模型預測控制(Model Predictive Control, MPC)能夠根據控制設計的實際需求，設置操作和被控變數的上下限，以確保控制系統之操作安全及最佳性能，尤其能對多變數程序進行有效控制。MPC的應用裡預測模型的凖確性是很重要的，然而由於化工操作程序大多具有非線性與多變數動態特性，傳統離散摺積模型只能獲得其線性近似，在操作範圍變大時會失去預測凖確性。隨著電腦計算能力的提升及計算工具的完備，類神經網路模型在實務上更適合用於化工程序的非線性預測，以滿足MPC對預測凖確性的要求。

本論文利用NARX類神經網路建模技術來建立連續攪拌槽反應器和活性污泥兩種多變數化工程序的非線性模型，透過NARX類神經網路模型的開環和閉環預測方法來確保模型的預測準確度，並且發現其對新數據集的預測能力優於其他常用模型。接著根據所得類神經網路模型進行兩種化工程序的模型預測控制，利用MATLAB的fmincon函數來計算滿足上下限設置條件的操作變數最佳值，以模擬各種設定點和擾動變化情況下的回饋控制系統。模擬結果顯示此控制方法在前期優於其他模型預測控制方法，但在後期會出現無法消除被控變數穩態誤差的缺點，為了解決此問題，本文提出結合了NARX類神經網路模型與線性ARX模型的混合式NARX模型，基於此混合式模型的預測控制不僅能在整個期間保持良好的控制性能，還能有效消除被控變數的穩態誤差。

Model predictive control (MPC) can set the upper and lower limits of manipulated and controlled variables according to the actual requirements of control design to ensure the operational safety and optimal performance of the control system, and is especially effective in controlling multivariable processes. The accuracy of the predictive model is very important in the application of MPC. However, due to the nonlinear and multivariate dynamic characteristics of most chemical operating processes, the conventional discrete convolution models can only obtain their linear approximations, and the prediction accuracy will be lost when the operating range becomes larger. With the improvement of computer computing power and the completeness of computing tools, artificial neural network models are more suitable for nonlinear prediction of chemical processes in practice, so as to meet the requirements of MPC for prediction accuracy.

In this thesis, the NARX (Nonlinear AutoRegressive with eXogenous input) neural network modeling technique is used to establish the nonlinear models of two multivariable chemical processes, continuous stirred-tank reactor and activated sludge. The prediction accuracy of the models is ensured through the open-loop and closed-loop prediction methods of the NARX neural network models, and they are found to outperform other commonly used models in their predictive power on new datasets. Then, according to the obtained neural network models, the model predictive control of the two chemical processes is carried out, and the fmincon function of MATLAB is used to calculate the optimal values of the manipulated variables that satisfy the upper and lower limit setting conditions, so as to simulate the feedback control systems under various set point and disturbance changes. The simulation results show that this control method is superior to other model predictive control methods in the early stage, but in the later stage there will be the disadvantage that the steady-state errors of the controlled variables cannot be eliminated. In order to solve this problem, this thesis proposes a combination of NARX neural network model and linear ARX, namely the hybrid NARX model. The predictive control based on this hybrid model can not only maintain good control performance throughout the control period, but also effectively eliminate the steady-state errors of the controlled variables.

