{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T07:00:32Z","timestamp":1777705232423,"version":"3.51.4"},"reference-count":33,"publisher":"SAGE Publications","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,3,2]]},"abstract":"<jats:p>This paper focuses on the development of a stable Mamdani type-2 fuzzy logic based controller for automatic control of servo systems. The stability analysis of the fuzzy controller has been done by employing the concept of Lyapunov. The Lyapunov approach results in the derivation of an original stability analysis that can be used for designing the rule base of our proposed online gain adaptive Interval Type-2 Fuzzy Proportional Derivative controller (IT2-GFPD) for servo systems with assured stability. In this approach a quadratic positive definite Lyapunov function is used and sufficient stability conditions are satisfied by the adaptive type-2 fuzzy logic control system. Illustrative simulation studies with linear and nonlinear models as well as experimental results on a real-time servo system validate the stability and robustness of the developed intelligent IT2-GFPD. A comparative performance study of IT2-GFPD with other controllers in presence of noise and disturbance also proves the superiority of the proposed controller.<\/jats:p>","DOI":"10.3233\/jifs-200802","type":"journal-article","created":{"date-parts":[[2020,12,8]],"date-time":"2020-12-08T21:56:38Z","timestamp":1607464598000},"page":"4187-4205","source":"Crossref","is-referenced-by-count":0,"title":["Lyapunov approach based design of a gain adaptive interval type-2 fuzzy controller for servo systems"],"prefix":"10.1177","volume":"40","author":[{"given":"Ritu Rani","family":"De (Maity)","sequence":"first","affiliation":[{"name":"Department of Instrumentation and Electronics Engineering, Jadavpur University, Kolkata, India"}]},{"given":"Rajani K.","family":"Mudi","sequence":"additional","affiliation":[{"name":"Department of Instrumentation and Electronics Engineering, Jadavpur University, Kolkata, India"}]},{"given":"Chanchal","family":"Dey","sequence":"additional","affiliation":[{"name":"Instrumentation Engineering, Department of Applied Physics, University of Calcutta, Kolkata, India"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-200802_ref1","doi-asserted-by":"crossref","first-page":"2346","DOI":"10.1016\/j.apm.2015.09.005","article-title":"Hardware-in-the loop simulation of interval type-2 fuzzy PD controller for uncertain nonlinear system using low cost microcontroller","volume":"40","author":"Ei.-Nagar","year":"2016","journal-title":"Applied Mathematical Modelling"},{"key":"10.3233\/JIFS-200802_ref3","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":"Information Sciences"},{"key":"10.3233\/JIFS-200802_ref4","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.isatra.2017.03.022","article-title":"A novel interval type-2 fractional order fuzzy PID controller: Design, performance evaluation and its optimal time domain tuning","volume":"68","author":"Kumar","year":"2017","journal-title":"ISA Transactions"},{"issue":"1","key":"10.3233\/JIFS-200802_ref5","first-page":"175","article-title":"Comparative Analysis of Noise Robustness of Type-2 Fuzzy Logic Controller","volume":"54","author":"Ontiveros-Robles","year":"2018","journal-title":"Kybernetika"},{"issue":"3","key":"10.3233\/JIFS-200802_ref7","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1109\/TFUZZ.2015.2471805","article-title":"Robust stability Analysis and Systematic Design of Single \u2013 Input Interval Type-2 Fuzzy Logic Controller, IEEE","volume":"24","author":"Kumbasar","year":"2016","journal-title":"Transactions on Fuzzy Systems"},{"issue":"1","key":"10.3233\/JIFS-200802_ref8","first-page":"125","article-title":"Industrial applications of type-2 fuzzy sets and systems: A concise review","volume":"62","author":"T\u00fcrkay","year":"2011","journal-title":"Computers in