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