Application of an Artificial Neural Network to Non-Linear Process Control 劉權輝、涂瑞澤
E-mail: [email protected]
ABSTRACT
Model predictive control (MPC) is one of the most frequently used process control strategies. The principle of MPC is to have a process model, which is able to predict the process response, in the MPC controller. The manipulated variable is tuned in order to minimize the deviation between the set point and the predicted response for a period of time in the feature. The goal of process control can therefore be achieved by regulating the manipulated variable. The MPC often uses a linear model to simulate the process. Hence, some modeling errors must exist. Some researchers have used an artificial neural network (ANN) to replace the linear model in the MPC control for a complex process, owing to the nonlinear mapping capability owned by an ANN. Usually, the neural predictive control is trained based on the autoregressive model with exogenous (ARX) form and/or autoregressive moving average model with exogenous (ARMAX) form. The ANN model uses the output value as input data iteratively. The drawback of the training pattern includes the induction of inaccuracy and time-consuming. To overcome the drawback, the process convolution model has been used to train the ANN. The proposed model has been named the neural network predictive control (NNPC) in this study. For the training proposes, the pseudo random binary sequence (PRBS) signal patterns are used to identify the process. Once the ANN has been trained, the MPC strategy determines a desired value for the manipulated variable by using the
Levenberg-Marquardt method. A CSTR with a nonlinear reaction has been chosen as an example to test the performance of the proposed control strategy. In this example, a temperature loop and a concentration loop and controlled simultaneously. Simulation results have shown that no matter the change of the set point or a load, the NNPC demonstrates a good control performance. When a process possesses a slow response (large time constant), e.g. a bioreactor, the ANN model in the NNPC has to increase the node number in the hidden layer, and therefore increase the training time. To overcome this disadvantage, a simplified neural network predictive control (SNNPC) has been proposed. In this simplified model, the node member of the output layer has been reduced to 3, and the training time has also been reduced substantially. In general, the control performance is still satisfactory, but the offset has been slightly increased.
Keywords : neural network ; model predictive control ; simplified neural network model predictive control Table of Contents
封面內頁 頁次 簽名頁 授權書1 iii 授權書2 iv 中文摘要 vi ABSTRACT viii 誌謝 x 目錄 xi 圖目錄 xv 表目錄 xviii 第一章 緒論 1 第二章 研究背景 5 2.1 前言 5 2.2 神經網路 (ANN) 6 2.2.1 節點(神經元)的組成 7 2.2.2 神經網路的拓蹼 8 2.3 神經網路的學 習訓練 10 2.4 模式預測控制 (MPC) 12 2.4.1 動態矩陣控制 (DMC) 14 2.4.2 DMC之簡化 19 符號說明 22 第三章 神經網路模式 預測控制 24 3.1 前言 24 3.2 NNPC控制架構 25 3.2.1 程序動態 26 3.2.1.1預測模式(ANN)的建立 27 3.2.1.2 訓練樣本的準備 28 3.2.1.3 訓練網路 29 3.2.1.4 ANN模式 33 3.2.2 模式預測控制 34 3.2.3 最適化運算 37 3.3 CSTR反應槽 39 3.3.1 溫度環路 42 3.3.2 濃度環路 42 3.4 結果與討論 43 3.4.1 程序的開環響應 43 3.4.1.1 冷卻水流率對程序之影響 43 3.4.1.2 進料流率對程序之 影響 45 3.4.2 溫度環路之控制 48 3.4.2.1 不同λ值之控制效果 50 3.4.2.2 NNPC與DMC控制結果之比較 52 3.4.3 濃度環路之 控制 54 3.4.3.1 不同λ值之控制效果 56 3.4.3.2 NNPC與DMC控制結果之比較 58 3.5 結論 60 符號說明 62 第四章 簡化神經 網路模式預測控制 65 4.1 前言 65 4.2 SNNPC控制架構 67 4.2.1 模式預測控制 67 4.2.2 最適化運算 69 4.3 SNNPC與NNPC之 控制差異 70 4.3.1 簡化神經網路模式預測控制結果 70 4.3.2 SNNPC與NNPC之控制結果比較 74 4.3.2.1 溫度環路 74 4.3.2.2 濃度環路 76 4.4 CASE STUDY--CSTR發酵槽 78 4.4.1 程序之模式建立 79 4.4.2 產生學習樣本 80 4.4.3 訓練樣本取決方式 81 4.4.4 以神經網路為模式 82 4.5 結果與討論 83 4.5.1 連續式發酵程序開環響應 83 4.5.2 控制結果及最適控制條件 84 4.5.3 與 其他控制器的比較 86 4.6 結論 88 符號說明 90 第五章 結論與展望 92 5.1 結論 92 5.2 展望 92 參 考 文 獻 94 附錄 99 附錄A 99 附錄B 101
