Elektrikli Araçlarda Optimal Tork Kontrolü Islam R.H. SHAMIA

** YÜKSEK LİSANS TEZİ **

Elektrik-Elektronik Mühendisliği Anabilim Dalı
**Nisan 2021 **

Optimal Torque Control for Electric Vehicles Islam R.H. SHAMIA

**MASTER OF SCIENCE THESIS **

Department of Electrical and Electronic Engineering April 2021

Optimal Torque Control for Electric Vehicles

A thesis submitted to the Eskişehir Osmangazi University Graduate School of Natural and Applied Sciences in partial fulfillment of the requirements for the degree of Master of Science

in Discipline of Control and Command Systems of the Department of Electrical and Electronic Engineering

By

Islam R.H. SHAMIA

Supervisor: Assistant Prof Dr. Kemal KESKİN

April 2021

**ETHICAL STATEMENT **

I hereby declare that this thesis study titled “Optimal Torque control for Electric Vehicles” has been prepared under the thesis writing rules of Eskişehir Osmangazi University Graduate School of Natural and Applied Sciences under the academic consultancy of my supervisor Assistant Prof Dr. Kemal KESKİN. I hereby declare that the work presented in this thesis is original. I also declare that I have respected scientific ethical principles and rules in all stages of my thesis study. All information and data presented in this thesis have been obtained within the scope of scientific and academic ethical principles and rules, all materials used in this thesis that are not original to this work have been fully cited and referenced, and all knowledge, documents, and results have been presented under scientific ethical principles and rules.

1/04/2021.

ISLAM R.H. SHAMIA

**ÖZET **

Bu tezde ana çalışma hedefi olarak dört tekerlek içi motorlu elektrikli araçlar için bir optimal Tork kontrol sistemi önermiştir. Sürüş Gücü kontrolü, önerilen sistemdeki ana denetleyicidir ve iç ve dış kontrol döngüsünden oluşur. Sürüş gücü kontrolü, hızlanma pedalıyla sürücüden istenen güce ulaşmak için, Entegratör I-kazanım kontrol parametresine ve sürüş gücü gözlemcisinden gelen tahmini sürüş gücü değerlerine bağlı olarak uygulanır.

Orantılı-türev PD kazanç parametreli bulanık mantık kontrolü, her bir tekerleğin hızını kontrol etmek, istenen tekerlek hızına ulaşmak, verilen torku tekerleklere yönlendirmek, çekiş işlemini desteklemek ve araçlar çalışırken kaymanın oluşmasını önlemek için iç döngü kontrolünde birinci tekerlek hız kontrolörü olarak uygulanır. Orantılı-İntegral kazanç PI denetleyicisi, önerilen araştırmayı geliştirmek için iki denetleyici arasında karşılaştırma yapmak amacıyla ikinci bir tekerlek hız denetleyicisi olarak sunulmuştur.

Toplam kayma oranını en aza indirerek, yalpalama momentini bastırarak ve aracın çekişini destekleyerek araç stabilitesini artırmak amacıyla her bir tekerlek içi motorun kuvvetine istenen girdi kuvveti dağıtım fonksiyonları uygulanmıştır. Bir aracın kısa yollarda düşük sürtünme katsayısı ile gitmesi durumunda kuvvetler, her bir tekerleğin kayma oranı değerine göre ön ve arka tekerlekler arasında dağıtılacak ve toplam itici güç korunacak ve çekiş işlemi devam edecektir. Ayrıca araç kısa bölünmüş kaygan yollarda hareket ettiğinde, itici kuvvetleri sol ve sağ tekerlekler arasında dağıtarak aracın sol ve sağ tarafları arasındaki yalpalama momenti bastırılacaktır.

**Anahtar kelimeler: Elektrikli araçlar, Bulanık Mantık Kontrolü, Tork optimizasyonu, Sürüş **
Gücü kontrolü, Kaymayı önleyici kontrol.

**SUMMARY **

This thesis proposed an optimal torque control system for electric vehicles with four in- wheel motors as the main objective, the driving force control is the main controller in the proposed system, and its consists of the inner and outer control loop. The driving force is controlled using the integrator gain control parameter and depending on estimated driving force values for each wheel coming from the driving force observer is implemented in order to reach the desired force requested from the driver by the acceleration pedal.

Fuzzy logic control with proportional-derivative PD gains parameter is applied as a first wheel speed controller in the inner loop control in order to control the speed of each wheel and reach the desired wheel speed. As well as avoid slip from occurring while vehicles run on roads with high slippage also directing the delivered torque to the wheels, and support traction operation. The proportional-Integral gain PI controller is presented as a second wheel speed controller with the aim of comparison between two controllers to enhance the proposed research.

Desired input force distribution functions have been applied on each in-wheel motor in
the interest of enhancing the vehicle stability by minimizing the total slip ratio, suppressing yaw
moment, and support the traction of the vehicle. In the case when a vehicle runs on the short
roads with a low friction coefficient the forces will be distributed between the front and rear
wheels based on the slip ratio value for each wheel and the total driving force will be retained
and traction operation will continue without significant effect. Besides, when the vehicle moves
on a short split slippery roads, the yaw moment between the left and right sides wheels
suppressed by distributing the driving forces between the four wheels based on the situation of
**each wheel. **

**Keywords: - Fuzzy Control, Torque Optimal Control, Driving Force Control, Yaw-Moment **
Suppression, Electric Vehicles, Anti-Slip.

