基于改进T-S模型的球杆系统控制方法研究

Controller Design Based on Improved T-S Fuzzy Model for Ball and Beam System

针对非线性球杆系统,提出一种基于Takagi-Sugeno(T-S)模糊模型的状态反馈控制方法。首先,通过扇区非线性方法为球杆系统建立具有较高逼近精度的T-S模糊模型,利用此T-S模型来描述球杆系统的非线性特性。然后,运用并行分布补偿(PDC)和线性矩阵不等式(LMI)方法设计状态反馈控制器。为了进一步说明系统的鲁棒性,在仿真实验中选择不同质量的小球。仿真研究结果表明:基于提出的T-S模型所设计的控制器使系统具有优良的动态特性和抗干扰特性。

A state feedback regulator based on the Takagi-Sugeno(T-S) fuzzy model is proposed forball and beam system. At first, the nonlinear ball and beam system is represented by a T-S fuzzy model with a high-precision, and the T-S fuzzy model is formulated by the sector nonlinear method. Then the T-S fuzzy model based state feedback regulator can be designed via the parallel distributed compensation ( PDC ) and linear matrix inequality ( LMI) technique. Finally, different mass of the small ball is chosen in the simulation to illustrate the effectiveness of the proposed controller, disturbance rejection performance of the system. The simulation results show that the proposed controller based on the given T-S model stabilizes the small ball at a desired position, and it gives the system excellent dynamic and disturbance rejection performance.