Enhancing Stability In Electric Vehicles With In-Wheel Motors

UNIVERSIDAD DE SEVILLA Escuela T´ecnica Superior de Ingenier´ıa Dept. Ingenier´ıa de Sistemas y Autom´atica DOCTORAL THESIS Enhancing Stability In Electric Vehicles With In-Wheel Motors Author: Ahmed Hassan Ahmed Ibrahim Supervisors: Dr. Jose Ramon Dominguez Frejo Dr. Jos´e Mar´ıa Maestre Torreblanca Seville, 2024 Acknowledgments I would like to express my special thanks and gratitude to my supervisors, Dr. Jos´e Mar´ıa Maestre Torreblanca, and Dr. Jose Ramon D. Frejo, for their great support and encouragement to conduct this research. Their extensive knowledge and significant experience have not only helped me throughout my research but have also allowed me to overcome any obstacles along this journey. Moreover, their choice to have me as a Ph.D. student and their efforts in integrating me into this exceptional group in Seville are sincerely acknowledged. I would like appreciatively to acknowledge the Egyptian Government for the financial support extended to this research project. I also extend my gratitude to Sara Ruiz-Moreno for her support, assistance, and encouragement. Additionally, my appreciation goes to the Spanish Government, and the University of Seville for their consistent technical backing during this study. I am also grateful to the previous students whose research provided valuable information that greatly contributed to the completion of my own research. Lastly, I want to convey my great appreciation to my family, without whom this journey would not have been possible. No words can describe my gratitude to my mother, my father, my sisters, and my wife for their emotional support and sacrifice. My warmest gratitude to my kid, Ziad, you are such a blessing. I hope that he will become a student at this great university in the future. v Abstract This thesis evaluates advanced control strategies aimed at improving the stability and maneuverability of electric vehicles (EVs) equipped with in-wheel motors (IWMs). It begins with an overview of the increasing importance of EVs for their environmental benefits and the potential of IWMs to enhance vehicle mobility and control adaptability. The thesis then focuses on addressing the challenge of lateral motion control during critical cornering scenarios. The primary focus is on the Direct Yaw Control (DYC) method, which utilizes the yaw moment to stabilize the vehicle and enhance handling characteristics. Particularly, addressing oversteering and understeering phenomena, ensuring better control and stability in various driving conditions. The research utilizes a fully functional prototype named FOX, serving as an ideal platform for implementing and evaluating the electronic stability control system. DYC includes two control levels: the upper controller, which determines the desired yaw moment and the lower controller, which allocates it to the four wheels using Torque Vector Control (TVC). The stability algorithm combines Model Predictive Control (MPC) with TVC to enhance vehicle stability. MPC determines corrective signals, while the TVC distributes them among the IWMs for effective stability control. Additionally, an alternative approach using a Nonlinear Model Predictive Control (NMPC) further improves stability by accounting for system dynamics, ensuring precise vehicle behavior control. Due to the high computational requirements of NMPC and the need for rapid control signal calculation, the thesis proposes integrating Nonlinear Autoregressive Exogenous (NARX) neural networks. In particularly, artificial neural networks (ANNs) were employed and trained using distinct simulation datasets to achieve this integration, So as to enhance lateral stability during cornering by emulating NMPC. The ANN model, trained on simulated NMPC data, includes tuning parameters as inputs, creating a versatile family of predictive controllers, that improve vehicle stability and handling while reducing computation time. Additionally, the thesis introduces a comprehensive benchmarking framework to evaluate vehicle lateral stability enhancement during double-lane change (DLC). This framework tests control strategies using simulations and performance vii viii Abstract metrics, supporting the development of advanced control strategies. Finally, the effectiveness of the proposed techniques has been evaluated through MATLAB/Simulink simulations. Abstract ix Resumen Esta tesis eval´ua estrategias de control avanzadas dirigidas a mejorar la estabilidad y maniobrabilidad de veh´ıculos el´ectricos (EVs, del ingl´es Electric Vehicles) equipados con motores en las ruedas (IWMs, del ingl´es In-wheel Motors). Comienza con una visi´on general de la creciente importancia de los EVs debido a sus beneficios ambientales y el potencial de los IWMs para mejorar la movilidad del veh´ıculo y la adaptabilidad del control. La tesis se centra en abordar el desaf´ıo del control del movimiento lateral durante escenarios cr´ıticos de giro. El enfoque principal es el m´etodo de Control de Gui˜nada Directa (DYC, del ingl´es Direct Yaw Control ), que utiliza el momento de gui˜nada para estabilizar el veh´ıculo y mejorar las caracter´ısticas de manejo. En particular, se abordan los fen´omenos de sobreviraje y subviraje, asegurando un mejor control y estabilidad en diversas condiciones de conducci´on. La investigaci´on utiliza un prototipo completamente funcional llamado FOX, que sirve como una plataforma ideal para implementar y evaluar el sistema de control de estabilidad electr´onica. El DYC incluye dos niveles de control: el controlador superior, que determina el momento de gui˜nada deseado, y el controlador inferior, que lo distribuye a las cuatro ruedas utilizando el Control Vectorial de Par (TVC, del ingl´es Torque Vector Control). El algoritmo de estabilidad combina el Control Predictivo de Modelos (MPC, del ingl´es Model Predictive Control) con el TVC para mejorar la estabilidad del veh´ıculo. El MPC determina las se˜nales correctivas, mientras que el TVC las distribuye entre los IWMs para un control de estabilidad efectivo. Adem´as, un enfoque alternativo utilizando Control Predictivo de Modelos No Lineal (NMPC, del ingl´es Non-linear Model Predictive Control) mejora a´un m´as la estabilidad al considerar la din´amica del sistema, asegurando un control preciso del comportamiento del veh´ıculo. Debido a los altos requisitos computacionales del NMPC y la necesidad de un c´alculo r´apido de se˜nales de control, la tesis propone integrar redes neuronales no lineales autorregresivas con ex´ogenos (NARX, del ingl´es Nonlinear Autoregressive Exogenous). En particular, se emplearon redes neuronales artificiales (ANNs, del ingl´es Artificial Neural Networks) entrenadas utilizando distintos conjuntos de datos de simulaci´on para lograr esta integraci´on, con el fin de mejorar la estabilidad lateral durante los giros emulando el NMPC. El modelo ANN, entrenado con datos de simulaciones del NMPC, incluye par´ametros de ajuste como entradas, 2Introduction 1.1 A summary of the state of the art Drive-by-wire (DBW) refers to a vehicle control system that replaces traditional mechanical components, such as the steering, braking, and acceleration mechanisms, with electronic systems. In a DBW system, the driver’s inputs, such as steering wheel movements, brake pedal pressure, and throttle position, are converted into electrical signals and then transmitted to the corresponding actuators that control the vehicle’s functions. In a DBW system, various sensors, such as position sensors and torque sensors, are used to detect the driver’s inputs and the current state of the vehicle. These sensor signals are then processed by a control unit, which determines the appropriate response and sends commands to the actuators. The emergence of new functionalities like collision avoidance, autonomous driving, lane-keeping assistance, and advanced stability control systems necessitates the integration of full by-wire systems. These systems allow for the control of all actuators through electronic control units, enabling the application of driver-independent signals. Consequently, the hazard severity associated with such systems is also elevated. However, it is crucial to have appropriate fail-safe mechanisms in place to ensure the system’s reliability and safety. Redundancies, backup power supplies, and fail-safe modes are typically implemented to prevent catastrophic failures and ensure that the vehicle can still be controlled in case of a system malfunction. Fig.1.1 demonstrates that the hazard severity of failures increases significantly when using DBW systems. The brake and steering systems in vehicles are safety-critical and must continue to operate without endangering human life in the event of failure. Among DBW systems, the steer-by-wire system poses the highest hazard severity because a malfunction in its single unit results in a complete loss of steering control. In contrast, if a single braking actuator fails, three alternate units remain, providing the driver with 75 percent of the normal braking force [1]. Some DBW systems are: •Brake by wire systems replace traditional hydraulic braking with electronic control, converting the driver’s brake pedal input into electronic signals processed by a control unit, which commands actuators to apply the brakes. This technology, divided into electro-hydraulic A summary of the state of the art 3 Figure 1.1: Safety risks in DBW and advanced control systems [1] brakes (EHB) and electro-mechanical brakes (EMB), as shown in Fig. 1.2. In EHB systems, a position sensor translates the driver’s braking request into an electrical signal, which is transmitted to the braking unit at each wheel. Each braking unit consists of an electric motor, a pump, and a hydraulic tank, all working together to generate the necessary braking pressure. Additionally, the brake pedal is connected to a hydraulic cylinder, enabling the driver to manually apply minimal braking pressure required in the event of an electronic failure. In EMB systems, the hydraulic components are eliminated, Figure 1.2: (a) EHB and (b) EMB concepts for brake-by-wire [2]. with braking pressure generated solely by an electric actuator. These actuators are controlled by an electronic control unit (ECU), which receives signals from a sensor on the brake pedal. To provide the driver with feedback on the braking pressure, a ”force feedback” ac- 4Introduction tuator is also used at the brake pedal. EMB systems require redundancy in both the power system and the ECU for safety. Notably, if one actuator fails, the independent nature of each wheel means that 75% of braking power remains available, compared to a typical EHB, a failure will cause half of the brakes to become ineffective. Advantages of EMB systems include being more environmentally friendly by eliminating hydraulic fluids, providing faster and more robust braking responses. •Steer-by-wire systems are the evolution of traditional setups based on mechanical or hydraulic power steering. Steer-by-wire eliminates mechanical linkages and uses force feedback actuators to maintain torque feedback and self-centering effects. Electro-mechanical power steering systems, which operate only during steering maneuvers, consume 8% less energy, are more sustainable, and eliminate environmentally harmful fluids [3]. These systems enable features like variable steering ratios and active steering, and their electronic control allows personalized steering feel. There are three different architectures to implement the steer-by-wire system: electro-hydraulic actuation (EHA), purely