多变量系统辨识与建模技术的研究
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摘要
多变量系统辨识与建模是研究生产过程多变量对象数学模型的理论和方法，是为提高控制系统质量、设计先进控制系统和实现优化控制提供依据的重要核心技术。本文主要研究用观测多变量过程的输入、输出数据来建立对象模型的辨识与建模方法。以几种典型的辨识方法为主线，研究了它们在多变量系统辨识建模中的应用，讨论了开环和闭环两种情况，并针对不同问题提出一些改进算法。阐述了算法在多变量系统开环、闭环在线辨识实现过程中涉及的理论研究、仿真实验，以及从实际应用角度出发的软件编制等问题。不仅对模型参数的辨识做了详细论述，还对模型结构辨识问题进行了探讨和研究。主要工作如下：
深入学习了多变量系统辨识与建模的理论和方法。研究了最小二乘法、辅助变量法、递阶梯度法的理论与算法的实现步骤。重点研究了这些算法在多变量闭环过程中在线辨识的实现步骤。通过仿真实验证明了方法的有效性和准确性。
针对不同问题提出改进算法。为克服数据饱和现象和坏数据对参数辨识的影响，引入加权辅助变量法和多新息梯度法。为让递阶梯度算法能解决有色噪声问题，提出了增广递阶梯度算法。并且针对多变量的闭环辨识提出了两阶段递阶梯度算法。仿真实例证明改进算法能得到满意结果。
探讨了模型结构的辨识。包括模型阶次和纯滞后时间的辨识方法。对用其中的AIC准则法来确定多变量系统模型的阶次给出了仿真研究实例，可以准确地得到模型的阶次。
设计和开发了多变量系统辨识软件包，将文中所述方法作为软件的核心算法加以实现。有利于实际生产过程中建立对象数学模型。
Multivariable system identification and modeling is the theory of multivariable system's mathematic model research in production process. And it is the core technique to improve control system's performance, design the advanced control system and carry out the optimization control. In this thesis, the identification methods using input and output data of the multivariable system to obtain model were studied. Some typical methods were studied into open-loop and close-loop, and some methods were put forward to solve different problems. The theories, simulation experiments and the identification software development were included in this thesis. The identification methods of model's structure were studied in addition to identification of model's parameters. Main work is shown as following.
The theory and methods of multivariable system identification were studied, emphasized on the study of least squares method, instrumental variable method and hierarchical gradient algorithm. The validity and veracity was checked by simulation experiments.
Some improved algorithms were proposed for different situation. Weighted instrumental variable method and multi-innovation gradient algorithm overcome the data saturation and bad data. Extended hierarchical gradient algorithm overcomes the color noise. And two-stage hierarchical gradient algorithm solves the close-loop problem. And the simulation experiments indicated the proposed algorithm has good performance.
The identification of Model's structure was studied, which included model order and lag time. The simulation experiment was given using AIC method.
Identification software for multivariable system was designed and developed. It used the main methods in this thesis as its core algorithms. And it is useful to obtain model in practical process.
深入学习了多变量系统辨识与建模的理论和方法。研究了最小二乘法、辅助变量法、递阶梯度法的理论与算法的实现步骤。重点研究了这些算法在多变量闭环过程中在线辨识的实现步骤。通过仿真实验证明了方法的有效性和准确性。
针对不同问题提出改进算法。为克服数据饱和现象和坏数据对参数辨识的影响，引入加权辅助变量法和多新息梯度法。为让递阶梯度算法能解决有色噪声问题，提出了增广递阶梯度算法。并且针对多变量的闭环辨识提出了两阶段递阶梯度算法。仿真实例证明改进算法能得到满意结果。
探讨了模型结构的辨识。包括模型阶次和纯滞后时间的辨识方法。对用其中的AIC准则法来确定多变量系统模型的阶次给出了仿真研究实例，可以准确地得到模型的阶次。
设计和开发了多变量系统辨识软件包，将文中所述方法作为软件的核心算法加以实现。有利于实际生产过程中建立对象数学模型。
Multivariable system identification and modeling is the theory of multivariable system's mathematic model research in production process. And it is the core technique to improve control system's performance, design the advanced control system and carry out the optimization control. In this thesis, the identification methods using input and output data of the multivariable system to obtain model were studied. Some typical methods were studied into open-loop and close-loop, and some methods were put forward to solve different problems. The theories, simulation experiments and the identification software development were included in this thesis. The identification methods of model's structure were studied in addition to identification of model's parameters. Main work is shown as following.
The theory and methods of multivariable system identification were studied, emphasized on the study of least squares method, instrumental variable method and hierarchical gradient algorithm. The validity and veracity was checked by simulation experiments.
