T-S型模糊系统的控制器设计

A New Method to Design Controller for T-S Model Fuzzy System

T- S型模糊系统可以描述工程中的许多非线性系统。为了研究该类系统的镇定问题 ,提出了将 T- S型模糊系统嵌入到区间系统的思想。利用区间系统的鲁棒控制理论 ,通过解代数 Riccati不等式方程 ,给出了一种镇定该类系统的控制器设计方法。最后通过对倒立摆系统的控制器设计 。

T S model fuzzy system can be used to describe many nonlinear systems in engineering. However, the controllers for this kind of system designed by the existing methods are either too conservative [2,3] or their gains are too large [4,5] . We present a new method to overcome these shortcomings. In section 1, we bring forward the idea that T S model fuzzy systems described by eqs.(1) through (3) are actually interval systems (eqs.(1) and (4)). To our best knowledge, we have not found any such report in the open literature. In section 2, we designed the controller by employing robust control theory of interval systems. Solving algebraic Riccati inequality (eq.(11)), we can get the controller (eq.(12)). Based on its T S fuzzy model (eq.(17)), we designed a controller for a handstand sway system described by eq.(16) with our method. Fig.1 is the response of the system without any control, and Fig.2 is the response of the system under the control law given by eq.(18) at the same initial state as Fig.1. It shows that our method is both effective and easy to implement.