為了增加產能及降低成本，設計良好的控制系統對於環安法規日益嚴格的化工產業愈趨重要，而優異的鑑別方法就是控制器設計的要素。但是化工程序複雜多變的非線性動態，大幅增添了鑑別的困難，而其普遍性更使得此非線性行為難以忽視。本論文針對各種非線性程序，應用Laguerre與Kautz離散展開式獲得極佳的Hammerstein與Wiener近似模型，適合控制器設計之用。
基於Hammerstein模型的鑑別法，採用多項式來描述非線性程序非線性靜態部分，以Laguerre ARX (外因輸入自動回歸)模型來代表線性動態部分，並成功地引用疊代式演算法來更新內部變數估測。此疊代鑑別法，有別於傳統線性鑑別法，不僅能夠處理完整的程序非線性特性，而且擁有極佳的收斂與準確性。數個實際程序之模擬鑑別結果顯示，所提Hammerstein鑑別法對於各種非線性動態與測試條件均有優異表現，經適當修改即可有效引入線性控制技術。
本文也提出Wiener模型的非疊代鑑別法，引用Laguerre FIR (有限脈衝響應)或Kautz FIR模型來代表線性動態，而靜態非線性則由逆反多項式函數來描述。此作法的優點在於，導出的回歸方程式將不含未知的內部變數，因此可進行非疊代式參數估測，有效解決了現有Wiener模型疊代式鑑別法的參數收斂性問題。另外，藉由調整逆反多項式的參考點，可降低測試實驗設計和量測雜訊的影響。此鑑別法可有效應用於多種程序非線性及範圍廣泛的測試條件，對於非線性控制器設計相當有用。

To increase production and reduce cost, well-designed control systems play an important role in chemical industry, subjected to stricter environmental constraints. On the other hand, a good identification method is crucial to controller design. However, complex nonlinear dynamics in chemical processes can cause considerable difficulties in identification, and such a nonlinear behavior cannot be ignored because of its prevalence. This thesis applies the Laguerre and Kautz descrete expansions to identify good Hammerstein and Wiener models, suited to controller design, for a wide variety of nonlinear processes.
The identification method based on the Hammerstein model describes the nonlinear static part by a polynomial, uses the Laguerre ARX (AutoRegressive with eXogenous input) model to represent the linear dynamic part, and successfully update the estimate of the internal variable by an iterative algorithm. Unlike conventional linear identification methods, the proposed method can not only deal with the entire nonlinear process characteristics, but also possesses excellent convergence and accuracy. Simulation results on several practical processes demonstrate that the proposed method performs well for a wide range of nonlinear dynamics and test conditions. The resultant Hammerstein model can be easily adapted to linear control techniques.
This thesis also proposes a non-iterative identification method based on a Wiener model. The method describes the linear dynamics by Laguerre FIR (Finit Impulse Response) or Kautz FIR models and approximates the static nonlinearity by an inverse polynomial function. As a result, the unknown internal variable does not appear in the regression equation, thereby allowing non-iterative parameter estimation. This resolves the convergence problem often encountered in available iterative methods for identifying Wiener models. Moreover, the influence of test experimental designs and measurement noise can be reduced by adjusting the reference point of the inverse polynomial. The identification method is effective for a wide range of process nonlinearities and test conditions, and is rather useful for nonlinear controller design.

Al-Duwaish, H.; Karim, M. N. A New Method for the Identification of Hammerstein Model. Automatica 1997, 33, 1871.
Bai, E. W. Decoupling the Linear and Nonlinear Parts in Hammerstein Model Identification. Automatica 2004, 40, 671.
Billings, S. A.; Fakhouri, F. Y. Identification of Nonlinear Systems Using the Wiener Model. Electronics Letters 13.
Bloemen, H. H. J.; Chou, C. T.; van den Boon, T. J. J.; Verdult, V.; Verhaegen, M.; Backx, T. C. Wiener Model Identification and Predictive Control for Dual Composition Control of a Distillation Column. J. Process Control 2001, 11, 601.