hydraulic actuation (PHA), and electromechanical actuation (EMA) [4]. As depicted in Fig.1.3.a, an EHA replaces the traditional steering column with an electric motor attached to the rack and pinion while adding a force feedback actuator to the steering wheel. However, it is associated with challenges related to packaging and weight. PHA is illustrated in Fig.1.3.b, which enables steering control by incorporating a set of hydraulic control valves into the power-assisted steering rack, offering control over the rack’s position. However, this solution still faces packaging and weight constraints due to the retention of the conventional power steering system. Finally, EMA is shown in Fig.1.3.c, which allows for wheel actuation using one motor to control both wheels through a steering rack or employing one motor for each wheel, enabling independent control of each wheel. This configuration offers the most practical and advantageous implementation of a steer-by-wire system [4]. •Throttle by wire (TBW) systems replace the traditional mechanical linkage with an electronic system. In TBW, a sensor on the throttle pedal communicates with an ECU, which processes the driver’s input and adjusts the engine’s power output by controlling the fuel and air mixture. This system enhances reliability and safety by allow- A summary of the state of the art 5 Figure 1.3: (a) EHA, (b) PHA, and (c) EMA [4]. ing the ECU to cut off power in case of failure, preventing accidents. TBW also offers flexibility in implementing various driving modes, such as eco-friendly or sports modes, based on the driver’s preferences [5]. •Anti-lock break system (ABS) prevents wheel lock-up during braking, enhancing vehicle control and safety. It employs wheel speed sensors, a hydraulic modulator, and an ECU to detect potential wheel lock-up and modulate brake pressure, ensuring wheels maintain traction with the road [6]. This pulsating brake action allows drivers to retain steering control during intense braking, particularly on slippery surfaces. Recognizing its importance, European manufacturers mandated ABS in all vehicles starting in 2003 [7]. •Traction Control system (TCS) prevents wheel slip during vehicle acceleration, by utilizing engine management controllers and brake systems to optimize traction and control [8]. TCS detects and intervenes in cases of wheel slip by reducing engine torque or applying brakes, enhancing stability and control. TCS improves vehicle stability, acceleration performance, and overall safety, particularly in challenging driving conditions. By eliminating mechanical connections, DBW systems offer several advantages. Firstly, they provide greater flexibility in vehicle design, as the absence of physical linkages allows for more freedom in cockpit layout and packaging. Secondly, these systems can enable advanced features such as adaptive cruise control, lane-keeping assist, and automated parking, as the control unit can seamlessly integrate with other vehicle systems. Moreover, DBW systems allow for more precise control and adjustments, as electronic signals can be rapidly processed and modulated. This can enhance the vehicle’s handling, responsiveness, and overall driving experience. Additionally, DBW systems can provide diagnostics and self-monitoring capabilities, making it easier to detect and 6Introduction address potential issues. Overall, DBW systems represent a significant advancement in vehicle control technology, offering increased functionality, flexibility, and precision. They are becoming more prevalent in modern vehicles, particularly in the development of autonomous and electric vehicles, where electronic control is essential for efficient and integrated vehicle operation. 1.1.1 Stability control systems Stability control systems like ESC, Electronic Stability Program (ESP), or Dynamic Stability Control (DSC) aim to enhance the vehicle’s lateral stability by monitoring its states and assisting drivers during emergencies or challenging road conditions [9]. Typically, drivers are accustomed to operating vehicles within their linear range, where steering inputs directly influence the vehicle’s direction with minimal delay. However, this linearity diminishes during high lateral acceleration situations, and there’s an increased delay between input and vehicle response, potentially resulting in accidents. ESC systems address these issues by interpreting data from angular speed sensors, steering wheel rotation, vehicle angular speed, and slip angle estimators. They compare this data with a reference model to determine the desired trajectory and take measures to avoid them by applying corrective actions such as independent wheel braking, active flywheel adjustments, or torque vectoring to stabilize the vehicle and align its behavior with driver intentions, thereby enhancing safety and stability [10]. The integration of electronic sensors and intelligent algorithms allows ESC to effectively manage vehicle response, improving overall stability and driver confidence, especially in hazardous conditions. Studies in [11–13] show ESC significantly reduces crashes and fatalities, leading to regulatory mandates and widespread adoption, contributing to safer driving experiences and effective accident prevention. In [14], a review on yaw rate and sideslip controllers is performed, showing that yaw rate control enhances driver confidence, while sideslip control has a greater impact on vehicle stability. ESCs based on braking systems, employ an ECU to control brakes independently, aiding drivers in maintaining control during emergencies. Loss of vehicle control can occur due to oversteer (the car turns more than intended) or understeer (the car doesn’t turn enough despite increased steering input). The intention to correct and address this issue with unsuitable steering angles often worsens the situation [15]. ESC systems intervene by ensuring the vehicle follows the intended direction A summary of the state of the art 7 as indicated by the steering wheel, eliminating the need for complex maneuvers by the driver. While effective in maintaining control, ESC activation typically results in a speed reduction. ESCs based on TVC systems in four-wheel drive vehicles enhance traction and stability by independently distributing torque between the front and rear axles and the wheels of each axle. These systems, incorporating active differentials, improve vehicle dynamics by modulating wheel speeds to ensure maximum traction and generate corrective angular momentum during maneuvers, such as oversteer and understeer situations [16]. Compared to conventional ESC systems that rely on active braking and reduce torque, torque vector control systems offer more efficient and less harmful stability management, especially at high speeds and during emergencies. 1.1.2 Direct yaw control (DYC) All-in-wheel drive vehicles provide traction to both front and rear wheels, which is crucial during cornering. Loss of traction at the front wheels can lead to oversteering, while loss of traction at the rear wheels can cause understeering. These scenarios, known as limit handling conditions, often occur near the traction limit in severe driving conditions. In [17], it is introduced the β-method, which links vehicle stability to sideslip and tire slip angles and uses this relationship to determine a corrective moment based on steering angles and longitudinal acceleration. This corrective moment is distributed as traction or braking torque between the rear wheels according to lateral and longitudinal acceleration, as shown in Fig 1.4. In [18], a study explores DYC using a feedback Proportional- Integral (PI) controller was then used to generate the required corrective moment, improving vehicle handling by reducing sideslip and yaw rate. Given the variability in driving conditions and vehicle parameters, Sliding Mode Controllers (SMCs) have emerged as robust solutions, as demonstrated by [19]. However, the discontinuous control term in SMCs can lead to chattering, prompting the development of quasi-SMC methods as in [20]. In [21], it is utilized Adaptive-SMC (ASMC), an adaptation mechanism developed based on the estimated cornering stiffness of the tires, as illustrated in Fig. 1.5. In [22], it is introduced a Linear parametric Variable (LPV)-H∞controller based on a 2-DOF bicycle model that accounts for various longitudinal speeds. The primary objective of this controller was to reject side wind effects during normal driving 8Introduction Figure 1.4: Corrective moment and vehicle sideslip at various steering angles [17]. conditions, thereby assisting the driver in maintaining the desired path. In [23], it is compared an H∞-based Internal Model Controller (IMC) with SMCs, finding that IMC offered robustness and managed actuator saturation using an anti-windup method. Both controllers showed good transient performance and minimal tracking error but underperformed on low-friction roads compared to uncontrolled vehicles in high-speed braking maneuvers. In [24], it is introduced an LPV-H∞controller with nonlinear tire characteristics for improved lateral stability via TVC. In [25], it is developed a robust gain-scheduling Linear Quadratic Regulator (LQR) controller, which outperformed conventional LQR controllers in stability and performance on dry roads. Most of the aforementioned controllers employed an upper-level controller to generate the corrective moment, with a lower-level controller to allocate and execute the control action, as shown in Fig. 1.6. Integrating a slip controller with the lower allocation controller was found to enhance the effectiveness of DYC using tire driving/braking forces. Optimization-based controllers were introduced to merge the two levels into a single controller, incorporating various optimal-constrained control signals and vehicle dynamics for improved performance. One of the most widely used optimization-based controllers is the A summary of the state of the art 9 Figure 1.5: Scheme of ASMC [21]. Figure 1.6: Upper and lower control scheme as shown [26]. MPC, which solves an optimization problem to satisfy a desired objective function and constraints based on predictions of vehicle states and control actions. In [27], an MPC that combined tire slip control and DYC was proposed utilizing the driving/braking force distribution on each wheel based on a 2-DOF bicycle model. This quadratic optimization minimized yaw rate, vehicle sideslip, and wheel velocity errors between the vehicle and desired signals. Despite these advantages, the linear bicycle model used in MPC design can struggle with nonlinear dynamic changes, necessitating a nonlinear MPC. In [28], it is developed an explicit NMPC for controlling vehicle lateral stability, offering an offline suboptimal solution to avoid the computational complexity of online NMPC. This method used multi-parametric quadratic program- 10 Introduction ming to approximate the solution, with controlled inaccuracy through iteration. The controller demonstrated improved handling performance and stability, but it required a high computational demand. 