**LIST OF CONTENTS **

**Page **

**ÖZET ...vi **

**SUMMARY ...vii **

**ACKNOWLEDGMENT ...viii **

**LIST OF CONTENTS ...ix **

**LIST OF FIGURES ...xii **

**LIST OF TABLES ... xvii **

**LIST OF SYMBOLS AND ABBREVIATIONS ...xviii **

**1. ** **INTRODUCTION AND PURPOSE ...1 **

**2. ** **LITERATURE REVIEW ...4 **

**2.1. Introduction ……….……….. 4 **

**2.2. A Brief Review on Traction Control and Antislip Control Systems for …..……….…..5 **

**2.3. A Brief Review on Torque Distribution Control Systems ………...…..6 **

**3. ** **VEHICLE DYNAMICS AND MODELLING ….………....11 **

3.1. Introduction ...11

3.2. Vehicle Dynamics and Modeling ……….11

3.2.1. Experimental vehicle characteristics ………..……... 11

3.2.2. Proposed vehicle dynamics ………13

3.2.3. Proposed vehicle Simulink modeling ………16

3.3. Tire-Road Friction and Tire Modeling ………16

3.3.1. A Brief Review on tire-road friction ………. 17

3.3.2. Tire friction modeling ...……… 19

3.4. Slip Ratio Definition and Calculation ………..20

3.4.1. Introduction …… ………...20

3.4.2. Longitudinal slip ratio ………...21

**4. METHOD ………25 **

**LIST OF CONTENTS (continued) **

**Page **

4.1. Introduction ………..25

4.2. Driving Force Control System………...25

4.3. Driving Force Controller and [ 𝜆 - Y ] ratio conversion function ……….27

4.4. Desired Wheel Speed (Vw*) and Angular Velocity (w*) Calculations ………31

4.5. Driving Force Observer ………32

4.6. Wheel Speed Control System ………...33

4.6.1. Wheel speed controller based on fuzzy logic control with PD (Proportional- Derivative gains) parameters ……….34

4.6.1.1. Fuzzy inputs membership functions ………..……36

4.6.1.2. Fuzzy output membership functions ………..………38

4.6.1.3. Fuzzy rules ……….38

4.6.1.4. Fuzzy inputs-output surface view ………..39

4.6.2. Wheel speed controller based on PI control (Proportional-Integral gains) parameters ……….………40

**5. DRIVING FORCE DISTRIBUTION ………41 **

**5.1. Introduction ………..41 **

**5.2. Driving Force Distribution Strategy ……….42 **

**5.3. Driving Force Distribution equations ………...43 **

**5.3.1. Distribution equations in the first interval (a) ………43 **

**5.3.2. Distribution equations in the second interval (b) ………44 **

**6. RESULTS AND DISCUSSION ………..45 **

6.1. Simulation Setup ……….. 45

6.2. Simulation Results Without Applying Control ………48

6.3. Simulation Results for Proposed Control System and Distribution Strategy while Driving on The First Experimental road - Split Slippery sheet ………51

**LIST OF CONTENTS (continued) **

**Page **
6.3.1. Simulation results using driving force control without applying distribution

strategy ………..51

6.3.1.1. Results based on PD-Fuzzy logic control as wheel speed controller …51 6.3.1.2. Results based on PI control as wheel speed controller ……….……….54

6.3.2. Simulation results using driving force control and distribution strategy ……...58

6.3.2.1. Results based on Fuzzy logic control as wheel speed controller ……….58

6.3.2.2. Results based on PI control as wheel speed controller ……….……….61

6.4. Simulation Results for Proposed Control System and Distribution Strategy while Driving on The Second Experimental road - Full Slippery Sheet ………..65

6.4.1. Simulation results using driving force control without applying distribution strategy ………..65

6.4.1.1. Results based on Fuzzy logic control as wheel speed controller ……….65

6.4.1.2. Results based on PI control as wheel speed controller ……….……….68

6.4.2. Simulation results using driving force control and distribution strategy …….72

6.4.2.1. Results based on Fuzzy logic control as wheel speed controller ……….75

6.4.2.2. Results based on PI control as wheel speed controller ………75

6.5. Comparison Between PD-Fuzzy Logic Controller and PI Controller Results ………...79

**7. CONCLUSION AND RECOMMENDATIONS ………..83 **

7.1. Future Work Recommendations ………...83

7.2. Conclusion ………...……… 83

**REFERENCES ………84 **

**LIST OF FIGURES **

**Figure ** **page **

2.1. EV with independent driven four-wheels.…...7

*3.1. The experimental Kanon-FPEV2 …...12 *

*3.2. The outer-rotor type in-wheel motor used in FPEV2-Kanon …...12 *

3.3. Wheel rotational motion …...14

3.4. Four-wheel vehicle longitudinal motion variables ...15

3.5. Longitudinal motion dynamics and the normal forces and for each tire of the vehicle … 15 3.6. Simulink model for One-wheel vehicle ...16

3.7. The Longitudinal Deformation and Interaction between Tires and Road ...17

3.8. Binding of the molecular bonds between the tire and road surfaces ...18

3.9. Longitudinal Slip ratio calculation for each wheel Simulink block diagram …...22

3.10. The relationship between longitudinal Slip and Friction Coefficient based on Magic Formula for main general road surfaces……….……..……....23

4.1. Flow chart of proposed control system ...26

4.2. The configuration of the proposed driving force control system ……….…….…..27

*4.3. The curve of ( Y – slip ratio ) relationship ………. ………..…..29 *

4.4. Driving force controller block diagram ………...30

4.5. Desired wheel speed and angular velocity calculation function …...31

4.6.*The range of desired wheel speed (Vω*) when ( V < σ ) ………....32 *

4.7. Calculation of Fd Estimation value from Driving Force Observer block-diagram ……….33

4.8. Wheel speed controller Block diagram ………...34

4.9. Wheel speed controller based on PD-Fuzzy Logic controller Block Diagram ………35

4.10. Fuzzy Logic controller Block diagram ………..36

4.11 Membership functions Fuzzy logic input 1 (Error) ………37

4.12 Membership functions of Fuzzy logic input 2 (Change Error) ..………37

4.13 Membership functions of Fuzzy logic output ……… 38

**LIST OF FIGURES (continued) **

**Figure ** **page **

4.14 Fuzzy Inputs-Output Surface ……… 39

4.15. PI controller Block diagram ………..40

**5.1. Flow chart for the proposed control system with distribution Function ………..41 **

6.1. First Experimental road description using Split Slippery Sheet ………..46

6.2. Second Experimental road description using Full Slippery Sheet ………...47

6.3. Slip ratio for each wheel – without control .………..………...49

6.4. Driving force for each wheel – without control ……… 49

6.5. Total driving force output – without control ………50

6.6. Total driving force output – without control ………50

6.7. Slip ratio for each wheel – PD-Fuzzy logic controller without distribution – Split slippery sheet ...51

6.8. Vehicle and wheels speed – PD-Fuzzy logic controller without distribution – Split slippery sheet ...52

6.9. Delivered Torque for each wheel – PD-Fuzzy logic controller without distribution – Split slippery sheet ...52

6.10. Driving Force for each wheel – Fuzzy logic controller without distribution – Split slippery sheet ...53

6.11. Total Driving Force output – Fuzzy logic controller without distribution – Split slippery sheet ...53

6.12. Total Yaw moment – PD-Fuzzy logic controller Without distribution – Split slippery sheet ...54

6.13. Slip ratio for each wheel – PI controller without distribution – Split slippery sheet ……...54

6.14. Vehicle and wheels speed – PI controller without distribution – Split slippery sheet ...55

**LIST OF FIGURES (continued) **

**Figure ** **page **

6.15. Delivered torque for each wheel – PI controller without distribution – Split slippery
sheet……….. 55
6.16. Driving Force for each wheel – PI controller without distribution – Split slippery sheet…56
**6.17. Total driving Force output –PI controller without distribution – Split slippery sheet ..… 56 **
6.18. Total Yaw moment – PI controller without distribution – Split slippery sheet ………….57
6.19. Slip ratio for each wheel – PD-Fuzzy logic controller with distribution – Split slippery
sheet ……….……….58
6.20. Vehicle and wheels speed – PD-Fuzzy logic controller with distribution – Split slippery
sheet ……….……….59
6.21. Delivered torque for each wheel – PD-Fuzzy logic controller with distribution – Split
slippery sheet ...59
6.22. Driving Force for each wheel – PD-Fuzzy logic controller with distribution – Split slippery

sheet……….……….60

6.23. Total Driving Force output – PD-Fuzzy logic controller with distribution – Split slippery sheet ……….……….60 6.24. Total Yaw moment – PD-Fuzzy logic controller with distribution – Split slippery sheet...61 6.25. Slip ratio for each wheel – PI controller with distribution – Split slippery sheet …………61 6.26. Vehicle and wheels speed – PI controller with distribution – Split slippery sheet ...62 6.27. Delivered torque for each wheel – PI controller with distribution – Split slippery sheet ...62 6.28. Driving Force for each wheel – PI controller with distribution – Split slippery sheet ...63 6.29. Total Driving Force output – PI controller with distribution – Split slippery sheet ...63 6.30. Total Driving Force output – PI controller with distribution – Split slippery sheet ...64 6.31.Slip ratio for each wheel – PD-Fuzzy logic controller without distribution – Full slippery sheet ……….……….65