Some improved algorithms were proposed for different situation. Weighted instrumental variable method and multi-innovation gradient algorithm overcome the data saturation and bad data. Extended hierarchical gradient algorithm overcomes the color noise. And two-stage hierarchical gradient algorithm solves the close-loop problem. And the simulation experiments indicated the proposed algorithm has good performance.
The identification of Model's structure was studied, which included model order and lag time. The simulation experiment was given using AIC method.
Identification software for multivariable system was designed and developed. It used the main methods in this thesis as its core algorithms. And it is useful to obtain model in practical process.
引文
[1] 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
[2] 方崇智，萧德云．过程辨识[M]．北京：清华大学出版社，1998
[3] Gopinath. On the Identification of Linear Time-invariant Systems from Input-Output Data [J]. Bell Dydtem Techn, 1969, 48: 1101-1113
[4] M, A. Budin. Minimal Realization of Discrete System from Input-Output Observation[J]. IEEE Trans, On Automatic Control, 1971, AC-16: 395-401
[5] M. A. Budin. A new Approachto System Identification[J]. IEEETrans, Mc, 1972, 2(5): 396-402
[6] P. Passeri, C. J. Herget. Parameter Identification of a Class of Multiple Input-Output Linear Discrete-time System[C]. JAAC, Stanford. 1977. 786-793
[7] R. D. Gupta, F. W. Fariman. Parameter Estimation for Multivariable Systems[J]. IEEE Trans, On Automatic Control, 1974, AC-19: 546-549
[8] R. Guidorzi. Canonical Structure in the Identification of Multivariable System[J]. Automatica, 1975, 11(4), 361-374
[9] N. K. Sinha, Y. H. Kwong. Recursive Identification of the Parameter of Multivariable System[C]. Proc, Of the 4th IFAC Symp, On Multivariable Technological System, 1976. 323-328
[10] Gautheser, I. D. Landau. On the Recursive Identification of the Multi-input-Multi-output System[J]. Automatica, 1978, 604-609
[11] H. EI. Sherief, N. K. Sinha. Stochastic Approximation Algorithm for the Identification of Linear Multivariable System[J]. IEEE Trans. on Automatic Control, 1979, AC-24: 331-332
[12] 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
[13] K. Diekmann, H. Unbehauen. Recursive Identification of Multi-input Multi-output Systems[C]. 5th IFAC Symp. Identification and System parameter Estimation, Darmstadt, FRG, 1979
[14] K. Diekmann, H. Unbehauen. International Conference on Control and its Application. Identification of Submodel of Muti-input Multi-output Systems. [C]. University of Warwick, 1981, 22-25
[15] K. Diekmann, H. Unbehauen. Proceeding of 6th IFAC Symposium: Identification and System Parameter Estimation. [C]. New York, Pergamon, 1983, 235-240
[16] J. Boker., L. Keviczky. Structural Preperties and Structure Estimation of Vector Difference Equations[J]. Int. J. Control, 1982, 36: 461-475
[17] 邓自立，郭一新．多变量CARMA模型的结构辨识．[J]．自动化学报，1986，12(1)：18-24
[18] Pan Lideng, Du Huaijing. Structure and parameters Identification of Multivariable CARMA Models Using SMM-Technique, [C]. IFAC, The 8th Identification and System Parameters Estimation Symposium, Beijing, Aug. 1988, 1003-1007
[19] 潘立登，杜怀京．多变量CARMA模型结构及参数辨识．[C]中国自动化学会控制理论与应用论文集．1988．436-439
[20] 潘立登．多变量系统辨识．[J]．炼油化工学报，1989，1
[21] 潘立登．多变量系统子子模型辨识．[J]．北京化工大学学报．1988，15(4)：80-90
[22] 潘立登，杜怀京．动态多变量CARMA模型结构及参数辨识．[J]．系统工程学报，1992，7(1)：136-144
[23] 张俊芝，熊淑燕．一种辨识多变量系统结构和参数的递推算法．[J]．控制理论与应用，1990，7(2)：78-82
[24] 赖晓平，李瑞胜，洪惠民．多维ARMAX系统辨识的一种新的递推预报误差算法．[J]．信息与控制，1991．1：1-7
[25] 龙茂林，刘永清．一种离散线性多变量系统结构辨识新方法．[J]．自动化学报，1991，17(5)：571-576
[26] 丁锋，谢新民．线性多变量系统的联合辨识算法．[J]．控制理论与应用，1992，9(5)：545-550
[27] FengDing, TongwenChen. Hierarchical gradient-based identification of multivariable discrete-time systems[J]. Automatica, 2005, 41: 315-325
[28] Soderstrom. T and Stoica. P. System Identification[M]. Hemel Hemptead, UK: PrenticeHall. 1989, 13-49