REFERENCES
王進德、蕭大全，類神經網路與模糊控制理論入門，全華科技圖書，台北市，1994。 黃明潔，簡化的模式預測控制，國立台灣科技大 學，碩士論文，台北，1990。 靳蕃、範俊波、譚永東，神經網路與神經計算機原理, 儒林, 台北，1992。 葉怡成，類神經網路模式應用 與實作，儒林，台北，1993。 蔡宏明、涂瑞澤，線上學習神經控制器結合最佳動態學習速率-應用於非線性系統的程序控制，中華民國
八十六年電腦程序控制研討會論文集，國立台灣大學，台灣，196-205，1997。 Aoyama, A., Internal model control framework using neural networks for the modeling and control of a bioreactor, Engng. Applic. Artif. Intell., 8(6), 689-701, 1995. Baheri, H. R., G. A. Hill, and W. J.
Roesler, Optimum design for production of tryptophan synthetase subunit from recombinant Escherichia coli in a two-stage continuous flow stirred tank reactor, The Chemical Engineering Journal, 62, 143-148, 1996. Chang, W. F., and M. W. Mak, A conjugate gradient learning algorithm for recurrent neural networks, Neurocompution, 24, 173-189, 1999. Chen, J., Systematic derivations of model predictive control based on artificial neural network, Chem. Eng. Comm., 164, 35-59, 1998. Chen, J., D. S. H. Wang, and S. L. Jang, Product and process development using artificial neural-network model and information analysis, AIChE Journal, 44(4), 876-887, 1998. Chien, I. L., and P. S. Fruehanf, Consider IMC tuning to improve controller performance, Chemical Engineering Progress, 86, 33-38, 1990. Cutler, C. R., and B. L. Ramaker, Dynamic matrix control: A computer control algorithm. Proc. American Control Conf., WP5-B, San Francisco, CA, 1980. Cutler, C. R., and R. B. Hawkins, Constrained multivariable control of a hydrocracker reactor, Proc. American Control Conf., Minneapolis, Minnesota, 1014-1020, 1987. Dutta, P., and R. R.
Rhinehart, Application of neural network control to distillation and an experimental comparison with other advanced controllers, ISA Transactions, 38, 251-278, 1999. Henson, M. A., and D. E. Sebrog, Nonlinear control strategies for continuous Fermentors, Proc. American Control Conf., San Diego, CA, 2723-2728, 1990. Hsu, Y. Y., and C. C. Yu, A self-learning fault diagnosis system based on reinforcement learning, Ind. Eng. Chem. Res., 31, 1937-1947, 1992. Hunt, K. J., and D. Sbarbaro, Neural networks for non-linear internal model control. Proc. IEE Pt. D, 138, 431-438, 1991. Hunt, K. J., D. Sbarbaro, R. Zbikowski, and P. J. Gawthrop, Neural networks for control systems-A survey, Automatica, 28, 1083-1112, 1992. Kambhampati, C., J. D. Mason, and K. Warwick. A stable one-step- ahead predictive control of non-linear system, Automatica.
36, 485-495, 2000. Kreyszig, E., Advanced Engineering Mathematics, 8th ed., Wiley, New York, 1999. Kurtanjek, Z., Principal component ANN for modeling and control of baker’s yeast production, Journal of Biotechnology, 65, 23-25, 1998. Lebourgois, F., IDCOM applications and experiences on a PVC production plant, JointAutomatic Control Conference, San Fransisco, FA9-C, 1980. Lippmann, R. P., An introduction to computing with neural nets, IEEE ASSP Mag, 68-76, 1987. Luyben, M. L., Essentials of Process Control, McGraw-hill, New York, 1999. Masters, T., Advanced Algorithms for Neural Networks: A C++ sourcebook, Wiley, New York, 1995. Masters, T., Practical neural network recipes in C++, Academic Press, New York, 1993. Maurath, P. R., D. A. Mellichamp, and D. E. Seborg, Predictive controller design for single-input/ single-output (SISO) system, Ind. Eng. Chem. Research, 27,956-966, 1988. Mayne, D. Q., and H. Michalska, Receding horizon control of nonlinear systems.