**LIST OF FIGURES (continued) **

**Figure ** **page **

6.32. Vehicle and wheels speed – PD-Fuzzy logic controller without distribution – Full slippery sheet ……….……….66 6.33. Delivered torque for each wheel – PD-Fuzzy logic controller without distribution – Full slippery sheet ...66 6.34. Driving Force for each wheel – PD-Fuzzy logic controller without distribution – Full slippery sheet ...67 6.35. Total Driving Force output – PD-Fuzzy logic controller without distribution – Full slippery sheet ...67 6.36. Total Yaw moment – PD-Fuzzy logic controller without distribution – Full slippery sheet...68 6.37. Slip ratio for each wheel – PI controller without distribution – Full slippery sheet ...68 6.38. Vehicle and wheels speed – PI controller without distribution – Full slippery sheet ...69 6.39. Delivered torque for each wheel–PI controller without distribution –Full slippery sheet...69 6.40. Driving Force for each wheel – PI controller without distribution – Full slippery sheet ...70 6.41. Total Driving Force output – PI controller without distribution – Full slippery sheet ...70 6.42. Total Yaw moment – PI controller without distribution – Full slippery sheet …………..71 6.43. Slip ratio for each wheel – PD-Fuzzy logic controller with distribution – Full slippery sheet ...72 6.44. Vehicle and wheels speed – PD-Fuzzy logic controller with distribution – Full slippery sheet ...73 6.45. Delivered torque for each wheel – PD-Fuzzy logic controller with distribution – Full slippery sheet ...73 6.46. Driving Force for each wheel – PD-Fuzzy logic controller with distribution – Full slippery sheet ...74

**LIST OF FIGURES (continued) **

**Figure ** **page **

6.47. Total Driving Force output – PD-Fuzzy logic controller with distribution – Full slippery

sheet ...74

6.48. Total Yaw moment – PD-Fuzzy logic controller with distribution – Full slippery sheet...75

6.49. Slip ratio for each wheel – PI controller with distribution – Full slippery sheet …………75

6.50. Vehicle and wheels speed – PI controller with distribution – Full slippery sheet ...76

6.51. Delivered torque for each wheel – PI controller with distribution – Full slippery sheet …76 6.52. Driving Force for each wheel – PI controller with distribution – Full slippery sheet ...77

6.53. Total Driving Force output – PI controller with distribution – Full slippery sheet ...77

6.54. Total Yaw moment – PI controller with distribution – Full slippery sheet ...78

6.55. Total Driving Force output _ PD-Fuzzy and PI controller – Split slippery sheet ...79

6.56. Total Yaw-moment Output _ PD-Fuzzy and PI controller – Split slippery sheet ...80

6.57. Total Driving Force output _ PD-Fuzzy and PI controller – Full slippery sheet ...80

6.58. Total Yaw-moment Output _ PD-Fuzzy and PI controller – Full slippery sheet ...81

**LIST OF TABLES **

**Table Page **

*3.1 Specifications and parameters of the FPEV2-Kanon model ………….………13 *

3.2 Values of magic formula parameters for main different road conditions ……….20

3.3 The maximum friction coefficient for main common road surfaces ……….24

4.1 Maximum and minimum values for Y and 𝜆 ………30

4.2 Rules of Applied Fuzzy Logic controller ………39

6.1. Simulation Parameters of the proposed Controller ……….45

6.2. Distribution coefficient for each wheel _ Split slippery sheet ………46

6.3. Distribution coefficient for each wheel _ Full slippery sheet ……….48

**LIST OF SYMBOLS AND ABBREVIATIONS **

**Abbreviations Statements **

EVs Electric vehicles

ICEVs Internal combustion engine vehicles

TCS Traction control system

DOF Degree of freedom

DYC Direct yaw moment control

*J * Wheel inertia

*ω * Wheel angular velocity

*ώ * Wheel angular acceleration

*T * Motor torque

*r * Wheel radius

*F**d* Driving force

*M * Vehicle total mass

*V * Vehicle velocity

𝑉𝜔 Wheel velocity

𝑉̇ Vehicle acceleration

*N * Normal force

𝜇(𝜆) Friction coefficient

𝜆 Longitudinal slip ratio

𝜀 Small positive number

𝐷𝑠 Driving stiffness

*σ * Small constant

*∅ * phi _ Force distribution coefficient

**1. INTRODUCTION AND PURPOSE **

With the worldwide rising of the industrial revolution and intellectual renaissance at the
beginning of the 20^{th} century to facilitate and meet the requirements and needs of life in various
fields, the production of vehicles in the world began (Forum, 2011). According to expectations
and with huge industrial and technological development, the number of vehicles will exceed two
and a half billion vehicles by 2050 such as modern transportation has become an essential part
of all aspects of life (Sher, 1998; Hajihosseinlu, 2015). By increasing the use and manufacturing
of traditional vehicles, which depend on the internal combustion engine for running, emitting
greenhouse gases, these gases have caused an increase in air pollution and global warming. The
effects of internal combustion engine vehicles (ICEVs) not only on the planet but also on human
lives too (Ewin, 2016; McTrustry, 2016). On the other hand, the depletion and instability of
fossil fuel sources are a significant challenge to the sustainability of industrial facilities in
general and ICEVs in particular, because of these issues automobile industries have tended to
develop and manufacture alternatives to ICEVs. (Sher, 1998; Martins et al., 2019)

In recent years, electric vehicles (EVs) manufacturing has received widespread attention, considering it more efficient in eliminating or reducing environmental noise and pollution comparing with ICEVs, besides, it is a perfect solution for environmental and energy problems (Jalali et al., 2012; Fazelpour et al., 2014; Xu et al., 2019). Furthermore, utilizing electric motors and inverters in EVs provides advantages over ICEVs, just like faster torque response, ease of applying torque allocation optimization, and accuracy of output torque measurement using motor current (Chiang et al., 2015; Maeda et al., 2017).

The revolution in electronics technology in the last 30 years has introduced many features in different sides of the automobile industry, many developments incorporated in the microcontroller devices to increase vehicle stability and handling efficiency while critically complex conditions. Fields like safety systems, traction torque control systems, and braking

torque control systems, and Anti-skid control systems have received notable attention (Schinkel and Hunt, 2002; Rahman et al., 2006; Yuan et al., 2016).

**Driving torque distribution control system such as traction control system (TCS), have **
good solutions for many issues during driving, problems like wheel spinning while driving on
slippery road or yaw moment difference between right and left side while driving on a split
slippery road, which is the main role to enhance vehicle’s stability and safety (Maeda et al.,
2017). In addition to maintaining the quality of the torque output to sustain vehicle stability, the
traction control system must also provide other control systems for EVs with certain and precise
information on different tire-road conditions (Mutoh et al., 2007; Hu et al., 2011; Ewin, 2016).

