Adaptive T-S Fuzzy Control for an Unknown Structure System With a Self-Adjusting Control Accuracy

Adaptive Takagi-Sugeno (T-S) fuzzy control was a real-time control method without off-line input and output data, but the approximate error between this T-S fuzzy model and the actual system model was rarely considered in the existing methods. This problem can lead to the degradation of controller accuracy in practical engineering. In order to solve this problem, the mathematical expression of the upper bound for the approximate error between adaptive T-S fuzzy logic system and the actual system was derived for the first time under any number of rules. This achievement was the key to the design of robust fuzzy controller based on Lyapunov synthesis method under finite number of rules, and this controller can achieve predictability of accuracy. Compared with existing T-S fuzzy control methods, the proposed method can realize the self-adjusting accuracy control for the unknown-structure system without the off-line input and output data. The unknown non-affine control system simulation and 3-DOF robotic arm experiment were carried out to verify the effectiveness of proposed method. Note to Practitioners—Due to the wide application of T-S fuzzy model in practice control system, such as the robot control, the unmanned vehicle control and so on, the actual control accuracy of T-S fuzzy controller was concerned by many scholars. However, the actual precision degradation of the controller was a difficult problem in on-line T-S fuzzy control. In order to solve this problem, a novel adaptive T-S fuzzy control method was proposed in this paper. In practical application, T-S fuzzy model often had a large approximate error with the actual model because of structure uncertainty, and this approximate error was the key factor affecting the actual accuracy of T-S fuzzy controller. Hence, the mathematical expression of the upper bound for the approximate error between adaptive T-S fuzzy logic system and the actual system was derived for the first time under any number of rules. Based on this mathematical expression, we can design a self-adjusting accuracy robust fuzzy controller based on Lyapunov synthesis method. 3-DOF robotic arm experiment verified that the proposed method can achieve the predefined control error with or without the feedforward of robot dynamics. 3-DOF robotic arm comparison experiments verified that the advantages of proposed method.

I. Introduction

Many systems cannot be mathematically modeled or were very difficult to model. Therefore, the traditional control algorithms that needed to know the mathematical analytic model of the original system cannot be used. In order to control unknown systems, model prediction control, data-driven control and T-S fuzzy control had been studied by scholars [1], [2], [3]. T-S fuzzy modeling strategy, as an arbitrary-approximation, describable, interpretable modeling method, had been widely studied in the control filed by scholars [4], [5], [6]. With the development of the T-S fuzzy control, online modeling and control accuracy for the unknown system began to get a lot of attention [7], [8], [9].