本論文主要探討非線性控制器設計，其中很多設計法採用連續線性化的概念，如非線性二次動態矩陣控制，但大範圍的設定點改變常會造成控制器過度反應。另外針對高度非線性程序進行線性化也有困難，失誤的線性化甚至會導致非線性控制器表現失靈。
Wiener模型為一種簡單的非線性程序模型，其結構為線性動態單元後接非線性靜態單元，由於程序的線性部分與非線性部分被區分開，因此大幅降低了線性化過程的困難度，極適合需採用線性化的非線性控制器。
吾人將非線性程序鑑別成Wiener模型，其原理是藉由Laguerre展開式與含可調參考點之逆多項式來分別描述線性動態部分與非線性靜態部分，如此導出的回歸方程式不含未知的內部變數，可有效解決參數估測的收斂性問題。
所提Wiener模型的逆多項式可直接加入回饋路徑，對非線性程序作全域線性化，使得被控程序轉成一線性系統，然後應用線性控制器來完成非線性控制器的設計。本文即利用全域線性化來設計非線性PI與動態矩陣控制器，模擬研究證實即使操作範圍增大也不會有過度反應或控制器失靈的情況發生。

This thesis investigates design methods for nonlinear controllers, many of which employ the concept of successive linearization, such as nonlinear quadratic dynamic matrix control. However, they would overreact to large changes in set-point. On the other hand, the linearization of a highly nonlinear process is rather difficult. Erroneous linearization may even cause the controller to malfunction.
A Wiener model is a kind of simple nonlinear process model, with the structure of a linear dynamic element followed by a nonlinear static element. Because the linear and nonlinear parts of the process are separated, the linearization procedure is greatly simplified. This implies that the Wiener model is suited to a nonlinear controller based on linearization.
We consequently identified the nonlinear processes as Wiener models, where we mainly used the principles of Laguerre expansions and inverse polynomials with an adjustable reference point to describe the linear dynamic element and nonlinear static element, respectively. With this approach, the derived regression equation would not contain any implicit (or unknown) internal variable. This may therefore effectively solve the convergence issue in parameter estimation.
The proposed inverse polynomial of the Wiener model was capable to be added directly to the feedback path, and then global linearization was conducted to the nonlinear processes. This enabled the controlled process to transform into a linear model, which this linear controller was then applied to complete the nonlinear controller design. In this study, global linearization was used to design a nonlinear PI controller and nonlinear dynamic matrix controller. Simulation results in this study demonstrated that even if the operational range increased, the process would not overreact or experience control failure.

Bequette, B. W., Process Control: Modeling, Design, and Simulation, Prentice Hall Professional Technical Reference, Upper Saddle River, 487-519, 2003.
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,” Journal of Process Control, 11, 601-620, 2001.
Boyd, S.; Chua, L. O.,“ Fading memory and the problem of approximating nonlinear operators with Volterra series,” IEEE Trans. Circuits Syst., 11, 1150-1171, 1985.
Cervantes, A. L.; Agamennoni, O. E.; Figueroa, J. L.,“ A nonlinear model predictive control system based on Wiener piecewise linear models,” Journal of Process Control, 11, 655-666, 2003.
Chien, I. L.; Fruehauf, P. S.,“ Consider IMC tuning to improve controller performance,” Chem. Eng. Prog., 86, 33-60, 1990
Clarke, D. W.; Mohtadi, C.; Tuffs, P. S.,“ Generalized predictive control-part I: the basic algorithm, ” Automatica, 23, 137-148, 1987.
Culter, C. R.; Ramaker, B. L.,“ Dynamic matrix control – a computer control algorithm,” Proc. J. Automat. Contr. Conf., Wp5-B, 1-6, 1980.
de Keyser, R. M. C.; van Cauwenberghe, A. R.,“ Extended prediction self-adaptive control,” Proc. IFAC 7th Series, 7, 1255-1260, 1985.
Garcia, C. E.; Morari, M.,“ Internal model control: 1. A unifying review and some new results,” Ind. Eng. Chem. Proc. Des. & Dev., 21, 308-320, 1982
Garcia, C. E.,“ Quadratic dynamic matrix control of nonlinear processes: a application to a batch reaction process,” AIChE Annual Meeting, San Francisco, CA, 1984.
Garcia, C. E.; Morshedi, A. M.,“ Quadratic programming solution of dynamic matrix control (QDMC),” Chemical Engineering Communications, 46, 73-87, 1986.