1.2 Motivation The motivation for this thesis lies in the need to enhance the stability and maneuverability of EVs equipped with IWMs. As EVs become more valuable for their environmental benefits, there is a demand for advanced control strategies to optimize their performance. IWMs offer significant potential for improving vehicle mobility and control adaptability but also pose challenges, particularly in maintaining stability during critical cornering scenarios. Addressing these challenges is essential for ensuring safe and reliable EV performance under various driving conditions. This PhD dissertation focuses on the DYC method, which stabilizes the vehicle by utilizing the yaw moment to improve handling and addressing oversteering and understeering issues. A fully functional prototype named FOX enables practical implementation and evaluation of the electronic stability control system, with its high-fidelity simulation model supporting virtual testing and simulations as discussed in [29–33]. Moreover, this thesis explores advanced control methodologies such as MPC and neural networks to optimize vehicle stability and performance. MPC is particularly suited for this application because it can account for dynamic constraints and optimize control inputs over a finite prediction horizon. By integrating MPC with neural networks, the thesis seeks to enhance the adaptability of vehicle control algorithms by utilizing machine learning (ML) techniques to model complex dynamics and environmental interactions, enhancing vehicle stability through precise distribution of corrective signals among the IWMs. Ultimately, this work aims to advance the understanding and implementation of sophisticated control strategies to optimize EV stability and performance, contributing to the development of safer, more efficient, and environmentally friendly vehicles. Objective 11 1.3 Objective The objectives of this thesis are as follows: •Evaluate the vehicle’s handling performance: This involves assessing a range of control methodologies aimed at enhancing the stability and maneuverability of EVs equipped with IWMs. This evaluation includes testing various approaches, such as MPCs and TVC implemented through DYC, to determine their effectiveness in improving vehicle performance. •Address lateral motion control challenges: This objective involves investigating challenges in critical cornering situations, emphasizing understanding factors like oversteering and understeering contributing to instability. The aim is to significantly improve the vehicle’s lateral stability by developing strategies to address these challenges, particularly during aggressive maneuvers and on low-traction surfaces, ensuring the following of the predefined path. •Evaluate stability control systems: Utilize a fully functional prototype (e.g., FOX) to perform and evaluate ESC systems. This involves integrating control algorithms into the vehicle’s structure and executing diverse tests to assess their performance under various driving conditions. •Optimize control algorithms: Develop approaches to optimize control algorithms and reduce computational complexities. Explore techniques like integrating NARX neural networks with MPCs to enhance computational efficiency. Moreover, evaluating the performance of neural networks to accelerate the computation of NMPC controllers dedicated to DYC. •Benchmarking and performance evaluation: Develop a comprehensive benchmarking framework to evaluate vehicle lateral stability enhancement during critical maneuvers, such as DLC, including standardized tests, simulations, and performance metrics to assess the efficacy of different control strategies accurately. •Validate through simulations: Validate the proposed control strategies and algorithms through extensive simulations using virtual vehicle models. This involves replicating real-world scenarios and evaluating the effectiveness of the control systems in achieving desired 18 Platform Environment Table 2.1: Vehicle parameters and model variables Symbol Description Value [Units] mVehicle mass 400.238 [kg] IzYaw moment of inertia 1047.52 [kg m2] lfDistance from CG to front axle 1.3004 [m] lrDistance from CG to rear axle 1.2204 [m] LWheelbase 2.5208 [m] CfCornering stiffness of front tire 47000 [N/rad] CrCornering stiffness of rear tire 53000 [N/rad] tfWidth of the front axle 1.55 [m] trWidth of the rear axle 1.48 [m] •Control unit: It operates with LabVIEW software, managing CAN bus communication and high-level tasks. The FOX vehicle’s internal architecture, including the ECU, IMU, electric motors, and communication interfaces. The ECU uses PC104 modules and the QNX realtime operating system, requiring code adaptation for implementation in the vehicle. 2.2 System modeling In this study, we utilize both linear and nonlinear models. The nonlinear model is a 14-DOF representation built upon vehicle dynamics, encompassing components such as the vehicle itself, tires, and IWMS. The linear model, on the other hand, is employed specifically for developing control strategies for electric vehicles equipped with IWMs. The symbols in the modeling process and their related physical meanings are listed in Table 2.1. 2.2.1 Linear vehicle model Firstly, the linear model that has been used for the computation of the controller is a bicycle model. It is a 2-DOF model widely used due to its simplicity and good performance where the left and right wheels for each axis are merged and it has been used in [37]. The bicycle model is shown in Fig. 2.3 with assumed moment Mzaround the Z axis to System modeling 19 maintain a balance with the applied forces. Figure 2.3: Vehicle Bicycle Model. The equations of motion for the vehicle lateral dynamics are mvx(˙ β+r) = Fyr +Fyf ,(2.1) Iz˙r=lfFyf −lrFyr +Mz,(2.2) Where βis the vehicle side slip angle, mis the vehicle mass, ris the vehicle yaw rate, Fyr is the rear axle lateral tire force, Fyf is the front axle lateral tire force, vxis vehicle longitudinal speed, lris the center of gravity (CG) to rear axle distance, lfis (CG) to front axle distance, Iz is the vehicle yaw moment of inertia. In turning conditions, the dynamic equations of the bicycle will be linearized in such a way that we will only take into account small values of the lateral drift angles or the sideslip angles, where sin (α)≈α, cos (α)≈1. Where the lateral front and rear tire forces are simplified with the linear tire models as Fyf =Cfαf,(2.3) 20 Platform Environment Fyr =Crαr,(2.4) where αf=δf−β+lf∗r vx,(2.5) αr=−β+ (lr∗r vx ).(2.6) In Eqs. 2.5, 2.6, αfand αrare the slip angles of the front and rear tires, respectively; vxis assumed to be constant for a short period of time. The dynamic tire model developed in [37] can be described as τlag ˙ F(yf,lag)+F(yf,lag)=Fyf ,(2.7) τlag ˙ F(yr,lag)+F(yr,lag)=Fyr,(2.8) Where Fyr lag and Fyf lag are the lagged lateral tire forces of the front and rear tires, respectively, and τlag is the relaxation time constant defined as [29] τlag =σ vx .(2.9) Where σ= 0.01, as in [37, 38], a vehicle model including the dynamic tire model can be obtained in state-space form as ˙x=Ax +Bδδf+BMMz,(2.10) where xl=    β ˙ β r ˙r     , A =       0 1 0 0 −Cf+Cr τlagmvx−1 τlag Crlr−Cflf τlagmv2 x−1 τlag −1 0 0 0 1 Crlr−Cflf τlagIz0−Cfl2 f+Crl2 r τlagIzvx−1 τlag       , (2.11) Bδ=     0 Cf τlagmvx 0 Cflf τlagIz      , BM=    0 0 0 1 τlagIz     .(2.12) System modeling 21 Figure 2.4: The vehicle’s simmechanics model. 2.2.2 Nonlinear vehicle model The nonlinear mathematical model, developed within ADAMS-Car, a comprehensive virtual prototype software for modeling, equation solving, optimization, simulation, and visualization, simulates the dynamic behavior of the real vehicle. SimMechanics, a Matlab/Simulink toolbox specializing in modeling mechanical systems through body and joint blocks, is utilized [29]. The FOX vehicle’s model (originally imported from SolidWorks CAD) comprises 35 bodies, and 38 joints, and considers 14-DOF, with simplifications such as considering rigid bodies, tire-road force at the wheel’s lowest point, flat surface, and factoring in air friction along the longitudinal axis as it is shown in Fig. 2.4. SimMechanics offers a versatile framework for in-depth analysis of vehicle dynamics. Furthermore, it accurately replicates the vehicle’s trajectory and serves as both an internal model for controllers and as a digital twin of the physical vehicle. 22 Platform Environment Figure 2.5: External forces. 2.2.3 External and tire forces on the vehicle Managing external and tire forces is crucial for optimal vehicle performance, handling, and safety, considering factors like road friction, aerodynamics, and gravity. Balancing these forces ensures a smooth driving experience while maximizing fuel efficiency and safety. Fig. 2.5 illustrates external forces on the vehicle, including gravity (Fg), vertical load (Fz), rolling resistance (Froll), friction road-to-wheel force (Fw) that includes both longitudinal (traction) and lateral (cornering) forces that oppose movement due to tire-road interaction, and air resistance (Fair). Gravity acts proportional to the vehicle’s mass, and gravitational acceleration and vertical load ensure tire-road alignment without violations, i.e., Fg=−mg. (2.13) Here, Froll denotes non-elastic tire force, partly dissipated upon pressure release, i.e., Froll =frollFz.(2.14) Where froll is the described coefficient, and Fzis the vertical load for each tire that is estimated from the shock absorber length measurement. The displacement of air during forward motion gives Fair, dependent on frontal area (Sfront), air density (ρair), and longitudinal speed (vx), with a shape-dependent drag coefficient (Cax), i.e., System modeling 23 Fair = 0.5CaxSfrontPairv2 x.(2.15) Where Sfront = 1.48m2,ρair = 1.16kg/m3, and Cax = 0.3. Fig. 2.6 depicts tire-road interaction, governed by longitudinal (µL) and lateral (µS) coefficients, influencing forces at the contact surface, which are described as follows: µL=µRes SL SRes , µS=µRes SS SRes ,(2.16) µRes =c1(1 −ec2SRes )−c3SRes, SRes =p(SL)2+ (SS)2.(2.17) , SL=vrsin α vw , SS=vrcos α−vw vrcos α,(2.18) where the values of the coefficients c1to c3depend on the type of road (asphalt, concrete, etc.) and of its conditions (dry, wet, etc.), vwis the wheel speed, vris a virtual speed aligned with the xiaxis, and αis for the slip angle between vwand vrthat can be described as follow: vr=ωwheelreff (2.19) Where ωwheel is the wheel rotational speed, reff is the effective wheel radius that is 253 mm and 270 mm for the front and the rear wheels respectively. The longitudinal and lateral forces (FL,FS) are the components of the force, respecting the wheel velocity reference system, i.e., FL=µLFZ, FS=µSFZ(2.20) Where FZis the vertical load. In the Simulink model, once the friction force is found, Fwl and Fws are the components of the force, respecting the wheel coordinate system that are calculated (it is simple, known α) and they are applied to the Simmechanics model that offers great versatility, enabling the selection of road types based on their adhesion characteristics (dry asphalt, rain, snow, etc.). 2.2.4 Constraints The brushless motors in the system have 7 KW of power and are supplied with alternating current through an inverter, which is more efficient 24 Platform Environment Figure 2.6: Tire’s forces. for prolonged use. These motors are chosen for their performance benefits, including reduced friction heat loss, and noise. They are directly connected to the wheels for maximum torque delivery efficiency. However, the manufacturer has set a maximum torque limit of Tmax = 80Nm, which serves as the ultimate constraint on torque application. The actuator’s primary function is to ensure control and safety by imposing constraints on the permissible additional yaw moment. These constraints may include limiting torque output, ensuring a specified response speed, or respecting the actuator’s physical limitations. In essence, the actuator’s role is to guarantee that the system operates within these defined limits while making necessary adjustments to the yaw moment. The following constraints need to be satisfied regardless of the model employed: |∆Mz|≤ 100 |Mz|≤ 1000 |Tmax|≤ 80 (2.21) where Mzis the control action, and ∆Mzis its rate of change. 