\chapter*{Introduction}\stepcounter{chapter}
\addcontentsline{toc}{chapter}{Introduction}

\label{chpt:introduction}

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\section[Background and Motivation]{Background and Motivation}
\label{sec: background and motivation}
The global automotive industry is currently undergoing a historic transition from Internal Combustion Engines (ICE) to Electric Powertrains (EP). This evolution represents a fundamental paradigm shift, particularly within the high-performance and motorsport sectors, and is not merely characterized by a change in energy source but also by a radical transformation in vehicle dynamics control capabilities. \\
The fundamental motivation for the shift from \gls{ice} to \gls{ep} in high-performance applications lies in the superior controllability of electromagnetic torque. As established by Hori et al. \cite{EVUotElectricMarch}, the torque response of an electric motor is approximately two orders of magnitude faster than that of an ICE, which is constrained by intake manifold dynamics, the delays of the ignition cycle and mechanical transmission latencies, unlocking the ability to modulate torque in sub-millisecond intervals. 
\newline\newline
In a motorsport context, this increased bandwidth allows for the implementation of Optimal Slip Ratio Control. This strategy ensures that the tire-road interface remains consistently at the peak of the friction coefficient curve, maximizing longitudinal force and acceleration efficiency regardless of rapid variations in road surface conditions. 
\newline\newline
Furthermore, electrification enables a transition from centralized propulsion to distributed drive systems, such as four or two independent In-Wheel Motors (\gls{iwm}). \\ 
De Novellis et al. discussed how this over-actuated configuration allows for sophisticated Torque Vectoring (TV) strategies \cite{DeNovellis2014TVComparison}: by independently modulating the torque at each wheel, the controller can generate a direct yaw moment. For a high-performance vehicle, this decouples lateral stability from longitudinal traction and, unlike traditional Electronic Stability Control (\gls{esc}) systems that rely on dissipative braking interventions, \gls{tv} enhances the vehicle's ability and agility by actively assisting cornering maneuvers, thereby reducing understeer and improving transient response without sacrificing kinetic energy.
\newline\newline
Despite these technical advantages, the implementation of high-performance traction control faces two major hurdles: the highly non-linear nature of tire dynamics and the \textit{sensory gap} experienced by the driver.\\
The tire-road friction coefficient is a non-linear function of the slip ratio, and its optimal peak is a moving target influenced by tire temperature, vertical load, and road surface variability. Consequently, the controller must exhibit extreme robustness to handle these unmodeled dynamics and parameter uncertainties.

Moreover, the lack of traditional acoustic and vibrational cues in electric vehicles can impede a professional driver's ability to perceive the limit of adhesion.\\
Research by Corno \cite{Corno2013HapticTC} addresses this by proposing Haptic Traction Control (\gls{htc}). This system integrates the control logic with the Human-Machine Interface (\gls{hmi}) by using an active accelerator pedal to provide force-feedback proportional to the wheel slip. By restoring this physical intuition, the system enables a driver-in-the-loop architecture where the human operator can modulate inputs in harmony with the automated slip regulation, ensuring safety and stability without compromising the \textit{fun-to-drive} factor essential in motorsport.

