基于LMI的随动系统满意PID调节器设计

臧文利; 王远钢; 郭治; 王艳霞

引用本文:	臧文利, 王远钢, 郭治, 王艳霞.基于LMI的随动系统满意PID调节器设计[J].控制理论与应用,2006,23(6):967~970.[点击复制]
	ZANG Wen-li, WANG Yuan-gang, GUO Zhi, WANG Yan-xia.Satisfactory PID design for servo systems based on iterative LMI technique[J].Control Theory and Technology,2006,23(6):967~970.[点击复制]

基于LMI的随动系统满意PID调节器设计

Satisfactory PID design for servo systems based on iterative LMI technique

摘要点击 1652 全文点击 1525 投稿时间：2005-06-17 修订日期：2006-01-04

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DOI编号 10.7641/j.issn.1000-8152.2006.6.023

2006,23(6):967-970

中文关键词 PID 线性矩阵不等式动态误差系数满意控制

英文关键词 PID linear matrix inequality dynamical error coefficients satisfactory control

基金项目国家自然科学基金资助项目(60174028); 教育部博士点基金资助项目(20040288002).

作者	单位
臧文利, 王远钢, 郭治, 王艳霞	南京理工大学自动化系, 江苏南京210094 南京理工大学理学院, 江苏南京210094

中文摘要

PID控制器在实际工程中应用广泛, 而且工程上对随动系统的性能要求往往是多方面的. 该文应用满意控制思想, 研究了期望指标: 扇形区域极点, 稳态输出方差和动态误差系数约束下随动系统的PID控制设计问题. 首先将PID控制参数设计转化为局部状态反馈问题, 导出了3项指标约束的双线性矩阵不等式(BMI)描述. 然后给出改进的迭代线性矩阵不等式(LMI)算法求解BMI可行解, 得到使闭环系统满足3项期望指标的PID参数. 最后给出了应用该方法数值算例.

英文摘要

In practical engineering, the PID controller is widely used to meet multiple system-specifications. Employing the idea of satisfactory control, the design of PID controller for a class of servo systems is investigated under desired indices in this paper. The desired indices include sector regional pole, steady output covariance and dynamical error coefficients. Firstly, the problem of PID design is transformed to one of partial state feedback, and the above three desired indices are formulated in terms of bilinear matrix inequality (BMI). An improved iterative linear matrix inequality (LMI) procedure is then presented to solve the BMI, and the resulting parameter of PID can also guarantee the closed-loop servo system satisfying the desired three indices. Finally, a numerical example is given to illustrate the proposed method.