{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T10:56:05Z","timestamp":1781693765391,"version":"3.54.5"},"reference-count":68,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T00:00:00Z","timestamp":1781654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"PubArt program of the National University of Science and Technology POLITEHNICA Bucharest"},{"name":"Experimental\u2014Demonstration project","award":["PN-IV-P7-7.1-PED-2024-0567"],"award-info":[{"award-number":["PN-IV-P7-7.1-PED-2024-0567"]}]},{"name":"Experimental\u2014Demonstration project","award":["58PED"],"award-info":[{"award-number":["58PED"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Permanent magnet synchronous motors (PMSMs) are widely used in industrial applications due to their high efficiency, compact structure, and excellent dynamic performance. However, achieving accurate speed control with high robustness under load disturbances and parameter uncertainties remains a significant challenge. Conventional proportional\u2013integral (PI) controllers often suffer from overshoot, slow dynamic response, and sensitivity to nonlinear operating conditions. To address these limitations, this paper proposes an intelligent control strategy that combines third-order sliding mode control (TOSMC) with the Golden Jackal Optimization (GJO) algorithm for optimal PMSM speed regulation. The proposed TOSMC-GJO approach aims to enhance the operational performance, robustness, and reliability of PMSM drives. The control structure consists of an optimized outer-loop speed controller and an inner-loop predictive current controller to improve current quality and eliminate the need for conventional PI tuning. The controller parameters are optimized using a fitness function designed to minimize tracking error, overshoot, settling time, torque ripples, and total harmonic distortion (THD). Simulation results under variable speed and load torque conditions demonstrate that the proposed TOSMC-GJO controller achieves superior performance compared with PI control and TOSMC optimized using Grey Wolf Optimization (GWO). The proposed strategy eliminates speed overshoot and reduces the response time to 0.0052 s, compared with 0.0056 s for TOSMC-GWO and 0.011 s for PI control. In addition, the THD of stator currents is reduced to 6.12%, improving current quality and reducing harmonic distortion. The proposed controller also provides smoother torque response, better disturbance rejection capability, and improved waveform symmetry. These results confirm that integrating high-order nonlinear control with metaheuristic optimization significantly improves the dynamic performance, operational reliability, and robustness of PMSM drive systems under demanding operating conditions.<\/jats:p>","DOI":"10.3390\/a19060486","type":"journal-article","created":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T10:19:53Z","timestamp":1781691593000},"page":"486","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Metaheuristic-Optimized Third-Order Sliding Mode Control for High-Performance Speed Regulation of Permanent Magnet Synchronous Motors"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8824-9761","authenticated-orcid":false,"given":"Benkaihoul","family":"Said","sequence":"first","affiliation":[{"name":"Applied Automation and Industrial Diagnostics Laboratory LAADI, Ziane Achour University of Djelfa, P.O. Box 3117, Djelfa 17000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1741-9209","authenticated-orcid":false,"given":"Bakria","family":"Derradji","sequence":"additional","affiliation":[{"name":"Applied Automation and Industrial Diagnostics Laboratory LAADI, Ziane Achour University of Djelfa, P.O. Box 3117, Djelfa 17000, Algeria"},{"name":"LASER Lab, Department of Electrical Engineering, Ziane Achour University of Djelfa, P.O. Box 3117, Djelfa 17000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8631-8172","authenticated-orcid":false,"given":"Ibrahim Farouk","family":"Bouguenna","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, University of Mascara, Mascara 29000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8253-4863","authenticated-orcid":false,"given":"Habib","family":"Benbouhenni","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Technology, Hassiba