The purpose of this thesis is to present optimal torque control strategies for an application like electric vehicles with four in-wheel motors. Desired driving force has been considered as the main input for the system, the requested driving force from the driver from the acceleration pedal are enters to the main outer loop control and it is controlled by utilizing an integrator gain control parameter also depending on the feedback coming from the driving force observer as driving force estimation values.

Moreover, the wheel speed controller is considered as the inner loop controller and it is proposed with two different types of control system with the aim of comparison between two controllers to enhance the proposed research. As a first wheel speed control in the inner loop control, the Fuzzy logic control with proportional-derivative PD gains parameter is applied in order to support the traction operation by controlling the speed of each wheel and achieving the desired wheel speed. Also, it works as an anti-slip controller to prevent slip value reaches extreme levels while the vehicle runs into roads with high slippage value, and directing the delivered torque to the wheels. Proportional-Integral gain PI control is presented as a second wheel speed controller.

Force distribution strategies are applied on the total requested driving force In the case of the vehicle moves on the short slippery roads or short split slippery roads. Which are enhance the vehicle stability by preventing the slip ratio from reaching high values also suppressing the yaw moment. If the vehicle enters into a short slipper road then the distribution function will distribute the input driving forces for each wheel taking into account the slip ratio values between the front and the rear wheels to maintain the total driving forces and keep the traction operation working without notable effect. Yaw moment between the left and right sides of the vehicle will be suppressed by distributing the driving forces between the four wheels of the vehicle depending on the situation of each wheel and which wheels still have traction on the normal road with high slippage when the vehicle runs into the short split slippery road.

**2. LITERATURE REVIEW **

**2.1. Introduction: **

Due to the reduction of fossil fuels and growing environmental emissions, interest in EVs has grown steadily over the last 20 years. EVs are considered a great solution to the issue of reliance on petrol and global energy resources problem (Wong et al., 2016; Wang et al., 2018).

EVs also offer major advantages for vehicles powered by internal combustion engines. Electric
vehicle motors respond to driving or braking torque requirements up to 100 times faster also
give the ability to calculate engine torque accuracy depending on engine current (Wang et al.,
**2011; Gu et al., 2013; Fujimoto and Harada, 2015). **

However, the restricted autonomy of EVs is one of the major challenges to the popularity of electric vehicles in the automobile markets. The range of electric vehicle’s autonomy is approximately between 150 - 200 km per hour and that is much lower than that of internal combustion engine vehicles (Koehler et al., 2014). Many researchers propose several methodologies to solve the restricted autonomy issue of EVs through enhancing advanced battery technologies and improvement of functional and more effective high power capacity storage devices (Santucci et al., 2014; Manzetti et al., 2015; Zhang et al., 2018). On the other hand by depending on available battery technologies for EVs and applying optimization functions on driving or braking torque to find an optimal value of torque to enhance total power efficiency which gives a good solution for cruising range limited problems(Sforza et al., 2019).

Because of the extraordinary structure opposed to ICEVs, the EVs with four in-wheel- motors attracted huge interest and became a focus of attention for many engineers and the automobile industry(Foito et al., 2008). EVs equipped with four in-wheel independent motors propose many advantages such as the capability of controlling the traction or braking torque of each wheel independently, increasing safety efficiency, and improving overall vehicle dynamic performance (Hori et al., 1998; He and Hori, 2006). Moreover, EVs by using in-wheel-motors

can direct the actuation of the four in-wheels with the absence of mechanical links, which is raising the overall operational efficiency, enhances the control flexibility and accuracy (Yuan et al., 2016).

**2.2. A Brief Review on Traction Control and Antislip Control Systems for EVs: **

For an overview of some main problems while driving throw slippery roads, wheel lock- up and spin out, the slip control mechanism such as the Anti-lock braking system or traction control system, has excellent treatment with both of them. They avoid wheel locking-up, spinning out while braking or traction operation, which is enhanced the vehicle’s stability and safety (Burton et al., 2004). At vehicle emergency braking actions, wheel slip must control to track the desired slip value, which helps to handle directional control and reach to the maximum friction force between wheel-surface to decrease the braking distance whereas plays a critical part in that situation (Burton et al., 2004; Bosch et al., 2007; Jalali et al., 2012; Jin et al., 2017).

The possibility of precise control of the traction torque and yaw moment for the four in- wheel motor EVs plus the previously mentioned advantages gives more precision to the configuration of the control strategies. Many research proposed several traction methods to prevent slipping on roads with a low friction coefficient. For instance, Ge and Chang (2011) proposed a torque blended control system as a traction method for EVs based on sliding mode control and using torque observer, then to enhance referencing of traction torque for each wheel they developed a computational-intelligence device. Yin and Hori (2008) by predicting the maximum active forces on four in-wheel EVs presented a developed anti-slip control system as a traction control on different road types test. In Guangcai et al. (2007) and Jin et al. (2017) slip ratio control system based on the dynamical fuzzy control system using sliding mode and estimated slip ratio for longitudinal vehicle motion respectively, as a traction control system improving handling stability and safety.

**2.3. A Brief Review on Torque Distribution Control Systems: **

As mentioned before, driving or braking torque can be controlled for each wheel independently for electric vehicles with four in-wheel motors, which makes unlimited solutions for torque allocation between the wheels to achieve the desired torque request from driver accelerator pedals by the driver. Because of that, distribution functions must be obtained with constraints to find the optimal solution for the torque allocation control system, the constraints of distribution functions must be affecting directly on the performance of EVs(Burgess, 2009;

Sforza et al., 2019).

A lot of research proposes torque allocation strategies aimed to enhance the total energy efficiency for EVs. For instance, in Chen and Wang (2010) as a function of the torque request form driver, the implemented approach was based on a predetermined efficiency curve. Despite the impact of changing in vehicle’s speed was not considered in the constraints, which have a significant effect on the performance, the result of the proposed method simulation show effective improving and increasing in energy efficiency.

Kang and Heo (2012) propose a control algorithm for an electric vehicle with one in- line motor for both front wheels and two in-wheel motors for each rear wheel as shown in Figure

.

2 1. For the driving control system, three main points are used to make the system, first by regulating the control mode and desirable dynamics based on the requested torque from the acceleration pedal and signals coming sensors, the main controller manages the appropriate control area. Second, calculate the yaw moment and the traction torque by applying an upper- level controller. Third, In order to reach the required yaw moment and traction torque, by finding an optimal solution for torque vectoring control, an optimization algorithm is proposed, which calculates the motors and braking modules commands and considering the needed constraints.

Besides supplying vehicle structure with independent brake modules, that enhancing braking operation also antislip control is designed to keep the slip ratio for each wheel under the maximum limits. The major goals of the study are enhancing vehicle manoeuvrability also reach vehicle lateral motion stability, and increasing total energy efficiency.

