{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:26:30Z","timestamp":1767338790696,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,5,31]],"date-time":"2021-05-31T00:00:00Z","timestamp":1622419200000},"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>The PID (proportional\u2013integral\u2013derivative) controller is the most widely used control method in modern engineering control because it has the characteristics of a simple algorithm structure and easy implementation. The traditional PID controller, in the face of complex control objects, has been unable to meet the expected requirements. The emergence of the intelligent algorithm makes intelligent control widely usable. The Quasi-Affine Transformation Evolutionary (QUATRE) algorithm is a new evolutionary algorithm. Compared with other intelligent algorithms, the QUATRE algorithm has a strong global search ability. To improve the accuracy of the algorithm, the adaptive mechanism of online adjusting control parameters was introduced and the linear population reduction strategy was adopted to improve the performance of the algorithm. The standard QUATRE algorithm, particle swarm optimization algorithm and improved QUATRE algorithm were tested by the test function. The experimental results verify the advantages of the improved QUATRE algorithm. The improved QUATRE algorithm was combined with PID parameters, and the simulation results were compared with the PID parameter tuning method based on the particle swarm optimization algorithm and standard QUATRE algorithm. From the experimental results, the control effect of the improved QUATRE algorithm is more effective.<\/jats:p>","DOI":"10.3390\/a14060173","type":"journal-article","created":{"date-parts":[[2021,5,31]],"date-time":"2021-05-31T21:42:06Z","timestamp":1622497326000},"page":"173","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["A PID Parameter Tuning Method Based on the Improved QUATRE Algorithm"],"prefix":"10.3390","volume":"14","author":[{"given":"Zhuo-Qiang","family":"Zhao","sequence":"first","affiliation":[{"name":"Fujian Provincial Key Laboratory of Big Data Mining and Applications, Fujian University of Technology, Fuzhou 350118, China"}]},{"given":"Shi-Jian","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Artificial Intelligence, Fujian University of Technology, Fuzhou 350118, China"}]},{"given":"Jeng-Shyang","family":"Pan","sequence":"additional","affiliation":[{"name":"Fujian Provincial Key Laboratory of Big Data Mining and Applications, Fujian University of Technology, Fuzhou 350118, China"},{"name":"College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,31]]},"reference":[{"key":"ref_1","first-page":"257","article-title":"Multi-group Flower Pollination Algorithm Based on Novel Communication Strategies","volume":"22","author":"Pan","year":"2021","journal-title":"J. Internet Technol."},{"key":"ref_2","first-page":"154","article-title":"Optimizing ontology alignment through hybrid population-based incremental learning algorithm","volume":"11","author":"Xue","year":"2018","journal-title":"Memet. Comput."},{"key":"ref_3","first-page":"1693","article-title":"A Novel Solution for Simultaneously Finding the Shortest and Possible Paths in Complex Networks","volume":"20","author":"Hlaing","year":"2019","journal-title":"J. Internet Technol."},{"key":"ref_4","first-page":"53","article-title":"An Uneven Clustering Routing Protocol based on Improved K-means Algorithm for Wireless Sensor Network in Coal-mine","volume":"10","author":"Dong","year":"2019","journal-title":"J. Inf. Hiding Multimed. Signal Process."},{"key":"ref_5","first-page":"11","article-title":"An Optimal Node Coverage in Wireless Sensor Network Based on Whale Optimization Algorithm","volume":"2","author":"Nguyen","year":"2018","journal-title":"Data Sci. Pattern Recogn."},{"key":"ref_6","first-page":"120","article-title":"Research of The WSN Routing based on Artificial Bee Colony Algorithm","volume":"8","author":"Wu","year":"2017","journal-title":"J. Inf. Hiding Multimed. Signal Process."},{"key":"ref_7","first-page":"162","article-title":"An Optimizing Cross-Entropy Thresholding for Image Segmentation based on Improved Cockroach Colony Optimization","volume":"11","author":"Pan","year":"2020","journal-title":"J. Inf. Hiding Multimed. Signal Process."},{"key":"ref_8","first-page":"41","article-title":"A Multi-group Grasshopper Optimisation Algorithm for Application in Capacitated Vehicle Routing Problem","volume":"4","author":"Pan","year":"2020","journal-title":"Data Sci. Pattern Recogn."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s10115-017-1101-x","article-title":"A Compact Co-Evolutionary Algorithm for sensor ontology meta-matching","volume":"56","author":"Xue","year":"2017","journal-title":"Knowl. Inf. