单变量系统辨识方法的研究与仿真
|
摘要
精确的对象数学模型是先进控制理论应用的必要前提,是否能够得到表征系统特性的模型对优化控制起至关重要的作用。本文对系统辨识的原理方法、信号的选择等方面重点介绍,并通过仿真采集数据信息进行辨识计算。针对实际工业应用情况做了以下几个方面的工作：
1、介绍系统辨识的发展情况以及现代辨识方法,描述了模型类型、建模方法以及误差准则的选取。对经典的辨识算法：最小二乘法、图解法、基于FIR模型的最小二乘法通过仿真对系统模型进行辨识得出各算法的优缺点。
2、研究NLJ、粒子群优化算法(PSO)以及遗传算法(GA)在系统辨识中的应用,并针对在实际应用中,遗传算法收敛速度慢、精度较低、易陷入局部最优等缺点,通过修改参数变化范围的上限对遗传算法进行改进,能够保证算法跳出局部最优所搜到参数的无偏一致估计。在满意度的概念上利用改进的遗传算法优化控制器参数,能够得到满足要求的控制系统。
3、针对实际应用过程中,控制回路不允许转换成开环形式但经典辨识算法无法直接应用于闭环辨识的情况,将粒子群算法的全局搜索能力和Rosenbrock算法的局部搜索能力结合,提出了PSO-Rosenbrock算法。该算法不需要控制器的先验知识,在闭环条件下,对任意测试信号都能获得待估对象的所有参数,不仅提高了收敛速度,缩短了辨识时间,同时极大地减小了模型辨识参数对参数初始值依赖性。
4、介绍常用的多项式预测滤波、中值滤波以及三次函数替代滤波算法,均具有较强的滤波能力。但是过于平滑的或有失真的波形会减少数据提供的有效信息,降低辨识精度。通过对中值滤波数据采用取均值的方式进行滤波,能够有效地去除脉冲废值并提供更多的信息量,与单纯中值滤波相比辨识结果大幅改善。
Application of advanced control theory is based on object's accurate mathematical model and the system character plays a critical role in optimal control. In this paper, the principle of system identification methods, signal selection and so on are focused and make identification calculations based on collected data information get by simulation. Based on practical industrial application, this paper make following contributions:
1、Introduce the development of system identification as well as modern methods and describe the model types, modeling methods and error criteria. Analysis classical identification algorithms:least squares method, graphical method, direct identification method for continuous by simulation and obtain the advantages and disadvantages of each method.
2、Research NLJ, particle swarm optimization (PSO) and genetic algorithm (GA) in system identification applications. In real applications, GA which is easy to fall into local optimum has low convergence speed, less precise. In this paper, GA is improved by adding high limit which ensure that the algorithm can jump out of local optimal search parameters to get consistent and unbiased estimates. Based on the concept of satisfaction, optimize the controller parameters by using the improved genetic algorithm meet the requirements of the control system.
3、For the practical application process, control loop is not allowed converted into the open-loop form, but classical identification algorithms can not be applied to the closed-loop identification directly. a novel identification method—PSO-Rosenbrock is proposed by integrating global identification ability of Particle Swarm Optimization (PSO) and local search competence of Rosenbrock. The algorithm does not require prior knowledge of controllers on closed loop conditions and can obtain the all of the parameters to be estimated based on arbitrary test signal. This algorithm can not only improve the convergence rate but also reduce the dependence of identification parameters on initial parameters.
4、Describe commonly used polynomial prediction filter, median filter and three alternative filtering algorithms function which all have strong filtering. But if the waveform is too smooth or anamorphic it will reduce useful information provided by data and identification accuracy. Take average valued of median filter can effectively remove the scrap value of the pulse and provide more information. Compared with the simple median filter, this method can improve identification results.