Boyd, S.; Chua, L. O. Fading Memory and the Problem of Approximating Nonlinear Operators with Volterra Series. IEEE Trans. Circuits Syst. 1985, CAS-32, 1150.
Cervantes, A. L.; Agamennoni, O. E.; Figueroa, J. L. A Nonlinear Model Predictive Control System Based on Wiener Piecewise Linear Models. J. Process Control 2003, 13, 655.
Chang, F. H. I.; Luss, R. A Noniterative Method for Identification Using Hammerstein Model. IEEE Trans. Autom. Control 1971, AC-16, 464.
Chen, H. F. Pathwise Convergence of Recursive Identification Algorithms for Hammerstein Systems. IEEE Trans. Autom. Control 2004, 49, 1641.
Clarke, D. W. Generalized Least Squares Estimation of Parameters of a Dynamic Model. First IFAC Symposium on Identification in Automatic Control Systems. Prague 1967.
Eskinat, E.; Johnson, S. H.; Luyben, W. L. Use of Hammerstein Models in Identification of Nonlinear Systems. AIChE J. 1991, 37, 255.
Fruzzetti, K. P.; Palazoglu, A.; McDonald, K. A. Nonlinear Model Predictive Control Using Hammerstein Models. J. Process Control 1997, 7, 31.
Gallman, P. G. An Iterative Method for the Identification of Nonlinear Systems Using Uryson Model. IEEE Trans. Autom. Control 1975, AC-20, 771.
Haber, R.; Unbehauen, H. Structure Identification of Nonlinear Dynamic Systems－A Survey on Input/Output Approaches. Automatica 1990, 26, 651.
Harris, K. R.; Colantonio, M. C.; Palazoglu, A. On the Computation of a Nonlinearity Measure Using Functional Expansions. Chem. Eng. Sci. 2000, 55, 2393.
Hasting-James, R.; Sage, M. W. Recursive Generalised-Least-Squares Procedures for On-Line Identification of Process Parameters. Proceedings IEE 1969, 116, 2057.
Henson, M. A.; Seborg, D. E. Input-Output Linearization of General Nonlinear Processes. AIChE J. 1990, 36, 1753.
Heuberger, P. S. C.; Van den Hof, P. M. J.; Bosgra, O. H. A Generalized Orthonormal Basis for Linear Dynamical Systems. IEEE Trans. Autom. Control 1995, AC-40, 451.
Hsia, T. C., On Multistage Least-Squares Approach to System Identification. Proceedings, IFAC Sixth World Congress, Paper 118.2, Boston 1975.
Hsia, T. C., System Identification – Least-Squares Methods; Lexington Books: Massachusetts, 1977.
Hu, X. L.; Chen, H. F. Strong Consistence of Recursive Identification for Wiener Systems. Automatica 2005, 41, 1905.
Huang, H. P.; Lee, M. W.; Tang, Y. T. Identification of Wiener Model Using Relay Feedback Test. J. Chem. Eng. Jpn. 1998, 31, 604.
Hwang, S. H.; Lin, M. L. A Method for Identification of Discrete Parametric Models with Unknown Orders and Delays. J. Chin. Inst. Chem. Engrs. 2002, 33, 373.
Hwang, S. H.; Lin, M. L. Unbiased Identification of Continuous Time Parametric Models Using a Time-Weighted Integral Transform. Chem. Eng. Commun. 2003, 190, 1170.
Jia, L.; Chiu, M. S.; Ge, S. S. A Noniterative Neuro-Fuzzy Based Identification Method for Hammerstein processes. Journal of Process Control 2005, 15, 749.
Johansson, R., System Modeling and Identification. Prentice Hall: Englewood Cliffs, New Jersey, 1993.
Kalafatis, A.; Arifin, N.; Wang, L.; Cluett, W. R. A New Approach to the Identification of pH Processes Based on the Wiener Model. Chem. Eng. Sci. 1995, 50, 3693.
Landau, I. D.; Zito, G. Digital Control Systems: Design, Identification and Implementation; Springer: Berlin, 2006.
