摘要
传统的系统辨识及其PID控制器的设计方法,虽然在很大程度上能满足工业系统的控制要求,但对一些具有MIMO、强藕合性、不确定性、非线性、信息不完全性和大纯滞后性等特征的工业控制系统,这些经典方法无法得到满意的效果,迫切需要对多变量系统的辨识及其PID参数整定进行研究,以求整定出合理的、最优的PID参数,以获得比传统的PID参数整定法更好的控制效果,更能适应复杂多变的工业生产过程的需要。
论文主要分成两部分来展开论述:多变量系统的辨识部分和PID整定方法部分,其中对多变量系统的辨识方法未涉及太深,只是做了初步研究,重点在多变量系统的PID整定方法上,做了大量工作,取得了一定的成果。
在进行多变量PID参数整定方法的研究之前,首先介绍了两种多变量系统的辨识方法:最小二乘法和递阶随机梯度法。在论述了算法基本原理和实现步骤的基础上,通过仿真实验证明了算法的有效性。
在多变量PID参数整定部分,首先对PID控制的基本原理与特点进行了概述,然后说明了PID参数整定的分类和传统方法,针对多变量系统的特点,概述了多变量PID的设计方法。而后对这些方法进行了具体研究,主要有预测PID参数整定、内模PID参数整定和鲁棒PID参数整定,分别在文中的第四章、第五章和第六章展开论述:
第四章在研究预测控制算法基本原理的基础上,将预测控制算法与PID参数整定相结合,形成预测PID整定算法,考虑到对预测PID参数的优化,提出了改进型预测PID整定算法,并将单变量预测PID控制推广,设计出符合多变量特点的预测PID控制器。比起传统的PID参数整定法(如Z-N整定法),预测PID整定法对模型失配、大滞后等传统整定法难以控制好的情况均有满意的控制效果。
第五章介绍了内模控制器的基本原理,在此基本上,将内模控制算法与PID参数整定相结合,形成IMC-PID整定算法,并将单变量IMC-PID控制推广,设计出符合多变量特点的IMC-PID控制器,主IMC-PID控制器用于保证输出的动态响应,副IMC-PID控制器用于及时克服回路间的耦合干扰,实现控制器解耦。并通过仿真实例证明了IMC-PID参数整定算法的有效性和鲁棒性。
第六章基于鲁棒控制的相关理论,介绍了两种多变量鲁棒PID控制器参数整定的方法,一种为多指标相容下多变量PID参数整定,该算法保证了闭环系统的稳定性,并具有一定衰减度,且符合鲁棒性能指标H_∞约束;另一种为基于结构Lyapunov矩阵的多变量PID参数整定,保证了闭环系统的稳定性,且符合鲁棒性能指标H_2/H_∞约束。最后对化工生产中的实际模型,进行了仿真,以证明算法的有效性。
在论文的最后,对所做的工作做了总结与前景展望。
The traditional identification and PID control are suitable for industry produce in many cases, but for model error, the system with big delay time and the multivariable system with coupling which often appear in industrial processes, the classical methods can not work well. Therefore, the reasonable methods for multivariable system should be studied, to get better control effect and adaptability for complex industrial processes.
The paper begins to research in two sections: identification of the multivariable system and the methods of tuning PID. The important point is how to tune PID parameters for multivariable system, many tests have been done and get some valuable conclusions.
Before the research for tuning PID, the two methods of identification are introduced: least squares algorithm and stochastic hierarchical gradient algorithm. After discussing the theory of the algorithms, the validity and veracity are checked by simulation experiments.
In the section of tuning PID, the summary about the basic principle and characteristic of PID controller firstly are introduced. Secondly, the paper explains the sort and traditional method of PID parameters tuning. Meantime, the methods for multivariable system are summarized, then the detailed studies are discussed: predictive-PID parameters tuning method, IMC-PID parameters tuning method and robust-PID parameters tuning method. These methods are studied in three chapters.
In the forth chapter, with the basic principle of prediction algorithm, the idea of GPC with PID control is provided. Considering to optimize PID parameters, an amelioration Predictive-PID parameters tuning method brings forward. Otherwise, GPC-PID is applied in multivariable system. Comparing with the traditional PID parameters tuning methods (for example, the Z-N tuning method), Predictive-PID tuning method not only has better dynamic response characteristic, but also has satisfying control effect for the instances which have difficulties in controlling for traditional tuning methods, for example, model error and big delay time.