1、介绍系统辨识的发展情况以及现代辨识方法,描述了模型类型、建模方法以及误差准则的选取。对经典的辨识算法：最小二乘法、图解法、基于FIR模型的最小二乘法通过仿真对系统模型进行辨识得出各算法的优缺点。
2、研究NLJ、粒子群优化算法(PSO)以及遗传算法(GA)在系统辨识中的应用,并针对在实际应用中,遗传算法收敛速度慢、精度较低、易陷入局部最优等缺点,通过修改参数变化范围的上限对遗传算法进行改进,能够保证算法跳出局部最优所搜到参数的无偏一致估计。在满意度的概念上利用改进的遗传算法优化控制器参数,能够得到满足要求的控制系统。
3、针对实际应用过程中,控制回路不允许转换成开环形式但经典辨识算法无法直接应用于闭环辨识的情况,将粒子群算法的全局搜索能力和Rosenbrock算法的局部搜索能力结合,提出了PSO-Rosenbrock算法。该算法不需要控制器的先验知识,在闭环条件下,对任意测试信号都能获得待估对象的所有参数,不仅提高了收敛速度,缩短了辨识时间,同时极大地减小了模型辨识参数对参数初始值依赖性。
4、介绍常用的多项式预测滤波、中值滤波以及三次函数替代滤波算法,均具有较强的滤波能力。但是过于平滑的或有失真的波形会减少数据提供的有效信息,降低辨识精度。通过对中值滤波数据采用取均值的方式进行滤波,能够有效地去除脉冲废值并提供更多的信息量,与单纯中值滤波相比辨识结果大幅改善。
Application of advanced control theory is based on object's accurate mathematical model and the system character plays a critical role in optimal control. In this paper, the principle of system identification methods, signal selection and so on are focused and make identification calculations based on collected data information get by simulation. Based on practical industrial application, this paper make following contributions:
1、Introduce the development of system identification as well as modern methods and describe the model types, modeling methods and error criteria. Analysis classical identification algorithms:least squares method, graphical method, direct identification method for continuous by simulation and obtain the advantages and disadvantages of each method.
2、Research NLJ, particle swarm optimization (PSO) and genetic algorithm (GA) in system identification applications. In real applications, GA which is easy to fall into local optimum has low convergence speed, less precise. In this paper, GA is improved by adding high limit which ensure that the algorithm can jump out of local optimal search parameters to get consistent and unbiased estimates. Based on the concept of satisfaction, optimize the controller parameters by using the improved genetic algorithm meet the requirements of the control system.
3、For the practical application process, control loop is not allowed converted into the open-loop form, but classical identification algorithms can not be applied to the closed-loop identification directly. a novel identification method—PSO-Rosenbrock is proposed by integrating global identification ability of Particle Swarm Optimization (PSO) and local search competence of Rosenbrock. The algorithm does not require prior knowledge of controllers on closed loop conditions and can obtain the all of the parameters to be estimated based on arbitrary test signal. This algorithm can not only improve the convergence rate but also reduce the dependence of identification parameters on initial parameters.
4、Describe commonly used polynomial prediction filter, median filter and three alternative filtering algorithms function which all have strong filtering. But if the waveform is too smooth or anamorphic it will reduce useful information provided by data and identification accuracy. Take average valued of median filter can effectively remove the scrap value of the pulse and provide more information. Compared with the simple median filter, this method can improve identification results.
引文
[1]邵惠鹤.工业过程高级控制[M].上海：上海交通大学出版社,1977
[2]俞金寿.新进控制技术与应用[J].世界仪表与自动化,2005,7：18-24
[3]B. Roffel, B. H. Betlem. Advanced Practical Process Control[M]. Berlin, Springer,2004
[4]潘立登,潘仰东.系统辨识与建模[M].北京：化学工业出版社,2004,81-133,197-206
[5]Zadeh L. A. From Circuit Theory to System Theory[J]. Proc. IRE,1962,50(5): 856-865
