manoeuvre

Figure 1.4: Parameter and state estimation with existing IVDC estimator.

1.4 Purpose of the Study

The purpose of the research is in making the existing IVDC controller robust and averse to physical uncertainties as much as possible with respect to the controller architecture perspective. Next, the observations gained from the development of different state estimators, are used to optimise the Kalman filter parameters. Thirdly, the vehicle handling characteristics with respect to the controller performance is discussed.

1.5 Limitations

Virtually with the vehicle kinematic and structural parameters as defined by the Five Mass Model (5MM), the estimator is robust. However, the implementation on the vehicle is not researched here which might be a point of interest for the future work.

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1.6 Thesis Outline

The brief sketch of each chapter is arranged accordingly as follows:

Chapter 2 introduces the existing IVDC architecture, the control structure, sub modules and the lower level controllers with a brief description of the mathematical models.

Chapter 3 describes the various methods of state estimation, proposes methods of adaption of process noise and measurement noise covariance matrices of the Kalman filter, techniques of improving the quality of estimation and development of estimator for both steady state and transient manoeuvres. The term Kalametric has been referred through out in the thesis which indicates the equations, parameters, characteristics and statistical interference dealing with the Kalman filter. The term eases the purpose of conveying the details and studies carried out in this thesis related to the state estimation.

Chapter 4 contributes to the research in supporting the robustness of the developed estimator with respect to the physical uncertainties and their effect on the quality of the estimated signals. The effect of the identified parameters which effect the most at certain frequencies are also discussed and observed. Certain parameters are identified, which can also change the vehicle’s handling behaviour.

Chapter 5 depicts the parameter variation of geometrical parameters and their effect on the quality of estimation such that optimising the former would result in better vehicle side slip (β) tracking.

The final value of the affecting parameter is identified henceforth.

Chapter 6 finally discusses about the results and contributions of the thesis and its effect on the vehicle handling characteristics. Besides, the possible future work to continue the work is mentioned.

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2 The IVDC Architecture

“An equation means nothing to me unless it expresses a thought of God”

-Srinivasa Aiyangar Ramanujan

2.1 IVDC Structure

The IVDC structure contains a vehicle model with lower level controllers, actuator dynamics, the state estimators and the feed forward function, which, through model predictive control (MPC), allocates the motor torque to the actuators. The IVDC structure in brief is shown in Fig. 2.1.

Figure 2.1: The IVDC structure.

The vehicle is defined in co-ordinate system with the origin defined at the mid point of rear axle as depicted in Fig. 2.2.

Figure 2.2: The 5MM. [5]

The vehicle model is based on the ”Five Mass Model (5MM)” structure depicted in Fig. 2.2, where the vehicle body is treated as a single mass and the wheels with subsystems and the respective hub motors are treated as one mass each, summing up to total five masses.

The 5MM structure with the system blocks is presented in Fig. 2.3. The vehicle model contains the aerodynamic maps and forces, dynamic steering model, suspension and steering kinematics, modular switchable tyre models, coordinated vehicle geometries and the mass of all the five

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IVDC 2. THE IVDC ARCHITECTURE

elements with the inertial properties. This makes the vehicle model quite realistic for the simulation study. The inputs to the vehicle model are the front wheel steering (FWS) angle, rear wheel steering (RWS) angle from the MPC as in Fig. 2.6, with lower level controllers including actuator dynamics, feed forward signals and the reference dynamics in order to generate the desired forces.

Figure 2.3: The 5MM structure.

The reference dynamics with the logic illustrated in Fig. 2.4 is generated based on the driver manoeuvre with the selected driving mode. The longitudinal force, Fxis generated based on the vehicle velocity Vxinitialised based on the manoeuvre through the pedal map. The steering wheel angle generated from the manoeuvre selection is fed into the extended single track model containing the roll dynamics which generates the reference lateral dynamics. The interesting feature of the steering dynamics is the variable steering ratio (VSR), which is speed dependent in order to reduce the steering trade offs and assists in driver feedback.

The feed forward structure portrayed in Fig. 2.5 generates the virtual lateral force Fyand virtual yaw moment Mz, to present a virtual sensor as described in [6], which would be discussed in section 3.4. This feeds as an input to the Kalman filter which is also discussed in section 3.4. Since the study also deals about the robust estimation, the Kalman filter architecture is presented along with.

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Figure 2.4: Reference Dynamics Generation based on manoeuvre selection and pedal mode.

Figure 2.5: The Feed forward dynamics.

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Figure 2.6: Model predictive control allocation.

2.2 Manoeuvre Definition

The manoeuvres are defined into two classes as defined in Fig. 2.7 from [7] as:

• Open Loop: Manoeuvres, in which the control signal is an input to the vehicle, as defined by the steering wheel angle (SWA), with respect to the manoeuvre standard outlined.

• Closed Loop: Manoeuvres, in which, the objective is to control the vehicle’s output, where driver correction is needed to make the vehicle follow the defined path.

Figure 2.7: Open and closed loop manoeuvre definition.[7]

Since, the IVDC evaluation in the scope of the thesis is based on objective validation, open loop manoeuvres are chosen, because the closed loop tests brings in driver intervention, hence influencing the vehicle behaviour. Moreover, the latter is used for subjective evaluation to express driver feel as described in [7].

There are two types of open loop manoeuvres used in this research and their definitions are presented as:

• Constant Velocity

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1. Step Steer according to according to ISO 7401, [8]: The initial speed should be within the deviation of 2 km/hr.

