Nonlinear System Real-World Control Based on an Adaptive T-S Fuzzy Controller

Abstract

In this study, an adaptive control system (ACS) has been applied to a nonlinear system control problem. The Takagi-Sugeno (T-S) fuzzy control method has been extensively applied to nonlinear systems by transforming them into T-S fuzzy models. Traditionally, T-S fuzzy controller gains are computed offline using MATLAB LMI control toolbox. The parameters of the T-S Fuzzy system mathematical model are derived from the linearization of each subsystem. While the linearization process simplifies the system, it also necessitates sacrificing the nonlinear characteristics of the system, which may lead to system distortion. This process sacrifices nonlinear characteristics, resulting in discrepancies between theoretical design and real-world performance. Furthermore, uncertainties in practical applications lead to parameter variations over time, making offline-computed gains suboptimal. In this study, the main contributions include: 1. This study proposes an adaptive T-S fuzzy control method to enhance the robustness of nonlinear systems and applies it to the real-world control of an omnidirectional inverted pendulum. 2. To address external disturbances and approximation errors, a T-S fuzzy controller with a compensated controller is designed to mitigate external disturbances and approximation errors, while a supervisory controller dynamically adjusts system output based on tracking errors. 3. Experimental results demonstrate that the proposed method effectively improves system stability and tracking accuracy compared to conventional T-S fuzzy controllers. By integrating adaptive control with a T-S fuzzy framework, this study enhances system reliability in dynamic environments, overcoming the limitations of traditional offline-designed controllers. The effectiveness of the proposed adaptive control system is validated through multiple experimental results.