In fifth chapter, firstly, the basic principle of IMC algorithm is introduced, then IMC-PID parameters tuning method that combines the idea of IMC with PID control is offered. Otherwise, IMC-PID is applied in multivariable system to form four PID controllers, two primary PID is used to satisfy the dynamic response of system and two assistant PID is used to eliminate disturb between two recycles. The validity and robustness are checked by simulation experiments.
In the sixth chapter, under the basic principle about robust algorithm, two PID parameters tuning methods for multivariable system are introduced .One is multivariable PID controller's design with multi-objective consistency, the other is the multivariable H_2/H_∞PID controller's design based on structureLyapunov matrix. Then, the validity and robustness are checked for real model in chemical process.
At last, the paper concludes by summarizing some key contents of what have been done and future work.
引文
[1]方崇智,萧德云.过程辨识[M].北京:清华大学出版社,1998
[2]陶永华.新型PID控制及其应用[M].第2版.北京:机械工业出版社,2002-1-11
[3]Gopinath.On the Identification of Linear Time-invariant Systems from Input-Output Data[J].Bell Dydtem Techn.,1969,48:1101-1113
[4]Budin M.A..Minimal Realization of Discrete System from Input-Output Observation[J].IEEE Trans.on Automatic Control,1971,AC-16:395-401
[5]王秀峰,卢贵章.多变量线性系统的递推辨识算法[J].自动化学报,1981,7(4):274-282
[6]FengDing,TongwenChen.Hierarchical gradient-based identification of multivariable discrete-time systems[J].Automatica,2005,41:315-325
[7]王顺晃,舒迪前.智能控制系统及其应用[M].机械工业出版社.1998
[8]朱豫才.过程控制的多变量系统辨识[M].长沙:国防科技大学出版社,2005,2-40
[9]潘立登、潘仰东.系统辨识[M].北京:化学工业出版社,2004
[10]Ding.F,J.B.,and Xu.Y.M,Hierarchical identification and its convergence for the transfer function matrix[A].Proceedings of IFAC Symposium on System identification[C].USA:Santa Barbara,2000
[11]Li.D.,Shah,S.L.,and Chen.T.Identification of fast-rate models from multirate data[J].International Journal of Control,2001,74(7):680-689
[12]Li.D.,Shah,S.L.,and Chen.T.Analysis of dual-rate inferential control systems[J].Automatica,2002,38(6):1053-1059
[13]Li.D.,Shah,S.L.,Chen.T.and Qi.K.Z.Application of dual-rate modeling to CCR octane quality inferential control.IEEE Transactions on Control Systems Technology.2003,11(1):43-51
[14]Dynamical hierarchical control[M].New York:North Holland Publishing Company,1980
[15]Sinha,Kwong.Recursive estimation of the parameters of linear multivariable systems[J].Automatica,1979,15:471-475
[16]Tamura,Yoshikawa.Large-scale systems control and decision making[M].New York and Basel:Marcel Dekker.inc,1990
[17]Drouin.M,Abou-Kandil.H and Maritom.M.Control of complex systems:methods and technology.New York,Lodon:Plenum Press,1991
[18]王伟,张晶涛,柴天佑.PID参数先进整定方法综述[J].自动化学报,2000,26(3):347-355
[19]Ho W.K,Lim K.W,XuW.Optimal gain and phase margin tuning for PID controllers[J].Automatica,1998,34(8):1009-1014
[20]柴天佑,张贵军.基于给定的相角裕度和幅值裕度PID参数自整定新方法[J].自动化学报,1997,23(2):167-172
[21]翁维勤,孙洪程.过程控制系统及工程[M].第2版.北京:化学工业出版社,1995.47-50
[22]Leonid Reznik,omar Ghanayem,Anna Bourmistror.PID plus fuzzy controller structures as a design base for industrial applications[J].Engineering Applications of Artificial Intelligence,2000,13(5):419-430
[23]Loh A P,Hang C C,Quek C K,VasnaniV U.Auto tuning of multiloop proportional integral controllers using relay feedback[J].Ind.Eng ng.Chem.Res.,1993,32:1102-1107
