【作者】 欧林林； 周佩冬； 陈宣光； 俞立；

【Author】 OU Linlin~1,ZHOU Peidong~1,CHEN Xuanguang~(1,2),YU Li~1 1.Department of Automation,Zhejiang University of Technology,Hangzhou 310023,P.R.China 2.Zhejiang Feiying Sewing Equipment CO.,LTD,Zhuji 311832,P.R.China

【机构】 浙江工业大学信息学院； 浙江飞鹰缝制设备有限公司；

【摘要】 针对离散时滞系统,采用一种简单的解析方法给出了满足H_∞性能指标的低阶控制器参数集合,位于该集合中的控制参数均能保证闭环系统稳定且满足相应的H_∞指标.因而,从理论上证明了满足某一H_∞指标的低阶控制器参数不是唯一的一组值,而是一个集合.首先,将满足H_∞指标的低阶控制器参数集求解问题转化成关于参数(?)的闭环特征多项式稳定性分析问题;然后,遍历(?)((?)∈[0,2π)),对每一个确定的参数(?),找出控制参数边界线并判断边界线的哪一侧具有更少的不稳定极点,从而确定参数(?)所对应的控制参数稳定域,这些稳定域的交集即为满足H_∞指标的PID控制器参数域.该方法为满足多性能指标的离散时滞系统低阶控制器设计提供了理论基础.更多还原

【Abstract】 For the discrete-time systems with time delay,the sets of the low-order controller parameters satisfying H∞performance are presented by using a simple analytical method.The parameter values in such the sets can not only guarantee the stability of the closed-loop system,but also satisfy the corresponding H∞performance.Thus,it can be theoretically proved that there exists a set of the low-order controller parameters satisfying the given H∞performance,but not only one group of values.Firstly,we convert the problem of determining the region of the control parameters satisfying H∞performance to a closed-loop characteristic polynomial stabilization problem with respect toφ;then,by sweeping overφ(φe[0,2π) ),the boundaries in the control parameters space is calculated for each fixedφ.Thus the stability region of PID parameters for the fixedφcan be determined by examining which side of each boundary has less unstable poles.The region of PID parameters satisfying H∞performance is the intersection of these stability regions.The proposed approach provides the theoretical basis for the low-order controller design satisfying multiple performance crideria.更多还原