{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T13:48:37Z","timestamp":1762004917626,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,9,22]],"date-time":"2017-09-22T00:00:00Z","timestamp":1506038400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["61673199"],"award-info":[{"award-number":["61673199"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Program for Liaoning Excellent Talents in University","award":["LR2015034"],"award-info":[{"award-number":["LR2015034"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Multivariable coupling, nonlinear and large time delays exist in the coil outlet temperature (COT) control system of the ethylene cracking furnace, which make it hard to achieve accurate control over the COT of the furnace in actual production. To solve these problems, an inverse controller based on an interval type-2 fuzzy model control strategy is introduced. In this paper, the proposed control scheme is divided into two parts: one is the approach structure part of the interval type-2 fuzzy model (IT2-FM), which is utilized to approach the process output. The other is the interval type-2 fuzzy model inverse controller (IT2-FMIC) part, which is utilized to control the output process to achieve the target value. In addition, on the cyber-physical system platform, the actual industrial data are used to test and obtain the mathematical model of the COT control system of the ethylene cracking furnace. Finally, the proposed inverse controller based on the IT2-FM control scheme has been implemented on the COT control system of the ethylene cracking furnace, and the simulation results show that the proposed method is feasible.<\/jats:p>","DOI":"10.3390\/info8040116","type":"journal-article","created":{"date-parts":[[2017,9,22]],"date-time":"2017-09-22T11:03:15Z","timestamp":1506078195000},"page":"116","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Interval Type-2 Fuzzy Model Based on Inverse Controller Design for the Outlet Temperature Control System of Ethylene Cracking Furnace"],"prefix":"10.3390","volume":"8","author":[{"given":"Taoyan","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Automation, Northwestern Polytechnical University, Xi\u2019an 710129, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3216-6246","authenticated-orcid":false,"given":"Ping","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, Liaoning Shihua University, Fushun 113001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiangtao","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, Liaoning Shihua University, Fushun 113001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tian","family":"Li","sequence":"additional","affiliation":[{"name":"Sinopec Tianjin Natural Gas Pipe Company, Tianjin 300457, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,22]]},"reference":[{"key":"ref_1","first-page":"2216","article-title":"Development and application of advanced process control system for the ethylene cracking heaters","volume":"62","author":"Li","year":"2011","journal-title":"Chem. Ind. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1177\/0020294015571498","article-title":"Advanced Process Control of an Ethylene Cracking Furnace","volume":"48","author":"Li","year":"2015","journal-title":"Meas. Control"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1293","DOI":"10.1007\/s00500-013-1144-1","article-title":"A simple design method for interval type-2 fuzzy pid controllers","volume":"18","author":"Kumbasar","year":"2014","journal-title":"Soft. Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1016\/j.engappai.2011.04.016","article-title":"Interval type-2 fuzzy inverse controller design in nonlinear IMC structure","volume":"24","author":"Kumbasar","year":"2011","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2986","DOI":"10.1016\/j.compchemeng.2008.03.010","article-title":"Control of a Nonlinear Continous Bioreactor with Bifurcation by a Type-2 Fuzzy Logic Controller","volume":"32","author":"Galluzzo","year":"2008","journal-title":"Comput. Chem. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2158","DOI":"10.1016\/j.ins.2008.12.028","article-title":"Optimization of Interval Type-2 Fuzzy Logic Controllers for a Perturbed Autonomous Wheeled Mobile Robot Using Genetic Algorithms","volume":"179","author":"Martinez","year":"2009","journal-title":"Inf. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5904","DOI":"10.1016\/j.eswa.2015.03.024","article-title":"Generalized type-2 fuzzy systems for controlling a mobile robot and a performance comparison with interval type-2 and type-1 fuzzy systems","volume":"42","author":"Sanchez","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1016\/j.engappai.2005.12.011","article-title":"Genetic Learning and Performance Evaluation of Interval Type-2 Fuzzy Logic Controllers","volume":"19","author":"Wu","year":"2006","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_9","first-page":"683","article-title":"Research of ethylene cracking furnace temperature control method based on IT2FIM","volume":"32","author":"Li","year":"2015","journal-title":"Chin. Comput. Appl. Chem."},{"key":"ref_10","first-page":"1053","article-title":"Observer-based adaptive interval type-2 fuzzy control of uncertain MIMO nonlinear systems with unknown asymmeteric saturation actuators","volume":"171","author":"Shahnazi","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.ins.2016.03.001","article-title":"A generalized type-2 fuzzy granular approach with applications to aerospace","volume":"354","author":"Castillo","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1016\/j.asoc.2014.05.036","article-title":"Information granule formation via the concept of uncertainty-based information with interval type-2 fuzzy sets representation and Takagi-Sugeno-Kang consequents optimized with Cuckoo search","volume":"27","author":"Sanchez","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.ins.2015.06.047","article-title":"Type-2 fuzzy logic aggregation of multiple fuzzy controllers for airplane flight control","volume":"324","author":"Cervantes","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.asoc.2016.12.015","article-title":"Ant colony optimization with dynamic parameter adaptation based on interval type-2 fuzzy logic systems","volume":"53","author":"Olivas","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Tai, K., EI-Sayed, A.R., Biglarbegian, M., Gonzalez, C.I., Castillo, O., and Mahmud, S. (2016). Review of recent type-2 fuzzy controller applications. Algorithms, 9.","DOI":"10.3390\/a9020039"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.asoc.2016.02.033","article-title":"Optimization of fuzzy controller design using a new bee colony algorithm with fuzzy dynamic parameter adaptation","volume":"43","author":"Caraveo","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/j.isatra.2011.10.007","article-title":"Type-2 Fuzzy Model Based Controller Design for Neutralization Processes","volume":"51","author":"Kumbasar","year":"2012","journal-title":"ISA Trans."