## 1 Introduction
### Proposed Work and Contributions  
The main contribution of this work is related to a novel back-EMF observer developed by integrating QPLL into the computation. The aim is to improve the control of BLDCMs by upgrading the rotor angular position estimation across a wider speed range compared to conventional back-EMF observers. The method retains the advantages of conventional back \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sensorless Technology** & & **Merits** & **Demerits** \\ \hline \multirow{4}{*}{Luenberger observer} & \(\bullet\) & Simple linear feedback mechanism & \(\bullet\) & Requires accurate parameter knowledge \\  & \(\bullet\) & Applicable in both stationary and synchronous frames & \(\bullet\) & Less effective at handling high-frequency disturbances \\  & \(\bullet\) & Robust gain tuning available & & \\ \hline \multirow{4}{*}{Linear disturbance observer (LDO)} & \(\bullet\) & Simplifies design & \(\bullet\) & Ineffective for high-frequency disturbances \\  & \(\bullet\) & Computationally efficient & \(\bullet\) & Requires tuning for sudden load changes \\ \cline{1-1} \cline{2-4}  & \(\bullet\) & Isolates fundamental components effectively & \(\bullet\) & Computationally demanding \\ \cline{1-1} \cline{2-4}  & \(\bullet\) & Excellent harmonic suppression & \(\bullet\) & Sensitive to parameter mismatches \\ \cline{1-1} \cline{2-4}  & \(\bullet\) & Eliminate low-order & \\ \cline{1-1} \cline{2-4}  & \(\bullet\) & harmonics dynamically & \(\bullet\) & High computational complexity \\ \cline{1-1} \cline{2-4}  & \(\bullet\) & Improve robustness & \(\bullet\) & Stability analysis \\ \cline{1-1} \cline{2-4}  & \(\bullet\) & against distortions & \(\bullet\) & poses challenges \\ \cline{1-1} \cline{2-4}  & \(\bullet\) & Effective for high-speed operation & & \\ \hline \multirow{4}{*}{Machine parameter-adaptive observers (RLS, MRAS, adaptive PI)} & \(\bullet\) & Dynamically adjusts resistance, inductance, and flux & \(\bullet\) & Convergence issues among estimators \\  & \(\bullet\) & Robust under varying conditions & \(\bullet\) & High computational burden \\ \cline{1-1} \cline{2-4}  & \(\bullet\) & Improves reliability & & \\ \cline{1-1} \cline{2-4}  & \(\bullet\) & across ranges & & \\ \hline \multirow{4}{*}{Saliency-based observers} & \(\bullet\) & Effective at low speeds & \(\bullet\) & Requires high-frequency signal injection \\  & \(\bullet\) & Leverage rotor anisotropy for position estimation & \(\bullet\) & Causes torque ripple and \\ \cline{1-1}  & \(\bullet\) & Robust to back-EMF limitations & & mechanical noise \\ \hline \multirow{4}{*}{Proposed QPLL-based back-EMF observer} & \(\bullet\) & Precise position estimation & \\ \cline{1-1}  & \(\bullet\) & Improved low & \\ \cline{1-1}  & \(\bullet\) & speed performance & \(\bullet\) & The addition of QPLL affects the dynamics response \\ \cline{1-1}  & \(\bullet\) & LPF is avoided & \(\bullet\) & Disturbances, such as in DC bus \\ \cline{1-1}  & \(\bullet\) & Speed-adaptive position estimation suitable for all operating speeds & & voltage, can affect the \\ \cline{1-1}  & \(\bullet\) & Avoids noise associated with the arc-tangent method & & QPLL performance \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._EMF observers while addressing their limitations, as developed in Table 1. The improved observer is well suited to provide sensorless control of BLDCM drives (Mclennan, Waco, TX, USA) used in light EVs. The novel observer modeling is performed in the stationary \(\alpha\beta\) frame, ensuring simpler computation compared to the other nonlinear observers. The estimator involved in the proposed method remains accurate across a wider speed range, especially in the challenging low-speed range, outperforming the accuracy of the conventional back-EMF observers. Through the proposed approach, the conventional arc-tangent method used for position estimation is replaced with the QPLL. This change not only improves low-speed performance but also reduces unwanted noise in position estimation.