Altman, N. S., An introduction to kernel and nearest-neighbor nonparametric
regression, The American Statistician, 46 (3), pp. 175-185, 1992
Clarke, D. W., C. Mohtadi and P. Tuffs, Generalized predictive control－Part I. The
basic algorithm, Automatica, 23 (2), pp.137-148, 1987.
Cortes, C. and V. Vapnik, Support-vector networks, Machine Learning, 20 (3), pp.
273-297, 1995.
Cutler, C. R. and B. L. Ramaker, Dynamic matrix control－A computer control
algorithm, Joint Automatic Control Conference, San Francisco, CA, Paper
WP5-B, 1980.
Diamantaras, K. I., Robust principal component extracting neural network,
International Conference on Neural Networks, 1, pp. 74-77, 1996.
Du, M. and P. Mhaskar, Isolation and handling of sensor faults in nonlinear systems,
Automatica, 50 (4), pp. 1066-1074, 2014.
Elman, J. L., Finding structure in time, Cognitive Science, 14, pp. 179-211, 1990.
Farley, B. and W. Clark, Simulation of self-organizing systems by digital computer,
IRE Professional Group on Information Theory, 4 (4), pp. 76-84, 1954.
Garcia, C. E. and A. Morshedi, Quadratic programming solution of dynamic matrix
control (QDMC), Chemical Engineering Communications, 46 (1), pp. 73-87,
1986.
Girosi, F., T. Poggio and B. Caprile, Extensions of a theory of networks for
approximations and learning: outliers and negative examples, Advances in
Neural Information Processing Systems, 3, pp. 750-756, 1991.
Hartman, E. J., J. D. Keeler and J. M. Kowalski, Layered neural networks with gaussian
hidden units as universal approximation, Neural Computation, 2 (2), pp. 210-
215, 1990.
Hassanpour, H., B. Corbett and P. Mhaskar, Integrating dynamic neural network
models with principal component analysis for adaptive model predictive
control, Chemical Engineering Research and Design, 161, pp. 26-37, 2020.
Hassanpour, H., B. Corbett and P. Mhaskar, Artificial neural network-based model
predictive control using correlated data, Industrial & Engineering Chemistry
Research, 61 (8), pp. 3075-3090, 2022.
Haykin, S., Neural Network: A Comprehensive Fundation, Prentice Hall, 1999.
Hebb, D. O., The Organization of Behavior, Wiley & Sons, 1954.
Jang, J. S. R., C. T. Sun and E. Mizutani, Neuro-Fuzzy and Soft Computing－A
Computational Approach to Learning and Machine Intelligence, Prentice Hall,
1997.
Jordan, M. I., Attractor dynamics and parallelism in a connectionist sequential
machine, IEEE Computer Society Neural Networks Technology Series, 5 (12),
pp. 112-127, 1990.
Lin, T., B. G. Horne, P. Tino and C. L. Giles, Learning long-term dependencies in
NARX recurrent neural networks Neural Networks, IEEE Transactions, 7 (6), pp.
1329-1338, 1996.
Ljung, L., System Identification: Theory for the User, Prentice-Hall, 1987.
Marlin, T. E., Process Control: Designing Process and Control Systems for Dynamic
Performance. McGraw-Hill, 1995.
Minsky, M. and S. Papert, An Introduction to Computational Geometry, MIT Press,
1969.
Nejjari, F., A. Benhammou, B. Dahhou and G. Roux, Non-linear multivariable
adaptive control of an activated sludge waste water treatment process,
International Journal of Adaptive Control and Signal Process, 13, pp. 347-365,
1999.
Olsson, G., State of the art in sewage treatment plant control, American Institute of
Chemical Engineers, 72 (159), pp. 52-76, 1976.
Pearson, K., On lines and planes of closest fit to systems of points in space,
Philosophical Magazine, 2, pp. 559-572, 1901.
Principe, J. C., D. Xu and C. Wang, Generalized Oja’s rule for linear discriminant
analysis with fisher criterion principe, IEEE International Conference, 4, pp.
3401-3404, 1997.
Richalet, J., A. Rault, J. L. Testud and J. Papon, Model predictive heuristic control:
applications to industrial processes, Automatica, 14 (5), pp. 413-428, 1978.
Rochester, N., J. H. Holland, L. H. Habit and W. L. Duda, Tests on a cell assembly
theory of the action of the brain using a large digital computer, IRE
Transactions on Information Theory, 2 (3), pp. 80-93, 1956.
Rosenblatt, F., The perceptron: a probalistic model for information storage and
organization in the brain, Psychological Review, 65 (6), pp. 386-408, 1958.
Vilanova, R. and R. Katebi, 2-DoF Decoupling controller formulation for set-point
following on decentraliced PI/PID MIMO Systems, IFAC Proceedings Volumes,
45 (3), pp. 235-240, 2012.
Werbos, P. J., Beyond Regression: New Tools for Prediction and Analysis in the
Behavioral Sciences, Harvard University, 1975.
Williams, R. J., G. E. Hinton and D. E. Rumelhart, Learning representations by back-
propagating errors, 323, pp. 533-536, 1986.
Yang, J. J., Memristive switching mechanism for metal/oxide/metal nanodevices,
Nature Nanotechnology, 3, pp. 429-433, 2008.
葉怡成，類神經網路應用，儒林書局2003。
張斐章、張麗秋和黃浩倫，類神經網路，東華書局2003。
陳正傑和李綱，結合類神經網絡及模型預測控制之智慧節能行車輔助系統 ，國立臺灣大
學 2019。
簡建州、鍾鴻源和莊堯棠，以遞迴式神經網路補償模型預測控制於永磁同步馬達定位，
國立中央大學 2018。