An Approach to Generate the LQR Based Takagi–Sugeno Fuzzy Model Controller for Nonlinear System

Abstract In this paper, we propose a general method for designing Takagi–Sugeno (T-S) fuzzy model controllers, applicable to a general class of nonlinear systems represented in state-space form. The method is an automated controller design process that introduces the BLOCK concept. Through the automatic division of BLOCKs, the system is divided into more subsystems, and corresponding fuzzy rules and membership functions are automatically generated, significantly shortening the development time for systems with known system models. According to T-S fuzzy theory, nonlinear systems are decomposed into multiple linear subsystems governed by fuzzy rules. Unlike conventional methods that rely on linear matrix inequalities (LMI), which may suffer from infeasibility or excessively large controller gains and generally involve higher computational complexity, we integrate the linear quadratic regulator (LQR) approach to enhance stability and performance. The LQR method offers a more computationally efficient solution while still achieving effective control. The effectiveness of the proposed automated process is demonstrated through its application to a two-link robotic manipulator, showcasing its ability to improve tracking accuracy. Experimental results confirm that the proposed controller outperforms conventional PID control, achieving reduced tracking errors and demonstrating the practicality of the method for broader nonlinear control applications.