Trans. IEEE on Aut. Control, 35, 814-824, 1990. Mehra, R. K., and R. Rouhani, Theoretical considerations on model algorithmic control for mon-minimum phase systems. Proc. American Control Conf., San Francisco, CA, TA8-B, 1980. Miller, W. T., R. S. Sutton, and P. J. Werbos, Neural networks for control. MIT Press, Cambridge, MA, 1990. Narendra, K. S., and A. M. Parthasarathy, Identification and control for dynamic systems using neural networks, IEEE Trans. on Neural Networks, 1, 4-27, 1990. Press, W. H., S. A. Teukolsky, W.T. Vetterling, and B. P.
Flannery, Numerical recipes in C. Second edition, Cambridge university press, New York, 1992 Robitaille, B., B. Marcos, M. Veillette, and G.
Payre, Modified quasi-newton methods for training neural networks, Computers Chem. Engng, 20, 1133-1140, 1996. Rohani, S., M. Haeri, and H. C. Wood, Modeling and control of a continuous crystallization process Part 2. Model predictive control, Computer and Chemical Engineering, 23, 279-286, 1999. Russell, N. T., H. H. C. Bakker, and R. I. Chaplin, Modular neural network modeling for long-range prediction of an evaporator, Control Engineering Practice, 8, 49-59, 2000. Saha, P. K., M. Shoib, and J. Kamruzzaman, Development of a neural network based integrated control system of 120 ton/h capacity boiler, Computers & Electrical Engineering, 24, 423-440, 1998. Salomon, R., and J. L. Hemmen, Accelerating Backpropagation through dynamic self-adaptation, Neural Networks, 9, 589-601, 1996. Smith, C. A., and A. B. Corripio, Principles and Practice of Automatic Process Control, 2nd ed., 471-475, Wiley, New York, 1997. Sorensen, P. H., M. Norgaard, O. Ravn, and N. K. Poulsen, Implementation of neural network based non-linear predictive control, Neurocomputing, 28, 37-51, 1999. Su, H. T., N. Bhat, P. A. Minderman, and T. J. McAvoy, Integrating neural networks with first principles models for dynamic modeling, In 3rd IFAC Symposium on Dynamics and Control of Chemical Reactors, Distillation Columns and Batch Processes, USA, 77-82, 1992. Syu, M. J., and C. L. Hou, Neural network dynamics identification of a fermentation system. in the proceedings of the 7th Congress of the Asian Pacific Confederation of Chemical Engineerings, TICC, Taipei, 2:625-630, 1996. Taso, J. H., and W. T. Wu, Global control of a continuous stirred tank bioreactor, The chemical Engineering Journal, 56, B69-B74, 1994. Temeng, K. O., P. D. Schnelle, and T. J. McAvoy. Model predictive control of an industrial packed bed reactor using neural networks, J. Proc. Cont., 5, 19-17, 1995. Trajanoski, Z., W. Regittnig, and P. Wach, Neural predictive controller for closed-loop control of glucose using the subcutaneous route: A simulation study, Control Eng. Practice, 5, 1727-1730, 1997. Trajanoski, Z., W. Regittnig, and P. Wach, Simulation studies on neural predictive control of glucose using the subcutaneous route, Computer Methods and Programs in Biomedicine, 56, 133-139, 1998. Wang, H., Y. Oh, and E. S. Yoon, Strategies for modeling and control of nonlinear chemical processes using neural networks, Computers Chem. Engng, 22, s823-s826, 1998. Werbos, P. J., Backpropagation through time: what it dose and how to do it?, Proc. of IEEE, 78, 1550-1560, 1990. Yu, X. H., and G. A. Chen. Efficient backpropagation learning using optimal learning rate and momentum, Neural Networks, 10(3), 517-527, 1997. Yu, X. H., G. A. Chen, and S. X. Cheng. Dynamic learning rate optimization of the backpropagation algorithm, IEEE Tran.
on Neural Networks, 6(3), 669-677, 1995. Zamarreno, J. M., and P. Vega, Neural predictive control. Application to a highly non-linear system, Engng. Applic. Artif. Intell., 12, 149-158, 1999。