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\section[Traction Control Challenges in Electric Vehicles]{Traction Control Challenges in Electric Vehicles} 
\label{sec: tract control challenges}
The primary objective of a Traction Control System (\gls{tcs}) is to modulate the drive torque such that the friction between the tire and the road surface is maximized, preventing wheel spin during acceleration. While the hardware advantages of electric powertrains provide the necessary bandwidth for superior control, the implementation of a robust and efficient slip control strategy involves significant challenges stemming from the highly non-linear nature of tire dynamics and environmental variability.
\subsection[The Physics of Tire-Road Interaction and Slip Control]{The Physics of Tire-Road Interaction and Slip Control}
\label{subsec: tire and slip physics background} 
The generation of longitudinal force between a vehicle and the ground is not a simple phenomenon of static friction, but a complex, distributed process occurring within the tire’s contact patch. This interaction is the foundation of traction control, as the controller’s primary task is to manage the physical states of this interface to prevent the transition from stable grip to unstable sliding.
\newline \newline
At the heart of traction control is the concept of the wheel slip ratio ($\sigma$) \nomenclature{$\sigma$}{Wheel slip ratio\nomunit{[-]}}, which defines the relative difference between the wheel's tangential velocity and the vehicle's longitudinal velocity.
\\
In the initial stage of torque application, the tire-road interface remains mostly in a \textit{stick} condition, where the rubber deforms but does not slide relative to the pavement. In this linear region, the traction force increases proportionally with the slip ratio. However, as torque increases, the rear part of the contact patch begins to \textit{slip} or \textit{micro-slide}. This represents a transition from elastic deformation to kinetic friction.
\newline\newline
The longitudinal force ($F_x$) \nomenclature{$F_x$}{Longitudinal tire force\nomunit{[N]}} generated at the contact patch is a non-linear function of this slip ratio; the relationship between the friction coefficient ($\mu$) \nomenclature{$\mu$}{Tire-road friction coefficient\nomunit{[-]}} and the slip ratio is fundamentally non-linear and is often described using semi-empirical models such as the Pacejka "Magic Formula" \cite{NovelTractionControlSingleWheel}.
The $\mu - \sigma$ characteristic curve typically exhibits three distinct zones:
\begin{figure}[H]
    \centering
    \includegraphics[width=0.65\textwidth]{images/FrictioSlip_GeneralRelationship.png}
    \caption{Friction coefficient as function of slip \cite{GeneralCurveMuSigmaFig}.}
    \label{fig: generic mu-sigma curve}
\end{figure}
\begin{description}[style=nextline]
    \item[The Linear Region] At low slip values (typically $\sigma<0.05$), the friction coefficient increases linearly. Here, the vehicle is easy to control, and the driver feels a direct correspondence between pedal input and acceleration.
    \item[The Peak Region] The curve reaches a maximum value, $\mu_{max}$ \nomenclature{$\mu_{max}$}{Peak friction coefficient \nomunit{[-]}}, at an \textit{optimal slip ratio} ($\sigma_{opt}$)\nomenclature{$\sigma_{opt}$}{Optimal slip ratio \nomunit{[-]}}. This point represents the physical limit of the tire's adhesion. In high-performance scenarios, maintaining the tire exactly at this peak yields the maximum possible longitudinal acceleration.
    \item[The Unstable Region] Beyond the optimal slip point, the friction coefficient begins to decrease. This is a critical instability: as the tire spins faster, it generates less force, leading to a runaway effect where the wheel accelerates rapidly toward a \textit{burnout} state.
\end{description}

\noindent
Overall, there exists an optimal slip ratio where the friction coefficient reaches its maximum. Beyond this point, the tire enters the unstable region where increasing the wheel speed leads to a decrease in traction, resulting in a loss of directional stability and acceleration.

The focus of modern EV traction control, as proposed in the seminal work of Hori et al. \cite{EVUotElectricMarch}, is to maintain the tire as close to this optimal point as possible. This \textbf{Optimal Slip Ratio Control} is far superior to the heuristic torque-reduction methods used in early ICE-based systems, as it directly manages the state of the tire-road interface.

A major challenge highlighted in the research by He \cite{AntiSkidControl} is that the optimal slip point is a moving target. The shape of the $\mu - \sigma$ curve changes drastically depending on road conditions (e.g., dry asphalt vs. wet concrete) and tire temperature. On a dry racing track, the peak might be sharp and at a relatively high slip ratio; on a wet surface, the peak is lower, flatter, and occurs at a lower slip ratio.
\begin{figure}[H]
    \centering
    \includegraphics[width=0.7\textwidth]{images/FrictionSlip_DifferentRoads.png}
    \caption{Friction coefficient as function of slip for different road surfaces \cite{DiffRoadsFig}.}
    \label{fig: mu-sigma curve for different roads}
\end{figure}
Furthermore, the operational limits of a tire are fundamentally governed by the \textit{Friction Ellipse} theory, a concept that defines the theoretical maximum resultant force that the tire-road interface can sustain. This principle points that the total transmissible traction force is a finite resource, determined by the product of the instantaneous vertical load and the local friction coefficient. From a vectorial perspective, the magnitude of the resultant force composed of both longitudinal ($F_x$) and lateral ($F_y$) \nomenclature{$F_y$}{Vertical tire force\nomunit{[N]}} components cannot exceed this adhesion limit without inducing \textit{macro-sliding}.

In high-performance maneuvers, this creates a critical coupling between traction and cornering stability. If a significant portion of the friction potential is consumed by longitudinal acceleration, the residual capacity for lateral force generation is proportionally diminished. Consequently, if a traction control system fails to regulate slip effectively, the saturation of the friction circle by longitudinal forces leads to a phenomenon known as \textit{contact patch saturation}. In such a state, the tire becomes incapable of providing the necessary centripetal force for steering, resulting in a total loss of directional stability. In a motorsport context, this loss of lateral authority is particularly hazardous, as it can lead to uncontrollable understeer or oversteer during high-speed transients.

