在實際工業控制系統中，水位的控制存在有時間延遲的特性，這種時間延遲的現象將會對工業控制系統的效能產生不良的影響。
因此本研究提出一類改良式基因模糊適應性 Smith-PID控制器之研究與應用來克服這種問題，利用Smith型式預估器控制的架構能有效地控制時間延遲系統，使用適應性模糊控制器，可以更快速達成控制目標並且改進控制器輸出曲線超越量的缺點。進一步使用基因演算法與改良式基因演算法則可以設計模糊歸屬函數及模糊規則函數。最後、應用此控制器於一類三個水箱的水位控制，模擬結果顯示此方法具有優良的性能。

In real industrial control systems, there exist time-delay characteris-tics in the liquid level control. Such time-delay phenomena will result in the bad performance in the industrial control systems. Therefore, in this study we propose a class of improved genetic fuzzy Smith-PID control-lers to conquer this problem. By using Smith-type predictor controllers, it can effectively control time-delay systems. By using adaptive fuzzy con-trollers, it can faster achieve the control objects and improve the over-shoot drawback in the output curve. Moreover, using Genetic Algorithm and Improved Genetic Algorithm, one can fine-tune the fuzzy member-ship and rule functions. Finally, we apply the proposed controller to a class of three tank water level control systems. Simulation results show that the proposed methods can achieve good performance.

[1]J.-Q. Deng and C. Hao, “The Smith-PID Control of Three-Tank-System Based on Fuzzy Theory,” Journal of Com-puters, vol. 6, no. 3, pp. 514-523, March 2011.
[2]Q.-L. Wang and X.-J. Xie, “Smith Control of Three Tank Water System Based on C++ Builder,” Journal of Qufu Normal Univer-sity (in Chinese), vol. 34, no. 1, pp. 33-35, January 2008.
[3]H.-Y. Sun, S.-H. Yu, J.-L. Du, Y. Tian, and Y.Hu, “The Level Con-trol of Three Water Tanks Based on Self-Tuning Fuzzy-PID Con-troller,” Electric Application(in Chinese), vol. 25, pp. 97-99, 2006.
[4]Y.-H. Wang, S.-H. Yu, J.-L. Du, Y. Tlan, and Y. Hu, “Adaptive Fuzzy Control of Uncertain Nonholonomic Mobile Robots,” Jour-nal of System Simulation (in Chinese), vol. 21, no. 2, pp. 469-473, January 2009.
[5]M.-C. Zhu, Y. Li, Y.-C. Li, and R.-H. Jiang, “Observer-based de-centralized adaptive fuzzy control for reconfigurable manipulator,” Control and Decision(in Chinese), vol. 24, no. 3, pp. 429-434, March 2009.
[6]N. Noroozi, M. Roopaei, and M.-Z. Jahromi, “Adaptive fuzzy slid-ing mode control scheme for uncertain systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, pp. 3978-3992, 2009.
[7]M. Roopaei, M. Zolghadri, and S. Meshksar, “Enhanced adaptive fuzzy sliding mode control for uncertain nonlinear systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, pp. 3670-3681, 2009,
[8]G.-G. Rigatos, “Adaptive fuzzy control of DC motors using state and output feedback,” Electric Power Systems Research, vol. 79, pp. 1579-1592, 2009.
[9]Z.-J. Li and C.-Q. Xu, “Adaptive fuzzy logic control of dynamic balance and motion for wheeled inverted pendulums,” Fuzzy Sets and Systems, vol. 160, pp. 1787-1803, 2009.
[10]S. Labiod and T.-M. Guerra, “Adaptive fuzzy control of a class of SISO non-affine nonlinear systems,” Fuzzy Sets and Systems, vol. 158, pp. 1126-1137, 2007.
[11]S.-C. Tong, Y.-M. Li and P. Shi, “Fuzzy adaptive back-stepping ro-bust control for SISO nonlinear system with dynamic uncertain-ties,” Information Sciences, vol. 179, pp. 1319-1332, 2009.
[12]H.-F. Ho, Y.-K. Wong, and A.-B. Rad, “Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO sys-tems,” Simulation Modeling Practice and Theory, vol. 17, pp. 1199-1210, 2009.
[13]S.-C. Tong, C.-Y. Li, and Y.-M. Li, “Fuzzy adaptive observer back stepping control for MIMO nonlinear systems,” Fuzzy Sets and Systems, vol. 160, pp. 2755-2775, 2009.
