第21卷第12期 2013年12月
文章编号
1004-924X(2013)12-3214-09
光学精密工程
Optics and Precision Engineering
确保稳定裕度的PID稳定域计算
赵秀伟1.2.3，任建岳1*
（1.中国科学院长春光学精密机械与物理研究所，吉林长春130033；
Vol. 21No.12
Dee.2013
2.中国科学院大学，北京100039；3.中国电子科技集团公司第四十五研究所，北京100176）
摘要：在PID控制器稳定参数域的研究中，要求控制系统具有一定的稳定裕度，以便补偿被控对象模型的不确定性和 PID控制器的参数漂移特性。本文扩展了传统稳定裕度（幅值裕度和相位裕度)的定义，定义了被控对象在PID控制下的4种稳定裕度。针对含有右半平面(RHP)极点和不含有RHP极点的两种被控对象，讨论了它们必然存在的稳定裕度。对于以这些稳定裕度作为性能指标约束的两类PID闭环控制系统利用扩展Hurmite-Biehler定理给出了其PID稳定参数域的详细构建方法，并通过两个伤真实例对该方法进行了验证。结果表明，利用本文提出的方法可以得到满足稳定裕度条件的PID参数稳定域。
关键调：PID控制器；PID稳定城：幅值格度；相位格度：扩展Hurmite-Biehler定理；
中图分类号：TP273;TP13
文献标识码：A
doi;10.3788/OPE.20132112.3214
ComputationofPiDstabilizingregionwithstabilizedmargins
ZHAO Xiu-weil-z3,REN Jian-yue'
(l.ChangchunInstitute of Optics，FineMechanics and Physics,
ChineseAcademyof Sciences，Changchun130033,China;
2.University of Chinese Academy of Sciences,Beijing 100039,China;
3.No.45 Research Institute,China Electronics Technology Group Corporation,Beijing 10o176,China)
Correspondingauthor,E-mailrenjy@ciomp.ac.cn
Abstract: On research of the stabilizing region of a PID controller,the control system is required a sta-bilized margin to compensate the uncertainty of plant modeling and the parameter deviation of PID controller, This paper defines four types of stability margins for the plant under PID controller to ex tend the conventional definition of stability margins (gain margin and phase margin). Based on the presences of Right Half Plane(RHP) poles or not, the closed-loop systems are classified into two cate gories and their necessary stabilized margins are stated. A method of constructing PID stabilizing re gions by using the generalized Hermite-Biehler theorems is proposed for the PID controlled closed-loop system to meet the prescribed performance of stability margins. Then, two examples are employed to lest the validity of the method proposed. Obtained results demonstrate that the PID stabilizing regions with stabilized margins can really be gotten by the proposed method for both cases.
收稿日期：2013-07-26；修订日期：2013-09-25
基金项目：国家863高技术研究发展计划资助项目(No.863-2-5-1-13B)