Benbouali University of Chlef, B.P 78C Ouled Fares, Chlef 02180, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6555-5785","authenticated-orcid":false,"given":"Riyadh","family":"Bouddou","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Technology, University of Naama, Naama 45000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8461-8702","authenticated-orcid":false,"given":"Y\u0131ld\u0131r\u0131m","family":"\u00d6z\u00fcpak","sequence":"additional","affiliation":[{"name":"Department of Electrical Energy, Silvan Vocational School, Dicle University, Diyarbak\u0131r 21280, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-1549-4334","authenticated-orcid":false,"given":"Nasreddine","family":"Bouchikhi","sequence":"additional","affiliation":[{"name":"Mechatronics Laboratory (LMETR), Department of Electrical Engineering, University of Setif, Setif 19000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3218-9218","authenticated-orcid":false,"given":"Alin-Gheorghita","family":"Mazare","sequence":"additional","affiliation":[{"name":"Pite\u0219ti University Centre, The National University of Science and Technology POLITEHNICA Bucharest, 110040 Pitesti, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9311-7598","authenticated-orcid":false,"given":"Nicu","family":"Bizon","sequence":"additional","affiliation":[{"name":"Pite\u0219ti University Centre, The National University of Science and Technology POLITEHNICA Bucharest, 110040 Pitesti, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,17]]},"reference":[{"key":"ref_1","first-page":"721","article-title":"Investigation of Dynamic Behavior of Double Feed Induction Generator and Permanent Magnet Synchronous Generator Wind Turbines in Failure Conditions","volume":"11","author":"Cakir","year":"2021","journal-title":"Int. J. Renew. Energy Res."},{"key":"ref_2","first-page":"197","article-title":"Modeling of a Permanent Magnet Synchronous Generator in a Power Wind Generation System with an Electrochemical Energy Storage","volume":"2","author":"Abdelhakim","year":"2018","journal-title":"Int. J. Smart Grid"},{"key":"ref_3","first-page":"139","article-title":"Assessing Wind Energy Conversion Systems Based on Newly Developed Wind Turbine Emulator","volume":"4","author":"Eldahshan","year":"2020","journal-title":"Int. J. Smart Grid"},{"key":"ref_4","first-page":"88","article-title":"A New Robust Control Strategy for a Wind Energy Conversion System Based on a T-S Fuzzy Model","volume":"4","author":"Sahbi","year":"2020","journal-title":"Int. J. Smart Grid"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Torres-Romero, L.A., Ruiz-Cruz, R., and Gonz\u00e1lez-Jim\u00e9nez, L.E. (2024). Path-Following Sliding Mode Controller for an Electric Vehicle Considering Actuator Dynamics. Machines, 12.","DOI":"10.3390\/machines12040219"},{"key":"ref_6","first-page":"149","article-title":"A Novel Solution to Eliminate Frequency Intermittency by Adding Spinning Reserve to the Micro-Hydro Turbine Generator Using Real-Time Control of Induction Motor through AC\u2013DC\u2013AC Power Converters","volume":"4","author":"Muhammad","year":"2020","journal-title":"Int. J. Smart Grid"},{"key":"ref_7","first-page":"120","article-title":"A Novel Fuzzy Control Strategy for Maximum Power Point Tracking of Wind Energy Conversion System","volume":"3","author":"Moez","year":"2019","journal-title":"Int. J. Smart Grid"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Krichi, M., Noman, A.M., Fannakh, M., Raffak, T., and Haidar, Z.A. (2025). Sustainable Electric Micromobility through Integrated Power Electronic Systems and Control Strategies. Energies, 18.","DOI":"10.3390\/en18082143"},{"key":"ref_9","first-page":"21","article-title":"Effect of Rotor Speed on the Thermal Model of AFIR Permanent Magnet Synchronous Motor","volume":"7","author":"Wahsh","year":"2017","journal-title":"Int. J. Renew. Energy Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1007\/s42835-020-00398-6","article-title":"A Review of State-of-the-Art Techniques for PMSM Parameter Identification","volume":"15","author":"Ahn","year":"2020","journal-title":"J. Electr. Eng. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"21450","DOI":"10.1038\/s41598-025-07282-1","article-title":"PMSM Integral Sliding Mode Control Based on Improved Power Exponential Reaching Law","volume":"15","author":"Shang","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"115699","DOI":"10.1109\/ACCESS.2023.3324419","article-title":"Critical Review on Torque Ripple Sources and Mitigation Control Strategies of BLDC Motors in Electric Vehicle Applications","volume":"11","author":"Prabhu","year":"2023","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Elele, M.J.M., Pau, D., Zhuang, S., and Facchinetti, T. (2025). Compensating PI Controller\u2019s Transients with Tiny Neural Network for Vector Control of Permanent Magnet Synchronous Motors. World Electr. Veh. J., 16.","DOI":"10.3390\/wevj16040236"},{"key":"ref_14","first-page":"183","article-title":"Neural Network Based Field Oriented Control for Doubly-Fed Induction Generator","volume":"2","author":"Samir","year":"2018","journal-title":"Int. J. Smart Grid"},{"key":"ref_15","first-page":"384","article-title":"Backstepping Control of Dual Stator Induction Generator Used in Wind Energy Conversion System","volume":"8","author":"Meryem","year":"2018","journal-title":"Int. J. Renew. Energy Res."},{"key":"ref_16","first-page":"1480","article-title":"Grid Connected Photovoltaic Energy Conversion System Modeling and Control Using SMC-BSC Approach","volume":"9","author":"Mohamed","year":"2019","journal-title":"Int. J. Renew. Energy Res."},{"key":"ref_17","first-page":"188","article-title":"Comparative Study Between Direct Vector Control and Fuzzy Sliding Mode Controller in Three-Level Space Vector Modulation Inverter of Reactive and Active Power Command of DFIG-Based Wind Turbine Systems","volume":"2","author":"Habib","year":"2018","journal-title":"Int. J. Smart Grid"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5636","DOI":"10.1038\/s41598-025-89636-3","article-title":"Solving the Problem of Power Ripples for a Multi-Rotor Wind Turbine System Using Fractional-Order Third-Order Sliding Mode Algorithms","volume":"15","author":"Benbouhenni","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Habib, B., and Bizon, N. (2021). Third-Order Sliding Mode Applied to the Direct Field-Oriented Control of the Asynchronous Generator for Variable-Speed Contra-Rotating Wind Turbine Generation Systems. Energies, 14.","DOI":"10.3390\/en14185877"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Chen, J., Zhu, H., Shu, T., Cao, C., and Deng, Y. (2026). Improved Grey Wolf Optimizer and Backpropagation Neural Network for Fractional-Order Control of PMSM. Appl. Sci., 16.","DOI":"10.3390\/app16031516"},{"key":"ref_21","first-page":"21","article-title":"Development of Hybrid Compensators for Enhancing Power Quality in Electrical Distribution Systems Using Innovative Optimization Techniques","volume":"9","author":"Vijaykumar","year":"2025","journal-title":"Int. J. Smart Grid"},{"key":"ref_22","first-page":"926","article-title":"Maximum Power Point Tracking of Wind Energy Conversion System Using Multi-Objective Grey Wolf Optimization of Fuzzy-Sliding Mode Controller","volume":"7","author":"Sami","year":"2017","journal-title":"Int. J. Renew. Energy Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1092","DOI":"10.1007\/s42235-023-00469-0","article-title":"An Improved Golden Jackal Optimization Algorithm Based on Multi-Strategy Mixing for Solving Engineering Optimization Problems","volume":"21","author":"Wang","year":"2024","journal-title":"J. Bionic Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"22189","DOI":"10.1038\/s41598-024-73473-x","article-title":"Hybrid Golden Jackal and Golden Sine Optimizer for Tuning PID Controllers","volume":"14","author":"Mou","year":"2024","journal-title":"Sci. Rep."},{"key":"ref_25","first-page":"1346","article-title":"Fuzzy Logic Controller Based Performance of SPMSM Fed with Improved Direct Torque Control","volume":"9","author":"Danduprolu","year":"2019","journal-title":"Int. J. Renew. Energy Res."