**Figure 2.1 EV with independent driven four-wheels proposed by (Kang and Heo, 2012) **
** **

Pennycott et al. (2013) and Plumlee et al. (2004) described another torque control allocation method by applying offline simulation-optimization based on the minimization of a direct quadratic cost function of the losses power from the motor, then using motor power map efficiency look-up table to compare with the schemes and get results for power losses at various speeds and forces. The presumption that the motor losses expressed quadratically in the function of the torque demand allowed using of the quadratic programming. Including permanent magnets, shifted reluctance, and brushless DC motors results and in order to investigate the impact of several kinds of motor characteristics, comparison depending on two main maneuvers between the results of three different kinds of motor applied.

The paper indicated for needed to future works with complex approximations because the result of simulation showed limitation in the optimal solution while applying cons function based on motor losses by quadratic approximation constraints for torque demand. In Lenzo et al. (2017) complex third-order polynomial function is proposed aiming to approximate values of motor losses, but this solution probable to have many minima solutions that make big challenges to apply online optimization and in the appropriateness of the system.

At the body level, the driver interpreter and stabilization controls function can be managed by using torque vectoring or differential braking as control behavior. This produces the requested response from the analytical model of the vehicle and compares this value for a stability controller with the sensor input (Liebemann et al., 2004). In general, to describe the vehicle and calculate the slip, pitch, and yaw motion for each wheel, bicycle models with two degrees of freedom (DOF) have been used. For stability control, there are several types of control systems that can enhance and deal with yaw moment to improve EVs for instance, proportional, optimal, sliding mood, and LQR strategies (Yang et al., 2009; De Novellis et al., 2013; Siampis et al., 2013; Goggia et al., 2014).

Four in-wheel motor EVs torque distribution control system have many effects on the steering and handling characteristics of EV, such as direct and indirect influence on the left and right wheels. Applying torque distribution control system based on moment distribution impacts on both energy consumption from power sources and stability of the EV. As the energy density of an EV is smaller than that of an internal combustion engine vehicle, the proper consumption of energy is a significant technological concern for improving driving control systems and designing EVs. That's why applied strategies must take both power-saving and increasing safety into account in order to enhance the overall performance of the EVs. Many studies proposed driving torque distribution from an economical perspective, which means they consider power saving distribution control strategies based on traction control system, motor model, and total feedback energy from the system (Dizqah et al., 2016; Li et al., 2017; Li et al., 2018; Wang et al., 2018; Zhao et al., 2020)

Li et al. (2018)and Chen and Wang (2013) and Pennycott et al. (2014) introduced a torque distribution optimization control structure for the management of energy efficiency, which benefits the development of an excrescent execution system. The torque allocation control based on an energy-efficient approach suggests that control efforts on over-actualized modules should be distributed by the specific inclusion of efficiency functions and operating modes of redundant actuators. In the level of realistic actuator power and efficiency functions, an optimization control system based on a Karush-Kuhn-Tucker is defined to find the local and

global minimum optimal solution for the optimization control system. However of considering the motor drive and regenerative brake control to reach maximum power saving and lowest consumption, also generalize a torque-related function by transforming the motor performance map using the wheel torque as the control variable, but the generalized motor performance map differs significantly from the real features. For this reason, this procedure is not feasible and has some disadvantages.

One of the driving torque control strategies that adjust the driving torque of EV to enhance active safety and stability of the vehicle is torque distribution control based on direct yaw moment control (DYC). The definition of DYC is the adjustment of generated yaw moment from applying torque distribution strategies throw transmission driving or braking torque to the vehicle’s right and left sides in order to change the vehicle's yaw rate specifically and reach the desired yaw rate (Geng et al., 2009; McTrustry, 2016).

In the last years, many researchers discussed and proposed various approaches about enhance the total efficiency and balance of the vehicle by applying DYC with different strategies and designs. Tahami et al. (2003) and Esmailzadeh et al. (2003) discuss an independent approach for optimum Yaw moment management to enhance car situational awareness. Because of simple configuration and great control influence on the vehicle, the semi-optimal control approaches have been considered more useful in their research. The controllability and balance of the car are boosted using this strategy in the control system.

Moreover, in Croft-White and Harrison (2006) aiming to increase the safety of the vehicle and handling stability, torque allocation based on linear and pitch angle of the tire’s weight parameters proposed. Such according to the outputs of their research, applying various weight allocation parameters makes a positive effect on the reaction and stability of vehicles.

Yu et al. (2016) developed a new direct yaw moment controller for four-wheel independent drive EV based on hierarchical control strategy with major aims increasing the safety of the vehicle and handling stability over several situations of driving moods. In the first

controller loop in the presented method, the main two parts have been described. The first is a control system for stat feedback by applying wheels lateral angle observer, and the second one is a controller for feed-forward aims to reach the requested optimal Yaw value for each wheel.

Over standard situations of operation, the steady-state response also in the transient response of vehicle handling and cost-effectiveness are enhanced by benefits of the proposed controller.

**3. VEHICLE DYNAMICS AND MODELLING **

**3.1. Introduction: **

In the automotive industry, the growing rivalry is encouraging automotive companies to focus on producing vehicles of high quality. A small change in the quality of handling, safety, and ride comfort systems may lead customers to choose one vehicle over another. As a result, integrating reliable mathematical models of the car is very important for the designing operation in the automobile industry. In recent years, the ability to apply model-based system construction approaches in order to deal with optimal performance and complexity in vehicle modeling considered a huge step in current automotive improvement and new engineering projects.

This chapter presents the proposed vehicle model and dynamics, tire-road friction definition, tire modeling, and longitudinal slip ratio calculation.

**3.2. Vehicle Dynamics and Modeling: **

The development of the study of vehicle dynamics and the related parts for longitudinal, lateral, and vertical motions have become the focus of attention of many researchers and developers in the car manufacturing and design fields. The experimental vehicle and proposed vehicle dynamics equations are explained as follows.

**3.2.1. Experimental vehicle characteristics: **

The properties and main parameters of the experimental vehicle are explained in this
*section. Authors of Maeda et al. (2017) developed and used the experimental (KANON-FPEV2) *
in many applications in their studies, as shown in Figure 3.1.

**Figure 3.1 The experimental Kanon-FPEV2 (Maeda et al., 2017) **

The proposed EV model in driving torque distribution control approaches are mainly
*depending on the design and characteristics of (FPEV2-KANON) and takes into account *
parameters specifications, which gives us the ability to verify from the performance of proposed
**vehicle modeling and simulation results. **

In addition, to increase control accuracy and enhance the overall operational efficiency an in-wheel motor with outer-rotor-type is set up for each wheel, as shown in Figure 3.2. Also with the in-wheel motors the traction or braking forces response can direct actuation to the motors without mechanical links or gear reduction because these types of motors depending on the direct drive system.

**Figure 3.2. The outer-rotor type in-wheel motor used in FPEV2-Kanon (Maeda et al., 2017) **

In Table 3.1. The specifications and parameters such as the maximum torque, Mass,
*Radius, and other properties of the Kanon-FPEV2 model are explained. *

**Table 3.1. Specifications and parameters of the FPEV2-Kanon model (Maeda et al., 2017) **

**# Name ** **Unit ** **QTY **

**1 Maximum Torque of Right and Left Front in-wheel motor ** Nm 500 ±
**2 Maximum Torque of Right and Left Rear in-wheel motor ** Nm 340 ±

**3 Mass of the Vehicle ** Kg 870

**4 The base of the Wheel ** meter 1.7

**5 Distance From the Front axle to the gravity center ** meter 0.99
**6 Distance From the Rear axle to the gravity center ** meter 0.701

**7 Base of Tread ** meter 1.3

**8 The Wheel Radius ** meter 0.302

**3.2.2. Proposed vehicle dynamics : **

As the major goal in this research is driving force distribution control, the illustrated vehicle dynamics equations and modeling are taken into account the longitudinal motion of the vehicle and rotational motion of four in-wheel motor EVs only, as shown in Figure 3.3; Figure 3.4, and Figure 3.5.

