{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T05:15:36Z","timestamp":1765343736952,"version":"3.46.0"},"reference-count":18,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,12,5]],"date-time":"2025-12-05T00:00:00Z","timestamp":1764892800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>This paper presents a physically constrained grey-box identification framework for electromechanical systems, illustrated through the dynamics of brushed DC motors. The method estimates all electromechanical parameters by minimizing a normalized residual that combines current, velocity, and steady-state algebraic constraints under a current-limit condition. Classical approaches such as least-squares and black-box identification often lack physical interpretability and do not explicitly enforce steady-state consistency, making their estimates susceptible to nonphysical parameter drift. The proposed formulation incorporates these physical constraints within a Levenberg\u2013Marquardt scheme with signal normalization, enabling the joint minimization of current and velocity errors. Validation was performed using step-response data from two DC motors under both synthetic and experimental conditions. When applied to unfiltered measurements, the method maintained steady-state relative errors below 1% and achieved low trajectory discrepancies, with NRMSE in velocity between 2.6 and 3.2% and NRMSE in current between 0.9 and 1.2% across both motors. Embedding physical and steady-state constraints directly into the cost function improves robustness and ensures physically consistent parameter estimates, even under high measurement noise and without filtering. The approach provides a general strategy for dynamic system identification under physical consistency requirements and is suitable for rapid calibration, diagnostic monitoring, and controller tuning in robotic and mechatronic applications.<\/jats:p>","DOI":"10.3390\/info16121079","type":"journal-article","created":{"date-parts":[[2025,12,5]],"date-time":"2025-12-05T13:17:07Z","timestamp":1764940627000},"page":"1079","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Constrained Gray-Box Identification of Electromechanical Systems Under Unfiltered Step-Response Data"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9476-4129","authenticated-orcid":false,"given":"Carlos","family":"Fuentes-Silva","sequence":"first","affiliation":[{"name":"Engineering Division, Technological University of Corregidora, Corregidora 76924, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8650-1185","authenticated-orcid":false,"given":"Omar","family":"Rodr\u00edguez-Abreo","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Aut\u00f3noma de Quer\u00e9taro, Santiago de Quer\u00e9taro 76010, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3267-8268","authenticated-orcid":false,"given":"Jes\u00fas Manuel","family":"Lugo-Quintal","sequence":"additional","affiliation":[{"name":"Tecnol\u00f3gico Nacional de M\u00e9xico, Instituto Tecnol\u00f3gico Superior Progreso, Progreso 97320, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0956-5994","authenticated-orcid":false,"given":"Alejandro","family":"Castillo-Atoche","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Aut\u00f3noma de Yucat\u00e1n, M\u00e9rida 97000, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5995-9510","authenticated-orcid":false,"given":"Mario A.","family":"Quiroz-Ju\u00e1rez","sequence":"additional","affiliation":[{"name":"Centro de F\u00edsica Aplicada y Tecnolog\u00eda Avanzada, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Boulevard Juriquilla 3001, Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2581-1921","authenticated-orcid":false,"given":"Enrique","family":"Camacho-P\u00e9rez","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Aut\u00f3noma de Yucat\u00e1n, M\u00e9rida 97000, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2430","DOI":"10.1017\/S0263574724000833","article-title":"Electro-mechanical Modeling and Identification of the UR5 e-series Robot","volume":"42","author":"Clochiatti","year":"2024","journal-title":"Robotica"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"G\u00f6k\u00e7e, C.O., \u0130pek, M.E., Day\u0131o\u011flu, M., and \u00dcnal, R. (2025). Parameter estimation and speed control of real DC motor with low resolution encoder. Results Control Optim., 19.","DOI":"10.1016\/j.rico.2025.100549"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Fazdi, M.F., and Hsueh, P.W. (2023). Parameters Identification of a Permanent Magnet DC Motor: A Review. Electronics, 12.","DOI":"10.3390\/electronics12122559"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Traversaro, S., Del