[14]C.-S. Chen, “Dynamic structure adaptive neural fuzzy control for MIMO uncertain nonlinear systems”, Information Sciences, vol. 179, pp. 2676-2688, 2009.
[15]J.-K. Liu, Advanced PID control and MATLAB simulation (in Chi-nese), the second edition. Publishing House of Electronics Industry, pp. 1-116, May 2007.
[16]X.-M. Shi and Z.-Q. Hao, Fuzzy control and MATLAB simulation (in Chinese), Publishing House of QingHua University, pp. 124-133, March 2008.
[17]S.-K. Tiwari and G.-D. Kaur, “Analysis of Fuzzy PID and Immune PID Controller for Three Tank Liquid Level Control,” International Journal of Soft Computing and Engineering (IJSCE), vol. 1, pp. 185-189, September 2011.
[18]Disha, P.-K. Pandey, and R. Chugh, “Simulation of Water Level Control in a Tank Using Fuzzy Logic,” IOSR Journal of Electrical and Electronics Engineering (IOSRJEEE), vol. 2, Issue 3, pp. 09-12, (Sep-Oct. 2012).
[19]S.-B. Baladi, “Water tank level control using (proportional integral derivative) controller,” Faculty of Electrical engineering Kolej Universiti Teknikal Kebangsaan Malaysia, pp. 12-20, March 2005.
[20]鄒治軍, 「基於模糊控制的Smith預估器的改進研究和設計」, 合肥工業大學論文，May 2008。
[21]石學文，王曉燕，王慶蘭，武玉強, “Decoupling Control of Three Tank Water System Based on C++ Builder,” 曲阜師範大學電氣信息與自動化學院, vol. 19, no. 12, pp. 57-58, June 2006.
[22]X.-Y. Wang and E.-D. Jir, “Smith Predictor Design and Simulation of Three Tank Water System(in china),” 計算機與現代化, no. 10, pp. 98-100, June 2007.
[23]朱晶，「基於模糊PID的三容水箱液位元控制系統應用研究」，大連理工大學軟體工程論文，November 2008。
[24]Z.-Y. Zou, D.-D. Zhao, N. Guo, J.-Y. Liu, D.-H. Yu and X.-J. Gui, “Fuzzy auto-tuning PID control of the temperature of a small elec-tric heating reactor,” Computer and Applied Chemistry, vol. 26, no. 8, pp. 1008-1012, August 2009.
[25]R.-C. Dorf and R.-H. Bishop 著，廖東成，陳志鏗，鍾翼能譯，「現代控制系統 第九版」，偉明圖書有限公司，台灣培生教育出版股份有限公司，October 2002。
[26]曾仲熙，「控制器設計與模擬範例」，東華書局，13-74頁，August 2009。
[27]王文俊，「認識 Fuzzy」，全華圖書股份有限公司，June 2008。
[28]李允中，王小璠，蘇木春，「模糊理論及其應用 3rd」，全華圖書股份有限公司，January 2012。
[29]H. Tia and J. Li, “Simulation Study of Fuzzy Self-tuning PID Con-troller Based on MATLAB,” industrial control computer, vol. 24, no. 6, June 2011.
[30]D.-D. Wen, “Temperature control system of resistance-heated fur-nace based on fuzzy immune PID,” 冶金自動化, vol. 06, pp. 43-46, 2007.
[31]D.-R. Coughanowr and L. B. Koppel, Process Systems Analysis and Control. New York:Mc-Graw Hill Book Company, 1965.
[32]T.-L. Tengku Mohamed, R.-H. Azman Mohamed, and Z. Mohamed, “Development of Auto Tuning PID Controller using Graphical User Interface (GUI),” Second International Conference on Com-puter Engineering and Applications, pp. 491-495, 2010.
[33]P. Persson, “A Matlab Toolbox for PID Controller Design,” De-partment of Electrical Engineering, pp. 230-234, 1993.
[34]A.-R. Benaskeur and A. Desbiens, “Backstopping-based adaptive PID control,” IEEE Process Control Theory Appl., Vol. 149, no. 1, pp. 54-59 , January 2002.
[35]H.-K. Liu, X. Zhang and W.-S. Chang, “PID Control to Maglev Train System,” International Conference on Industrial and Infor-mation Systems, pp. 341-343, 2009.