The equations of longitudinal motion for vehicle body and rotational motion for each wheel can be described as the following equations:-

, 1, 2, 3, 4

*n* *n* *n* *dn*

*J* *T* *rF* *n* (3.1)

*The first equation represents the dynamics for rotational motion of each wheels such J *
(Nm^{2}*) is the wheel inertia, ω (rad/s) is the wheel angular velocity, * 𝜔̇ (rad/s^{2}) represent the wheel
*angular acceleration that is the first derivative of wheel angular velocity. T (Nm) is the motor *

torque, it represents the delivered torque to the wheel by assuming the requested torque applied
*directly to each wheel, r (m) is the actual wheel radius and F**d* is the driving force at the contact
area between tire and road, as shown in Figure 3.3. In addition, n = 1, 2, 3, 4 are indices for
(front right, front left, rear right, rear left) respectively.

**Figure 3.3 Wheel rotational motion. **

The longitudinal motion of the vehicle is presented based on Newton’s second law, (the Newtonian relationship of force is equal to the product of mass and acceleration) i.e. Newton’s second law. Using this relationship, the total applied longitudinal forces on the vehicle can be calculated as the following equation:

1 2 3 4

*d* *d* *d* *d*

*MV* *F* *F* *F* *F* (3.2)

The second equation represents the dynamics of the vehicle while running on a straight
path and steering angles are the same for each wheel with longitudinal motion, as shown in
*Figure 3.4. Such M (Kg) represent the vehicle total mass, V (m/s) is the vehicle velocity and 𝑉̇ *

(m/s^{2}*) is the vehicle acceleration. F**d* is the total driving force, and 𝐹_{𝑑1}+ 𝐹_{𝑑2}+ 𝐹_{𝑑3} + 𝐹_{𝑑4} are
represent the driving force for (front right, front left, rear right, rear left) wheels respectively.

**Figure 3.4. Four-wheel vehicle longitudinal motion variables **

The driving force 𝐹_{𝑑} can be defined by the following equations:-

###

*n*

*n*

*F**d n* *N* (3.3)

*N* *M**n**g* (3.4)

*Where N is the normal force on the wheel and it occurred due to the vehicle's weight and *
*it is assumed to be equal for all wheels, as shown in Figure 3.5. M**n *represents the mass applied
on the n^{th} wheel (one wheel) and it is equal to a quarter of the total vehicle mass. Where g is the
gravity force. 𝜇(𝜆) is the friction coefficient for each wheel, which is a function of the slip ratio
𝜆. The tire-road friction coefficient, slip ratio, and the relationship between them explained in
detail in the tire-road friction section.

**Figure 3.5. Dynamics of the longitudinal motion and applied Normal Force on each tire. **

**3.2.3. Proposed vehicle Simulink modeling: **

In this section, Simulink modeling for One-wheel vehicle model has been proposed, as shown in Figure 3.6. Slip ratio calculation and the 𝜆 − 𝜇 function is explained in the next sections.

**Figure 3.6. Simulink model for One-wheel vehicle. **

**3.3. Tire-Road Friction and Tire Modeling: **

Beneficial to apply control on the driving forces generated from friction between tire and road, the nature of adhesion must be considered while defining the tire-road friction on the driving mode. The development and complexity of studying the friction between the tire-road contribute to the development and improvement of proposed driving torque control systems and traction control.

**3.3.1 A brief review on tire-road frictions: **

As mentioned before, the applied normal weight to the vehicle tires during straight path motion of the vehicle generates friction between tire and road. The generated friction in the contact area between them is occurred due to many aspects and very complex interactions.

Figure 3.7 describes the longitudinal deformation and interaction between tires and road (Moore, 1975; Gillespie, 1992).

**Figure 3.7. The Longitudinal Deformation and Interaction Between Tires and Road copied from **
(Moore, 1975)

The generated friction forces between tire and road have three types of mechanisms, and they described as following:

**First, the Adhesion Friction: because of sticking between the tire and the road surface, **
the adhesion friction arises. In general, rubber is resists slipping on the surface due to adhesion.

The molecular bonding between the rubber and road surfaces because the actual contact between the tire and surface is too less than the observed one, adhesion friction occurred as a result of this molecular binding, as shown in Figure 3.8.

The adhesion friction corresponds to the force needed to split these molecular limits and partition the surfaces. Also, it depends on the applied load on the tire, thus if load increase the contact area between the tire and road surface will increases too, providing higher bounding and rising of requested friction forces for binding operation. The adhesion friction is considered a major contributor to tire traction under dry road surfaces situation. on the surfaces covered by low friction coefficients, such as wet or icy roads, the adhesion friction significantly reduces because the direct interaction is limited in the wet surfaces which decreases the creation of friction in the contact area between tire and road (Siampis, 2016; Jazar, 2017).

**Figure 3.8 Binding of the molecular bonds between the tire and road surfaces copied from **
(Jazar, 2017).

**Second, The Deformation Friction: The effect of deforming rubber and completing the **
tiny irregularities when tire moves on the road surface called deformation friction. The street's
surface has various sharp edges, or peaks, and valleys. When a tire passes over rough roads, the
rubber deforms due to peaks and high points on different road surfaces. The peaks of
abnormalities enter the tire whenever there is a load on it, as well as the tire drapes over them.

Because of that, the deformation friction is considered as a fundamental contribution to enhance the tire traction while the vehicle running on wet surfaces (Jazar, 2017).

**Third, The Wear Friction, such it is caused by extreme localized stress on the rubber's **
tensile strength. After the flexible point, the excess local pressure distorts the frame structure of
the tire surface (Jazar, 2017).

The combination of the above friction mechanisms demonstrate the tire force as a function of the tire’s load and the road conditions according to the previously mention equation (3.3)

**3.3.2. Tire friction modeling: **

Tire friction modeling is a difficult but very necessary aspect of vehicle modeling.

Theoretical and Empirical tire models are the two primary types of tire models identified in this review as follows:

Theoretical Models:

These models utilize physical equations to describe the relationship between both tires and the different road surfaces. Besides, Strain-stress relationships or friction models, just like Dahl and LuGre, are widely used in these models. Moreover, the outcomes generally contain combined of non-linear equations, sophisticated computational methods might be required to deal with results (De Wit and Tsiotras, 1999; Tönük et al., 2001; Canudas-de-Wit et al., 2003;

**Åström and De Wit, 2008). **

Empirical Models:

In Empirical models, to define the tire properties and characteristics such as Pacejka Magic Formula, the experimental findings are used. furthermore, sophisticated computational techniques are not needed for these models, which makes them more efficient, easier, and less costly (Pacejka and Bakker, 1992b). Because of that, for vehicle stability management and handling simulation implementations, Empirical Models are often recommended.