[29] Ljung L. System Identification: Theory for the Users [M]. Englewood Caffs, NI: Prentice-Hall Inc., 1987, 34-67
[30] Gustavsson, Ljung L, and Soderstrom T. Identification of processes in closed loop-identifiability and accuracy aspects[J]. Automatrca. 1977, 13(4): 59-75
[31] 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，2002，19(1)：9-14．
[32] 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
[33] R. J. P. Schrama. An Open-loop Solution to the Approximate Closed-loop Identification[A]. Proc. 9th IFAC/IFORS Symposium Idention and System Parameter Estimation.[C], IEEE Publish Society, Budapest, Magyarorszag, 1991, 1602-1607
[34] Zhang W. X., C. B. Feng. A Bias-correction method for Indirect Identification of Closed-loop System[J]. Automatica, 1995, 31 (7): 1019-1024
[35] Zhang W. X. Identification of Closed-loop System with Low-order Controllers[J]. Automatica, 1996, 32(12): 1753-1757
[36] J. Tugnait. Identification of Multivariable Stochastic Linear System Via Poly spectral Analysis Given Noisy Input-output Time-domain [J]. IEEE Trans. Automatic Control, 1998, 43(8): 1084-1100
[37] 潘立登、潘仰东．系统辨识[M]．北京：化学工业出版社，2004
[38] Sinha. Dynamical hierarchical control[M]. New York: Noah Holland Publishing Company, 1980
[39] Sinha, Kwong. Recursive estimation of the parameters of linear muitivariable systems[J]. Automatica, 1979, 15: 471-475
[40] Tamura, Voshikawa. Large-scale systems control and decision making[M]. New York and Basel: Marcel Dekker. Inc, 1990
[41] Drouin. M, Abou-Kandil. H and Maritom. M, Control of complex systems: methods and technology. New York, Lodon: Plenum Press, 1991
[42] 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
[43] 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
[44] Li.D.,Shah,S.L., and Chen.T. Analysis of dual-rate inferential control systems[J].Automatica,2002,38(6): 1053-1059
[45] 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
[46] Moustafa. Identification of stochastic time-varying systems[J].IEE Proc,Rart D,1983,130(4): 137-142
[47] 丁锋，谢新民，方崇智．时变系统辨识的多新息方法[J]．自动化学报．1996，22(1)：85-91
[48] 丁锋．鞅超收敛定理与遗忘因子最小二乘算法的收敛性分析[J]．控制理论与应用，1997，14(1)：90-95
[49] 丁锋，谢新民，方崇智．辨识时变系统遗忘因子算法的收敛性[J]．控制理论与应用，1994，11(5)：634-638
[50] 冯纯伯，史维．自适应控制[M]．北京：电子工业出版社，1986
[51] 谢新民，丁锋．自适应控制系统[M]．北京：清华大学出版社，2002
[2] 方崇智，萧德云．过程辨识[M]．北京：清华大学出版社，1998
[3] Gopinath. On the Identification of Linear Time-invariant Systems from Input-Output Data [J]. Bell Dydtem Techn, 1969, 48: 1101-1113
[4] M, A. Budin. Minimal Realization of Discrete System from Input-Output Observation[J]. IEEE Trans, On Automatic Control, 1971, AC-16: 395-401
[5] M. A. Budin. A new Approachto System Identification[J]. IEEETrans, Mc, 1972, 2(5): 396-402
[6] P. Passeri, C. J. Herget. Parameter Identification of a Class of Multiple Input-Output Linear Discrete-time System[C]. JAAC, Stanford. 1977. 786-793
[7] R. D. Gupta, F. W. Fariman. Parameter Estimation for Multivariable Systems[J]. IEEE Trans, On Automatic Control, 1974, AC-19: 546-549
[8] R. Guidorzi. Canonical Structure in the Identification of Multivariable System[J]. Automatica, 1975, 11(4), 361-374
[9] N. K. Sinha, Y. H. Kwong. Recursive Identification of the Parameter of Multivariable System[C]. Proc, Of the 4th IFAC Symp, On Multivariable Technological System, 1976. 323-328
[10] Gautheser, I. D. Landau. On the Recursive Identification of the Multi-input-Multi-output System[J]. Automatica, 1978, 604-609
[11] H. EI. Sherief, N. K. Sinha. Stochastic Approximation Algorithm for the Identification of Linear Multivariable System[J]. IEEE Trans. on Automatic Control, 1979, AC-24: 331-332
[12] 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
[13] K. Diekmann, H. Unbehauen. Recursive Identification of Multi-input Multi-output Systems[C]. 5th IFAC Symp. Identification and System parameter Estimation, Darmstadt, FRG, 1979
