{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T18:17:30Z","timestamp":1775067450779,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,25]],"date-time":"2021-06-25T00:00:00Z","timestamp":1624579200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper presents an efficient coronavirus optimization algorithm (CVOA) to find the optimal values of the PID controller to track a preselected reference speed of a brushless DC (BLDC) motor under several types of disturbances. This work simulates how the coronavirus (COVID-19) spreads and infects healthy people. The initial values of PID controller parameters consider the zero patient, who infects new patients (other values of PID controller parameters). The model aims to simulate as accurately as possible the coronavirus activity. The CVOA has two major advantages compared to other similar strategies. First, the CVOA parameters are already adjusted according to disease statistics to prevent designers from initializing them with arbitrary values. Second, the approach has the ability to finish after several iterations where the infected population initially grows at an exponential rate. The proposed CVOA was investigated with well-known optimization techniques such as the genetic algorithm (GA) and Harmony Search (HS) optimization. A multi-objective function was used to allow the designer to select the desired rise time, the desired settling time, the desired overshoot, and the desired steady-state error. Several tests were performed to investigate the obtained proper values of PID controller parameters. In the first test, the BLDC motor was exposed to sudden load at a steady speed. In the second test, the continuous sinusoidal load was applied to the rotor of the BLDC motor. In the third test, different operating points of reference speed were selected to the rotor of the BLDC motor. The results proved that the CVOA-based PID controller has the best performance among the techniques. In the first test, the CVOA-based PID controller has a minimum rise time (0.0042 s), minimum settling time (0.0079 s), and acceptable overshoot (0.0511%). In the second test, the CVOA-based PID controller has the minimum deviation about the reference speed (\u00b14 RPM). In the third test, the CVOA-based PID controller can accurately track the reference speed among other techniques.<\/jats:p>","DOI":"10.3390\/a14070193","type":"journal-article","created":{"date-parts":[[2021,6,27]],"date-time":"2021-06-27T22:24:57Z","timestamp":1624832697000},"page":"193","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Optimal Coronavirus Optimization Algorithm Based PID Controller for High Performance Brushless DC Motor"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3993-2265","authenticated-orcid":false,"given":"Mohamed A.","family":"Shamseldin","sequence":"first","affiliation":[{"name":"Mechanical Department, Faculty of Engineering, Future University in Egypt, Cairo Governorate 11835, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,25]]},"reference":[{"key":"ref_1","first-page":"113","article-title":"Modeling of brushless dc drive using genetic algorithm based tuning of pid con-troller","volume":"4","author":"Kumar","year":"2014","journal-title":"IJEEER"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1177\/1687814017737724","article-title":"Design and implementation of double-integral sliding-mode controller for brushless direct current motor speed control","volume":"9","author":"Chen","year":"2017","journal-title":"Adv. Mech. Eng."},{"key":"ref_3","first-page":"125","article-title":"Tuning of PID Controller for A Linear Brushless DC Motor using Swarm Intelligence Technique Pooja Sharma, Rajeev Gupta","volume":"4","author":"Kota","year":"2014","journal-title":"J. Eng. Res. Appl."},{"key":"ref_4","first-page":"13","article-title":"Optimal PID control of a brushless DC motor using PSOtechnique","volume":"10","author":"Navatakke","year":"2015","journal-title":"IOSR J. Electr. Electron. Eng."},{"key":"ref_5","first-page":"431","article-title":"Comparative Study of Intelligent Controllers for Brushless. Dc Motor","volume":"63","author":"Selvakumar","year":"2014","journal-title":"J. Theor. Appl. Inf. Technol."},{"key":"ref_6","first-page":"55697187","article-title":"Performance Analysis of BLDC Motor Drive using New Simulation Model with Fuzzy and ANFIS Speed Controllers","volume":"14","author":"Reddy","year":"2014","journal-title":"Glob. J. Res. Eng. F Electr. Electron. Eng."