2.3 Problem description In real-world environments, road-vehicle dynamics are highly nonlinear and sensitive to model uncertainties and disturbances, especially during Problem description 25 Figure 2.7: TVC, oversteering and understeering. critical driving conditions such as severe cornering maneuvers. These dynamics can be affected by variations in parameters such as road surface adhesion coefficients, tire cornering stiffness, vehicle mass, vehicle speed, and moment of inertia [39]. Therefore, appropriate control strategies and algorithms are necessary to address these issues. The primary goal of the control system is to enhance vehicle stability and maneuverability during the DLC maneuver, ensuring safe and smooth navigation through corners. During the DLC maneuver, the vehicle is subjected to rapid lateral acceleration, which can lead to instability and loss of control if not properly managed. Oversteering occurs when the vehicle turns more sharply than intended, causing the rear end to slide outwards, while understeering happens when the vehicle fails to turn as much as intended, resulting in a wider turning radius than desired, as seen in Fig. 2.7. Both of these phenomena pose significant safety risks and can lead to accidents if not corrected efficiently. The control system aims to address these challenges by utilizing advanced techniques. Traditional stability control systems, like ESC-based brakes, often exhibit limitations in their ability to efficiently manage vehicle dynamics, as they primarily target specific tires, leading to aggressive actions and significant speed changes. To overcome these limitations, we integrate ESC with TVC as depicted in Figs. 2.7, 2.8. Unlike ESC-based brakes, ESC-based TVC utilizes TVC to engage all vehicle wheels for corrective action, thereby improving efficiency. By adjusting torque symmetrically, it maintains the driver’s desired speed, minimizing abrupt speed 26 Platform Environment Figure 2.8: Control structure. changes. The hierarchical structure in Fig. 2.8 has been used for the proposed controllers. Additionally, the combination of DYC with TVC further enhances vehicle stability and maneuverability: DYC creates rotational motion around the vehicle’s vertical axis, while TVC optimizes torque distribution to individual wheels, effectively addressing oversteering and understeering to ensure safe and precise vehicle operation, even in challenging driving conditions. By implementing DYC and TVC, the control system also manages oversteering and understeering during the DLC maneuver effectively, ensuring that the vehicle maintains its intended trajectory without loss of control. 2.3.1 Torque vector controller The torque for each motor is computed by a low-level TVC as proposed in [31]. The TVC distributes the torque between the four motors to generate the desired angular momentum, by dividing the generated the angular momentum as: Mz,front = 0.5Mz, Mz,rear = 0.5Mz,(2.22) Mz,front =Fx,fr tf 2+Fx,fl tf 2,(2.23) The longitudinal forces on right and left sides are distributed as in [40] according to the vertical forces and road friction as: Fx,f =q(µFz)2−F2 y,(2.24) ISO 3888 Test 27 Figure 2.9: The double change lane(ISO 3888) Fx,f =Mz,front tf .(2.25) where Fx,fr, Fx,fl, Fx,rr, Fx,rl are the longitudinal forces of the frontright, front-left, rear-right, and rear-left wheels, respectively, and tf, tr are the width of the front and rear axles, and µis the tire-road friction coefficient. By doing the same for the rear ones, we have Fx,r =Mz,rear tr .(2.26) The high-level controller obtains the required angular momentum that must be applied to the vehicle to correct its trajectory, then the required torque from the electric motor is obtained as: Tm−Fxrdyn =Iyy ˙ω, (2.27) Tm,i =rdyn tf Mz,front +Iyy ˙ω, (2.28) where Tmis the torque generated by the electric motor, rdyn is the dynamic radius of the tire, Iyy is the moment of inertia of the wheel on its axis turning, and ωis the angular speed of the wheel. 2.4 ISO 3888 Test This test evaluates vehicle lateral stability enhancement during DLC to provide in-depth insights. ISO 3888 standard defines essential tests like the DLC dual track maneuver, where two consecutive lane changes are executed within a predefined distance, assessing the vehicle’s responsiveness and stability during rapid lateral transitions [30]. This involves 34 Lateral Stability Using MPC Here, the relationship between the matrices M,Nand Qand the nonincremental matrices A,Band Ccan easily be obtained by comparing Eqs. 3.3, 3.4 with Eq. 3.5. Using the incremental model, the systems outputs are obtained as: ˆy(t+j) = QMjˆx(t) + j−1 X i=0 QMj−i−1N∆u(t+i).(3.6) The predictions along the horizon are given by y=  ˆy(t+ 1|t) ... ˆy(t+Np|t)  =Fˆx(t) + Hu (3.7) Where u=∆u(t)... ∆u(t+Nu−1)Tis the vector of future control increments, His a block lower triangular matrix with its nonnull elements defined by Hij =QMi−jNand F=QM ... QMNpT. Notice that Eq. 3.7 is composed of two terms: the first depends on the current state and therefore is known at instant t, while the second depends on the vector of future control actions, which is the decision variable that must be calculated. The control sequence uis calculated minimizing the objective function in Eq. 3.2, assuming for simplicity (δ(j) = 1 and λ(j) = λ) that can be written as [44,45]: J= (Fˆx(t) + Hu −r)T(Fˆx(t) + Hu −r) + λuTu. (3.8) It should be noted that all states are measurable ˆx(t). We have employed a quadratic objective function and the system is linear, the actuation signal can be represented as follows: u= (HTH+λI)−1HT(w−F˙x(t))u(3.9) As a receding horizon strategy is used, only the first element of the control sequence, ∆u(t), is sent to the plant and all the computation is repeated at the next sampling time. 3.3 Simulation Results A comparison using simulation between PID and MPC has been made to highlight their respective strengths and weaknesses. Such simulations Simulation Results 35 illustrate these control strategies in the considered application. The required outputs (such as the yaw rate and side slip angle) and also other parameters have been computed to evaluate the control system as shown in Figs. 3.2- 3.7: Figure 3.2: The vehicle’s trajectory Figure 3.3: The yaw rate response 36 Lateral Stability Using MPC Figure 3.4: The side slip response Figure 3.5: steering wheel Fig. 3.2 shows the trajectory followed by the vehicle with the PID and the MPC controllers. The MPC controller was able to follow the Simulation Results 37 required trajectory with a low tracking error. Figs 3.3 and 3.4 represent the evaluation of the angular speed and the angle side slip. The MPC controller gave results closer to the required values. The designed MPC controller was also, able to prevent the occurrence of an oscillation yielding smoother behavior for the driver. This is relevant to avoid accidents, as sudden maneuvers on the road usually result in this phenomenon. Regarding side slip, with the PID controller, the maximum values are approximately in the range [-1.4 , 1.4 ] degrees. With the MPC controller, range is reduced to approximately [-1 , 1] degree, which guarantees better maneuverability and predictability. Finally, in Fig. 3.5, a comparison has been made between the steering wheel obtained with each controller. With the PID controller, the range becomes [-6 , 6] degrees. On the other hand, the MPC controller, the extreme values are reduced to [-4 , 4] degrees. In Fig. 3.6, the evaluation of hysteresis was obtained by measuring the relation between the yaw rate and the angle of the steering wheel. Figure 3.6: Hysteresis response 38 Lateral Stability Using MPC Figure 3.7: Lateral Acceleration In general, the definition of hysteresis is the energy lost and not returned when tires are subjected to stress in any direction. Lost energy is converted to heat through molecular interaction and since rubber has poor thermal conductivity, the internal temperatures of a tire can accumulate rapidly under repeated flexing. Usually, for simulation studies, hysteresis is expressed as a time delay or as linear functions. The width of this curve shows the relation between the value of the steering wheel and the capacity of vehicle response, how closer the vehicle becomes to it; there is a lower delay between the steering wheel and the time it takes the vehicle to spin. This is very important, since delayed systems are difficult to control. As noted in Fig. 3.6, the width and length of the MPC curve is less than that of PID, so the car behavior can be easily managed and easily controlled. In Fig. 3.7, the last variable is lateral acceleration. The MPC was able to reduce the peak value of lateral acceleration with respect to the PID controller. This increases the security and comfort of the driver. 3.4 Chapter Summary This chapter presents the design and implementation of two controllers, PID and MPC, to achieve yaw stability in a four-wheel drive electric Chapter Summary 39 vehicle. A linearized model of the vehicle was used by the predictive controller to anticipate the car’s future behavior. The results demonstrate that the MPC controller outperforms the PID controller in terms of yaw rate and side slip angle reduction. Additionally, the MPC offers several advantages over the PID, including the ability to incorporate constraints into the control strategy, enhancing overall vehicle stability and handling performance. For this reason, future chapters will explore more deeply the potential of MPC for the considered application. Chapter 4 Enhancing Performance Using NMPC This chapter introduces a NMPC to improve vehicle performance and minimize tracking errors in yaw angle and sideslip while following reference values. The main objective is to produce more yaw moments to improve handling stability and guarantee accurate trajectory tracking. This method combines ride comfort, lateral stability, and handling concerns to create a complete approach to vehicle management. The control sequence is optimized to enhance efficacy through a comprehensive process that includes calculating the overall needed torque and determining individual wheel torques based on yaw moment and longitudinal force. The robustness of the controller is demonstrated by comparative simulations between MPC and NMPC in MATLAB/Simulink under varied road conditions. The contents of this chapter have been published in [46]. CONTENTS 4.1 The Nonlinear MPC controller .................................. 42 4.2 Simulation results ............................................... 43 4.2.1 Dry road test ............................................ 44 4.2.2 Wet Road Test ........................................... 45 4.3 Chapter Summary ............................................... 