## 5 Conclusions  
Using notions of fractional calculus, this article has presented several integer-order or FO controllers that have been integrated into the structure of the PMSM-SCS, based on the DTC strategy, to improve performance. Thus, starting from PI-type controllers, the features of the control system was improved by using the EOA-type algorithm for optimal tuning of controller parameters and by using FO-type controllers: FOPI, TID, and FO-Lead-Lag speed controllers. These types of controllers, embedded in the DTC strategy, are based on a constant reference flux for the flux control loop. When the reference flux is variable, the features of the control system are improved by using an integer-order SMC-type controller and the improved fractional FOSMC-type controller. The performance indicators of the PMSM-SCS based on the DTC strategy are the usual ones: response time, settling time, overshoot, steady-state error, speed ripple, and FD of the PMSM rotor speed signal.  
The parametric robustness property of the control system based on the DTC strategy is also demonstrated by the fact that good control performance is obtained by increasing the \(J\) parameter, which represents the combined inertia of the PMSM rotor and the load.  
The deployment of the software application in embedded system for a real-time HIL stage follows the stages presented in the controller synthesis and numerical simulations for the SIL stage, and good control performance of the PMSM based on the DTC strategy is obtained for the real-time control system.  
Future work will build on the development of controller vendor libraries to implement specific machine-learning capabilities in Simulink to design and implement PMSM-SCS that deliver superior performance.  
Conceptualization, M.N., C.-I.N. and D.S.; data curation, M.N., C.-I.N., D.S. and D.S.; formal analysis, M.N., C.-I.N., C.I. and D.S.; funding acquisition, M.N., investigation, M.N., C.-I.N., D.S., C.I. and D.S.; methodology, M.N., C.-I.N., D.S., C.I. and D.S.; project administration, M.N.; resources, M.N.; software, M.N. and C.-I.N.; supervision, M.N., C.-I.N., D.S. and C.I.; validation, M.N., C.-I.N., D.S., C.I. and D.S.; visualization, M.N., C.-I.N., D.S. and D.S.; writing--original draft, M.N. and C.-I.N.; writing--review and editing, M.N. and C.-I.N. All authors have read and agreed to the published version of the manuscript.  
This paper was elaborated as part of the NUCLEU Program within the framework of the National Research, Development, and Innovation Plan for 2022-2027, developed with the support of the Ministry of Research, Innovation, and Digitization, Project No. PN 23 33 02 04 and partially funded by Installation of National Interest \"System for generating, measuring and recording short circuit currents\"--SPMICS.  
**Institutional Review Board Statement:** Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type of Controller for PMSM Sensorless Real-Time Control System** & **Response Time [ms]** & **Settling Time** & **Speed Ripple** & **FD of PMSM Speed Signal** \\ \hline PI-EOA & 18.2 & 70 & 16.76 & 0.96900 +/ \(-\) 0.065622 \\ FOPI & constant flux & 25.8 & 60 & 15.83 & 0.97465 +/ \(-\) 0.060998 \\ SMC & 34.5 & 34.5 & 14.95 & 0.98009 +/ \(-\) 0.060727 \\ FOSMC & variable flux & 33.9 & 33.9 & 10.61 & 0.98533 +/ \(-\) 0.031485 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Performance of the proposed controllers for PMSM-SCS in real-time implementation.