},{"key":"ref_7","first-page":"2226","article-title":"Modeling and Analysis of PI Controller Based Speed Control of Brushless DC Motor Drive","volume":"2","author":"Reddy","year":"2013","journal-title":"IJESRT"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1016\/j.protcy.2013.12.296","article-title":"Testing Performance of 10 kW BLDC Motor and LiFePO4 Battery on ITB-1 Electric Car Prototype","volume":"11","author":"Purwadi","year":"2013","journal-title":"Procedia Technol."},{"key":"ref_9","unstructured":"Shamseldin, M., Eissa, M.A., and EL-Samahy, A. (2015, January 15\u201317). Practical Implementation of GA-Based PID Controller for Brushless DC Motor. Proceedings of the 17th International Middle East Power System Conference (MEPCON\u201915), Mansoura University, Mansoura, Egypt."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1431","DOI":"10.1002\/oca.2419","article-title":"Comparison of PID and FOPID controllers tuned by PSO and ABC algorithms for unstable and integrating systems with time delay","volume":"39","author":"Bingul","year":"2018","journal-title":"Optim. Control Appl. Methods"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Sun, C., Gong, G., Wang, F., Yang, H., and Ouyang, X. (2016, January 29\u201331). Single neuron adaptive PID control for hydro-viscous drive clutch. Proceedings of the 2016 12th IEEE\/ASME International Conference on Mechatronic and Embedded Systems and Applications (MESA), Auckland, New Zealand.","DOI":"10.1109\/MESA.2016.7587118"},{"key":"ref_12","first-page":"111","article-title":"LabVIEW implementation of an enhanced nonlinear PID controller based on harmony search for one-stage servomechanism system","volume":"10","author":"Shamseldin","year":"2020","journal-title":"J. Comput. Appl. Res. Mech. Eng."},{"key":"ref_13","first-page":"8","article-title":"A new model reference self-tuning fractional order PD control for one stage servomechanism system","volume":"14","author":"Shamseldin","year":"2019","journal-title":"WSEAS Trans. Syst. Control"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4161","DOI":"10.15282\/jmes.12.4.2018.13.0359","article-title":"Real-time implementation of an enhanced nonlinear PID controller based on harmony search for one-stage servomechanism system","volume":"12","author":"Shamseldin","year":"2018","journal-title":"J. Mech. Eng. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Pillai, B., and Nair, K.T. (2017, January 6\u20137). Intelligent adaptive controller for DC servo motor position control in LabVIEW. Proceedings of the 2017 International Conference on Intelligent Computing, Instrumentation and Control Technologies (ICICICT), Kannur, India.","DOI":"10.1109\/ICICICT1.2017.8342700"},{"key":"ref_16","first-page":"4","article-title":"Optimal Nonlinear PID Speed Control Based on Harmony Search for An Electric Vehicle Optimal Nonlinear PID Speed Control Based on Harmony Search for An Electric","volume":"2","author":"Shamseldin","year":"2021","journal-title":"Future Eng. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1109\/TCST.2017.2699166","article-title":"Nonlinear Adaptive Control of Hydraulic System With Observing and Compensating Mismatching Uncertainties","volume":"26","author":"Wang","year":"2017","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Dinc, A., and Otkur, M. (2020, January 14\u201317). Optimization of Electric Vehicle Battery Size and Reduction Ratio Using Genetic Algorithm. Proceedings of the 2020 11th International Conference on Mechanical and Aerospace Engineering (ICMAE), Athens, Greece.","DOI":"10.1109\/ICMAE50897.2020.9178899"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2020\/8857346","article-title":"Measuring and Preventing COVID-19 Using the SIR Model and Machine Learning in Smart Health Care","volume":"2020","author":"Alanazi","year":"2020","journal-title":"J. Healthc. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Kozio\u0142, K., Stanis\u0142awski, R., and Bialic, G. (2020). Fractional-Order SIR Epidemic Model for Transmission Prediction of COVID-19 Disease. Appl. Sci., 10.","DOI":"10.3390\/app10238316"},{"key":"ref_21","unstructured":"\u00c1guila-Le\u00f3n, J., Chi\u00f1as-Palacios, C.D., Vargas-Salgado, C., Hurtado-Perez, E., and Garc\u00eda, E.X. (2020, January 24\u201325). Optimal PID Pa-rameters Tunning for a DC-DC Boost Converter. Proceedings of the 2020 IEEE Conference on Technologies for Sustainability (SusTech) Optimal, Las Vegas, NV, USA."