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Wang, X., Liu, Z., Zhou, P., Jia, B., Li, R., and Xu, Y. (2025). A Saturation Adaptive Nonlinear Integral Sliding Mode Controller for Ship Permanent Magnet Propulsion Motors. J. Mar. Sci. Eng., 13.","DOI":"10.3390\/jmse13050976"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3558","DOI":"10.1002\/cta.3929","article-title":"Speed\u2013Current Single-Loop Control of PMSM Based on Model-Assisted Cascaded Extended State Observer and Sliding Mode Control","volume":"52","author":"Wang","year":"2024","journal-title":"Int. J. Circuit Theory Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"7922","DOI":"10.48084\/etasr.4585","article-title":"Chaos Control and Stabilization of a PID Controlled Buck Converter Using the Spotted Hyena Optimizer","volume":"11","author":"Bakria","year":"2021","journal-title":"Eng. Technol. Appl. Sci. Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"102416","DOI":"10.1016\/j.rineng.2024.102416","article-title":"Improved Robust Model Predictive Control for PMSM Using Backstepping Control and Incorporating Integral Action with Experimental Validation","volume":"23","author":"Djouadi","year":"2024","journal-title":"Results Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"356","DOI":"10.3311\/PPee.37217","article-title":"Robust Intelligent Nonlinear Predictive Control Based on Artificial Neural Network for Optimizing PMSM Drive Performance","volume":"68","author":"Kasri","year":"2024","journal-title":"Period. Polytech. Electr. Eng. Comput. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Bouguenna, I.F., Tahour, A., Kennel, R., and Abdelrahem, M. (2021). Multiple-Vector Model Predictive Control with Fuzzy Logic for PMSM Electric Drive Systems. Energies, 14.","DOI":"10.3390\/en14061727"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2735","DOI":"10.1002\/cta.4249","article-title":"Enhanced Active Disturbance Rejection Speed Controller for Permanent Magnet Synchronous Motors Using Virtual Friction Feedback Technique","volume":"53","author":"Dong","year":"2025","journal-title":"Int. J. Circuit Theory Appl."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Kant, S., Sreejeth, M., Singh, M., Devanshu, A., Alotaibi, M.A., Malik, H., and M\u00e1rquez, F.P.G. (2025). Development of Intelligent Hybrid Controller for Torque Ripple Minimization in Electric Drive System with Adaptive Flux Estimator: An Experimental Case Study. PLoS ONE, 20.","DOI":"10.1371\/journal.pone.0312946"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"22","DOI":"10.37394\/232017.2025.16.3","article-title":"Sliding Mode Predictive Control Using Model Reference Adaptive System of Permanent Magnet Synchronous Motor","volume":"16","author":"Bouguenna","year":"2025","journal-title":"WSEAS Trans. Electron."},{"key":"ref_35","first-page":"71","article-title":"Advanced Dual-Loop Control Architecture for Superior PMSM Performance Utilizing Finite-Control-Set Model Predictive Control and Exponential Reaching Law Sliding Mode Control","volume":"10","author":"Karboua","year":"2024","journal-title":"J. Eng. Technol. Ind. Appl."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Tuyen, T.T., Yang, J., Liao, L., and Zhou, J. (2025). Integrated Sliding Mode Control for Permanent Magnet Synchronous Motor Drives Based on Second-Order Disturbance Observer and Low-Pass Filter. Electronics, 14.","DOI":"10.3390\/electronics14071466"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"7","DOI":"10.51485\/ajss.v10i1.222","article-title":"Application of Third-Order SMC Technique to Improve the Performance of Backstepping Control of Induction Motors Using Modified SVM Techniques","volume":"10","author":"Zellouma","year":"2025","journal-title":"Alger. J. Signals Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"10","DOI":"10.3311\/PPee.20333","article-title":"Backstepping Control Based on a Third-Order Sliding Mode Controller to Regulate the Torque and Flux of Asynchronous Motor Drive","volume":"67","author":"Zellouma","year":"2023","journal-title":"Period. Polytech. Electr. Eng. Comput. