From 8563bf2dcbee3423398084121fae24595211ff0b Mon Sep 17 00:00:00 2001 From: Nolan Date: Tue, 12 May 2026 15:39:44 +0200 Subject: [PATCH] Ajout de la partie related work --- Sécurité/main.tex | 68 ++++++++++++++++++++++++++++++++++++++++++++++- 1 file changed, 67 insertions(+), 1 deletion(-) diff --git a/Sécurité/main.tex b/Sécurité/main.tex index 528ad9e..8a9fb91 100644 --- a/Sécurité/main.tex +++ b/Sécurité/main.tex @@ -103,7 +103,73 @@ We also argue the need for general public's safety when it comes to these bikes, product from laMAD than what is publicly available? -\section{Litterature review} +\section{Related Work} + +\subsection{Modeling of BLDC Motor} +The electromechanical model of a BLDC motor is foundational for understanding its behavior under different control +schemes. BLDC motors are categorized by their back-electromotive force (back-EMF) waveform: trapezoidal or sinusoidal. +This distinction is crucial, as the trapezoidal shape inherently leads to torque ripple when the supplied phase currents +are not perfectly aligned, directly influencing the choice and effectiveness of the control strategy +\cite{patil_analysis_2025}. For a BLDC motor with trapezoidal back-EMF, the electromagnetic torque is given by: +\[ +T_e = \frac{e_a i_a + e_b i_b + e_c i_c}{\omega_m} +\] +where \( e_x \) is the back-EMF and \( i_x \) is the phase current \cite{li_quantitative_2019}. The classical d-q +reference frame model, ideal for sinusoidal machines, is less suitable for trapezoidal BLDC motors because it assumes +sinusoidal flux distribution. Phase-variable modeling in the natural (abc) frame is therefore more appropriate, as it +directly accounts for the non-sinusoidal, trapezoidal nature of the back-EMF and the associated harmonics +\cite{mohammd_taher_new_2021}. + +\subsection{Trapezoidal Commutation (Six-Step Control) for BLDC Motors} +% Trapezoidal commutation, or six-step control, uses Hall-effect sensors to synchronize phase current switching every +% 120 electrical degrees. +Trapezoidal commutation, or Six-Step control, uses bipolar conduction, with two motor phases conducting at any time and +current commutation occurring every 120 electrical degrees \cite{gieras_modern_2023}. As commutation depends on rotor +position, Six-Step control requires either position sensors (e.g. Hall sensors, encoders, or resolvers) or sensorless +estimation based on back-EMF detection or observers \cite{gieras_modern_2023, gasc_conception_2004}. This method is +renowned for its simplicity of implementation and low hardware cost \cite{bhatiya_bldc_2024}. It enables effective +torque control but introduces significant torque ripple during commutation events, especially under high load +\cite{jomsa-nga_torque_2024}. This ripple generates noise, increases mechanical stress, and reduces overall efficiency +\cite{mohammd_taher_new_2021}. Although PWM techniques can mitigate this ripple, they do not completely eliminate it +\cite{li_quantitative_2019}. + +\subsection{Field-Oriented Control (FOC) for BLDC Motors} +FOC is a vector control strategy that decouples the stator flux and torque components. It transforms three-phase +currents into orthogonal \( I_d \) and \( I_q \) components, enabling precise torque control and significant ripple +reduction \cite{jomsa-nga_torque_2024}. FOC is particularly effective for BLDC motors with sinusoidal back-EMF but can +also be applied to trapezoidal back-EMF motors, albeit with less impressive ripple suppression results +\cite{li_quantitative_2019}. It requires greater computational power and more precise position sensors (e.g. encoders). +Comparative analysis shows that FOC yields a more stable stator current profile and significantly reduces torque +variations compared to trapezoidal control \cite{patil_analysis_2025}. + +\subsection{Comparative Analysis: FOC vs. Trapezoidal for Light Electric Vehicles} + +\subsubsection{Torque Ripple and User Comfort} +Firstly, torque ripple can be reduced for both control methods by selecting appropriate motor parameters, such as the +number of stator slots and rotor poles \cite{gasc_conception_2004}. +FOC substantially reduces torque ripple compared to Six-Step control, directly enhancing ride comfort and minimizing +vibrations. Experimental results show a torque ripple of \SI{18.38}{\percent} for FOC versus \SI{35.67}{\percent} for +Six-Step control at \SI{500}{\rpm} \cite{jomsa-nga_torque_2024}. +Commutation torque ripple (CTR), prominent in Six-Step control, can be specifically targeted and mitigated using +advanced control techniques like Model Predictive Control (MPC) while retaining the fundamental simplicity of +trapezoidal commutation \cite{mohammd_taher_new_2021}. + +\subsubsection{Energy Efficiency} +FOC optimizes torque per ampere (MTPA), improving efficiency at low loads. Six-Step control exhibits lower switching +losses at high speeds \cite{li_quantitative_2019}. + +\subsubsection{Complexity, Cost, and Low-Tech Suitability} + +Six-Step control is inherently simpler, cheaper, and more robust, making it a prime candidate for low-tech applications. +Research focused on reducing propulsion system costs proposes simplified hardware topologies, such as 4-switch inverters +(instead of 6) coupled with direct current control strategies, maintaining acceptable performance while significantly +lowering hardware costs \cite{lee_advanced_2001}. FOC, while superior in performance, is more complex to implement and +carries higher hardware costs (sensors, processing power). + +\subsubsection{Dynamic Response} + +FOC provides faster response times and better load disturbance rejection \cite{jomsa-nga_torque_2024}. + \section{Research gap} Despite this progress, limited research has examined the adaptation of open-source motor controllers to LowTech and