Industry"},{"key":"10.3233\/JIFS-200802_ref9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0020-7373(75)80002-2","article-title":"An experiment in linguistic systhesis with a fuzzy logic controller","volume":"7","author":"Mamdani","year":"1975","journal-title":"Int J Man-Machine Studies"},{"key":"10.3233\/JIFS-200802_ref10","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1016\/S0020-7373(76)80028-4","article-title":"Advances in the linguistic synthesis of fuzzy controllers","volume":"8","author":"Mamdani","year":"1976","journal-title":"Int J Man-Machine Studies"},{"issue":"C","key":"10.3233\/JIFS-200802_ref11","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/j.engappai.2017.09.007","article-title":"A review on stability analysis of continuous\u2013 time, fuzzy-model-based control systems","volume":"67","author":"Lam","year":"2018","journal-title":"Engineering Applications of Artificial Intelligence"},{"issue":"11","key":"10.3233\/JIFS-200802_ref12","first-page":"48","article-title":"Design of stable Type-2 Fuzzy Logic Controllers using a Lyapunov Approach","volume":"2","author":"Asradj","year":"2014","journal-title":"International Journal of Industrial Electronics and Electrical Engineering"},{"key":"10.3233\/JIFS-200802_ref13","first-page":"1347","article-title":"Stability Analysis of Type-2 Fuzzy Logic Controllers","volume":"17","author":"Galluzzo","year":"2009","journal-title":"Chemical Engineering Transactions"},{"issue":"1","key":"10.3233\/JIFS-200802_ref14","first-page":"3","article-title":"Stability Analysis approach for Fuzzy Logic control systems with Mamdani Type Fuzzy Logic Controllers","volume":"9","author":"Precup","year":"2007","journal-title":"Applied Informatics"},{"key":"10.3233\/JIFS-200802_ref16","first-page":"429","article-title":"An improved Lyapunov function based stability analysis method for Fuzzy logic control systems","volume":"1","author":"Wong","year":"2000","journal-title":"Proceedings of Ninth IEEE International conference on Fuzzy Systems"},{"key":"10.3233\/JIFS-200802_ref17","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1007\/s11071-010-9817-0","article-title":"Adaptive interval type-2 fuzzy sliding mode control for unknown chaotic system","volume":"63","author":"Hawang","year":"2011","journal-title":"Nonlinear Dynamics"},{"key":"10.3233\/JIFS-200802_ref18","first-page":"303","article-title":"Design and Stability Analysis of Single-Input Fuzzy Logic Controller","volume":"30","author":"Choi","year":"2000","journal-title":"IEEE Trans Fuzzy Systems"},{"issue":"2","key":"10.3233\/JIFS-200802_ref19","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1109\/91.755401","article-title":"On Stability of Fuzzy Systems Expressed by Fuzzy Rules with Singleton Consequents","volume":"7","author":"Sugeno","year":"1999","journal-title":"Fuzzy Systems"},{"key":"10.3233\/JIFS-200802_ref20","first-page":"791","article-title":"Conventional fuzzy control and its enhancement\u2019","volume":"25","author":"Li","year":"1996","journal-title":"IEEE Trans Systems Man and Cybernetics"},{"issue":"4","key":"10.3233\/JIFS-200802_ref21","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1109\/TFUZZ.2004.832538","article-title":"A hierarchical Type-2 fuzzy logic control architecture for autonomous mobile robots","volume":"12","author":"Hagras","year":"2004","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"10.3233\/JIFS-200802_ref22","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1080\/21642583.2015.1013644","article-title":"Interval Type-2 Fuzzy Logic Controller design for Speed Control of DC motors","volume":"3","author":"Hassani","year":"2015","journal-title":"Systems Science and Control Engineering"},{"key":"10.3233\/JIFS-200802_ref23","unstructured":"Documents for Quanser SRV02 Rotary Servo Base Unit, Canada, (2015)."