{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T01:28:41Z","timestamp":1783042121609,"version":"3.54.6"},"reference-count":25,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T00:00:00Z","timestamp":1750982400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"CIDESI","award":["2001MD1001"],"award-info":[{"award-number":["2001MD1001"]}]},{"name":"SECIHTI","award":["2001MD1001"],"award-info":[{"award-number":["2001MD1001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This study proposes an enhanced derivative control strategy, named PI-D\u00c6, designed to overcome key limitations of the derivative (D) term, such as noise amplification, derivative kick (D-k), and tuning difficulties. These issues often arise in high-frequency or rapidly changing systems, in which traditional PID controllers struggle. The proposed solution introduces a novel adaptive exponent algorithm (\u00c6) that dynamically modulates the D term based on the evolving relationship between system output and setpoint. This yields the PI-D\u00c6 controller, which adapts in real time to changing conditions. The results show significant performance improvements. Simulation results on two systems demonstrate that PI-D\u00c6 achieves a 90% faster response time, a 35% reduction in peak time, and a 100% improvement in settling time compared with conventional PID controllers, all while maintaining a near-zero steady-state error even under external disturbances. Unlike more-complex alternatives such as fuzzy logic, neural networks, or sliding mode control, PI-D\u00c6 retains the simplicity and robustness of PID, avoiding high computational costs or intricate setups. This adaptive exponent strategy offers a practical and scalable enhancement to classical PID, improving performance and robustness without added complexity, and thus provides a promising control solution for real-world applications in which simplicity, adaptability, and reliability are essential.<\/jats:p>","DOI":"10.3390\/a18070391","type":"journal-article","created":{"date-parts":[[2025,6,30]],"date-time":"2025-06-30T12:10:31Z","timestamp":1751285431000},"page":"391","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["PI-D\u00c6: An Adaptive PID Controller Utilizing a New Adaptive Exponent (\u00c6) Algorithm to Solve Derivative Term Issues"],"prefix":"10.3390","volume":"18","author":[{"given":"Juan M.","family":"Barrera-Fern\u00e1ndez","sequence":"first","affiliation":[{"name":"Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-7464-0670","authenticated-orcid":false,"given":"Juan Pablo Manzo","family":"Hern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6638-448X","authenticated-orcid":false,"given":"Kevin Miramontes","family":"Escobedo","sequence":"additional","affiliation":[{"name":"Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9911-4328","authenticated-orcid":false,"given":"Alberto","family":"V\u00e1zquez-Cervantes","sequence":"additional","affiliation":[{"name":"Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4745-0175","authenticated-orcid":false,"given":"Julio-C\u00e9sar","family":"Solano-Vargas","sequence":"additional","affiliation":[{"name":"Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,27]]},"reference":[{"key":"ref_1","unstructured":"Karl, J. 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