[24]QING-GUO WANG,BIAO ZOU,TONG-HENG LEE,QIANG BI.Auto-tuning of Multivariable PID Controllers from Decentralized Relay Feedback[J].Chemical Engineering Science,2002,46(20):496-510
[25]蒋蔚孙,叶银钟.多变量控制系统分析与设计[M].第2版.北京:中国石化出版社,1997.256-260
[26]薛美胜,吴刚,孙德敏等.工业过程的先进控制[J].化工自动化及仪表,2002,29(2):1-9
[27]王树青.先进控制技术及应用[M].北京:化学工业出版社,2001.45-55
[28]刘金锟.先进PID控制及其MATLAB仿真[M].北京:电子工业出版社,2003.49-50
[29]邵惠鹤,任正云.预测PID控制算法的基本原理和研究现状[J].自动化软件技术,2004,6:17-21
[30]K.K.Tan,S.N.Huang,T.H.Lee.Development of a GPC-based PID controller for unstable systems with deadtime[J].ISA Transactions,2000,39:57-70
[31]Lu Jialiang,Chen Guanrong,Ying Hao.Predictive fuzzy PID control theory[J],design and simulation,Information Sciences,2001,137:157-187
[32]李林欢,苏宏业,褚健.一类多输入多输出系统的预测PID控制算法仿真[J].系统仿真学报,2004,16(3):495-503
[33]R.M.Miller,S.L.Shah,R.K.Wood,E.K.Kwok.Predictive PID[J],ISA Transaction,1999,38:11-23
[34]陈增强,袁著祛.PI型广义平均预测控制器及其仿真[J].决策与控制,1996,11(6):702-706
[35]Garcia,C.E.and Morari,M.Intemal Model Control.1.A Unifying Review and Some New Results[J].Int.Eng.Chem.Process Des.Dev.,1982,21:308-323
[36]林艳春.多变量内模控制方法的研究[D].北京:北京化工大学,2006
[37]H.T.Toivonen,K.V.Sandstrom,R.H.Nystrom.Internal model control of nonlinear systems described by velocity-based linearizations[J].Journal of Process Control,2003,13:215-224
[38]Hu Qiuping,Gade Pandu Rangaiah.Adaptive internal model control of nonlinear process [J].Chemical Engineering Science.,1999,54:1205-1220
[39]Wang Qing-Guo,C.C.Hang,Yang Xue-Ping.Single-loop controller design via IMC principles[J].Automatica,2001,37:2041-2048
[40]王文新,潘立登.IMC-PID鲁棒控制器设计及其在蒸馏装置上的应用[J].北京化工大学学报,2004,31(5):93-96
[41]刘国华.鲁棒PID控制器的研究[D].东华大学,2006.
[42]解学书,钟宜生.鲁棒控制理论[M].北京:清华大学出版社,1994.
[43]俞立.鲁棒控制-线性矩阵不等式处理方法[M].北京:清华大学出版社,2003.
[44]臧文利,郭治.基于LMI的随动系统PID控制下的多指标相容性[J].吉林大学学报(工学版),200636(5):745-750.
[45]Zheng Feng,Wang Qingguo,Lee Tongheng.On the design of multivariable PID controller via LMI approach[J].Automatica,2002,38:517-526
[46]Garcia-Alvarado M A,Ruiz-Lopez I I,Torres-Ramos T.Tuning of multivariate PID controllers based on characteristic matrix eigenvalues,Lyapunov functions and robustness criteria[J].Chemical Engineering Science,2005,60:897-905.
[47]Cao Y Y,Lam J,Sun Y X.Static output feedback stabilization:an LMI approach[J].Automatica,1998,34(12):1641-1665.
[48]Boyd S,Feron E,Balakrishnan V et al.Linear matrix inequality in system and control theory[M].Philadelphia:SLAM,1994.
[49]Masubuchi I,Kamitane Y,Ohara A,et al.H_∞ control for descriptor systems:A matrix inequalities approach[J].Automatica,33(4),1997:669-673.
[50]Prempain E,Postlethwaite I.Static output feedback stabilisation with H_∞ performance for a class of plants[J].Systems & Control Letters,2001,43:159-166
[51]Chien I L,Huang H P.A simple multi-loop tuning method for PID controllers with no proportional kick[J].Ind.Eng.Chem.Res.,1999,38:1456-1468
[52]王钊,李树荣.基于H_∞控制的Smith预估器及其在Wood-Berry精馏塔设计中的应用[J].石油大学学报,2004,28(4):134-140
[53]Benton R E,Jr,Smith D.Static output feedback stabilization with prescribed degree of stability[J].IEEE Trans on Automat Contr,1998.43(10):1493-1496.
[54]Kim J S,Moon H Y.Structurally constrained H_2 and H_∞ control:A rank-constrained LMI approach[J].Automatic,2006,42:1583-1588
[55]项基,张晓宇,苏宏业.基于结构Lyapunov矩阵的静态输出反馈镇定[J].控制与决策,2004,19(9):978-993.
[56]Gahinet P,Nemirovski A,Laub A J,et al.LMI Control Toolbox[M].The Mach Works Inc,1995.