Gerksic, S.; Juricic, S.; Strmcnik, S.; Matko, D.,“ Wiener-model-based nonlinear predictive control,” International Journal of Systems Science, 31, 189-202, 2002.
Haber, R.; Unbehauen, H.,“ Structure identification of nonlinear dynamic systems-a survey on input/output approaches,” Automatica, 26, 651-677, 1990.
Huang, H. P.; Lee, M. W.; Tang, Y. T.,“ Identification of Wiener model using relay feedback test,” J. Chem. Eng. Jpn., 31, 604-612, 1998.
Hwang, S. H.; Lin, M. L.,“ Unbiased Identification of Continuous Time Parametric Models Using a Time-Weighted Integral Transform,” Chem. Eng. Commun., 190, 1170-1199, 2003.
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., 50, 3693-3701, 1995.
Kwon, W. H.; Byun, D. G.,“ Receding horizon tracking control as a predictive control and its stability properties,” International Journal of Control, 50, 1807-1824, 1989.
Lebourgeois, F.,“ IDCOM application and experiences on a PVC production plant,” Proc Joint Aut. Control Conf., San Francisco, California, Fa9-c, 1980.
Lecchini, A.; Gevers, M.,“ Explicit expression of the parameter bias in identification of Laguerre models from step responses,” Systems and Control Letters, 52, 149-165, 2004.
Lee, M. W.; Huang, H. P.,“ Identification and control of Hammerstein-type nonlinear process,” J. Chin. Inst. Chem. Engrs., 32, 361-371, 2001.
Lawarynczuk, M.,“ Efficient nonlinear predictive control based on structured neural models,” Int. J. Appl. Math. Comput. Sci., 19, 233-246, 2009
Marchettl, J. L.; Mellichamp, D. A.; Seborg, D. E.,“ Predictive controller design for single-input/single-output (SISO) systems,” Ind. Eng. Chem. Res., 27, 956-963, 1988.
Marquis, P.; Broustal, J. P.,“ SMOC, a bridge between state space and model predictive controllers: application to the automation of a hydro treating unit,” Proceedings of the IFAC workshop on model based process control, 82, 37-43, 1988.
McDonald, K. A.; McAvoy, T. J.,“ Application of dynamic matrix control to moderate and high-purity distillation tower,” Ind. Eng. Chem. Res., 26, 1011-1018, 1987.
Morshedi; Cutler, C. R.; Skrovanek, T. A.,“ Optimal solution of dynamic matrix control with linear programming techniques (LDMC),” American Control Conference, 10, 199-208, 1985.
Nahas, E. P.; Henson, M. A.; Seborg, D. E.,“ Nonlinear Internal Model Control Strategy for Neural Network Models,” Comput. Chem. Eng., 16, 1039-1057, 1992.
Norquary, S. J.; Palazoglu, A.; Romagnoli, J. A.,“ Model predictive control based on Wiener models,” Chem. Eng. Sci., 53, 75-84, 1998.
Palancar, M. C.; Aragon, J. M.; Torrecilla, J. S.,“ pH-control systems based on artificial neural networks,” Ind. Eng. Chem. Res., 37, 2729-2740, 1998.
Pang-Yen Ho; Cheng-Ching Yu,“ Two-degree-of-freedom dynamic matrix control for distillation columns,” Journal of the Chinese institute of Engineers, 16, 101-111, 1993.
Peterson, T.; Herandez, E.; Arkun, Y.; Schork, F. J.,“ A nonlinear DMC algorithm and its application to a semi-batch polymerization reactor,” Chemical Engineering Science, 47, 737-742,1992
Rawlings, J. B.; Muske, K. R.,“ Stability of constrained receding horizon control,” IEEE Trans. Auto. Cont., 38, 1512-1516, 1993.
Richalet, J.; Rault, A.; Testud, J. L.; Papon J.,“ Model predictive heuristic control: applications to industrial processes,” Automatica, 14, 413-428, 1978.
Ricker, N. L.,“ Model Predictive Control with State Estimation,” Ind. and Eng. Chem. Res., 29, 374-382, 1990.
Wahlberg, B.,“ System identification using Laguerre models,” IEEE Transactions on Automatic Control, 36, 551-562, 1991.
Ydstie, B. E.,“ Extended horizon adaptive control,” Proc. IFAC 9th Series, 1, 133-138, 1985.
陳厚岑,以方塊導向模型為基礎之非線性程序鑑別,成功大學化學工程學系博士論文,2009