Accordingly, the strong coupling between longitudinal and lateral tire dynamics requires the traction control system to regulate slip with high precision, ensuring that the resultant tire force remains within the admissible friction-ellipse boundary. The synthesis of such a controller is further complicated by the strongly non-linear and time-varying nature of the tire-road interface. As reported by Yang et al. \cite{NovelTractionControlSingleWheel}, once the slip ratio exceeds the optimal threshold ($\sigma > \sigma_{opt}$), the local system behavior transitions from a stable to an unstable regime, so that further increases in wheel speed induce a positive-feedback effect driving the tire rapidly toward full sliding.

Furthermore, as previously noted, the plant is subject to high degrees of environmental stochasticity. The friction peak is not a static parameter but a moving target that shifts according to the road surface composition, instantaneous vertical load, and the tire's thermal state \cite{AntiSkidControl}. Under these unsteady conditions, traditional linear control strategies, such as the Proportional-Integral-Derivative (PID) controller, often prove inadequate. Linear controllers are typically tuned for a specific operating point and lack the structural robustness required to manage the sudden gain jumps and parameter uncertainties typical of near-limit vehicle operation.

Consequently, the academic literature has explored a diverse array of advanced architectures, ranging from Model Predictive Control (MPC) to \textit{smart paradigms} such as Fuzzy Logic (FL) and artificial Neural Networks (NN). In this context, Sliding Mode Control (SMC) emerges as a particularly compelling solution due to its inherent robustness to bounded uncertainties.
\subsection[Slip-Based Control Strategy]{Slip-Based Control Strategy}
\label{subsec: slip based ctrl strategy}
The shift toward slip-based control in electric vehicles offers different advantages that are particularly critical in motorsport and high-performance environments.
First and foremost, the quasi-instantaneous torque modulation capability of electromagnetic actuators allows the controller to track the optimal slip ratio even under transient conditions, such as rapid vertical load shifts during cornering.
Furthermore, this strategy transforms the electric motor into a sophisticated sensor, providing a high-fidelity estimation of the tire-road interface states without the latency associated with traditional mechanical observers

Despite its theoretical superiority, slip-based control introduces several engineering trade-offs:
\begin{description}[style=nextline]
    \item[Robustness and Smoothness] A highly aggressive slip controller is necessary to catch sudden instabilities; however, this often leads to the phenomenon of \textbf{\gls{chattering}}, especially when using robust frameworks like Sliding Mode Control. Chattering can induce mechanical fatigue in the drivetrain and degrade the driving experience.
    \item[Estimation Lag] While the motor response is fast, the calculation of the slip ratio depends on an accurate estimation of the vehicle's longitudinal velocity ($v$) \nomenclature{$v$}{Vehicle's speed \nomunit{[m/s]}}. In motorsport, where all wheels may be near the limit of adhesion, obtaining a true ground speed reference is difficult, and errors in this estimate can lead to improper control interventions.
    \item[Sensory Gap] A highly efficient automated slip controller can effectively mask the physical limits of the car from the driver. By instantly correcting every micro-slip, the system removes the tactile cues that professional drivers use to sense the limit. This necessitates the integration of feedback mechanisms to restore the driver-in-the-loop synergy without sacrificing the safety provided by the control system.
\end{description}