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Kumar, M., and Chaursiya, K. (2017, January 20\u201322). Position control of brushless DC motor using harmony search algorithm optimization technique. Proceedings of the 2017 International conference of Electronics, Communication and Aerospace Technology (ICECA), Coimbatore, India.","DOI":"10.1109\/ICECA.2017.8203644"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Mukhtar, A., Tayal, V.K., and Singh, H. (2019, January 10\u201311). PSO Optimized PID Controller Design for the Process Liquid Level Control. Proceedings of the 2019 3rd International Conference on Recent Developments in Control, Automation & Power Engineering (RDCAPE), Noida, India.","DOI":"10.1109\/RDCAPE47089.2019.8979108"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Bennaoui, A., Saadi, S., and Ameur, A. (2020, January 25\u201327). Performance Comparison of MFO and PSO for Optimal Tuning the fractional order fuzzy PID Controller for A DC-DC Boost Converter. Proceedings of the 2020 International Conference on Electrical Engineering (ICEE), Istanbul, Turkey.","DOI":"10.1109\/ICEE49691.2020.9249778"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5246","DOI":"10.1109\/TIE.2019.2931501","article-title":"Adaptive Threshold Correction Strategy for Sensorless High-Speed Brushless DC Drives Considering Zero-Crossing-Point Deviation","volume":"67","author":"Yang","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"7826","DOI":"10.1109\/TPEL.2018.2880916","article-title":"Design of Speed Control and Reduction of Torque Ripple Factor in BLdc Motor Using Spider Based Controller","volume":"34","author":"Maharajan","year":"2019","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Gaurav, A., and Gaur, A. (2020, January 10\u201311). Modelling of Hybrid Electric Vehicle Charger and Study the Simulation Results. Proceedings of the 2020 International Conference on Emerging Frontiers in Electrical and Electronic Technologies (ICEFEET), Aarhus, Denmark.","DOI":"10.1109\/ICEFEET49149.2020.9187007"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Shamseldin, M.A., El-Samahy, A.A., and Ghany, A. (2016, January 27\u201329). Different techniques of self-tuning FOPID control for Brushless DC Motor. Proceedings of the 2016 Eighteenth International Middle East Power Systems Conference (MEPCON), Cairo, Egypt.","DOI":"10.1109\/MEPCON.2016.7836913"},{"key":"ref_29","first-page":"184","article-title":"A PSO-Based Optimum Design of PID Controller for a Linear Brushless DC Motor","volume":"1","author":"Nasri","year":"2007","journal-title":"Int. J. Electr. Robot. Electron. Commun. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"88","DOI":"10.14445\/22315381\/IJETT-V17P219","article-title":"Genetic Tuned PID Controller Based Speed Control of DC Motor Drive","volume":"17","author":"Deraz","year":"2014","journal-title":"Int. J. Eng. Trends Technol."},{"key":"ref_31","first-page":"348","article-title":"Optimal Tuning of PID Controllers for Hydrothermal Load Frequency Control Using Ant Colony Optimization","volume":"5","author":"Omar","year":"2013","journal-title":"Int. J. Electr. Eng. Inform."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"12","DOI":"10.22161\/ijaers\/nctet.2017.eee.3","article-title":"Load Frequency Control of a Two-Area Power System Using FOPID with Harmony Search Algorithm","volume":"6495","author":"Kiran","year":"2017","journal-title":"Natl. Conf. Trends Eng. Technol."},{"key":"ref_33","first-page":"1","article-title":"Reduced Size Harmony Search Algorithm for Optimization","volume":"1","author":"Omar","year":"2016","journal-title":"J. Electr. Eng."},{"key":"ref_34","first-page":"255","article-title":"Tuning of PID Controller for Load Frequency Control Problem via Harmony Search Algorithm","volume":"1","author":"Omar","year":"2016","journal-title":"Indones. J. Electr. Eng. Comput. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Banu, U.S., and Lakshmanaprabu, S.K. (2015, January 10\u201311). Multivariable Centralized Fractional Order PID Controller tuned using Harmony search Algorithm for Two Interacting Conical Tank Process. Proceedings of the SAI Intelligent Systems Conference, London, UK.","DOI":"10.1109\/IntelliSys.2015.7361162"},{"key":"ref_36","first-page":"407","article-title":"Harmony Search based PID for Multi Area Load Frequency Control Including Boiler Dynamics and Nonlinearities","volume":"14","author":"Omar","year":"2015","journal-title":"WSEAS Trans. Circuits Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1089\/big.2020.0051","article-title":"Coronavirus Optimization Algorithm: A Bioinspired Metaheuristic Based on the COVID-19 Propagation Model","volume":"8","author":"Torres","year":"2020","journal-title":"Big Data"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/7\/193\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:24:30Z","timestamp":1760163870000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/7\/193"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,25]]},"references-count":37,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["a14070193"],"URL":"https:\/\/doi.org\/10.3390\/a14070193","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,25]]}}}