## 1 Introduction
### Sensorless Control of BLDCMs
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sensorless Technology** & **Merits** & **Demerits** \\ \hline Back-EMF zero-crossing & \(\bullet\) & Only 2 voltage sensors required & \(\bullet\) & Position estimation is not \\  & \(\bullet\) & Less computational burden & & accurate at low speed \\  & \(\bullet\) & Direct position estimation & \(\bullet\) & LPF introduces phase lag \\  & & using comparator & \(\bullet\) & Compensator is required \\  & & & \(\bullet\) & Delay is not fully compensated \\ \hline Third harmonic back-EMF variation & \(\bullet\) & Neutral point voltage & \(\bullet\) & High filtering requirement \\  & \(\bullet\) & fluctuation is avoided & \(\bullet\) & Estimated position pulses are \\  & \(\bullet\) & Similarly to conventional & & twice the actual frequency of \\  & & back-EMF zero-crossing & & Hall pulses \\  & & back-EMF zero-crossing & \(\bullet\) & Lag-lead compensation required \\  & & & for delay compensation \\ \hline Conventional back-EMF observer & \(\bullet\) & Easy computation compared to other nonlinear observers & \(\bullet\) & Suitable for medium- to \\  & \(\bullet\) & Observer modeling is further & \(\bullet\) & high-speed range \\  & & made easier in the stator & \(\bullet\) & LPF is required which \\  & & reference frame & \(\bullet\) & introduces delay \\  & \(\bullet\) & Fast dynamic response under & \(\bullet\) & Obtaining theta using \\  & & full-load variation & & arc-tangent method adds \\  & & full-load variation & & unwanted noise \\ \hline Sliding mode observer & \(\bullet\) & Both speed and position & \(\bullet\) & Complex computation \\  & & estimation are possible & \(\bullet\) & Chattering problem \\  & \(\bullet\) & Continuous position & \(\bullet\) & Additional filtering requirement \\  & & information is obtained & \(\bullet\) & Low-speed performance \\  & & information is obtained & & affected due to \\  & & & high-order harmonics \\ \hline Super-twisting SMO (STO) & \(\bullet\) & Reduces chattering compared to & \\  & & conventional SMO & \(\bullet\) & Complex gain design \\  & \(\bullet\) & Maintains robust tracking & \(\bullet\) & Computationally intensive \\  & \(\bullet\) & Suitable for noisy environments & & \\ \hline Flux-based observer & \(\bullet\) & Torque can also be estimated & \(\bullet\) & Complex computation \\  & & along with speed and position & \(\bullet\) & Estimated flux has offset \\  & \(\bullet\) & Suitable for wide speed & & problem due to integration \\  & & range application & & operation at low speed \\  & & Minimum position error due to & \(\bullet\) & Magnitude attenuation due to \\  & & adaptive control & & lowpass filter \\ \hline \multirow{4}{*}{Extended Kalman Filter (EKF)} & \(\bullet\) & Near optimal estimation & \(\bullet\) & High computational cost \\  & \(\bullet\) & Robust to noise & \(\bullet\) & Complex tuning of \\ \cline{1-1}  & \(\bullet\) & Adaptive feedback & & covariance matrices \\ \cline{1-1}  & \(\bullet\) & gain adjustment & \(\bullet\) & Sensitive to \\ \cline{1-1}  & \(\bullet\) & Effective under varying loads & & parameter variations \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparative analysis of sensorless BLDCM control methods.