Prete, A., Muradore, R., Natale, L., and Nori, F. (2013, January 15\u201317). Inertial parameter identification including friction and motor dynamics. Proceedings of the 2013 13th IEEE-RAS International Conference on Humanoid Robots (Humanoids), Atlanta, GA, USA.","DOI":"10.1109\/HUMANOIDS.2013.7029957"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wu, W. (2012). DC Motor Parameter Identification Using Speed Step Responses. Model. Simul. Eng., 2012.","DOI":"10.1155\/2012\/189757"},{"key":"ref_6","first-page":"14","article-title":"Identificaci\u00f3n de par\u00e1metros din\u00e1micos de motores de corriente directa usando el m\u00e9todo de Steiglitz\u2013McBride","volume":"8","author":"Cruz","year":"2019","journal-title":"Mecatr\u00f3nica M\u00e9x."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Siddiqi, F.U.R., Ahmad, S., Akram, T., Ali, M.U., Zafar, A., and Lee, S.W. (2024). Artificial Neural Network-Based Data-Driven Parameter Estimation Approach: Applications in PMDC Motors. Mathematics, 12.","DOI":"10.3390\/math12213407"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Kim, P.S., Kim, S.M., and Kim, S.Y. (2024, January 19\u201322). Model Parameter Identification for DC Motor Using Rapid Control Prototyping System. Proceedings of the 2024 International Conference on Artificial Intelligence in Information and Communication (ICAIIC), Osaka, Japan.","DOI":"10.1109\/ICAIIC60209.2024.10463479"},{"key":"ref_9","first-page":"1301","article-title":"Review and Comparative Analysis of System Identification Methods for Perturbed Motorized Systems","volume":"143","author":"Wee","year":"2025","journal-title":"Comput. Model. Eng. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Jimenez-Gonzalez, J., Gonzalez-Monta\u00f1ez, F., Jimenez-Mondragon, V.M., Liceaga-Castro, J.U., Escarela-Perez, R., and Olivares-Galvan, J.C. (2021). Parameter Identification of BLDC Motor Using Electromechanical Tests and Recursive Least-Squares Algorithm: Experimental Validation. Actuators, 10.","DOI":"10.3390\/act10070143"},{"key":"ref_11","first-page":"130","article-title":"System identification of servo drive using simulation-based parameter estimation","volume":"113","author":"Chakraborty","year":"2021","journal-title":"ISA Trans."},{"key":"ref_12","first-page":"99","article-title":"Parameter Identification of a Separately Excited DC Motor via Inverse Problem Methodology","volume":"17","author":"Hadef","year":"2009","journal-title":"Turk. J. Electr. Eng. Comput. Sci."},{"key":"ref_13","first-page":"401","article-title":"Different identification methods with application to a DC motor","volume":"56","author":"Hassan","year":"2007","journal-title":"J. Eng. Appl. Sci."},{"key":"ref_14","unstructured":"Hamza, B., El Mehdi, A.S.A., Houcine, C., and Mouloud, D. (2021, January 9\u201310). A New Method for the Parametric Identification of DC Machines Using MATLAB Identification Toolbox and Experimental Measurements. Proceedings of the International Conference on Energy and Green Computing (ICEGC 2021), Meknes, Morocco."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Munci\u00f1o, D.M., Damian-Ram\u00edrez, E.A., Cruz-Fern\u00e1ndez, M., Montoya-Santiyanes, L.A., and Rodr\u00edguez-Res\u00e9ndiz, J. (2024). Metaheuristic and Heuristic Algorithms-Based Identification Parameters of a Direct Current Motor. Algorithms, 17.","DOI":"10.3390\/a17050209"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Jesenik, M., Ravber, M., and Trbu\u0161i\u0107, M. (2024). Innovative Approach for the Determination of a DC Motor\u2019s and Drive\u2019s Parameters Using Evolutionary Methods and Different Measured Current and Angular Speed Responses. Mathematics, 12.","DOI":"10.3390\/math12010042"},{"key":"ref_17","first-page":"1101","article-title":"Practical Parameter Identification of DC Motor Using Rapid Control Prototyping System","volume":"15","author":"Demirtas","year":"2020","journal-title":"J. Electr. Eng. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Ar\u00e9valo, E., Herrera Hern\u00e1ndez, R., Katselis, D., Reusser, C., and Carvajal, R. (2025). On Modelling and State Estimation of DC Motors. Actuators, 14.","DOI":"10.3390\/act14040160"}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/12\/1079\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T05:13:13Z","timestamp":1765343593000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/12\/1079"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,5]]},"references-count":18,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["info16121079"],"URL":"https:\/\/doi.org\/10.3390\/info16121079","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2025,12,5]]}}}