## 5 Conclusions and Future Work  
The highly nonlinear behavior, rapidly varying dynamics, and practically unavailable measurements make PMSM a challenging estimation and control problem. In order to cope with such challenges, a novel hybrid strategy of MPC-UKF is proposed that provides advantages over the previously used algorithms in the shape of fewer current ripples, short peak time, improved settling time, controlled overshoot regarding speed variations, and an overall improved estimation. Therefore, the MPC-UKF hybrid approach, as a whole, is less susceptible to speed variations. In an effort to present an insightful discussion, the MPC-UKF has been compared with the MPC-EKF and MPC-SMO and it has been shown that the MPC-UKF has a good dynamic response even in a wide range with safer starting procedures. The superiority of the MPC-UKF over the other two approaches particularly originates from the fact that the UKF copes with the high nonlinearities, uncertainties, and unobservability more efficiently as compared to the EKF and SMO. It can be concluded from the presented results that the combination of MPC and the UKF is comparatively an efficient and better choice for high-performance AC drives. The proposed method seems amenable to highly nonlinear AC drives based on Doubly Fed Induction Motor (DFIM) and would \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline \multirow{2}{*}{**Dynamic Property**} & \multirow{2}{*}{**MPC-UKF**} & \multirow{2}{*}{**MPC-EKF**} & \multirow{2}{*}{**MPC-SMO**} & **Percentage Improvement for UKF** \\ \hline
**Step 1 (0–25\% of rated speed)** & & & & \\ \hline Speed peak time & 0.75 ms & 1.07 ms & 1.59 ms & 29.90\% \\ Speed settling time & 0.97 ms & 1.15 ms & 3.50 ms & 15.65\% \\ Speed overshoot & 1.26\% & 1.78\% & 24.9\% & 29.21\% \\ \hline
**Step 2 (25–50\% of rated speed)** & & & & \\ \hline Speed peak time & 0.68 ms & 1 ms & 1.48 ms & 32\% \\ Speed settling time & 0.67 ms & 0.87 ms & 3.06 ms & 22.98\% \\ Speed overshoot & 0.92\% & 1.43\% & 19.6\% & 35.66\% \\ \hline
**Step 3 (50–75\% of rated speed)** & & & & \\ \hline Speed peak time & 0.65 ms & 0.91 ms & 2.05 ms & 28.57\% \\ Speed settling time & 0.34 ms & 0.52 ms & 2.59 ms & 34.61\% \\ Speed overshoot & 0.56\% & 0.99\% & 15.4\% & 43.43\% \\ \hline
**Step 4 (75–100\% of rated speed)** & & & & \\ \hline Speed peak time & 0.42 ms & 0.61 ms & 2.60 ms & 31.14\% \\ Speed settling time & 0.26 ms & 0.35 ms & 2.36 ms & 25.71\% \\ Speed overshoot & 0.29\% & 0.78\% & 11.56\% & 62.82\% \\ \hline
**Step 5 (40\% of rated speed)** & & & & \\ \hline Speed peak time & 1.21 ms & 1.36 ms & 4.89 ms & 11.03\% \\ Speed settling time & 0.97 ms & 1.15 ms & 3.50 ms & 15.65\% \\ Speed overshoot & 1.26\% & 1.78\% & 24.9\% & 29.21\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: PMSM parameters used in the Simulations. potentially prove advantageous. In the future, we will intend to validate the proposed hybrid MPC-UKF technique through practical experimentation [35; 36]. Moreover, state-of-the-art observers, such as the improved non-singular fast terminal SMC and second-order SMC, will be implemented and compared in a hybrid combination with MPC. Conceptualization, K.S., M.J., K.A. and J.A. ; methodology, K.S., M.J., K.A., J.A. and I.K. ; validation, M.J., I.K., M.B., E.E.E. and S.K. ; formal analysis, K.S., M.J., K.A. and J.A. ; investigation K.S., M.J., K.A., J.A. and I.K. ; resources, M.B., E.E.E. and S.K. ; data curation, M.J., M.B., E.E.E. and S.K. ; writing--original draft preparation, K.S., M.J., K.-A. and J.A. ; writing--review and editing, I.K., M.B., E.E. and S.K., visualization, K.S. and M.J.; supervision, M.J., K.A. and M.B., S.K. ; project administration M.B., E.E.E. and S.K. All authors have read and agreed to the published version of the manuscript. This work was supported by Taif University Researchers Supporting Project number (TURSP-2020/86): Taif University, Taif, Saudi Arabia. Not applicable.