Computation of PID stabilizing region with stabilized margins

ZHAO Xiu-wei1; 2; 3; REN Jian-yue1

doi:10.3788/OPE.20132112.3214

您当前的位置：

首页 >

文章列表页 >

Computation of PID stabilizing region with stabilized margins

更新时间：2020-08-12

- Computation of PID stabilizing region with stabilized margins
- Optics and Precision Engineering Vol. 21, Issue 12, Pages: 3214-3222(2013)
- 作者机构：
  
  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
  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
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20132112.3214
  CLC： TP13;TP273
- Received：26 June 2012，
  
  Revised：29 October 2012，
  
  Published Online：25 December 2013，
  
  Published：25 December 2013
- 稿件说明：
移动端阅览
赵秀伟任建岳. 确保稳定裕度的PID稳定域计算[J]. 光学精密工程, 2013,21(12): 3214-3222

ZHAO Xiu-wei REN Jian-yue. Computation of PID stabilizing region with stabilized margins[J]. Editorial Office of Optics and Precision Engineering, 2013,21(12): 3214-3222
赵秀伟任建岳. 确保稳定裕度的PID稳定域计算[J]. 光学精密工程, 2013,21(12): 3214-3222 DOI： 10.3788/OPE.20132112.3214.

ZHAO Xiu-wei REN Jian-yue. Computation of PID stabilizing region with stabilized margins[J]. Editorial Office of Optics and Precision Engineering, 2013,21(12): 3214-3222 DOI： 10.3788/OPE.20132112.3214.

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，并通过两个仿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。

Abstract

On research of the stabilizing region of a PID controller

the control system is required a stabilized 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 extend 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 categories and their necessary stabilized margins are stated. A method of constructing PID stabilizing regions 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 test 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.

关键词

Keywords

references

［1］STRM K J,HGGLUND T. PID Controllers: Theory, Design, and Tuning ［M］.North Carolina: Instrument Society of America, 1995.［2］AIDAN ODWYER. Handbook of PI and PID controller tuning rules ［M］. London: Imperial College Press, 2009.［3］HUANG Y J,WANG Y J. Robust PID tuning strategy for uncertain plants based on the Kharitonov theorem ［J］. ISA Transactions, 2000, 39(4):419-431.［4］CHAPELLAT H,MANSOUR M,BHATTACH-ARYYA S P. Elementary proofs of some classical stability criteria ［J］. IEEE Transactions on Education, 1990, 33(3):232-239.［5］MATUU R.Calculation of all stabilizing PI and PID controllers ［J］. International Journal of Mathematics and Computers in Simulation, 2011, 5(3): 224-231.［6］李银伢, 盛安冬, 王远钢. 期望指标集约束下一类随机系统的满意PID控制［J］. 控制与决策, 2007, 22(3): 252-257.LI Y Y, SHENG A D, WANG Y G. On satisfactory PID control for a class of stochastic systems with desired index set constraint ［J］. Control and Decision, 2007, 22(3): 252-257. (in Chinese)［7］马建伟, 李银伢. 满意PID控制设计理论与方法［M］. 北京: 科学出版社, 2007.MA J W,LI Y Y. Satisfactory PID Control Design: Theorem and Methods［M］. Beijing: Science Press, 2007. (in Chinese)［8］HO M T,DATTA A,BHATTACHARYYA S P. Bhattacharyya generalizations of the Hermite-Biehler theorem ［J］. Linear Algebra and its Applications, 1999, 302-303:135-153.［9］BHATTACHARYYA S P,DATTA A,KEEL L H. Control Theory: Structure, Robustness and Optimization ［M］. Florida:CRC Press, 2009.［10］SILVA G J,DATTA A,BHATTACHARYYA S P. PID Controller for Time-Delay Systems ［M］. Boston: Birkhuser, 2005.［11］BHATTACHARYYA S P,CHAPELLAT H,KEEL L H. Robust Control: The Parametric Approach ［M］. London:Prentice Hall PTR, 1995.［12］DATTA A,HO M T, BHATTACHARYYA S P. Structure and Synthesis of PID Controller ［M］. London: Springer, 2000.［13］HO M T,DATTA A,BHATTACHARYYA S P. A linear programming characterization of all stabilizing PID controllers ［C］. Proceedings of the 1997 American Control Conference, 1997,6:3922-3928.［14］ACKERMANN J,KAESBAUER D. Design of robust PID controllers ［C］. Proc. European Control Conference, Porto, 2001.［15］BAJCINCA N. The method of singular frequencies for robust control design in an affine parameter space ［J］. IEEE Transactions on Automatic Control, 2001, 100-105.［16］BAJCINCA N. Design of robust PID controllers using decoupling at singular frequencies ［J］. Automatica, 2006, 42(11):1943-1949.［17］方斌. 时滞系统PID控制器参数稳定域的实现［J］. 电子科技大学学报, 2011, 40(3):411-417.FANG B. Realization of PID controller parameter stable regions for time delay systems ［J］. Journal of University of Electronic Science and Technology of China, 2011, 40(3):411-417. (in Chinese)［18］方斌. 基于稳定裕量的二阶时滞系统PID 控制器参数稳定域［J］. 信息与控制, 2011, 40(2), 192-197.FANG B. Second-order time delay system stable regions of PID controller parameter based on stability margins ［J］. Information and Control, 2011, 40(2), 192-197. (in Chinese)［19］彭瑞, 岳继光. 基于区间分析的参数不确定系统PID鲁棒控制器设计［J］.电机与控制学报, 2006, 10(4):411-419.PENG R,YUE J G. Robust design of PID controller for interval plants based on interval analysis ［J］. Electronic Machines and Control, 2006, 10(4):411-419. (in Chinese)［20］KEEL L H,BHATTACHARYYA S P. Fixed order multivariable controller synthesis: A new algorithm ［C］. Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico,2008: 977-982.［21］KNAP M J,KEEL L H,BHATTACHARYYA S P. Robust stability of complex systems with applications to performance attainment problems ［C］. Proceedings of the 2010 American Control Conference, Baltimore, 2010: 3907-3912.［22］HO M T,DATTA A, BHATTACHARYYA S P. Generalizations of the HermiteBiehler theorem: the complex case ［J］. Linear Algebra and its Applications, 2000, 320:23-36.［23］HO M T,WANG H S. PID controller design with guaranteed gain and phase margins ［J］. Asian Journal of Control, 2003, 5(3):374-381.

Views

675

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

High-gain PID controller for nanometer positioning

Related Author

LU Li-hua

GUO Yong-feng

Tachikawa Hiroyuki

LIANG Ying-chun

Shimokohbe Akira

Related Institution

Precision Engineering Research Institute, Harbin Institute of Technology

Precision and Intelligent Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan

AI问答

Address：No.3888 Dong Nanhu Road, Changchun, Jilin, China Postal code：130033
Tel：0431-86176855 Email：gxjmgc@ciomp.ac.cn
Technical support is provided by Beijing Founder electronics co., LTD 吉ICP备11002662号-17 京公网安备11010802024621
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