## 6 Conclusions  
In this paper, a novel sensorless DSMC-based sliding mode observer is proposed to achieve a reliable and smooth start. It was demonstrated that, with the proposed method, the motor can start promptly from any arbitrary initial position. The starting was achieved without an initial jerk. At higher speeds, the accuracy of the speed and displacement measurements of the DSMC-based SMO are reasonably good (within \(\pm 2\%\)). The chattering phenomena were reduced to a minimal extent and tracked the speed in less than 0.005 s only. The sensorless DSMC-based SMO gave accurate rotor displacement, position and speed measurements with any sudden change of loading conditions and reference values, as compared with the SMC-based SMO. Hence, the DSMC-based SMO method is very suitable for the sensorless control of the BSRM at higher speeds with any consideration of internal and external disturbances. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & \multicolumn{2}{c}{**SMC Based-SMO**} & \multicolumn{2}{c}{** DSMC-Based SMO**} \\ \hline Change of system parameters & \begin{tabular}{c} Difference in \\ speed \\ \end{tabular} & \begin{tabular}{c} \% of \\ Chattering \\ \end{tabular} & \begin{tabular}{c} Difference in \\ speed \\ \end{tabular} & \begin{tabular}{c} \% of \\ Chattering \\ \end{tabular} \\ \hline \begin{tabular}{c} Change of Switching angle to \\ 13 degree \\ \end{tabular} & 3000 & \(\pm 8\) & 1000 & \(\pm 3\) \\ \hline \begin{tabular}{c} Varying of supply voltage \\ \end{tabular} & 3500 & \(\pm 8\) & 1500 & \(\pm 5\) \\ \hline \begin{tabular}{c} Varying in load Torque \\ \end{tabular} & 3500 & \(\pm 8\) & 1500 & \(\pm 5\) \\ \hline \begin{tabular}{c} Decrease of moment of inertia \\ by 10\% \\ \end{tabular} & 3000 & \(\pm 5\) & 800 & \(\pm 4\) \\ \hline \
\begin{tabular}{c} Increase of moment of inertia \\ by 10\% \\ \end{tabular} & 2000 & \(\pm 5\) & 800 & \(\pm 4\) \\ \hline
\begin{tabular}{c} Change of Switching angle to \\ 11 degree \\ \end{tabular} & 2000 & \(\pm 8\) & 1000 & \(\pm 3\) \\ \hline \hline \end{tabular} Note: SMC-sliding mode controller; DSMC-dynamic sliding mode controller; SMO-sliding mode observer  
\end{table} 
Table 4: Comparisons of speeds between the proposed and conventional methods. Figure 29: Change in the switching angle to 13 degrees. [Note: ACT_SMC: actual speed under sliding mode controller; EST_SMC: estimated speed under sliding mode controller; ACT_DSMC: actual speed under dynamic sliding mode controller; EST_DSMC: estimated speed under dynamic sliding mode controller; SPEED_REF: reference speed]. **Author Contributions:** Data curation, P.N.R. ; formal analysis, P.N.R. and N.M.K. ; funding acquisition, S.P. (towards APC); methodology, P.N.R. and N.M.K. ; resources, S.P. ; software, P.N.R. ; visualisation, N.M.K. ; writing--original draft, P.N.R. and N.M.K. and writing--review and editing, P.N.R., N.M.K., S.P, M.S.P.S. and A.A.C. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Acknowledgments:** We authors acknowledge the Department of Energy Technology, Aalborg University, Esbjerg, Denmark for sharing technical experts. **Conflicts of Interest:** The authors declare no conflict of interest.