[6]I. Gustavsson, L.Ljung. Sodersrtrom T. Identification of Process in Closed Loop-Identification and Accuracy Aspects [J]. Automatica,1977,13(4):59-75
[7]张嗣瀛,高立群.现代控制理论[M].北京：清华大学出版社,2006,
[8]Von Lennart Ljung.System Identification- Theory for the User[M]. NJ:, Englewood Cliffs,1999:133-258
[9]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
[10]张勇,杨慧中.有色噪声干扰输出误差系统的偏差补偿地退最小二乘辨识算法[J].自动化学报,2007,33(10),1053-1060
[11]高颖,李月,杨宝俊.加性噪声背景下基于ICA的线性系统辨识算法[J].系统仿真学报,2008,20(18),4813-4816
[12]Anna Hagenblada, Lennart Ljung, Adrian Wills. Maximum likelihood identification of Wiener models[J]. Automatica,2008(44),2697-2705
[13]Roberto Diversi, Roberto Guidorzi, Umberto Soverini. Maximum Likehood Identification of Noisy-input-output Models[J]. Automatica,2007,4,464-472
[14]朱幼莲.一种新的基于极大似然估计的系统辨识算法[J].现代雷达,1998,20(1),33-38
[15]王永,李旺,梁青.多变量频域极大似然辨识算法研究[J].东南大学学报(自然科学版),2005,35(增刊Ⅱ)：15-21
[16]Landau I.D, Karimi A. Recursive for Identification in Closed loop- a Unified Approach and Evaluation[J]. Decision and Control,1996(2),1391-1396
[17]Giannakis G B. Polyspectral and cylostationary approaches for identification of closed- loop systems[J]. Automatic Control,1995,40(5):882-885
[18]莫建林,王伟,许晓鸣,张卫东.系统辨识中的闭环问题[J].控制理论与应用,2002,4(9)：15-16
[19]潘立登.最优化在在线调节器整定中的应用[J].北京化工大学学报,1984,11(2),17-20
[20]马俊英,罗元浩,潘立登.用改进的NLJ方法辨识闭环系统的模型参数及滤波器设计[J].北京化工大学学报,2003,30(4),95-98
[21]Van den Hof P M J, Schrama R J P. An Indirect Method for Transfer Function Estimation from Closed-loop Data[J]. Automatica,1993,29(6),1523-1527
[22]曹江涛,李平,郭丹.两阶段闭环辨识算法仿真[J].石油化工高等学校学报,2003,16(3),70-74
[23]Timothy I. Salsbury. Continuous-time model identification for closed loop control performance assessment[J]. Control Engineering Practice,2007(15),109-121
[24]Hua Mei, Shaoyuan Li, Wen-Jia Cai, QiangXiong. Decentralized Closed-loop Parameter Identification for Multivariable Processes from Step Responses[J]. Mathematica and Computers in Simulation,2005(68),171-192
[25]靳其兵,夏丹阳.一种闭环条件下的多变量系统辨识方法[J].微计算机信息,2007,23(7-1),282-284
[26]L Miskovic, A Kzrimi, D Bonvin, M Gevers. Closed-loop Identification of Multivariable System:With or Without Excitation of All Reference?[J]. Automatica,2008(44),2048-2056
[27]Linard N. Anderson B D O and De Bruyne F. Identification of a nonlinear plant under nonlinear feedback using left coprime fractional based representations [J]. Automatica,1999,35(4):655-667
[28]刘德,王先上.多变量线性系统的在线辨识[J].系统工程,1989,7(16),59-63
[29]甄新平,李全善,姜景杰,潘立登,闻光辉.一种可在线实现的对象辨识新方法[J].北京化工大学学报,2006,33(6),74-77
[30]Oscar Gomez, Yury Orlov, Ilya V Kolmanovsky. On-line Identification of SISO Linear Time-invariant Delay Systems from Output Measurements [J]. Automatica, 2007(43),2060-2069
[31]王琳,马平.系统辨识方法综述[J].电力情报,2001,4：63-66
[32]张言俊,张科.系统辨识理论及应用[M].北京：国防工业出版社,2004
[33]郑大钟.线性系统理论[M].北京：清华大学出版社,2005
[34]历玉鸣,马召坤,王晶.自动控制原理[M].北京：化学工业出版社,2005
[35]夏天长.系统辨识——最小二乘法[M].北京：清华大学出版社,1983
[36]Jie Ding, Feng Ding, Shi Zhang. Parameter Identification of Multi-input, Single-output Systems Based on FIR Models and Least Squares Principle[J], Applied Mathematics and Computation,2007,2(187):658-668
[37]樊厉,林红权,高东杰.过程控制常用连续模型的直接辨识法及应用[J].控制工程,2006,13(4),310-314
[38]Luss R, Jaakola. T.H.I, Optimization by Direct Search and Systematic Reduction of the Size of Search Region-AIChE[J].1973,19(4):760-765
[39]沈佳宁,孙俊,须文波.运用QPSO算法进行系统辨识的研究[J].计算机工程与应用,2009,45(9),67-70
[40]Gen M, Cheng R W. Genetic Algorithms and Engineering Design[M]. New York: John Wiley and Sons,1997.
