{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:39:52Z","timestamp":1747190392321,"version":"3.40.5"},"reference-count":29,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,12,5]],"date-time":"2020-12-05T00:00:00Z","timestamp":1607126400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2020,12,5]]},"abstract":"<jats:p>This article provides a representation of the double inverted pendulum system that is shaped and regulated in response to torque application at the top rather than the bottom of the pendulum, given that most researchers have controlled the double inverted pendulum based on the lower part or the base. To achieve this objective, we designed a dynamic Lagrangian conceptualization of the double inverted pendulum and a state feedback representation based on the simple convex polytypic transformation. Finally, we used the fuzzy state feedback approach to linearize the mathematical nonlinear model and to develop a fuzzy controller <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                        <a:msub>\n                           <a:mrow>\n                              <a:mi>H<\/a:mi>\n                           <\/a:mrow>\n                           <a:mrow>\n                              <a:mi>\u221e<\/a:mi>\n                           <\/a:mrow>\n                        <\/a:msub>\n                     <\/a:math>\n                  <\/jats:inline-formula>, given its great ability to simplify nonlinear systems in order to reduce the error rate and to increase precision. In our virtual conceptualization of the inverted pendulum, we used MATLAB software to simulate the movement of the system before applying a command on the upper part of the system to check its stability. Concerning the nonlinearities of the system, we have found a state feedback fuzzy control approach. Overall, the simulation results have shown that the fuzzy state feedback model is very efficient and flexible as it can be modified in different positions.<\/jats:p>","DOI":"10.1155\/2020\/8835511","type":"journal-article","created":{"date-parts":[[2020,12,8]],"date-time":"2020-12-08T19:30:26Z","timestamp":1607455826000},"page":"1-9","source":"Crossref","is-referenced-by-count":2,"title":["T-S Fuzzy System Controller for Stabilizing the Double Inverted Pendulum"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3100-1407","authenticated-orcid":true,"given":"Boutaina","family":"Elkinany","sequence":"first","affiliation":[{"name":"Laboratory of Engineering Systems and Applications, Sidi Mohammed Ben Abdellah University, Fez, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammed","family":"Alfidi","sequence":"additional","affiliation":[{"name":"Laboratory of Engineering Systems and Applications, Sidi Mohammed Ben Abdellah University, Fez, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Redouane","family":"Chaibi","sequence":"additional","affiliation":[{"name":"Department of Physics, Sidi Mohammed Ben Abdellah University, LESSI, Fez, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0838-4152","authenticated-orcid":true,"given":"Zakaria","family":"Chalh","sequence":"additional","affiliation":[{"name":"Laboratory of Engineering Systems and Applications, Sidi Mohammed Ben Abdellah University, Fez, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","first-page":"34","article-title":"Inverted pendulum control: an overview","volume":"1","author":"K. Perev","year":"2011","journal-title":"Information Technologies and Control"},{"article-title":"Classical double inverted pendulum\u2013a complex overview of a system","author":"S. Jadlovska","key":"2","doi-asserted-by":"crossref","DOI":"10.1109\/SAMI.2012.6208937"},{"author":"H. Biglari","key":"3","article-title":"The double pendulum numerical analysis with Lagrangian and the Hamiltonian equations of motions 2 the double pendulum numerical analysis with Lagrangian and the Hamiltonian equations of motions"},{"author":"L. Chen","key":"4","article-title":"Research on the nonlinear dynamical behavior of double pendulum"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/1221\/1\/012049"},{"author":"L. Song Qing-kun","key":"6","article-title":"The design and stability study of double inverted pendulum controller"},{"author":"D. Ali","key":"7","article-title":"Control of double inverted pendulum first approach"},{"first-page":"4117","article-title":"Experimental estimation of a second order, double inverted pendulum parameters for the study of human balancing","author":"A. Cerda-Lugo","key":"8"},{"key":"9","unstructured":"BogdanovA.Optimal control of a double inverted pendulum on a cart2004Portland, OregonOregon Health & Science UniversityTechnical Report CSE-04-006"},{"volume-title":"Robust Control Using Incremental Sliding Mode for Underactuated Systems with Mismatched Uncertainties","year":"2008","author":"Y. Hao","key":"10"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1504\/ijcat.2007.014556"},{"issue":"2","key":"12","doi-asserted-by":"crossref","first-page":"239","DOI":"10.25088\/ComplexSystems.28.2.239","article-title":"Neural control model for an inverted double pendulum","volume":"28","author":"M. C. Alexander","year":"2019","journal-title":"Complex Systems Journal"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.14311\/ap.2013.53.0883"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3531-0"},{"issue":"2","key":"15","first-page":"41","article-title":"LMI-based control of a double pendulum crane, applications of modeling and simulations","volume":"2","author":"M. Muhammad","year":"2018","journal-title":"Journal"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2018.06.005"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1109\/tii.2020.3006179"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1109\/tie.2020.2992972"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2017.08.1975"},{"author":"J. Slavka","key":"20","article-title":"Inverted pendula simulation and modeling-a generalized approach"},{"issue":"1","key":"21","first-page":"27","article-title":"Control of a double-inverted pendulum for nonlinear system","volume":"8","author":"M. Demirci","year":"2007","journal-title":"Journal of Applied Mathematics"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.phpro.2012.02.246"},{"key":"23","unstructured":"MoysisL.Balancing a double inverted pendulum using optimal control and laguerre functions2016Thessaloniki, GreeceAristotle University of ThessalonikiTechnical Report"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.5121\/ijcsa.2015.5508"},{"article-title":"Swing up control of a double pendulum","author":"M. Yamakita","key":"25","doi-asserted-by":"crossref","DOI":"10.23919\/ACC.1993.4793279"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1016\/s1474-6670(17)57101-3"},{"issue":"3","key":"27","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/0165-0114(95)00156-5","article-title":"Fuzzy optimal control for double inverted pendulum","volume":"79","author":"B. Al-Hadithi","year":"1996","journal-title":"Fuzzy Sets and Systems Journal"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1109\/tfuzz.2004.825992"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2020.2965884"}],"container-title":["Advances in Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2020\/8835511.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2020\/8835511.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2020\/8835511.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,8]],"date-time":"2020-12-08T19:31:33Z","timestamp":1607455893000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/afs\/2020\/8835511\/"}},"subtitle":[],"editor":[{"given":"Ping-Feng","family":"Pai","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2020,12,5]]},"references-count":29,"alternative-id":["8835511","8835511"],"URL":"https:\/\/doi.org\/10.1155\/2020\/8835511","relation":{},"ISSN":["1687-711X","1687-7101"],"issn-type":[{"type":"electronic","value":"1687-711X"},{"type":"print","value":"1687-7101"}],"subject":[],"published":{"date-parts":[[2020,12,5]]}}}