In this thesis, the main function that describes friction coefficient and its relation with longitudinal slip ratio is based on Pacejka’s Magic formula. The equation of Magic formula that calculates friction as a function of slip ratio is written as follows:

###

^{n}*n*

*D*

^{sin}

##

*C*

^{arctan}

*B*

^{n}*E*

^{(}

*B*

^{n}^{arctan}

###

*B*

^{n}###

(3.5)

B is the stiffness coefficient, C is the shape coefficient, D is the peak coefficient, and E is the curvature factor, the values of these factors are different depends on road condition are written, as shown in Table 3.2 (Pacejka and Bakker, 1992a).

𝜆_{𝑛} Represent the slip ratio for each wheel. Longitudinal slip ratio is and mathematical
calculation are defined in the next section

**Table 3.2 values of magic formula parameters for main different road conditions (Pacejka and **
Bakker, 1992a)

**Types of roads ****Dry road ** **Wet road ** **Snow surface ** **Icy surface **

* B * 10 12 5 4

* C * 1.9 2.3 2 2

* D * 1 0.82 0.3 0.1

* E * 0.97 1 1 1

**3.4 Slip Ratio Definition and Calculation: **

**3.4.1 Introduction: **

For assessing the efficiency, increasing handling stability, and safety of the Electric vehicles, there are several essential quality attributes strategies and target performance indicators widely determined and applied in the control system (Burgess, 2009; Yin and Hori,

2010; De Novellis et al., 2013). By utilizing prediction models or determining using measurement items, these parameters can be estimated or measured, relying on the vehicle design setup and the required applied control system. One of these approaches is slip ratio control, which is used to optimize the vehicle's performance while also increasing its efficiency and safety (McTrustry, 2016).

**3.4.2 Longitudinal slip ratio: **

The longitudinal Slip ratio describes the relationship between the following main three parts, vehicle speed, wheel speed, and tire-road surface. As mentioned before in the tire-road friction section, applied driving or braking force on each wheel of the vehicle makes rubber deformation occurred on the contact area between tire and road surface due to many reasons.

Because of this deformation and other factors, a difference between the observed wheel speed and calculated real vehicle speed occurred which makes a slip, the ratio of the difference between the vehicle and wheel speed is known as the slip ratio. There are many approved procedures for calculating and describing a vehicle's longitudinal slip (Gillespie, 1992;

McTrustry, 2016).

In this thesis, the longitudinal slip ratio calculated as a function of vehicle speed, and wheel speed for driving or braking mode as follows:

Slip ratio for driving mode:

###

^{,}

###

^{max}

###

^{n}^{, , }

^{n}###

*n* *n* *n*

*n* *n*

*V* *V*

*V* *V* *V*

(3.6)

Slip ratio for braking mode:

###

^{,}

###

^{max}

###

^{n}^{, , }

^{n}###

*n* *n* *n*

*n* *n*

*V* *V*

*V* *V* *V*

(3.7)

*n* *n*

*V* *r* (3.8)

Where 𝑉 is the vehicle velocity, 𝜀 is a small positive number and it has added for benefit of prevents division by zero. In addition, 𝑉𝜔 is the wheel velocity, which is described as the product of wheel angular velocity and wheel radius.

Figure 3.9 described Simulink-block modeling of the slip ratio calculation for each wheel in the vehicle. The upper and lower boundaries of the saturation block for the slip ratio are explained in the driving force controller section in chapter 4.

**Figure 3.9. Longitudinal Slip ratio calculation for each wheel Simulink block diagram. **

Figure 3.10. Presents the relationship between longitudinal slip ratio and the friction coefficient for different major road conditions based on Magic formula from equation (3.5) (Pacejka and Bakker, 1992b).

**Figure 3.10. The relationship between longitudinal Slip and Friction Coefficient based on **
Magic Formula for main general road surfaces.

As shown in Figure 3.10. There are two peaks for each curve in the above relation between 𝜆 and 𝜇 and it depends on the type of road condition. The 𝜇 friction coefficient value is rising proportionally as a function of slip while 𝜆 value increasing and still inside the domain of maximum and minimum peaks. As well as the 𝜇 friction coefficient value is falling proportionally as a function of slip when the absolute of 𝜆 values increase in the outer range of maximum and minimum peaks.

The maximum positive peak values of the previously mentioned friction coefficient for main common road surfaces are demonstrated in table 3.3.

**Table 3.3. The maximum friction coefficient for main common road surfaces (Pacejka and **
Bakker, 1992a).

* Type of road surface * 𝝁

_{𝟏}

**Dry road**𝝁

_{𝟐}

**Wet road**𝝁

_{𝟑}

**Snowy road**𝝁

_{𝟒}

**Icy road**

**Maximum friction **

* coefficient * 0.9 – 1 0.8 – 0.85 0.2 0.1

**4. METHOD **

**4.1. Introduction: **

This chapter presents the proposed operations and methods of designing and carrying out suitable control strategies for driving force. Different types of control system strategies are obtained and evaluated in terms of their capability to boost the overall performance of the vehicle, simplicity to obtain feedback. Also depending on the ability to develop the dynamics of the vehicle.

The proposed control system consists of the inner and outer loop inside the main controller. The control system is applied to each wheel of the vehicle model. Controllers like wheel speed and driving force controllers have been obtained. Simulink-MATLAB simulations are used to examine and compare the output performance of the applied approaches. The main objective of the proposed method is to contribute the vehicle traction while driving on a normal or slippery road as well as increase the total efficiency and stability of the vehicle.

The mechanism of the proposed control system and operation steps are described in the flow chart as shown in Figure 4.1.

**4.2. Driving Force Control system: **

The proposed driving force control system as traction control, total yaw moment control, and anti-slip control systems are included in the control method in this section, which gives the ability to control delivered torque for each wheel, consequently enhance the stability of the vehicle.

**Figure 4.1. Flow chart of proposed control system **

The configuration of the proposed driving force control system consists of main two control loops, the first loop is an outer control loop, and it controls the driving force by depending on the feedback coming from the driving force observer. The second loop is an inner control loop, and it controls the speed of each wheel in order to manage the slip ratio for the vehicle, as shown in Figure 4.2.

**Figure 4.2. The configuration of the proposed driving force control system – one wheel vehicle **
model

By looking at the aforementioned relationship between 𝜆 – 𝜇, the values of friction coefficient can be controlled by applying a control system on each wheel to prevent an increase in the slip for the wheel as well as limits saturation of applied driving force for each wheel.

The relation between the slip ratio of each wheel and driving force, the operational strategies, inputs, and outputs values for each part of the proposed control system are discussed in the following sections.

**4.3. Driving Force Controller and ( 𝝀 - Y ) Ratio Conversion Function: **

The relation between the slip ratio of each wheel and the driving force can be described as the driving stiffness. Depending on the defined driving force equation (3.3) from the previous chapter, driving stiffness for each wheel can be calculated as the following equation:

*dn*
*n*

*n*

*Ds* *F*

(4.1)

Where 𝐷𝑠 is the driving stiffness for each wheel, 𝐹_{𝑑} is the driving force, and 𝜆 represents
the longitudinal slip ratio.