Test Speed: 100 km/hr

SWA rate: 30°/s Turning direction: Left (Right can also be implemented, but the study is restricted to left only)

Time to reach the final SWA: 3 s

2. Sine Steering at defined Frequency: A sine wave steering input is generated based on the defined steering amplitude and frequency.

SWA: 27°

Frequency: 0.5 to 5 Hz

3. Linear Chirp Steering at defined start frequency to defined end frequency: The SWA is excited from a start frequency to the end frequency in order to evaluate the vehicle performance at increasing sine steer excitation.

SWA: 45°

Start Frequency: 0.1 Hz

End Frequency: 2 to 5 Hz (2 Hz is considered as the baseline frequency)

• Variable Velocity

1. Braking from Steady-State Circular Motion according to ISO 7975:

SWA: 30°

Radius: 100 m

2. Sine with Dwell (Critical Evasive Manoeuvre), [9]: A sine frequency, with initial turning direction, i.e. left or right, pause time period (dwell), nominal SWA, and if SWA is used for both turning directions, SWA increments (if multiple tests are executed, then, the SWA should increase), with maximum SWA and initial speed.

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3 Robust state and parameter estimation

अक्षराणामकारोऽ स्म न् ः सामा सकस्य च । अहमेवाक्षयः कालो धाताहं िवश्वतोमुखः ॥

“Of letters I am the letter A, and among compound words I am the dual compound. I am also inexhaustible time, and of creators I am Brahmā.”

-Shrimad Bhagavad Gita An important category of practical problems in active control systems is of the statistical nature which can be described through, (i) Prediction of random signals; (ii) separation of random signals from random noise; (iii) detection of signals of known form (pulses, sinusoids) in the presence of random noise [10].

Kalman filter, which is an exclusive first hand tool available to the engineering fraternity for the state estimation or the parameter estimation is also deployed in the study. Since 1960, when Rudolf Emil Kálmán published his famous paper, which described a recursive solution to the discrete-data linear filtering problem and due to large advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation [10].

First, a short introduction of various possible ways of estimation of signals are highlighted. Then, a focus is laid on the methods of state and parameter estimation and the effectiveness of each of them is discussed with respect to the manoeuvres performed with the quality of estimation.

3.1 System Dynamics

The data acquired from on board sensors in the vehicle has noisy signals which also pose challenge to the estimation of the states. The system is linearly quite easy to estimate, although in practicality the contradiction holds true. The observer is based on the plant dynamics and it’s behaviour under different conditions as applied to. The plant dynamics are described by a linear/ non-linear function f defined by the user with state variables x, the system inputs u, h is a measurement function, w and v as process and measurement noise signals respectively. The system can be described as:

˙

x = f (x, u, w)

y = h(x, u, v) (3.1)

Furthermore, expressing the plant dynamics in the state space, where A is the state evolution matrix, B is the input matrix, C being the output matrix and D is the feed through matrix gives the following over time period t:

x(t) = Ax(t) + Bu(t) + w(t)˙

y(t) = Cx(t) + Du(t) + v(t) (3.2)

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IVDC 3. ROBUST STATE AND PARAMETER ESTIMATION

3.1.1 Random Variables and Random Processes

There are two types of systems, namely Deterministic System and the system including Random Process. Deterministic system are described as the perfect plant having no noise in the input signals which is observed. The depiction of Deterministic and Random process systems are as demonstrated in Fig. 3.1.

The objective of including random processes is to use it for better estimation of parameters and state of the process with the target of understanding, analysing and evaluate the performance of the estimator.

3.1.2 System Observability

The system is observable and the determination of the system state x(t) is possible if for any t>0 through measurements y(t) and inputs u(t) which lie in the interval of [0,t] as explained in [11]. The observability of the system is of great practical interest as it clarifies the absence of the

“hidden dynamics,” thus aiding in determining that the sensors used are enough for the system controlling.

Figure 3.1: a) Deterministic System, b) The observed output from the system is noisy and does not fit the model properly, and c) Explicit modelling the process with the error included in the Random Process as Process and Measurement Noise respectively.

The linear system expressed in equation (3.2) is observable, if the observability matrix O, given by equation (3.3) has full rank n (i.e. n linearly independent rows) [11].

O = [CCACA²....CAⁿ⁻¹]^T (3.3)

The local stability of the system is discussed in [12] and [13], by which a system is locally observable at x0, if there exists a neighbourhood of x0such that every x in that neighbourhood other than x0

is distinguishable from x0. Lie derivatives of hifunction is used in the local observability analysis.

The Lie derivative at (r+1) order is defined in equations (3.4) and (3.5), where i is the number of measurements ranging from i = 1,...,p and with x as the state and u as the input.

L^r+1_f h_i(x) = ∂L^r_fh_i(x)

∂x f (x, u) (3.4)

Improvement of an existing Integrated Vehicle Dynamics Control System influencing an urban electric car

Improvement of an existing Integrated Vehicle Dynamics Control System influencing an urban electric car

ARIHANT SUREKA

Improvement of an existing Integrated Vehicle Dynamics Control System influencing an

urban electric car

Arihant Sureka

Abstract

Sammanfattning

Acknowledgement

Contents

List of Figures

List of Tables

List of Symbols

List of abbreviations

Research questions

1 Introduction

2 The IVDC Architecture

3 Robust state and parameter estimation