Lecchini, A.; Gevers, M. Explicit Expression of the Parameter Bias in Identification of Laguerre Models from Step Responses. Syst. Control Lett. 2004, 52, 149.
Lee, M. W.; Huang, H. P. Identification and Control of Hammerstein-Type Nonlinear Process. J. Chin. Inst. Chem. Engrs. 2001, 32, 361.
Lee, Y. W. Synthesis of Electrical Networks by Means of the Fourier Transforms of Laguerre Functions. J. Math Physics. 1933, 11, 83-113.
Ljung, L.; Söderstrom, T. Theory and Practice of Recursive Identification; MIT Press: Cambridge, 1983.
Ljung, L. On the Estimation of Transfer Functions. Automatica 1985, 21, 677.
Ljung, L. System Identification: Theory for the User; Prentice Hall: Englewood Cliffs, New Jersey, 1987.
Ljung, L. System Identification: Theory for the User; Prentice Hall: Upper Saddle River, NJ, 1999.
Murray-Smith, R.; Johansen, T. A. Multiple Model Approaches to Modeling and Control, Taylor and Francis: London, 1997.
Nahas, E. P.; Henson, M. A.; Seborg, D. E. Nonlinear Internal Model Control Strategy for Neural Network Models. Comput. Chem. Eng. 1992, 16, 1992.
Narenda, K. S.; Gallman, P. G. An Iterative Method for the Identification of Nonlinear Systems Using the Hammerstein Model. IEEE Trans. Autom. Control 1997, AC-11, 546.
Norquary, S. J.; Palazoglu, A.; Romagnoli, J. A. Model Predictive Control Based on Wiener Models. Chem. Eng. Sci. 1998, 53, 75.
Palancar, M. C.; Aragon, J. M.; Torrecilla, J. S. pH-Control Systems Based on Artificial Neural Networks. Ind. Eng. Chem. Res. 1998, 37, 2729.
Söderstrom, T. Convergence Properties of the Generalized Least Squares Identification Method. Automatica 1974, 10, 617.
Söderstrom, T.; Stöica, P. G. Comparison of Some Instrumental Variable Methods – Consistency and Accuracy Aspects. Automatica 1981, 17, 101.
Söderstrom, T.; Stöica, P. G. Instrumental Variable Methods for System Identification; Springer: Berlin, 1983.
Söderstrom, T.; Stöica, P. G. System Identification; Prentice Hall Interational: UK, 1989.
Szabo, Z.; Heuberger, P. S. C.;Bokor, J.; Van den Hof, P. M. J. Extended Ho-Kalman Algorithm for Systems Represented in generalized orthonormal base. Automatica 2000, 36, 1809-1818
Voros, J. Modeling and Identification of Wiener Systems with Two-Segment Nonlinearities. IEEE Trans. Contr. Sys. Tech. 2003, 11, 253.
Voros, J. Parameter Identification of Wiener Systems with Multisegment Piecewise-Linear Nonlinearities. Syst. Control Lett. 2007, 56, 99.
Wahlberg, B. System Identification Using Laguerre Models. IEEE Trans. Autom. Control 1991, 36, 551.
Wahlberg, B. System Identification Using Kautz Models. IEEE Trans. Autom. Control 1994, 39, 6.
Wahlberg, B. Makila, P., M.; On Approximation of Stable Linear Dynamical Systems using Laguerre and Kautz Function,” Automatica 1996, 32, 693.
Wigren, T. Recursive Prediction Error Identification Using the Nonlinear Wiener Model. Automatica 1993, 29, 1011.
Wong, K. Y.; Polak, E. Identification of Linear Discrete Time Systems Using the Instrumental Variable Approach. IEEE Trans. Automat. Contr. 1967, AC-12, 707.
陳厚岑, 以方塊導向模型為基礎之非線性程序鑑別, 成功大學化學工程研究所博士論文, 2009.
邱瑩鵑, 非線性離散系統之疊代式鑑別, 成功大學化學工程研究所碩士論文, 2004.