45 41 42 Enhancing Performance Using NMPC Figure 4.1: yaw stability control structure In real-world environments, road-vehicle dynamics are highly nonlinear and sensitive to model uncertainties and perturbances, especially during critical driving conditions such as severe cornering maneuvers. These dynamics can be affected by variations in parameters such as road surface adhesion coefficients, tire cornering stiffness, vehicle mass, vehicle speed, and moment of inertia [39]. Therefore, appropriate control strategies and algorithms are necessary to address these issues. The structure of the proposed controller for yaw stability is shown in Fig. 4.1, the inputs to the model are front-wheel steer angle δf, vehicle velocity V, horizontal acceleration ax, and vertical acceleration ay, while the output variables to be controlled are vehicle sideslip βand yaw rate r. The integrated controller consists of an upper-level controller and a lower-level controller. The linear/nonlinear MPC works as an upperlevel controller, using sideslip and yaw rate as inputs and generating the required moment Mz, while the TVC is responsible for distributing torque between the four motors to generate the desired angular momentum and acts as a low-level controller by dividing the generated angular momentum. This hierarchical structure has been used for both linear and nonlinear MPC controllers. 4.1 The Nonlinear MPC controller Linear controllers are not effective for processes with severe nonlinearities [47]. In fact, the control of lateral stability in 4-wheeled vehicles is a challenging control problem due to the nonlinearity of tire characteristics [48]. The proposed yaw stability controller for in-wheel-motored Simulation results 43 EVs is shown in Fig. 4.1. The NMPC acts as an upper-level controller, using sideslip and yaw rate as inputs and generating the required moment Mz. The TVC is responsible for distributing torque among the four motors to generate the desired angular momentum and acts as a lowlevel controller by dividing the generated angular momentum. NMPC can explicitly take constraints into account and handle multiple objectives in nonlinear systems, making it an appropriate method for solving the control problem in in-wheel-motored EVs [49]. To achieve yaw stability control in an in-wheel-motored EV, the following objectives must be considered: good handling and stability, anti-slip on low-friction coefficient roads, and smooth driving for the comfort of the driver. The criterion for minimizing the deviation between predicted outputs and given references is usually chosen in a quadratic form. Therefore, an objective function based on the tracking problem has been designed to achieve precise yaw stability control of the EV as follows: J= Np X j=1 Q1[y(t+j|t)−r(t+j)]2+ Nu X j=1 Q2[∆M(t+j−1)]2(4.1) subject to the constrains in (2.21). Here Q1 and Q2 are weight matrices for adjusting tracking performance between the output and the reference, y(t+j|t) is the predicted output, r(t+j) is the reference value, and ∆M(t+j−1) is the change in control input. Therefore, the EV yaw stability control problem is described as a tracking problem of the yaw rate while reducing the side slip angle. In linear MPC, the predicted output sequence yis obtained using model (3.1), which was discretized in MATLAB using a zero-order hold, and the problem is solved using the Matlab function quadprog. In NMPC, the Simmechanics model predicts how the system behaves, providing outputs β[k] and r[k] during the prediction horizon Np. Then, we utilize the interior-point algorithm through fmincon to minimize the cost function. As customary, at each time step, we apply solely the initial input from the sequence of optimal inputs, and this process is reiterated in every time step. 4.2 Simulation results In this section, we present the results of the simulation. ISO 3888 or the DLC maneuver has been chosen to evaluate the stability of the vehicle. 50 Emulating Vehicle Dynamics Using Neural Network 5.1 Artificial neural networks and NARX model ANNs are versatile tools utilized for a wide range of applications, including clustering, recognition, pattern classification, optimization, function approximation, and prediction [99–102]. Inspired by the biological neural system, ANNs possess remarkable abilities to learn, store, and recall information [103, 104]. As black-box modeling tools, they excel at performing nonlinear mappings from an m-dimensional input space to an n-dimensional output space, even when the relationships between the input and output spaces are unknown [79,105,106]. In our vehicle simulation model, continuous measurements of yaw rate and side slip angle, used for comprehending, controlling, and simulating dynamic behavior, create a time series dataset, which can be used to train NARX neural networks yielding a powerful predictor for the corresponding time series data due to their feedback connections to improve its performance in nonlinear time series prediction [103,104,107]. Fig. 5.1 shows two NARX neural network architectures: series-parallel (open-loop) and parallel (closed-loop), respectively represented in (5.1) and (5.2), ˆx(k+ 1) = F(x(k), . . . , x(k−d), u(k), . . . , u(k−d)) (5.1) ˆx(k+ 1) = F(ˆx(k),...,ˆx(k−d), u(k), . . . , u(k−d)) (5.2) where F(·) is the mapping function of the neural network, ˆx(k+ 1) is the predicted output of the NARX at time k+ 1, ˆx(k) is the past predicted output of the NARX, x(k) is the corresponding true value, u(k) is the input of the NARX, and dis the number of delays. In the series-parallel architecture, predictions for each time step kare made by providing both present and past exogenous inputs u(k), . . . , u(k−d) and the past true values of the time series x(k), . . . , x(k−d). These inputs are utilized to forecast the next time step, k+ 1. Conversely, in the parallel architecture, the prediction is made using the present and past values of exogenous inputs u(k), . . . , u(k−d) and the past predicted values of the time series ˆx(k),...,ˆx(k−d). The series-parallel architecture is chosen for training due to the availability of true past values of side slip β, yaw rate r, and control input Mz(see Fig.6.1). It offers two advantages: more precise predictions using true values as inputs and a pure feedforward structure allowing the use of standard training algorithms for Multi- Layer Perceptron (MLP). After training, the NARX model is converted to parallel architecture via the feedback connection of the predicted Artificial neural networks and NARX model 51 Feed Forward Network Feed Forward Network Time delay Time delay 𝒙(𝐤) series-parallel parallel ෝ 𝒙(𝒌 + 𝟏) ෝ 𝒙(𝒌 + 𝟏) 𝒖(𝐤) 𝒖(𝐤) Time delay Time delay Figure 5.1: Architectures of the NARX neural network. outputs, benefiting multi-step ahead prediction for (ˆ β, ˆr). The NARX neural network model uses the structure of MLP to approximate the mapping function, a powerful structure capable of learning continuous nonlinear mappings [108]. It consists of three layers: input, hidden, and output, where each neuron’s output is given by a(l) i=g(l)( n(l−1) X j=1 w(l−1) ji a(l−1) j+b(l−1) i) (5.3) where al iis the output of node iand layer l,wl ji is the weight vector between neurons jand i,g(l)is the activation function, and bl iis the bias unit. 5.1.1 NARX training The neural network parameters are determined iteratively through initialization, error calculation, and weight adjustment until a specified criterion is met. Back-propagation is used to compute errors for networks with hidden layers. The appropriate number of nodes in an MLP is found through a trial-and-error process [109,110]. The data gathering process involved conducting 20 separate simulations under different conditions on various roadways with profiles as those depicted in Fig. 5.3. A total of 20020 samples were generated from 52 Emulating Vehicle Dynamics Using Neural Network Figure 5.2: Training and deployment phases. these simulations, comprising input values of Mzand the corresponding output data for slip angle βand yaw rate r. The dataset has been split into a training set (70%), a validation set (15%) and a test set (15%), randomly chosen. The neural dynamics prediction model can be described as ˆx(k+ 1) = F(x[k], Mz[k]),(5.4) where x[k] = β[k], r[k]T. In this way, the equations of the neural network are planned as follows [111–113]: Z1=W1(x[k], Mz[k]) + B1 H1=g(Z1) ˆx(k+ 1) = W2H1+B2 (5.5) where W1,W2,B1and B2are the weight matrices of the neural network, Z1is the weighted sum of inputs, H1is the activation value, and gis the activation function, which in this case is the hyperbolic tangent function. Eq. (5.5) can be extended for multiple layers. To learn the matrices, the mean square error function is defined, and the gradient descent algorithm is utilized to optimize the parameters. The training process adjusts neural network weights iteratively to match the targets closely using the given inputs and desired outputs. Tanh activation function is used in all layers, except the output layer, which Artificial neural networks and NARX model 53 Figure 5.3: Roads schemes for training and validation. Table 5.1: Training parameters of the neural networks. Range Transfer function µ µ increase ratio µdecrease ratio Max µMax epochs Min gradient Max validation checks [1,−1] tansig pureling 10−310 10−11010 10310−76 employs a linear function. For more details, see Table 5.1. In this work, several neural networks underwent training with various hidden layer configurations. After utilizing the neural network toolbox, we obtained the Pearson correlation coefficient (R) results, which measure the correlation between outputs and targets of an open-loop NARX model. Subsequently, a feedback NARX model is employed in the simulation. The resulting values are shown in Table 5.2, where a regression value close to R= 1 indicates a very strong positive linear relationship between the variables, suggesting an excellent fit for the data. The chosen trained neural networks are thoroughly evaluated and compared to each other. This evaluation encompasses an assessment of their overall performance, accuracy, and efficiency, considering the complete model. The objective is to identify the most effective and suitable model by making comparisons among these neural networks. 5.1.2 Machine learning with MPC MPC-NPL stands for a MPC algorithm with nonlinear prediction and linearization. The approach involves finding a local linear approximation of the nonlinear neural model online at each sampling instant, allowing 54 Emulating Vehicle Dynamics Using Neural Network Table 5.2: The regression R values of different NNS R ( training ) R ( validation ) R ( test ) 5 0.9974 0.9985 0.9979 10-5 0.9978 0.9983 0.9981 15-10 0.9983 0.9981 0.9987 20-15-10 0.9987 0.9977 0.9973 the output predictions to depend on the calculated control policy in a linear manner. This feature enables the MPC-NPL algorithm to solve a quadratic programming problem online efficiently [111, 112]. That is, MPC-NPL improves conventional linear MPC by handling nonlinear behavior, adapting to complexity, and maintaining accuracy. In this approach, the NN model is linearized yielding the incremental space state representation: ˆxe(k+ 1) = Aexe[k] + Be∆Mz y[k] = Cex[k](5.6) where xe[k], Ae,Beand Ceare: xe[k] = ∆x[k] y[k]Ae=Am0m CmAmI Be=Bm CmBmCe=0mI To obtain the system matrices, the partial derivative of the function F(x[k], u[k]) with respect to the current state x[k] and the input Mz[k] is found [111,112] as follows Am=∂ˆx[k+ 1] ∂x[k], Bm=∂ˆx[k+ 1] ∂Mz[k], Cm=1 0 1 0  Therefore, we can predict these future states using the augmented model as ˆ Y=Fx[k] + Φ∆Mz(5.7) here F=hCeAeCeA2 eCeA3 e. . . CeANp eiT, Simulation results 55 Φ =        CeBe0· · · 0 CeAeBeCeBe· · · 0 CeA2 eBeCeAeBe· · · 0 . . .. . ..... . . CeANp−1 eBeCeANp−2 eBe· · · CeANp−Nc eBe        (5.8) To optimize the increments of the control signal ∆Mz, the optimization problem is formulated as in Eq. 4.1, and solved using the Matlab function quadprog. 