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 <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msub> <mrow> <mi>H</mi> </mrow> <mrow> <mi>∞</mi> </mrow> </msub> </math> , 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.

Boutaina Elkinany

Mohammed Alfidi

Redouane Chaibi

Zakaria Chalh

Advances in Fuzzy Systems

Advances in Fuzzy Systems is an international journal which aims to provide a forum for original research articles in the theory and applications of fuzzy subsets and systems. The goal of the journal is to help promote the advances in the development and practice of fuzzy system technologies in the areas of engineering, management, medical, economic, environmental, and societal problems. Advances in Fuzzy Systems is intended to provide a rapid communication of fully refereed papers through the open access publication model, which will enable the journal to reach a far greater audience than traditional subscription-based journals.

Advances in Fuzzy Systems is an international journal that aims to provide a forum for original research articles in the theory and applications of fuzzy subsets and systems. The journal's goal is to promote the development and practice of fuzzy system technologies in various fields, including engineering, management, medicine, economics, environmental issues, and societal problems. Advances in Fuzzy Systems is designed to facilitate the rapid communication of fully refereed papers through an open access publication model, enabling the journal to reach a much wider audience than traditional subscription-based journals.

《Advances in Fuzzy Systems》是一本国际期刊，旨在为模糊子集和系统的理论与应用提供原创研究文章的论坛。期刊的目标是促进模糊系统技术在工程、管理、医学、经济、环境和社会问题等领域的发展与实践。《Advances in Fuzzy Systems》旨在通过开放获取出版模式快速传播经过严格审稿的论文，使期刊能够接触到比传统订阅制期刊更广泛的受众。

T-S Fuzzy System Controller for Stabilizing the Double Inverted Pendulum

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Journal Info

Category	Quartile
MATHEMATICS, APPLIED	2