Within this framework, the control architecture is typically structured hierarchically: a \textit{high-level supervisor} determines the target slip ratio based on the desired vehicle dynamics and actual road conditions, while a \textit{low-level slip regulator} modulates the motor torque to track this reference. By maintaining the tire at the peak of the $\mu - \sigma$ curve, the system effectively decouples the driver's longitudinal demand from the physical limits of the tire-road interface. This ensures that the vehicle remains in a high-performance envelope where traction and lateral stability are simultaneously optimized. Consequently, slip-based control does not replace the driver’s authority but rather allows for the safe exploitation of the electric powertrain's full potential.
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\section[Project Goals and Research Questions]{Project Goals and Research Questions}
\label{sec: project goals}
The preceding analysis of the tire-road interface and the advantages of electric powertrains highlights a major control challenge: maintaining the optimal slip ratio in a highly non-linear, dynamic and unsteady environment. Although \acrlong{smc} provides the robustness required for this task, its practical implementation in high-performance EVs introduces specific technical challenges that this thesis aims to address.
\paragraph[short]{Problem Statement.}
Standard \acrshort{smc} is often plagued by the chattering phenomenon, where high-frequency switching of the control law excites drivetrain resonances and causes mechanical fatigue.\\ Furthermore, while a smoother switching function (e.g., using a saturation function) can mitigate chattering, it often introduces a steady-state error, preventing the tire from reaching the ideal peak of the friction curve. In a motorsport context, where a 1-2\% deviation from the optimal slip ratio translates to lost lap time, this represents an inadmissible compromise. \\ Additionally, the controller must remain adaptive to varying road conditions without requiring manual re-tuning for every surface change.
\paragraph[short]{Project Goals.}
The primary goal of this research is the design, implementation, and validation of an Adaptive Conditional Integral Sliding Mode Controller (ACISMC) tailored for a high-performance electric vehicle. The specific technical objectives are:
\begin{itemize}
    \item Chattering Suppression: to implement a continuous approximation of the switching law that minimizes high-frequency torque ripples without sacrificing the response time of the electromagnetic actuators.
    \item Environmental Adaptation: to develop an adaptive algorithm capable of identifying and compensating diverse track conditions (e.g., dry vs. wet asphalt).
    \item Simulation Validation: to verify the controller’s performance using a high-fidelity co-simulation environment (e.g., CarMaker and CarMaker4Simulink) under realistic racing maneuvers.
    \item Comparative Performance Benchmarking: to perform a rigorous cross-evaluation between the proposed ACISMC and baseline control strategies, such as standard \acrshort{pid} and Traditional SMC. This objective aims to quantify the trade-offs between computational complexity and the resulting improvements in tracking accuracy and vehicle stability.
\end{itemize}
\paragraph{Research Questions.} The investigation first examines the tracking accuracy of the slip ratio under highly dynamic conditions, evaluating how the integration of a Conditional Integral term can mathematically eliminate the residual errors inherent in standard boundary-layer Sliding Mode Control. This phase of the study aims to quantify the \textit{performance gap} between traditional robust methods and the proposed integral-augmented architecture. \\
Subsequently, the analysis shifts toward the adaptive capabilities of the controller. The study investigates the algorithm's internal mechanisms for compensating for the  shifts in the tire-road friction peak, simulating transitions between heterogeneous surfaces (e.g., dry asphalt to wet concrete). The goal is to determine the controller's ability to maintain the \textit{optimal slip} without requiring manual calibration for environmental changes.
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\section[Thesis Structure]{Thesis Structure}
\label{sec: thesis structure}
This dissertation is organized into five primary chapters, following a path that transitions from theoretical modeling to the synthesis and comparative validation of advanced non-linear control laws. The methodology adopted ensures that the final controller design is rooted in a deep physical understanding of the tire-road interface and is benchmarked against established industry standards.
\paragraph[short]{State-of-the-Art.} A systematic review of existing literature is performed to situate the research within the broader control landscape. This chapter explores diverse methodologies, ranging starting from the foundational \acrshort{pid} regulators to more sophisticated \textit{intelligent paradigms} such as \acrshort{fl} and \acrshort{mpc}. By evaluating the performance trade-offs inherent in these established strategies, the chapter identifies the specific technical gaps and limitations, particularly regarding robustness and environmental adaptability, that justify the development of advanced \acrshort{smc} variants as the primary focus of this dissertation.
\paragraph[short]{Vehicle and Tire Modeling.} This chapter establishes the analytical foundation of the research. It provides a comprehensive derivation of the longitudinal vehicle and tire dynamics, with a specific focus on the non-linearities of the tire-road interaction. By employing semi-empirical models, such as the Pacejka Magic Formula, the chapter defines the state-space representation of the plant and identifies the critical implications that these physical constraints impose on the controller’s architecture.
\paragraph[short]{Baseline Controller Design.} To provide a rigorous basis for comparison, this chapter details the design process of the baseline control strategies. It covers the tuning of a standard PI  and the formulation of a \acrlong{tsmc}.
\paragraph[short]{Adaptive CISMC Design.} This chapter details the mathematical derivation of the \acrlong{acismc}. It explains the integration of the conditional integral term for error elimination and the development of the adaptive law used to track the variable friction peak. The stability of the proposed control law is formally analyzed using Lyapunov’s direct method.
\paragraph[short]{Simulation, Results, and Comparative Analysis.} The final technical chapter presents the results obtained from high-fidelity co-simulations. A comparative performance analysis is conducted across the three implemented technologies, evaluating their robustness, tracking accuracy, and impact on vehicle stability under diverse track conditions.