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.ijar.2008.03.003","article-title":"Sets with type-2 operations","volume":"50","author":"Walker","year":"2009","journal-title":"Int. J. Approx. Reason."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/j.ijar.2012.08.009","article-title":"A 2uFunction representation for non-uniform type-2 fuzzy sets: Theory and Design","volume":"54","author":"Molaeezadeh","year":"2013","journal-title":"Int. J. Approx. Reason."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.ins.2016.03.026","article-title":"A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems","volume":"354","author":"Castillo","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.ijar.2008.03.001","article-title":"New geometric inference techniques for type-2 fuzzy sets","volume":"49","author":"Coupland","year":"2008","journal-title":"Int. J. Approx. Reason."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0020-0255(01)00069-X","article-title":"Centroid of a type-2 fuzzy set","volume":"132","author":"Karnik","year":"2001","journal-title":"Inf. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1109\/TFUZZ.2002.803496","article-title":"Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems","volume":"10","author":"Wu","year":"2002","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1021\/i200017a016","article-title":"Internal model control. A unifying review and some new result","volume":"21","author":"Garcia","year":"1982","journal-title":"Ind. Eng. Chem. Process. Des. Dev."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Liu, D., and Fujii, F. (2014, January 3\u20136). An adaptive interval model control system of a piezo-ceramic actuator with two RBF neural networks. Proceedings of the 2014 IEEE Interval Conference on Mechatronics and Automation, Tianjin, China.","DOI":"10.1109\/ICMA.2014.6885697"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Toshiki, H., Hiromitsu, O., Hiroki, S., Ryo, T., and Yoshihisa, I. (2016, January 27\u201329). Simplified internal model control for time delay processed. Proceedings of the 35th Chinese Control Conference, Chengdu, China.","DOI":"10.1109\/ChiCC.2016.7553101"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Talange, D.B., Laware, A.R., and Bandal, V.S. (November, January 30). Development of an internal model sliding mode controller for cascade control system. Proceedings of the 2015 International Conference on Energy Systems and Applications, Pune, India.","DOI":"10.1109\/ICESA.2015.7503312"},{"key":"ref_28","unstructured":"Sun, Z.P., Chen, J., and Zhu, X.T. (July, January 29). Multi-model internal model control applied in temperature reduction system. Proceedings of the 11th World Congress on Intelligent Control and Automation, Shenyang, China."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Kumbasar, T., Eksin, I., Guzelkaya, M., and Yesil, E. (2011, January 17\u201319). Adaptive fuzzy internal model control design with bias term compensator. Proceedings of the IEEE International Conference on Mechatronics, Kuala Lumpur, Malaysia.","DOI":"10.1109\/ICMECH.2011.5971302"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1109\/TII.2012.2205581","article-title":"Fuzzy adaptive internal model control schemes for PMSM speed-regulation system","volume":"8","author":"Li","year":"2012","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1109\/TFUZZ.2003.819835","article-title":"Nonlinear internal model control: Application of inverse model based fuzzy control","volume":"11","author":"Boukezzoula","year":"2003","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/j.ijar.2012.11.005","article-title":"Exact inversion of decomposable interval type-2 fuzzy logic systems","volume":"54","author":"Kumbasar","year":"2013","journal-title":"Int. J. Approx. Reason."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2665","DOI":"10.1007\/s00500-015-1966-0","article-title":"An inverse controller design method for interval type-2 fuzzy models","volume":"21","author":"Kumbasar","year":"2017","journal-title":"Soft Comput."},{"key":"ref_34","unstructured":"Kumbasar, T., Eksin, I., Guzelkaya, M., and Yesil, E. (September, January 28). Type-2 fuzzy model inverse controller design based on BB-BC optimization method. Proceedings of the 18th IFAC World Congress, Milano, Italy."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1109\/2.53","article-title":"Fuzzy Logic","volume":"21","author":"Zadeh","year":"1988","journal-title":"Computer"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Karnik, N.N., and Mendel, J.M. (1998, January 4\u20139). Introduction to type-2 fuzzy logic systems. Proceedings of the IEEE World Congress on IEEE International Conference on Fuzzy Systems, Anchorage, AK, USA.","DOI":"10.1109\/FUZZY.1998.686240"},{"key":"ref_37","unstructured":"Babuska, R. (1998). Fuzzy Modeling for Control, Springer Science Business Media, LLC."},{"key":"ref_38","unstructured":"Zhang, X.Y., She, H., and Zheng, Y.Y. (2016, January 27\u201329). Operation optimization based on cyber-physical system for smart converter steelmaking. Proceedings of the 35th Chinese Control Conference, Chengdu, China."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/8\/4\/116\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:45:36Z","timestamp":1760208336000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/8\/4\/116"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,22]]},"references-count":38,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["info8040116"],"URL":"https:\/\/doi.org\/10.3390\/info8040116","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2017,9,22]]}}}