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"186740","DOI":"10.1109\/ACCESS.2020.3028845","article-title":"Integral Super-Twisting Sliding Mode Based Sensorless Predictive Torque Control of Induction Motor","volume":"8","author":"Sami","year":"2020","journal-title":"IEEE Access"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Karboua, D., Mebkhouta, T., Benkaihoul, S., and Chouiha, Y. (2025). Model Reference Adaptive System and Pseudo-Sliding Mode Control with Exponential Reaching Law for Sensorless-Speed Control of PMSM. PLoS ONE, 20.","DOI":"10.1371\/journal.pone.0321985"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Kong, L., Zhang, H., Zhang, T., Wang, J., Yang, C., and Zhang, Z. (2024). Adaptive Control Parameter Optimization of Permanent Magnet Synchronous Motors Based on Super-Helical Sliding Mode Control. Appl. Sci., 14.","DOI":"10.3390\/app142310967"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Bian, F. (2025). PMSM Speed Control Based on Improved Adaptive Fractional-Order Sliding Mode Control. Symmetry, 17.","DOI":"10.3390\/sym17050736"},{"key":"ref_43","first-page":"1","article-title":"Improving the Response of Permanent Magnet Synchronous Motors to Disturbances Using PSO Techniques","volume":"12","author":"Alfadli","year":"2025","journal-title":"Int. J. Eng. Technol. Manag. Res."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"e32669","DOI":"10.1016\/j.heliyon.2024.e32669","article-title":"Optimal Third-Order Sliding Mode Controller for Dual Star Induction Motor Based on Grey Wolf Optimization Algorithm","volume":"10","author":"Terfia","year":"2024","journal-title":"Heliyon"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"103916","DOI":"10.1016\/j.rineng.2025.103916","article-title":"IbI Logics Optimization Algorithm-Based High-Order Sliding Mode Control for DSIG within a Wind Turbine System","volume":"25","author":"Benzaoui","year":"2025","journal-title":"Results Eng."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Jegha, A.D.G., Subathra, M.S.P., Kumar, N.M., Subramaniam, U., and Padmanaban, S. (2020). A High Gain DC\u2013DC Converter with Grey Wolf Optimizer Based MPPT Algorithm for PV Fed BLDC Motor Drive. Appl. Sci., 10.","DOI":"10.3390\/app10082797"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"3329","DOI":"10.1049\/rpg2.13138","article-title":"Improving Maximum Power Point Tracking Efficiency in Solar Photovoltaic Systems Using Super-Twisting Algorithm and Grey Wolf Optimizer","volume":"18","author":"Deghfel","year":"2024","journal-title":"IET Renew. Power Gener."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"7844084","DOI":"10.1155\/2024\/7844084","article-title":"Optimal Adaptive Fractional Order Integral Sliding Mode Controller-Energy Management Strategy for Electric Vehicles Based on Bald Eagle Search Algorithm","volume":"2024","author":"Ghadbane","year":"2024","journal-title":"Int. J. Energy Res."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Ghadbane, H.E., and Mohamed, A.F. (2025). Optimizing Fuel Economy in Hybrid Electric Vehicles Using the Equivalent Consumption Minimization Strategy Based on the Arithmetic Optimization Algorithm. Mathematics, 13.","DOI":"10.3390\/math13091504"},{"key":"ref_50","first-page":"662","article-title":"A Stand-Alone PV-PEMFC System Based SM-ANN-MPPT Controller: Solar Pumping Application Using PMSM","volume":"11","author":"Badreddine","year":"2021","journal-title":"Int. J. Renew. Energy Res."},{"key":"ref_51","first-page":"691","article-title":"Minimizing Cogging Torque in Permanent Magnet Synchronous Generators for Small Wind Turbine Applications","volume":"11","author":"Ercan","year":"2021","journal-title":"Int. J. Renew. Energy Res."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"33","DOI":"10.2516\/stet\/2025010","article-title":"Online Intelligent Parameter and Speed Estimation of Permanent Magnet Synchronous Motors Using Bacterial Foraging Optimization","volume":"80","author":"Alrashed","year":"2025","journal-title":"Sci. Technol. Energy Transit."},{"key":"ref_53","first-page":"157","article-title":"Direct Reactive and Active Power Regulation of DFIG Using an Intelligent Modified Sliding-Mode Control Approach","volume":"6","author":"Habib","year":"2022","journal-title":"Int. J. Smart Grid"},{"key":"ref_54","first-page":"9","article-title":"Power Quality Improvement Based on Five-Level Shunt APF Using Sliding Mode Control Scheme Connected to a Photovoltaic System","volume":"1","author":"Yousfi","year":"2017","journal-title":"Int. J. Smart Grid"},{"key":"ref_55","first-page":"209","article-title":"Neuro-Second Order Sliding Mode Field Oriented Command for DFIG-Based Wind Turbine","volume":"2","author":"Benbouhenni","year":"2020","journal-title":"Int. J. Smart Grid"},{"key":"ref_56","first-page":"1977","article-title":"A Comparative Study of Different Sliding Mode Control Strategies for PMSG-Based Standalone WECS","volume":"11","author":"Hoa","year":"2021","journal-title":"Int. J. Renew. Energy Res."