[41]沈春华,浮点数编码的遗传算法在系统辨识中的应用[J].应用科学学报,2001, 19(4),299-302
[42]王振雷.基于实值遗传算法的模糊神经网络辨识器[J].东北大学学报(自然科学版),2000,21(4),354-356
[43]郭治.满意控制与估计概述[C].中国控制与决策学术年会论文集,大连：大连海事大学出版社,1998
[44]李艳红.基于满意度的NLJ算法在火电厂锅炉控制系统中的研究与应用[D].安徽：合肥工业大学,2009
[45]方崇智,萧德云.过程辨识(第一版)[M].北京：清华大学出版社,1998
[46]T.C.Hsia系统辨识与应用[M].长沙：中南工业大学出版社,1986
[47]林川,泻全源.基于微Ⅰ暾群本质特征鹃混沌微粒群优化算法.[J].西南交通大学学报,2007,42(6),665-669
[48]Shi Y, Eberhant R C A Modified Particle Swarm Optimazer[R]. Alaska, IEEE International Conference of Evolutionary Computation,1998
[49]袁亚湘,孙文瑜,石钟慈,李岳生.最优化理论与方法[M].北京：科学出版社,1997
[50]Paul M, R. J. P. Schrama. Identification and Control — Closed-loop Issuse[J]. Automatica,1995,31(12),1751-1779
[51]徐小平,钱富才,刘丁,王峰.基于PSO算法的系统辨识方法[J].系统仿真学报.2008,20(13),3525-3528
[2]俞金寿.新进控制技术与应用[J].世界仪表与自动化,2005,7：18-24
[3]B. Roffel, B. H. Betlem. Advanced Practical Process Control[M]. Berlin, Springer,2004
[4]潘立登,潘仰东.系统辨识与建模[M].北京：化学工业出版社,2004,81-133,197-206
[5]Zadeh L. A. From Circuit Theory to System Theory[J]. Proc. IRE,1962,50(5): 856-865
[6]I. Gustavsson, L.Ljung. Sodersrtrom T. Identification of Process in Closed Loop-Identification and Accuracy Aspects [J]. Automatica,1977,13(4):59-75
[7]张嗣瀛,高立群.现代控制理论[M].北京：清华大学出版社,2006,
[8]Von Lennart Ljung.System Identification- Theory for the User[M]. NJ:, Englewood Cliffs,1999:133-258
[9]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
[10]张勇,杨慧中.有色噪声干扰输出误差系统的偏差补偿地退最小二乘辨识算法[J].自动化学报,2007,33(10),1053-1060
[11]高颖,李月,杨宝俊.加性噪声背景下基于ICA的线性系统辨识算法[J].系统仿真学报,2008,20(18),4813-4816
[12]Anna Hagenblada, Lennart Ljung, Adrian Wills. Maximum likelihood identification of Wiener models[J]. Automatica,2008(44),2697-2705
[13]Roberto Diversi, Roberto Guidorzi, Umberto Soverini. Maximum Likehood Identification of Noisy-input-output Models[J]. Automatica,2007,4,464-472
[14]朱幼莲.一种新的基于极大似然估计的系统辨识算法[J].现代雷达,1998,20(1),33-38
[15]王永,李旺,梁青.多变量频域极大似然辨识算法研究[J].东南大学学报(自然科学版),2005,35(增刊Ⅱ)：15-21
[16]Landau I.D, Karimi A. Recursive for Identification in Closed loop- a Unified Approach and Evaluation[J]. Decision and Control,1996(2),1391-1396
[17]Giannakis G B. Polyspectral and cylostationary approaches for identification of closed- loop systems[J]. Automatic Control,1995,40(5):882-885
[18]莫建林,王伟,许晓鸣,张卫东.系统辨识中的闭环问题[J].控制理论与应用,2002,4(9)：15-16
[19]潘立登.最优化在在线调节器整定中的应用[J].北京化工大学学报,1984,11(2),17-20
[20]马俊英,罗元浩,潘立登.用改进的NLJ方法辨识闭环系统的模型参数及滤波器设计[J].北京化工大学学报,2003,30(4),95-98
[21]Van den Hof P M J, Schrama R J P. An Indirect Method for Transfer Function Estimation from Closed-loop Data[J]. Automatica,1993,29(6),1523-1527
[22]曹江涛,李平,郭丹.两阶段闭环辨识算法仿真[J].石油化工高等学校学报,2003,16(3),70-74