5.1.3 Machine learning with NMPC NMPC–NO denotes the optimal control action obtained providing NMPC with the nonlinear ML model, with fmincon performing the nonlinear optimization. The proposed approach generates control signals that exhibit almost the same characteristics as NMPC, but with significantly lower execution time [112]. Here, the future states are iteratively predicted as ˆx[k+ 1] = W2·tanh(W1·(x[k],(Mz[k] +∆Mz[1]) + B1) + B2 ˆx[k+ 2] = W2·tanh(W1·(ˆx[k+ 1],(Mz[k] +∆Mz[2]) + B1) + B2 . . . ˆx[k+Np] = W2·tanh(W1·(ˆx[k+Np−1],(Mz[k] +∆Mz[k+Nc]) + B1) + B2 (5.9) The predicted output of the system at each time step is y[k+ 1] = 1 0 1 0 ·ˆx[k+ 1] (5.10) Again, the increments of the control signal ∆Mzare optimized following Eq. 4.1. 5.2 Simulation results The control strategies are tested through a DLC and a slalom maneuver through both wet and dry roads. The simulation is conducted within SimMechanics, demonstrating the vehicle’s ability to navigate a curve 56 Emulating Vehicle Dynamics Using Neural Network effectively [30]. The tire model parameters in SimMechanics were configured as follows: c1= 1.1973, c2= 25.168, c3= 0.5373 in case of dry road and c1= 0.857, c2= 33.822, c3= 0.347 in case of wet road [29]. Figure 5.4: A double lane change and A slalom Maneuvers 5.2.1 Double-lane change road test As depicted in Figs. 5.5,5.7 the MPC-NPL controller out-performs conventional linear MPC, demonstrating superior performance with decreased tracking error and oscillations, resulting in smoother driving behavior. In terms of RMSE performance as shown in Table 5.3, different neural network models were employed to evaluate controllers across various road conditions. Meanwhile, the performance of NMPC-NO approaches that of NMPC in terms of stability when tracking the desired values. Figure 5.5: A DLC dry road Simulation results 57 0 1 2 3 4 5 6 7 8 9 10 Time[s] -100 0 100 Tfl [Nm] MPC-NPL NMPC-NO MPC NMPC 0 1 2 3 4 5 6 7 8 9 10 Time[s] -100 0 100 Tfr [Nm] MPC-NPL NMPC-NO MPC NMPC 0 1 2 3 4 5 6 7 8 9 10 Time[s] -100 0 100 Trl [Nm] MPC-NPL NMPC-NO MPC NMPC 0 1 2 3 4 5 6 7 8 9 10 Time[s] -100 0 100 Trr [Nm] MPC-NPL NMPC-NO MPC NMPC Figure 5.6: Dry road response for motors’ torques Figure 5.7: A DLC wet road 5.2.2 Slalom road test As Figs. 5.9, 5.10 show, the stability of NMPC-NO is close to that of NMPC. On the other hand, the MPC-NPL controller surpasses the performance of conventional MPC, exhibiting reduced tracking error, oscillations, and smoother driving behavior. In terms of RMSE performance as shown in Table 5.3, different neural network models were employed to evaluate controllers across various road conditions, with NMPC-NO showing convergence to NMPC stability levels and improved computational efficiency as in the second column. Additionally, a deep learning neural network with two hidden layers highlighted the superior RMSE 58 Emulating Vehicle Dynamics Using Neural Network 0 1 2 3 4 5 6 7 8 9 10 Time[s] -100 0 100 Tfl [Nm] MPC-NPL NMPC-NO MPC NMPC 0 1 2 3 4 5 6 7 8 9 10 Time[s] -100 0 100 Tfr [Nm] MPC-NPL NMPC-NO MPC NMPC 0 1 2 3 4 5 6 7 8 9 10 Time[s] -100 0 100 Trl [Nm] MPC-NPL NMPC-NO MPC NMPC 0 1 2 3 4 5 6 7 8 9 10 Time[s] -100 0 100 Trr [Nm] MPC-NPL NMPC-NO MPC NMPC Figure 5.8: Wet road response for motors’ torques Figure 5.9: Slalom response dry road performance of the MPC-NPL controller over the linear MPC controller. As illustrated in Figs. 5.6, 5.8, 5.11, 5.12 these findings provide additional perspective on the controller’s efficacy in maintaining vehicle stability across diverse scenarios, all while ensuring that each motor remains below the maximum torque threshold of 80 N.m. 5.2.3 Computation time In control systems, computation time typically refers to the time required for a controller to calculate and execute its control actions and is a relevant indicator in determining the performance in real-time applications where the system must respond quickly to changes in the en- Simulation results 59 Figure 5.10: Slalom response wet road 0 1 2 3 4 5 6 7 8 9 10 Time[s] -100 0 100 Tfl [Nm] MPC-NPL NMPC-NO MPC NMPC 0 1 2 3 4 5 6 7 8 9 10 Time[s] -100 0 100 Tfr [Nm] MPC-NPL NMPC-NO MPC NMPC 0 1 2 3 4 5 6 7 8 9 10 Time[s] -100 0 100 Trl [Nm] MPC-NPL NMPC-NO MPC NMPC 0 1 2 3 4 5 6 7 8 9 10 Time[s] -100 0 100 Trr [Nm] MPC-NPL NMPC-NO MPC NMPC Figure 5.11: Slalom response for motors’ torques dry road vironment. The computation time depends on several factors, including the processing speed of the control hardware, the complexity of the control algorithm and the system being controlled. In the context of vehicle lateral stability, the sample time is also related to the collection of lateral dynamics measurements, influencing the frequency of adjustments that determine the real-time response and its stability. Considering a 10 milliseconds sample time, only MPC-NPL and NMPC-NO fit the requirement, with MPC-NPL being much faster. However, note that our simulations were performed in Matlab, which is good for mathematical prototyping but slow, therefore admitting much faster execution times if implemented in programming languages such as C. In particular, the computation times shown in Table 5.4 and Fig. 5.13 were evaluated using Matlab on a computer equipped with 16 GB RAM, a 2.6 GHz Intel Core i7 processor, and a 512 GB SSD. Also, note that the computation 66 Emulating NMPC Using Neural Network Figure 6.2: A double lane change dry road. ing parameters post-training, which are included into the input vector x=r, rref, β, βref, Q, R, NT. The ANN output is the torque y=Mz. 6.2 Simulation results The efficacy of the proposed control strategy was evaluated through simulations, utilizing a DLC scenario, across diverse road conditions including dry, wet, and icy surfaces. These simulations, conducted within Matlab´s toolbox SimMechanics, demonstrated the vehicle’s adeptness in navigating curves efficiently. The neural network architecture was selected using MATLAB’s Deep Learning Toolbox through a trial-and-error process, exploring various configurations comprising two and three hidden layers. Ultimately, an ANN with 20 neurons in the input layer, 15 neurons in the first hidden layer, and 10 neurons in the second hidden layer was chosen. This configuration yielded R coefficients of 0.9964, 0.9973, and 0.9969 for the Simulation results 67 Figure 6.3: A double lane change wet road. training, validation, and test subsets, respectively. Subsequently, this neural network underwent testing across three distinct road conditions to assess its performance and validate its efficacy. The graphical results, are supplemented by corresponding numerical data provided in Table 6.1. As shown in Fig. 6.2, under identical conditions employed for training the ANNs (dry road), the ML controller closely approaches the performance of the NMPC. Numerically, the ML controller also approximates the performance of the NMPC in tracking the desired trajectory (RMSE of 0.19 vs. 0.17), yaw rate (2.79 vs. 2.67), and sideslip angle (0.24 vs. 0.22). As road conditions shift, the proposed ML controller showcases its capacity for post-training re-tuning, facilitating dynamic adaptation to changing environmental conditions. For instance, in the wet scenario, the RMSE using parameters optimized for dry roads is 6.98. However, after parameter retuning, the RMSE decreases to 4.97. Notably, this error substantially improves upon the one obtained with the retuned NMPC (6.12) and approaches the performance achieved with the retuned NMPC (4.54). Additionally, the consistent trend of improved per- 68 Emulating NMPC Using Neural Network Figure 6.4: A double lane change ice road. formance under varying conditions can be observed in Figs. 6.3 and 6.4. These figures depict the trajectory tracking and yaw rate response, respectively, under different road conditions. As it can be seen in the figures, tuning the ML controller enables to maintain more stable and accurate control in wet and icy scenarios. This approach not only approaches the performance of the NMPC with the same parameter values but also enhances the performance of the NMPC using parameters selected for dry road conditions. Furthermore, the computation time utilizing ML is significantly reduced compared to NMPC, plummeting from the range of 10.8−16.9 seconds to a mere 0.51 −0.75 milliseconds. This reduction ensures seamless and responsive execution, rendering it highly conducive for real-time applications. Simulation results 69 Table 6.1: RMSE and mean computation time of double lane change. Set [1] - (Q=155, R=335, N=11) Dry road Beta [deg] YawR [deg] Traj [m] Time [s] ML 0.24 2.79 0.19 5.1·10−4 NMPC 0.22 2.67 0.17 5.6 Wet road ML 2.96 6.98 0.39 5.3·10−4 NMPC 2.35 6.12 0.34 6.1 Ice road ML 5.56 11.69 1.87 5.7·10−4 NMPC 4.91 10.86 1.08 6.3 Set [2] - (Q=250, R=295, N=13) Dry road Beta [deg] YawR [deg] Traj [m] Time [s] ML 0.39 3.98 0.29 6.4·10−4 NMPC 0.36 3.06 0.27 7.7 Wet road ML 1.92 4.97 0.23 6.6·10−4 NMPC 1.76 4.54 0.18 8.2 Ice road ML 4.23 10.43 1.05 6.8·10−4 NMPC 3.98 8.89 0.77 8.9 Set [3] - (Q=395, R=220, N=15) Dry road Beta [deg] YawR [deg] Traj [m] Time [s] ML 0.48 4.88 0.38 6.9·10−4 NMPC 0.44 4.12 0.33 10.4 Wet road ML 2.27 5.92 0.32 7.1·10−4 NMPC 1.98 5.35 0.28 10.7 Ice road ML 2.32 8.29 0.72 7.5·10−4 NMPC 1.91 7.79 0.59 11.3 70 Emulating NMPC Using Neural Network 6.3 Chapter Summary In this chapter, a novel approach to enhance lateral stability during cornering by using ML techniques has been presented to emulate the behavior of NMPC. The methodology involves training a ANN model on a dataset derived from simulated NMPC-controlled vehicle dynamics, incorporating tuning parameters to enable post-training adaptability. This ANN model effectively replicates NMPC decision-making processes, significantly reducing computation time compared to traditional NMPC methods. This reduction is relevant for real-time applications, demonstrating the practical feasibility of our solution for in-vehicle control systems. Additionally, our exploration of the ML-based approach’s adaptability to various driving conditions, addresses both performance and computational challenges associated with the use of NMPC for lateral stability control in EVs. Chapter 7 Conclusions and Future Research This chapter summarizes the key findings of the thesis, emphasizing how they align with the stated research objectives. It also identifies several promising directions for future research, such as the development of advanced control strategies with enhanced stability assurances, the refinement of simulation models for greater accuracy, and the execution of experimental validations to strengthen the robustness and applicability of the results. Ultimately, this chapter aims to offer a synthesis of the research contributions of this thesis and to propose a strategic plan for ongoing exploration and innovation in this field. CONTENTS 7.1 Conclusions ....................................................... 72 7.2 Future research ................................................... 