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/S1367-5788(01)00005-0","article-title":"The past of PID controller","volume":"25","author":"Stuart","year":"2001","journal-title":"Annu. Rev. Control"},{"key":"ref_11","first-page":"759","article-title":"Optimum Setting for Automatic Controllers","volume":"64","author":"Ziegler","year":"1942","journal-title":"Trans. ASME"},{"key":"ref_12","first-page":"827","article-title":"Theoretieal Consideration of Retarded Control","volume":"75","author":"Cohen","year":"1953","journal-title":"Trans. ASME"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1016\/0005-1098(84)90014-1","article-title":"Automatic Tuning of Simple Regulators with Specfications on Phase and Amplitude Margrins","volume":"20","author":"Astrom","year":"1984","journal-title":"Automatiea"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1021\/i200032a041","article-title":"Interal model control-4.PID controller design","volume":"25","author":"Rivera","year":"1986","journal-title":"Ind. Eng. Chem. Process. Des. Dev."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1049\/ip-d.1991.0015","article-title":"How Rfinements of the Ziegler-Nichols Tuning Formula","volume":"137","author":"Hang","year":"1991","journal-title":"IEEE Proc."},{"key":"ref_16","first-page":"303","article-title":"Derivation of Fuzzy Rules for Parameter Free PID Gain Tuning","volume":"27","author":"Baras","year":"1994","journal-title":"Adv. Control Chem. Process."},{"key":"ref_17","unstructured":"Zhu, M. (2021, April 01). Research on the Design of Fuzzy PID Controller. Available online: http:\/\/cdmd.cnki.com.cn\/Article\/CDMD-10056-2006053125.htm."},{"key":"ref_18","unstructured":"Wang, K.Q., Cao, J., Jiao, J., and Zhang, X.D. (2021, April 01). Self Tuning of PID Controller Parameters Based on Neural Network. Available online: https:\/\/www.cnki.com.cn\/Article\/CJFDTotal-DBLY199603015.htm."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/S0016-0032(96)00094-4","article-title":"A hybrid method for parameter tuning of PID controllers","volume":"334","author":"Wu","year":"1997","journal-title":"J. Frankl. Inst."},{"key":"ref_20","unstructured":"Li, W., and Zhao, Q. (2021, April 01). A Multivariable Fuzzy Self Tuning PID Controller Based on Neural Network. Available online: https:\/\/en.cnki.com.cn\/Article_en\/CJFDTotal-DLTD801.010.htm."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Shao, Y.Y. (2013, January 24). PID Parameters Tuning Based on a Self-Adaptive Immunity Ant Colony Algorithm. Proceedings of the 2013 3rd Interational Conference on Electric and Electronics (EEIC 2013), Hong Kong, China.","DOI":"10.2991\/eeic-13.2013.67"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"23","DOI":"10.4316\/AECE.2011.04004","article-title":"PID Neural Network Based Speed Control of Asynchronous Motor Using Programmable Logic Controller","volume":"11","author":"Maraba","year":"2001","journal-title":"Adv. Electr. Comput. Eng."},{"key":"ref_23","unstructured":"Zou, H.B., Chai, T., and Bao, G. (2021, April 01). Application of Improved BBO Algorithm in PID Parameter Tuning. Available online: https:\/\/www.cnki.com.cn\/Article\/CJFDTotal-ZHJC201912019.htm."},{"key":"ref_24","first-page":"92","article-title":"PID parameter tuning of hydro generator unit based on improved particle swarm optimization algorithm","volume":"19","author":"Wang","year":"2019","journal-title":"Sinotrans"},{"key":"ref_25","first-page":"90","article-title":"Application of multi-objective particle swarm optimization algorithm in PID optimization design","volume":"18","author":"Zhou","year":"2019","journal-title":"Wuhan Voc. Tech. Coll. Acta Sin. Sin."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.knosys.2016.06.029","article-title":"QUasi-Affine TRansformation Evolutionary (QUATRE) algorithm: A cooperative swarm based algorithm for global optimization","volume":"109","author":"Meng","year":"2016","journal-title":"Knowl. Based Syst."},{"key":"ref_27","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle Swarm Optimization\/Icnn95-international Conference on Neural Networks. Proceedings of the ICNN\u201995\u2014International Conference on Neural Networks, Perth, WA, Australia."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"105908","DOI":"10.1016\/j.knosys.2020.105908","article-title":"Enhancing QUasi-Affine TRansformation Evolution (QUATRE) with adaptation scheme on numerical optimization","volume":"197","author":"Meng","year":"2020","journal-title":"Knowl. Based Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/MCS.2006.1580152","article-title":"PID control system analysis and design","volume":"26","author":"Li","year":"2006","journal-title":"IEEE Control Syst. Mag."},{"key":"ref_30","unstructured":"Crowe, J., Chen, G.R., Ferdous, R., Greenwood, D.R., Grimble, M.J., Huang, H.P., Jeng, J.C., Johnson, M.A., Katebi, M.R., and Kwong, S. (2005). PID Control: New Identification and Design Methods, Springer."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/6\/173\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:09:33Z","timestamp":1760162973000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/6\/173"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,31]]},"references-count":30,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["a14060173"],"URL":"https:\/\/doi.org\/10.3390\/a14060173","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2021,5,31]]}}}