[14] K. Diekmann, H. Unbehauen. International Conference on Control and its Application. Identification of Submodel of Muti-input Multi-output Systems. [C]. University of Warwick, 1981, 22-25
[15] K. Diekmann, H. Unbehauen. Proceeding of 6th IFAC Symposium: Identification and System Parameter Estimation. [C]. New York, Pergamon, 1983, 235-240
[16] J. Boker., L. Keviczky. Structural Preperties and Structure Estimation of Vector Difference Equations[J]. Int. J. Control, 1982, 36: 461-475
[17] 邓自立，郭一新．多变量CARMA模型的结构辨识．[J]．自动化学报，1986，12(1)：18-24
[18] Pan Lideng, Du Huaijing. Structure and parameters Identification of Multivariable CARMA Models Using SMM-Technique, [C]. IFAC, The 8th Identification and System Parameters Estimation Symposium, Beijing, Aug. 1988, 1003-1007
[19] 潘立登，杜怀京．多变量CARMA模型结构及参数辨识．[C]中国自动化学会控制理论与应用论文集．1988．436-439
[20] 潘立登．多变量系统辨识．[J]．炼油化工学报，1989，1
[21] 潘立登．多变量系统子子模型辨识．[J]．北京化工大学学报．1988，15(4)：80-90
[22] 潘立登，杜怀京．动态多变量CARMA模型结构及参数辨识．[J]．系统工程学报，1992，7(1)：136-144
[23] 张俊芝，熊淑燕．一种辨识多变量系统结构和参数的递推算法．[J]．控制理论与应用，1990，7(2)：78-82
[24] 赖晓平，李瑞胜，洪惠民．多维ARMAX系统辨识的一种新的递推预报误差算法．[J]．信息与控制，1991．1：1-7
[25] 龙茂林，刘永清．一种离散线性多变量系统结构辨识新方法．[J]．自动化学报，1991，17(5)：571-576
[26] 丁锋，谢新民．线性多变量系统的联合辨识算法．[J]．控制理论与应用，1992，9(5)：545-550
[27] FengDing, TongwenChen. Hierarchical gradient-based identification of multivariable discrete-time systems[J]. Automatica, 2005, 41: 315-325
[28] Soderstrom. T and Stoica. P. System Identification[M]. Hemel Hemptead, UK: PrenticeHall. 1989, 13-49
[29] Ljung L. System Identification: Theory for the Users [M]. Englewood Caffs, NI: Prentice-Hall Inc., 1987, 34-67
[30] Gustavsson, Ljung L, and Soderstrom T. Identification of processes in closed loop-identifiability and accuracy aspects[J]. Automatrca. 1977, 13(4): 59-75
[31] 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，2002，19(1)：9-14．
[32] 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
[33] R. J. P. Schrama. An Open-loop Solution to the Approximate Closed-loop Identification[A]. Proc. 9th IFAC/IFORS Symposium Idention and System Parameter Estimation.[C], IEEE Publish Society, Budapest, Magyarorszag, 1991, 1602-1607
[34] Zhang W. X., C. B. Feng. A Bias-correction method for Indirect Identification of Closed-loop System[J]. Automatica, 1995, 31 (7): 1019-1024
[35] Zhang W. X. Identification of Closed-loop System with Low-order Controllers[J]. Automatica, 1996, 32(12): 1753-1757
[36] J. Tugnait. Identification of Multivariable Stochastic Linear System Via Poly spectral Analysis Given Noisy Input-output Time-domain [J]. IEEE Trans. Automatic Control, 1998, 43(8): 1084-1100
[37] 潘立登、潘仰东．系统辨识[M]．北京：化学工业出版社，2004
[38] Sinha. Dynamical hierarchical control[M]. New York: Noah Holland Publishing Company, 1980
[39] Sinha, Kwong. Recursive estimation of the parameters of linear muitivariable systems[J]. Automatica, 1979, 15: 471-475
[40] Tamura, Voshikawa. Large-scale systems control and decision making[M]. New York and Basel: Marcel Dekker. Inc, 1990
[41] Drouin. M, Abou-Kandil. H and Maritom. M, Control of complex systems: methods and technology. New York, Lodon: Plenum Press, 1991
[42] 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
[43] 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
[44] Li.D.,Shah,S.L., and Chen.T. Analysis of dual-rate inferential control systems[J].Automatica,2002,38(6): 1053-1059
[45] 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
[46] Moustafa. Identification of stochastic time-varying systems[J].IEE Proc,Rart D,1983,130(4): 137-142
[47] 丁锋，谢新民，方崇智．时变系统辨识的多新息方法[J]．自动化学报．1996，22(1)：85-91
[48] 丁锋．鞅超收敛定理与遗忘因子最小二乘算法的收敛性分析[J]．控制理论与应用，1997，14(1)：90-95
[49] 丁锋，谢新民，方崇智．辨识时变系统遗忘因子算法的收敛性[J]．控制理论与应用，1994，11(5)：634-638
[50] 冯纯伯，史维．自适应控制[M]．北京：电子工业出版社，1986
[51] 谢新民，丁锋．自适应控制系统[M]．北京：清华大学出版社，2002