75 71 72 Conclusions and Future Research 7.1 Conclusions This thesis addresses the critical need to enhance stability and maneuverability in EVs equipped with IWMs. Advanced control systems such as ESC, DYC, and TVC are essential in achieving these objectives. These systems maintain vehicle stability by adjusting brakes or motor torque in response to real-time driving conditions, providing a dynamic and adaptive response to varying scenarios. To achieve optimal performance, TVC selectively distributes torque to individual wheels, refining stability and enhancing cornering performance. By minimizing understeer and oversteer, TVC significantly improves the vehicle’s maneuverability. The integration of ESC with TVC ensures smooth coordination between power distribution and braking interventions, optimizing traction and handling across various driving scenarios. Additionally, DYC plays a crucial role in managing the vehicle’s yaw rate to maintain lateral stability during aggressive maneuvers or on low-friction surfaces. This multi-faceted approach significantly enhances safety, performance, and driver confidence, showcasing the combined effectiveness of these advanced control systems. Despite these advancements, achieving lateral stability in EVs presents several challenges. One major issue is managing weight distribution, which affects the vehicle’s balance and stability, particularly during highspeed maneuvers. Controlling high torque and acceleration poses another challenge, as the instant torque delivery of electric motors can lead to instability if not properly managed. Adapting to diverse road conditions requires control systems that can handle a wide range of environmental variables, from wet and slippery surfaces to dry and uneven terrain. The design and testing of complex control systems, particularly the upper controller for DYC, are challenging due to their nonlinear and uncertain characteristics, and high computational demands further limit the optimization of stability control systems. Additionally, effectively addressing oversteering and understeering during cornering and abrupt maneuvers requires sophisticated control algorithms and real-time adjustments. Accurately modeling the nonlinear dynamics of EVs, considering varying load conditions and tire characteristics, adds another layer of complexity to the design process. Furthermore, integrating these control systems into real vehicles incurs high costs and consumes significant time and resources. These factors highlight the need for new industry-level EV control algorithms to facilitate the effective development and deployment Conclusions 73 of these advanced control techniques. To address these challenges, this thesis focuses on utilizing the DYC method, which operates through two control levels: an upper controller that determines the desired yaw moment and a lower controller that allocates it to the four wheels using TVC. By precisely distributing yaw moments to individual wheels, vehicle handling characteristics are significantly enhanced, reducing oversteering and understeering during cornering and abrupt maneuvers. Many studies have explored different controllers for DYC, such as PID, SMC, LQR, H∞, and fuzzy logic controllers. Among these, MPC has shown the most significant potential for vehicle stability control due to its ability to predict multiple states, handle diverse control objectives, and outperform traditional control methods. This thesis explores the application of MPC, particularly its nonlinear variant (NMPC), to improve lateral stability in EVs. However, its implementation requires a high computing demand. To reduce the computational load, we integrated MPC with NARX neural networks. These networks, capable of simulating dynamic processes more efficiently within the MPC framework, helped reduce computational burdens. Additionally, a ML model was designed to be more flexible, enabling it to represent a family of MPCs by taking the tuning parameters as inputs. This adaptability allows the model to adjust to varying road conditions, making it suitable for various dynamic scenarios and enhancing the robustness and performance of the vehicle’s stability control system. A key component of this research is the use of a fully functional prototype vehicle named FOX. The FOX vehicle serves as an ideal platform for implementing and evaluating the proposed electronic stability control systems. Equipped with 4 IWMs, FOX allows for precise control and testing of the DYC and TVC strategies. High-fidelity simulations are conducted using MATLAB/Simulink to validate the effectiveness of these advanced control techniques. The FOX vehicle’s comprehensive benchmarking framework is utilized to assess vehicle lateral stability enhancement during DLC maneuvers, providing robust data for analyzing and refining control strategies. By combining the theoretical development of advanced control methods with evaluations on the FOX prototype, this thesis demonstrates significant improvements in the stability and performance of EVs with IWMs. The integration of these control systems not only addresses the computational challenges but also ensures the applicability of the proposed 74 Conclusions and Future Research methods in real-world scenarios. Finally, we summarize the key insights from each chapter of the thesis as follows: •Chapter 2: Platform Environment provides a comprehensive overview of the FOX vehicle’s, which serves as the benchmark for the thesis. It details the system modeling process, starting with the linear vehicle model and progressing to the nonlinear vehicle model, capturing the complexities of vehicle dynamics more accurately. Additionally, it discusses the use of a comprehensive vehicle model with nonlinear dynamics developed through ADAMS-Car®and its integration into MATLAB®SimMechanics/Simulink, successfully emulating a real vehicle from the University of Seville. Finally, it outlines the specific problem this research aims to address, setting the stage for developing and implementing advanced control strategies to enhance vehicle performance and stability. •Chapter 3: Lateral Stability Using MPC designed and evaluated two controllers, PID and MPC, to achieve yaw stability for the FOX EV. The MPC controller, using a linearized model of the vehicle, provided more precise control and improved vehicle stability in terms of yaw rate and side slip angle compared to the PID controller. Moreover, the MPC controller’s ability to incorporate constraints and use cost functions that go beyond single reference tracking further enhanced vehicle handling and stability, which is shown in the numerical simulations highlighting the superior performance of the MPC controller. •Chapter 4: Enhancing Performance Using NMPC uses and evaluates NMPC to achieve better performance in yaw stability control, building on the problem analyzed in the previous chapter with MPC and PID. As expected, NMPC achieves superior performance due to its use of a more accurate model with enhanced predictive capabilities, demonstrating significant advantages in terms of yaw rate and side slip angle compared to linear MPC. However, implementing NMPC poses considerable computational challenges, particularly for real-time applications. This chapter sets the stage for exploring machine learning techniques in subsequent chapters to address these computational issues. •Chapter 5: Emulating Vehicle Dynamics Using Neural Network explores the use of Artificial Neural Networks to substitute the model within the NMPC framework for vehicle stability control. The Conclusions 75 training process for the NARX model is carried out using a dataset created through simulations with the previously explained FOX vehicle model. The results demonstrate that using ANNs significantly reduces computational load without a substantial decrease in performance. Additionally, the chapter analyzes the computation time associated with these approaches, showing that they can be calculated in real-time, making them feasible for implementation in vehicle control systems while maintaining maneuverability and stability in challenging driving scenarios. •Chapter 6: Emulating NMPC Using Neural Network proposes and evaluates a novel approach using ANNs to emulate the behavior of NMPC for vehicle stability control. Unlike Chapter 5, where ANNs were used to substitute the model within the NMPC framework, this chapter focuses on replacing the entire NMPC controller with a ANN. The ANN model is trained on a comprehensive dataset generated from simulated NMPC-controlled vehicle dynamics, including tuning parameters as additional inputs. The results demonstrate that ANNs can effectively replicate the NMPC’s performance while significantly reducing computational demands. This novel approach has the potential to achieve even better results than the methods discussed in Chapter 5, although the training process is more complex and the robustness of the ANN needs to be studied further. This chapter shows that ANNs offer a viable solution for real-time vehicle control by maintaining high performance in terms of yaw rate and side slip angle. Furthermore, the flexibility of ANNs allows them to adapt to varying driving conditions, enhancing the robustness and overall performance of the vehicle’s stability control system. Thanks to all the above-mentioned contributions, this thesis has advanced the state-of-the-art in lateral stability control methods, paving the way for their application in more sophisticated scenarios in a scalable manner. Despite these advancements, there are still open challenges and questions that need to be addressed. The subsequent section will discuss these remaining issues and potential directions for future research to further enhance the robustness and performance of vehicle stability control system. 82 Bibliography [48] B. Ren, H. Chen, H. Zhao, and L. Yuan, “Mpc-based yaw stability control in in-wheel-motored ev via active front steering and motor torque distribution,” Mechatronics, vol. 38, pp. 103–114, 2016. [49] X. Zhang, P. Wang, Z. Li, F. Wang, and H. Chen, “Estimation and analysis of vehicle stability region under complex road conditions,” in 2020 Chinese Automation Congress (CAC), pp. 3036– 3041, IEEE, 2020. [50] A. Hassan, S. Ruiz-Moreno, J. R. D. Frejo, J. M. Maestre, and E. F. Camacho, “Neural-Network Based MPC For Enhanced Lateral Stability In Electric Vehicles,” IEEE Access, 2024. [51] L. Zhang, H. Ding, Y. Huang, H. Chen, K. Guo, and Q. Li, “An analytical approach to improve vehicle maneuverability via torque vectoring control: theoretical study and experimental validation,” IEEE Transactions on Vehicular Technology, vol. 68, no. 5, pp. 4514–4526, 2019. [52] A. El Kharki, Z. Boulghasoul, L. Et-Taaj, and A. Elbacha, “A new intelligent control strategy of combined vector control and direct torque control for dynamic performance improvement of induction motor drive,” Journal of Electrical Engineering & Technology, vol. 17, no. 5, pp. 2829–2847, 2022. [53] E. Siampis, E. Velenis, S. Gariuolo, and S. Longo, “A real-time nonlinear model predictive control strategy for stabilization of an electric vehicle at the limits of handling,” IEEE Transactions on Control Systems Technology, vol. 26, no. 6, pp. 1982–1994, 2017. [54] A. Parra, D. Tavernini, P. Gruber, A. Sorniotti, A. Zubizarreta, and J. P´erez, “On nonlinear model predictive control for energyefficient torque-vectoring,” IEEE Transactions on Vehicular Technology, vol. 70, no. 1, pp. 173–188, 2020. [55] M. Kvasnica, P. Bakar´aˇc, and M. Klauˇco, “Complexity reduction in explicit mpc: A reachability approach,” Systems & Control Letters, vol. 124, pp. 19–26, 2019. [56] A. Pavlov, M. M¨uller, C. Manzie, and I. Shames, “Complexity minimisation of suboptimal mpc without terminal constraints,” IFAC-PapersOnLine, vol. 53, no. 2, pp. 6089–6094, 2020. Bibliography 83 [57] D. Masti, T. Pippia, A. Bemporad, and B. De Schutter, “Learning approximate semi-explicit hybrid mpc with an application to microgrids,” IFAC-PapersOnLine, vol. 53, no. 2, pp. 5207–5212, 2020. [58] H. Peng, W. Wang, Q. An, C. Xiang, and L. Li, “Path tracking and direct yaw moment coordinated control based on robust mpc with the finite time horizon for autonomous independent-drive vehicles,” IEEE Transactions on Vehicular Technology, vol. 69, no. 6, pp. 6053–6066, 2020. [59] R. N. Liang, E. A. Anacleto, and C. N. Meneses, “Data structures