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

作　　者：臧文利[1] 王远钢[2] 郭治[1] 王艳霞[1] 

机构地区：[1]南京理工大学 自动化系,江苏南京210094 [2]南京理工大学 理学院,江苏南京210094

出　　处：《控制理论与应用》2006年第6期967-970,975,共5页Control Theory & Applications

基　　金：国家自然科学基金(60174028);教育部博士点基金(20040288002).

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．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.

关 键 词：PID 线性矩阵不等式 动态误差系数 满意控制 

分 类 号：TP275[自动化与计算机技术—检测技术与自动化装置]