},{"key":"10.3233\/JIFS-200802_ref24","doi-asserted-by":"crossref","unstructured":"Drainkov D. , Hellendroon H. and Reinfrank M. , An Introduction to Fuzzy Control, New York: Springer-Verlag, (1993).","DOI":"10.1007\/978-3-662-11131-4_5"},{"issue":"1","key":"10.3233\/JIFS-200802_ref25","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0005-1098(79)90084-0","article-title":"A linguistic self-organizing process controller","volume":"15","author":"Procyk","year":"1979","journal-title":"Automatica"},{"key":"10.3233\/JIFS-200802_ref26","first-page":"62","article-title":"A gain adaptive fuzzy logic controller","volume":"2275","author":"Mudi","year":"2002","journal-title":"Proceedings of 2002 AFSS International Conference on Advances in Fuzzy Systems, Springer \u2013 LNCS"},{"key":"10.3233\/JIFS-200802_ref27","first-page":"35","article-title":"A non-fuzzy self-tuning scheme of PD type FLC for overhead crane control","volume":"199","author":"Pal","year":"2013","journal-title":"Proceedings of 2012 FICTA International Conference on Frontiers of Intelligent Computing: Theory and Applications, Springer"},{"key":"10.3233\/JIFS-200802_ref28","doi-asserted-by":"publisher","DOI":"10.1109\/FUZZ-IEEE.2013.6622576"},{"issue":"1","key":"10.3233\/JIFS-200802_ref29","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/91.746295","article-title":"A Robust Self-Tuning Scheme for PI and PD Type Fuzzy Controllers","volume":"7","author":"Mudi","year":"1999","journal-title":"IEEE Trans on Fuzzy Systems"},{"issue":"C","key":"10.3233\/JIFS-200802_ref30","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.engappai.2017.02.011","article-title":"Parallel realization for self-tuning interval type-2 fuzzy controller","volume":"61","author":"EI-Nagar","year":"2017","journal-title":"Engineering Applications of Artificial Intelligence"},{"issue":"4","key":"10.3233\/JIFS-200802_ref31","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1109\/TFUZZ.2010.2045386","article-title":"Towards General Type-2 Fuzzy Logic Systems Based on Z-Slices","volume":"18","author":"Wagner","year":"2010","journal-title":"IEE Transactions on Fuzzy Systems"},{"issue":"8","key":"10.3233\/JIFS-200802_ref32","doi-asserted-by":"crossref","first-page":"643","DOI":"10.5505\/pajes.2016.49344","article-title":"Interval type-2 fuzzy PID controllers and an online self-tuning mechanism","volume":"22","author":"Kumbasar","year":"2016","journal-title":"Pamukkale University Journal of Engineering Sciences"},{"issue":"4","key":"10.3233\/JIFS-200802_ref33","doi-asserted-by":"crossref","first-page":"8476","DOI":"10.1016\/j.eswa.2008.10.072","article-title":"A rule base modification scheme in fuzzy controllers on time-delay systems","volume":"36","author":"Genc","year":"2009","journal-title":"Expert Systems with Applications"},{"issue":"5","key":"10.3233\/JIFS-200802_ref34","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1109\/TFUZZ.2006.883415","article-title":"A survey on analysis and design of model-based fuzzy control systems","volume":"14","author":"Feng","year":"2006","journal-title":"IEEE Transaction on Fuzzy Systems"},{"issue":"4","key":"10.3233\/JIFS-200802_ref36","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1016\/S0019-0578(07)60228-6","article-title":"A simplified type-2 fuzzy logic controller for real-time control","volume":"45","author":"Dongrui","year":"2006","journal-title":"ISA Transaction"},{"issue":"Supplement 2","key":"10.3233\/JIFS-200802_ref37","first-page":"363","article-title":"Robust Control Of Shunt Active Power Filter Using Interval Type-2 Fuzzy Logic Controller for Power Quality Improvement","volume":"24","author":"Acikgoz","year":"2017","journal-title":"Technical Gazette"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-200802","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:43:16Z","timestamp":1777455796000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-200802"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,2]]},"references-count":33,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.3233\/jifs-200802","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,2]]}}}