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Habib, B., and Bizon, N. (2021). Improved Rotor Flux and Torque Control Based on the Third-Order Sliding Mode Scheme Applied to the Asynchronous Generator for the Single-Rotor Wind Turbine. Mathematics, 9.","DOI":"10.3390\/math9182297"},{"key":"ref_58","first-page":"517","article-title":"Amelioration Effectiveness of Torque and Rotor Flux Control Applied to the Asynchronous Generator for Dual-Rotor Wind Turbine Using Neural Third-Order Sliding Mode Approaches","volume":"35","author":"Benbouhenni","year":"2022","journal-title":"Int. J. Eng. Trans. C Asp."},{"key":"ref_59","first-page":"197","article-title":"Artificial Neural Network-Based Deadbeat Predictive Current Control with Dead-Time Compensation for PMSMs","volume":"11","author":"Slimani","year":"2025","journal-title":"J. Eng. Technol. Ind. Appl."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"165","DOI":"10.2478\/pead-2023-0012","article-title":"Chaos Elimination for a Buck Converter Using the Multi-Objective Grey Wolf Optimiser","volume":"8","author":"Bakria","year":"2023","journal-title":"Power Electron. Drives"},{"key":"ref_61","first-page":"181","article-title":"Hybrid Algorithm of PSO and GWO Based PITIDF Controller for Load Frequency Control of Two-Area Power System","volume":"15","author":"Abdessamade","year":"2025","journal-title":"Int. J. Renew. Energy Res."},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Manoharan, P., Ravichandran, S., Kumar, J.S.V.S., Abdullah, M., Sin, T.C., and Hashim, T.J.T. (2025). Electrical Equivalent Circuit Parameter Estimation of Commercial Induction Machines Using an Enhanced Grey Wolf Optimization Algorithm. Biomimetics, 10.","DOI":"10.3390\/biomimetics10040228"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"15869","DOI":"10.1038\/s41598-025-00204-1","article-title":"An Optimized Shunt Active Power Filter Using the Golden Jackal Optimizer for Power Quality Improvement","volume":"15","author":"Bakria","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1002\/acs.3985","article-title":"Classification of Inter-Turn Insulation Faults in Three-Phase Induction Motors and Optimum Detection Using GJO-GBDT Method","volume":"39","author":"Williams","year":"2025","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1007\/s10586-024-04987-2","article-title":"Diversity-Enhanced Adaptive Golden Jackal Optimization Based on Multi-Strategy and Its Engineering Applications","volume":"28","author":"Wang","year":"2025","journal-title":"Clust. Comput."},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Zeghlache, A., Djerioui, A., Mekki, H., Zeghlache, S., and Benkhoris, M.F. (2025). Robust Sensorless PMSM Control with Improved Back-EMF Observer and Adaptive Parameter Estimation. Electronics, 14.","DOI":"10.3390\/electronics14071238"},{"key":"ref_67","first-page":"117","article-title":"Active Disturbance Rejection Control Based Sensorless Model Predictive Control for PMSM","volume":"57","author":"Dahnoun","year":"2024","journal-title":"J. Eur. Syst. Autom."},{"key":"ref_68","first-page":"261","article-title":"FEM Study of a Synchronous Motor with Different Permanent Magnet Topologies","volume":"85","author":"Craiu","year":"2023","journal-title":"UPB Sci. Bull. Ser. C Electr. Eng. Comput. Sci."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/6\/486\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T10:29:11Z","timestamp":1781692151000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/6\/486"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,17]]},"references-count":68,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["a19060486"],"URL":"https:\/\/doi.org\/10.3390\/a19060486","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,17]]}}}