[23]Timothy I. Salsbury. Continuous-time model identification for closed loop control performance assessment[J]. Control Engineering Practice,2007(15),109-121
[24]Hua Mei, Shaoyuan Li, Wen-Jia Cai, QiangXiong. Decentralized Closed-loop Parameter Identification for Multivariable Processes from Step Responses[J]. Mathematica and Computers in Simulation,2005(68),171-192
[25]靳其兵,夏丹阳.一种闭环条件下的多变量系统辨识方法[J].微计算机信息,2007,23(7-1),282-284
[26]L Miskovic, A Kzrimi, D Bonvin, M Gevers. Closed-loop Identification of Multivariable System:With or Without Excitation of All Reference?[J]. Automatica,2008(44),2048-2056
[27]Linard N. Anderson B D O and De Bruyne F. Identification of a nonlinear plant under nonlinear feedback using left coprime fractional based representations [J]. Automatica,1999,35(4):655-667
[28]刘德,王先上.多变量线性系统的在线辨识[J].系统工程,1989,7(16),59-63
[29]甄新平,李全善,姜景杰,潘立登,闻光辉.一种可在线实现的对象辨识新方法[J].北京化工大学学报,2006,33(6),74-77
[30]Oscar Gomez, Yury Orlov, Ilya V Kolmanovsky. On-line Identification of SISO Linear Time-invariant Delay Systems from Output Measurements [J]. Automatica, 2007(43),2060-2069
[31]王琳,马平.系统辨识方法综述[J].电力情报,2001,4：63-66
[32]张言俊,张科.系统辨识理论及应用[M].北京：国防工业出版社,2004
[33]郑大钟.线性系统理论[M].北京：清华大学出版社,2005
[34]历玉鸣,马召坤,王晶.自动控制原理[M].北京：化学工业出版社,2005
[35]夏天长.系统辨识——最小二乘法[M].北京：清华大学出版社,1983
[36]Jie Ding, Feng Ding, Shi Zhang. Parameter Identification of Multi-input, Single-output Systems Based on FIR Models and Least Squares Principle[J], Applied Mathematics and Computation,2007,2(187):658-668
[37]樊厉,林红权,高东杰.过程控制常用连续模型的直接辨识法及应用[J].控制工程,2006,13(4),310-314
[38]Luss R, Jaakola. T.H.I, Optimization by Direct Search and Systematic Reduction of the Size of Search Region-AIChE[J].1973,19(4):760-765
[39]沈佳宁,孙俊,须文波.运用QPSO算法进行系统辨识的研究[J].计算机工程与应用,2009,45(9),67-70
[40]Gen M, Cheng R W. Genetic Algorithms and Engineering Design[M]. New York: John Wiley and Sons,1997.
[41]沈春华,浮点数编码的遗传算法在系统辨识中的应用[J].应用科学学报,2001, 19(4),299-302
[42]王振雷.基于实值遗传算法的模糊神经网络辨识器[J].东北大学学报(自然科学版),2000,21(4),354-356
[43]郭治.满意控制与估计概述[C].中国控制与决策学术年会论文集,大连：大连海事大学出版社,1998
[44]李艳红.基于满意度的NLJ算法在火电厂锅炉控制系统中的研究与应用[D].安徽：合肥工业大学,2009
[45]方崇智,萧德云.过程辨识(第一版)[M].北京：清华大学出版社,1998
[46]T.C.Hsia系统辨识与应用[M].长沙：中南工业大学出版社,1986
[47]林川,泻全源.基于微Ⅰ暾群本质特征鹃混沌微粒群优化算法.[J].西南交通大学学报,2007,42(6),665-669
[48]Shi Y, Eberhant R C A Modified Particle Swarm Optimazer[R]. Alaska, IEEE International Conference of Evolutionary Computation,1998
[49]袁亚湘,孙文瑜,石钟慈,李岳生.最优化理论与方法[M].北京：科学出版社,1997
[50]Paul M, R. J. P. Schrama. Identification and Control — Closed-loop Issuse[J]. Automatica,1995,31(12),1751-1779
[51]徐小平,钱富才,刘丁,王峰.基于PSO算法的系统辨识方法[J].系统仿真学报.2008,20(13),3525-3528