{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T14:59:21Z","timestamp":1776956361393,"version":"3.51.4"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T00:00:00Z","timestamp":1631059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["F2019501012"],"award-info":[{"award-number":["F2019501012"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The coupling between variables in the multi-input multi-output (MIMO) systems brings difficulties to the design of the controller. Aiming at this problem, this paper combines the particle swarm optimization (PSO) with the coefficient diagram method (CDM) and proposes a robust controller design strategy for the MIMO systems. The decoupling problem is transformed into a compensator parameter optimization problem, and PSO optimizes the compensator parameters to reduce the coupling effect in the MIMO systems. For the MIMO system with measurement noise, the effectiveness of CDM in processing measurement noise is analyzed. This paper gives the control design steps of the MIMO systems. Finally, simulation experiments of four typical MIMO systems demonstrate the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/e23091180","type":"journal-article","created":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T10:12:03Z","timestamp":1631095923000},"page":"1180","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Robust Controller Design for Multi-Input Multi-Output Systems Using Coefficient Diagram Method"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5594-6798","authenticated-orcid":false,"given":"Kai","family":"Liu","sequence":"first","affiliation":[{"name":"College of Department of Control Science and Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6852-7173","authenticated-orcid":false,"given":"Fanwei","family":"Meng","sequence":"additional","affiliation":[{"name":"College of Department of Control Science and Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengya","family":"Meng","sequence":"additional","affiliation":[{"name":"College of Department of Control Science and Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7530-5659","authenticated-orcid":false,"given":"Chonghui","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Department of Control Science and Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1109\/TSMC.2016.2608799","article-title":"Improved results on asymptotic stabilization for stochastic nonlinear time-delay systems with application to a chemical reactor system","volume":"47","author":"Liu","year":"2016","journal-title":"IEEE Trans. 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