朱嵘涛 陈希湘

摘  要： 文中主要研究单级倒立摆的模糊控制，首先根据单级倒立摆数学模型和T?S模糊规则，采用三角隶属函数实现对倒立摆摆角的模糊化，接着对T?S模糊控制器的方法作了具体介绍，并给出T?S模糊系统稳定的判定依据，即线性矩阵不等式，然后运用YAPLMI工具箱对线性矩阵不等式求解出控制器的增益，最后采用并行分布式补偿的方法设计出单级倒立摆的T?S模糊控制器，并对两种模糊规则的控制器进行了深入对比研究。实际测试结果表明，8条模糊规则的控制器在角速度最大值和盲区控制上的表现都优于4条模糊规则的控制器，且能在不超过2.3 s时间内实现对倒立摆角度和角速度的有效控制，因此在相应的控制领域应优先采用8条模糊规则的控制器。

关键词： 模糊控制; T?S模糊模型; 单级倒立摆; 系统设计; 并行分布式补偿; 仿真测试

中图分类号： TN876?34; TP242                   文献标识码： A                     文章编号： 1004?373X（2020）08?0179?04

Control of T?S fuzzy model in single inverted pendulum

ZHU Rongtao， CHEN Xixiang

（Yangtze University College of Technology & Enginerring， Jingzhou 434020， China）

Abstract： The fuzzy control of the single inverted pendulum is mainly studied. On the basis of the mathematical model of single inverted pendulum and T?S fuzzy rules， the fuzzification of inverted pendulum′deflection angle is realized by means of the triangular membership function. The method of T?S fuzzy controller is introduced in detail， and the criterion for judging the stability of T?S fuzzy system??linear matrix inequality is given. The gain of the controller is solved with the YAPLMI toolbox. The T?S fuzzy controller of single inverted pendulum is designed by means of the method of parallel distributed compensation， and two kinds of fuzzy rule controllers are comparative studied in detail. The actual testing results show that the performance of the controller with 8 fuzzy rules is better than that of the controller with 4 fuzzy rules in the maximum angular velocity and blind area control. It can effectively control the angle and angular velocity of inverted pendulum in no more than 2.3 s. Therefore， the controller with eight fuzzy rules should be preferred in the corresponding control field.

Keywords： fuzzy control; T?S fuzzy model; single inverted pendulum; system design; parallel distributed compensation; simulation test

单级倒立摆系统是一种特殊的单力臂机器人被控对象，是一种复杂的非线性、多变量、强耦合和快速运动的不稳定系统，也是检验新的控制理论和方法有效性的典型理想模型[1?2]。它具有线性的T?S模糊模型，采用模糊规则的方法，并利用系统局部信息和专家控制经验，可在极高精度下拟合实际被控对象，且T?S模糊系统的稳定性条件可用线性矩阵不等式的形式表达出来[3]。

1  系统整体设计

文中首先根据单级倒立摆数学模型和T?S模糊规则，采用三角隶属函数实现了……