for speeding up tabu search when solving sparse quadratic unconstrained binary optimization problems,” Journal of Heuristics, vol. 28, no. 4, pp. 433–479, 2022. [60] F. Truger, J. Barzen, M. Bechtold, M. Beisel, F. Leymann, A. Mandl, and V. Yussupov, “Warm-starting and quantum computing: A systematic mapping study,” arXiv preprint arXiv:2303.06133, 2023. [61] A. Cano, “A survey on graphic processing unit computing for large-scale data mining,” Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, vol. 8, no. 1, p. e1232, 2018. [62] T. M. Blaha, E. J. J. Smeur, and B. D. W. Remes, “A survey of optimal control allocation for aerial vehicle control,” in Actuators, vol. 12, p. 282, MDPI, 2023. [63] J. Hou, G. Chen, J. Huang, Y. Qiao, L. Xiong, F. Wen, A. Knoll, and C. Jiang, “Large-scale vehicle platooning: Advances and challenges in scheduling and planning techniques,” Engineering, 2023. [64] Z. Zhou, C. Rother, and J. Chen, “Event-triggered model predictive control for autonomous vehicle path tracking: Validation using carla simulator,” IEEE Transactions on Intelligent Vehicles, 2023. [65] B. Wang, J. Huang, C. Wen, J. Rodriguez, C. Garcia, H. B. Gooi, and Z. Zeng, “Event-triggered model predictive control for power converters,” IEEE Transactions on Industrial Electronics, vol. 68, no. 1, pp. 715–720, 2020. [66] C. Wu, S. Jiang, S. Gao, Y. Liu, and H. Han, “Event-triggered model predictive control for dynamic energy management of 84 Bibliography electric vehicles in microgrids,” Journal of Cleaner Production, vol. 368, p. 133175, 2022. [67] S. Yang, W. Chen, and M. P. Wan, “A machine-learning-based event-triggered model predictive control for building energy management,” Building and Environment, vol. 233, p. 110101, 2023. [68] J. Yoo and K. H. Johansson, “Event-triggered model predictive control with a statistical learning,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 51, no. 4, pp. 2571– 2581, 2019. [69] J. Chen, X. Meng, and Z. Li, “Reinforcement learning-based eventtriggered model predictive control for autonomous vehicle path following,” in 2022 American Control Conference (ACC), pp. 3342– 3347, IEEE, 2022. [70] Y. Xiao, X. Zuo, I. Kaku, S. Zhou, and X. Pan, “Development of energy consumption optimization model for the electric vehicle routing problem with time windows,” Journal of Cleaner Production, vol. 225, pp. 647–663, 2019. [71] Y. Xu, W. Tang, B. Chen, L. Qiu, and R. Yang, “A model predictive control with preview-follower theory algorithm for trajectory tracking control in autonomous vehicles,” Symmetry, vol. 13, no. 3, p. 381, 2021. [72] L. Xiang, C. W. Lee, O. Zikanov, and C.-C. Hsu, “Efficient reduced order model for heat transfer in a battery pack of an electric vehicle,” Applied Thermal Engineering, vol. 201, p. 117641, 2022. [73] N. Rama and D. Robinette, “Computationally efficient reducedorder powertrain model of a multi-mode plug-in hybrid electric vehicle for connected and automated vehicles,” tech. rep., SAE Technical Paper, 2019. [74] S. Ruiz-Moreno, J. R. D. Frejo, and E. F. Camacho, “Model predictive control based on deep learning for solar parabolic-trough plants,” Renewable Energy, vol. 180, pp. 193–202, 2021. [75] D. Piga, M. Forgione, S. Formentin, and A. Bemporad, “Performance-oriented model learning for data-driven mpc design,” IEEE control systems letters, vol. 3, no. 3, pp. 577–582, 2019. Bibliography 85 [76] L. Hewing, K. P. Wabersich, M. Menner, and M. N. Zeilinger, “Learning-based model predictive control: Toward safe learning in control,” Annual Review of Control, Robotics, and Autonomous Systems, vol. 3, pp. 269–296, 2020. [77] A. Norouzi, H. Heidarifar, H. Borhan, M. Shahbakhti, and C. R. Koch, “Integrating machine learning and model predictive control for automotive applications: A review and future directions,” Engineering Applications of Artificial Intelligence, vol. 120, p. 105878, 2023. [78] B. Paden, M. ˇ C´ap, S. Z. Yong, D. Yershov, and E. Frazzoli, “A survey of motion planning and control techniques for self-driving urban vehicles,” IEEE Transactions on Intelligent Vehicles, vol. 1, no. 1, pp. 33–55, 2016. [79] Y. Xiao, X. Zhang, X. Xu, X. Liu, and J. Liu, “Deep neural networks with koopman operators for modeling and control of autonomous vehicles,” IEEE Transactions on Intelligent Vehicles, vol. 8, no. 1, pp. 135–146, 2023. [80] M. T. Gillespie, C. M. Best, E. C. Townsend, D. Wingate, and M. D. Killpack, “Learning nonlinear dynamic models of soft robots for model predictive control with neural networks,” in 2018 IEEE International Conference on Soft Robotics (RoboSoft), pp. 39–45, IEEE, 2018. [81] L. A. Basina, B. K. Irdmousa, J. M. Velni, H. Borhan, J. D. Naber, and M. Shahbakhti, “Data-driven modeling and predictive control of maximum pressure rise rate in rcci engines,” in 2020 IEEE conference on control technology and applications (CCTA), pp. 94–99, IEEE, 2020. [82] L. C. Sousa and H. V. H. Ayala, “Nonlinear tire model approximation using machine learning for efficient model predictive control,” IEEE Access, vol. 10, pp. 107549–107562, 2022. [83] K. Bieker, S. Peitz, S. L. Brunton, J. N. Kutz, and M. Dellnitz, “Deep model predictive flow control with limited sensor data and online learning,” Theoretical and computational fluid dynamics, vol. 34, pp. 577–591, 2020. 86 Bibliography [84] Y. Vaupel, N. C. Hamacher, A. Caspari, A. Mhamdi, I. G. Kevrekidis, and A. Mitsos, “Accelerating nonlinear model predictive control through machine learning,” Journal of process control, vol. 92, pp. 261–270, 2020. [85] M. Toub, M. Shahbakhti, R. D. Robinett, and G. Aniba, “Mpctrained anfis for control of microcsp integrated into a building hvac system,” in 2019 American Control Conference (ACC), pp. 241– 246, IEEE, 2019. [86] M. Novak and T. Dragicevic, “Supervised imitation learning of finite-set model predictive control systems for power electronics,” IEEE Transactions on Industrial Electronics, vol. 68, no. 2, pp. 1717–1723, 2020. [87] R. Koh´ut, L. Galˇc´ıov´a, K. Fedorov´a, T. ´ Abelov´a, M. Bakoˇsov´a, and M. Kvasnica, “Hidden markov model-based warm-start of active set method in model predictive control,” in 2021 23rd International Conference on Process Control (PC), pp. 60–65, IEEE, 2021. [88] D. Masti and A. Bemporad, “Learning binary warm starts for multiparametric mixed-integer quadratic programming,” in 2019 18th European Control Conference (ECC), pp. 1494–1499, IEEE, 2019. [89] N. Karnchanachari, M. I. Valls, D. Hoeller, and M. Hutter, “Practical reinforcement learning for mpc: Learning from sparse objectives in under an hour on a real robot,” in Learning for Dynamics and Control, pp. 211–224, PMLR, 2020. [90] L. Wei, X. Wang, L. Li, Z. Fan, R. Dou, and J. Lin, “Ts fuzzy model predictive control for vehicle yaw stability in nonlinear region,” IEEE transactions on vehicular technology, vol. 70, no. 8, pp. 7536–7546, 2021. [91] C. Greatwood and A. G. Richards, “Reinforcement learning and model predictive control for robust embedded quadrotor guidance and control,” Autonomous Robots, vol. 43, pp. 1681–1693, 2019. [92] K. P. Wabersich and M. N. Zeilinger, “A predictive safety filter for learning-based control of constrained nonlinear dynamical systems,” Automatica, vol. 129, p. 109597, 2021. Bibliography 87 [93] M. Zanon and S. Gros, “Safe reinforcement learning using robust mpc,” IEEE Transactions on Automatic Control, vol. 66, no. 8, pp. 3638–3652, 2020. [94] A. Cheng and Y. M. Low, “Improved generalization of narx neural networks for enhanced metamodeling of nonlinear dynamic systems under stochastic excitations,” Mechanical Systems and Signal Processing, vol. 200, p. 110543, 2023. [95] P. Takyi-Aninakwa, S. Wang, H. Zhang, Y. Xiao, and C. Fernandez, “A narx network optimized with an adaptive weighted square-root cubature kalman filter for the dynamic state of charge estimation of lithium-ion batteries,” Journal of Energy Storage, vol. 68, p. 107728, 2023. [96] A. Jain, N. Framke, A. Tiwari, and M. Spasov, “Application of feedforward neural networks in battery electric vehicle air conditioning system simulations,” 2022. [97] E. ˇ Sabanoviˇc, V. ˇ Zuraulis, O. Prentkovskis, and V. Skrickij, “Identification of road-surface type using deep neural networks for friction coefficient estimation,” Sensors, vol. 20, no. 3, p. 612, 2020. [98] J. Zhu, Q. Jiang, Y. Shen, C. Qian, F. Xu, and Q. Zhu, “Application of recurrent neural network to mechanical fault diagnosis: A review,” Journal of Mechanical Science and Technology, vol. 36, no. 2, pp. 527–542, 2022. [99] B. Widrow, D. E. Rumelhart, and M. A. Lehr, “Neural networks: applications in industry, business and science,” Communications of the ACM, vol. 37, no. 3, pp. 93–106, 1994. [100] F. Mumali, “Artificial neural network-based decision support systems in manufacturing processes: A systematic literature review,” Computers & Industrial Engineering, p. 107964, 2022. [101] E. Camacho and A. Gallego, “Optimal operation in solar trough plants: A case study,” Solar Energy, vol. 95, pp. 106–117, 2013. [102] Y. Huang, J. Du, Z. Yang, Z. Zhou, L. Zhang, and H. Chen, “A survey on trajectory-prediction methods for autonomous driving,” IEEE Transactions on Intelligent Vehicles, vol. 7, no. 3, pp. 652– 674, 2022. 88 Bibliography [103] S. Mohanty, P. K. Patra, and S. S. Sahoo, “Prediction of global solar radiation using nonlinear auto regressive network with exogenous inputs (narx),” in 2015 39th National Systems Conference (NSC), pp. 1–6, IEEE, 2015. [104] L. G. B. Ruiz, M. P. Cu´ellar, M. D. Calvo-Flores, and M. D. C. P. Jim´enez, “An application of non-linear autoregressive neural networks to predict energy consumption in public buildings,” Energies, vol. 9, no. 9, p. 684, 2016. [105] M. A. Sadeeq and A. M. Abdulazeez, “Neural networks architectures design, and applications: A review,” in 2020 International Conference on Advanced Science and Engineering (ICOASE), pp. 199–204, IEEE, 2020. [106] A. Kusiak, “Convolutional and generative adversarial neural networks in manufacturing,” International Journal of Production Research, vol. 58, no. 5, pp. 1594–1604, 2020. [107] E. Cadenas, W. Rivera, R. Campos-Amezcua, and C. Heard, “Wind speed prediction using a univariate arima model and a multivariate narx model,” Energies, vol. 9, no. 2, p. 109, 2016. [108] T. Fine, “Feedforward neural network methodology (softcover reprint of the original 1st ed. 1999), ed,” 2013. [109] B. J. Erickson, “Basic artificial intelligence techniques: machine learning and deep learning,” Radiologic Clinics, vol. 59, no. 6, pp. 933–940, 2021. [110] J. Spicer and A. N. Sanborn, “What does the mind learn? a comparison of human and machine learning representations,” Current opinion in neurobiology, vol. 55, pp. 97–102, 2019. [111] M. Lawry´nczuk, “A family of model predictive control algorithms with artificial neural networks,” International Journal of Applied Mathematics and Computer Science, vol. 17, no. 2, pp. 217–232, 2007. [112] E. Szczerbicki, Intelligent systems for knowledge management, vol. 252. Springer, 2009. [113] J. Zamarreno, P. Vega, L. Garcıa, and M. Francisco, “State-space neural network for modelling, prediction and control,” Control Engineering Practice, vol. 8, no. 9, pp. 1063–1075, 2000. Bibliography 89 [114] A. Hassan, S. Ruiz-Moreno, J. R. D. Frejo, and J. M. Maestre, “Enhancement of lateral stability control in 4-wheel electric vehicles using deep learning,” IEEE Conference on Decision and Control (CDC), 2024. [115] M. T. Hagan and M. B. Menhaj, “Training feedforward networks with the marquardt algorithm,” IEEE Transactions on Neural Networks, vol. 5, pp. 989–993, 1994.