As described before in equations (3.6) and (3.7), the formula for calculating the
longitudinal slip ratio is different such it depends on the driving mode. Where it is in the case of
*acceleration, the wheel speed is greater than the vehicle’s speed (Vω ≥ V) and the slip ratio *
calculated as written in equation (3.6). Conversely, in the case of deceleration, the wheel speed
*becomes less than the speed of the vehicle (Vω < V), and the slip ratio is found by different *
formula as described in equation (3.7). Accordingly, the definition of slip ratio must be
alternated while applying different control commands, which is negatively affecting the
operation of implementing the control system.

Such as the input of the wheel speed controller (desired wheel speed) in the inner loop control will be calculated depending on the driving force controller ( 𝜆 ) output results. Because of that, it is not convenient to use lambda directly in the plant of the driving force controller.

*Consequently, the definition of controller Y has been developed as a function of vehicle *
and wheel speed for all driving mode for the purpose of utilizing it as controller input instead of
𝜆, and its described as the following equation:

*n* 1

*n*
*n*

*Y* *V*
*V*

(4.2)

*Through the above equation, it is notable that the definition of Y is the same as the *
definition of slip ratio (𝜆) in the case of braking (Vω < V), and the relationship between
*controller output Y and (𝜆) in the case of acceleration (Vω ≥ V) is defined as the following *
equation:

, 1

,

*n*

*for driving*
*Y*

*for braking*

(4.3)

*Figure 4.3. Presents the curve of ( Y – slip ratio ) relationship, and it shows that while *
*the magnitude of slip ratio value is much less than 1 (|λ| ≪ 1 ) then slip ratio equals to Y. *

according to that reason, it is appropriate to apply Y in the controller instead of 𝜆. The equation
(4.1) can be written like 𝐹_{𝑑} = 𝐷_{𝑠}* × 𝜆 while considering (| 𝜆 | << 1). By assuming the transfer *
*function from Y to *𝐹_{𝑑}* be zero-order, also depending on the (Y−𝜆) relation, the driving force *
controller’s transfer function can be described as:

,

*d* *s* *s*

*F* *D* *Y* *D* *such Y* (4.4)

**Figure 4.3. The curve of ( Y – slip ratio ) relationship. **

The proposed driving force controller has one controller, which is limited integrator
control with gain, the input of the control system is desired driving force 𝐹_{𝑑} and it is defined by
*the user (driver), the output of the controller is Y as the difference between desired *𝐹_{𝑑} and
estimation 𝐹_{𝑑} coming from driving force observer as feedback, as shown in Figure 4.4.

**Figure 4.4. Driving force controller block diagram. **

*The upper and lower boundaries of the integrator are obtained on the Y output based on *
the maximum and minimum peaks from (𝜆 − 𝜇) relation and the relation between (𝜆 − 𝑌). The
*initial value of Y**0** is defined as equal to zero, and the upper and lower boundaries for both Y and *
λ are described as shown in Table 4.1.

**Table 4.1. Maximum and minimum values for Y and 𝜆. **

Name Value

𝑌_{𝑚𝑎𝑥} 0.25

𝑌_{𝑚𝑖𝑛} - 0.20

λ_{ 𝑚𝑎𝑥} 0.20

λ_{ 𝑚𝑖𝑛} - 0.20

The main aims of applying these boundaries are explained as follows:

Keeps the slip ratio (𝜆) inside the range where friction coefficient is monotonic with 𝜆.

Keeps Y and slip ratio (𝜆) values within the range where (𝑌 ≅ 𝜆) satisfied.

**4.4. Desired Wheel Speed (Vω*) and Angular Velocity (ω*) Calculations: **

The input of the inner control loop (wheel speed controller) is defined based on the
*output of driving force controller Y and the calculated vehicle body velocity in vehicle model, *
as shown in Figure 4.5.

**Figure 4.5. Desired wheel speed and angular velocity calculation function. **

*From equation (4.2), the desired wheel speed (Vω*) and angular velocity (ω*) as a *
reference for the wheel speed controller can be defined as the following equation:

*V* * *V* *Y* *V* (4.5)

*

* *V*

*r*

(4.6)

*According to equation (4.5), the required wheel speed (Vω*) calculated value in the *
*starting operating will remain equal to zero regardless of the Y value, due to the initial velocity *
*of a vehicle is defined to be zero (V**0 **= 0). *

*To avoid the problem of start operating, the desired wheel speed (Vω*) calculating *
*formula is redefined by adding a small constant (σ) instead of vehicle speed value in the case *
*that the vehicle speed (V) is less than (σ), as described in the following equation: *

###

###

*

, ( ) ,

*V* *Y* *V*

*V*

*V* *Y* *V* *V*

(4.7)

*As shown in Figure 4.6. When vehicle velocity (V) is less than (σ), the range of the *
*desired wheel speed (Vω*) can be defined depends on the upper and lower boundaries of Y as *
follows:

###

*min*

###

^{ }

^{*}

^{ }

###

*max*

###

*V* *Y* *V* *V* *Y*

(4.8)

**Figure 4.6. The range of desired wheel speed (Vω*) when ( V < σ ). **

**4.5. Driving Force Observer: **

The main purpose of the proposed driving torque observer is to calculate the estimated driving force for each wheel in the vehicle and give it as feedback for the outer loop of the driving force control system. Depending on the equation (3.1), and vehicle dynamics, the presented driving force observer is consist of two main input and one output.

As shown in Figure 4.7. The first input is the desired torque command for each wheel in
*the vehicle (T*), which is the output from the wheel speed controller. The second input is the *

angular acceleration, which is can be calculated in the vehicle model, where r and J are defined previously as the wheel radius and wheel inertia respectively. The output of the driving torque observer is the estimated driving force (est. Fd) for each wheel.

**Figure 4.7. Calculation of F**d Estimation value from Driving Force Observer block diagram.

**4.6. Wheel Speed Controller: **

In the proposed driving force control system, the inner loop controller is represented by the wheel speed controller, and it is explained in this section.

Different types of control systems applied as wheel speed controllers aiming to control the delivered torque to the wheel, also prevent slip ratio value from exceeding the saturation limits while driving on low friction coefficient roads as well as reaching the desired wheel speed.

The input of this controller is the desired wheel angular velocity ω^{∗} and the feedback
comes from the calculated actual wheel angular velocity in the vehicle model. The output of the
controller is the desired delivered torque 𝑇^{∗}, and to enhance the speed response driving torque
(r*Fd) is added to the output of the system as a feed-forward, as shown in Figure 4.8.

**Figure 4.8. Wheel speed controller main Block diagram **

The main objectives of applying wheel speed controller are explained as follows:

- Reach to the desired wheel speed as well as Prevents slip and support the vehicle traction when the vehicle runs into slippery roads.

- Control on the delivered torque for each wheel.

Two types of control systems have been applied and compared in the same simulation situation and parameters in order to contribute to this research.

**4.6.1. Wheel speed controller based on fuzzy logic control with PD (Proportional-**
**Derivative gains) parameters: **

In this section, the PD-Fuzzy logic control system as a wheel speed controller is presented, as shown in Figure 4.9.