Observer Design for RIP Stability Using Takagi-Sugeno Fuzzy Model and Mean Value Theorem

• Published in: Journal of Applied Science and Engineering Vol. 28; no. 9; pp. 1843 - 1855
• Main Authors: Quy-Thinh Dao, Bao-Trung Dong, Thi-Van-Anh Nguyen
• Format: Journal Article
• Language: English
• Published: Tamkang University Press 01.02.2025
• Subjects: mean value theorem; observer design; rotary inverted pendulum; stability control; takagi-sugeno fuzzy model
• ISSN: 2708-9967; 2708-9975
• DOI: 10.6180/jase.202509_28(9).0019

This paper presents an observer design for the Rotary Inverted Pendulum (RIP) system using the Takagi-Sugeno (T-S) fuzzy model and the mean value theorem. The proposed method addresses the nonlinear and inherently unstable dynamics of the RIP by transforming the error dynamics into a linear parametric varying system. A non-quadratic Lyapunov function candidate is employed to ensure the global exponential convergence of the estimation error to zero. By combining the differential mean value theorem with sector nonlinearity transformation, the observer guarantees robust performance in the presence of unmeasured premise variables. The stability conditions are derived based on the Lyapunov function, leading to the solvability of a set of linear matrix inequalities. Simulation results demonstrate the effectiveness of the proposed observer in significantly reducing dynamic errors and enhancing the overall stability and accuracy of state estimations. The proposed approach outperforms traditional methods, providing a reliable and precise solution for real-time control applications in nonlinear systems.