[36]A. Oi, C. Nakazawa, T. Matsui1, H. Fujiwara, K. Matsumoto, and H. Nishida, “PID Optimal Tuning Method by Particle Swarm Op-timization,” SICE Annual Conference The University Elec-tro-Communications (Japan), pp. 3470-3473, August 2008.
[37]C.-W. Li and J.-D. Lian, “The Application of Immune Genetic Al-gorithm in PID Parameter Optimization for Level Control System,” Proceedings of the IEEE International Conference on Automation and Logistics, pp. 782-786, August 2007.
[38]G.-L. Yuan, J.-H. Liu, T. Wen and X.-G. Liu, “The Research and Application of Immune Feedback Control in the Load Control System of Tube Mill,” Zhangjiajie Hunan China, pp. 350-353, July 2007.
[39]C.-Y. Hsu, S.-J. Lin, W.-L. Chien, and C.-C. Tong, “An Auto-tuning PID Regulator Using Grey Predictor,” Electrical En-gineering, 2006.
[40]C.-N. Jutarut, A. Numsomran, T. Suesut, T. Trisuwannawat, and V. Tipsuwanporn, “PID Controller Design using Characteristic Ratio Assignment Method for Coupled-Tank Process,” IEEE computer society, 2005.
[41]S.-H Ma and W. Li, “Non-linear PID control method with feed-forward in smart car,” Chinese Control and Decision Confer-ence, pp. 462-465, 2009.
[42]Y.-H. Zhang and Y.-M. Hu, “On PID Controllers Based on Simu-lated Annealing Algorithm,” Proceedings of the 27th Chinese Con-trol conference, pp. 16-18, July 2008.
[43]J.-X. Xu and D.-Q. Huang, “Optimal Tuning of PID Parameters Using Iterative Learning Approach,” 22nd IEEE International Symposium on Intelligent Control Part of IEEE Multi-conference on Systems and Control Singapore, pp. 226-231, October 2007.
[44]J.-X. Xu and D. Huang, “Optimal Tuning of PID Parameters Using Iterative Learning Approach,” 22nd IEEE International Sympo-sium on Intelligent Control Part of IEEE Multi-conference on Sys-tems and Control Singapore, pp. 226-231, October 2007.
[45]J. Wei, P. Yin and L.-T. Cao, “On Fuzzy Self-tuning PID MAT-LAB Simulation for Central Heating,” Proceedings of the 26th Chinese Control Conference, pp. 425-429, July 2007.
[46]J.-J. Gu, Y.-J. Zhang, and D.-M. Gao, “Application of Nonlinear PID Controller in Main Steam Temperature Control,” Power and Energy Engineering Conference, pp. 27-31, March 2009.
[47]J. Rocca and S.-X. Yang, “Fuzzy Control of Dissolved Oxygen Concentration in a Bioreactor for Wastewater Applications,” Automation and Logistics, pp. 108-113, August 2009.
[48]D.-S. He, X.-W. Fan, and S.-H. Tong, “Simulation Study of CO2-based Outdoor Air Rate Control in Public Buildings,” School of Energy and Environment and Zhongyuan University of Tech-nology, pp. 3210-3214, 2009.
[49]H.-Q. Zang and Q. Li, “The Automatic Temperature System with Fuzzy Self-adaptive PID Control in Semiconductor Laser,” Pro-ceedings of the IEEE International Conference on Automation and Logistics Shenyang, pp. 1691-1694, August 2009.
[50]J. Zeng, Y.-C. Xie, and L. Chen, “Design of Main Steam Tem-perature Cascade Control System Based on Fuzzy Self-tuning PID Controller,” International Conference on Intelligent Computation Technology and Automation, pp. 878-881, 2008.
[51]X.-K. Wang, Z.-L. Sun, L. Wang, and D.-Q. Feng, “Design and Research Based on Fuzzy PID parameters Self-tuning Controller with MATLAB,” International Conference on Advanced Computer Theory and Engineering, pp. 996-999, 2008.
[52]S.-Q. Wang, Z.-P. Zhang, and H. Liu, “Research on Fuzzy-PID Composite Control Strategy for Hydroelectric Generating Unit,” International Conference on Artificial Intelligence and Computa-tional Intelligence, pp. 36-39, 2009.
[53]X.-L. Fang, T. Shen, X.-H. Wang, and Z.-G. Zhou, “Application and Research of Fuzzy PID in Tank System,” Fourth International Conference on Natural Computation, pp. 326-330, 2008.
[54]M.-H. Li and Q. Zhang, “The Design and Application of Fuzzy PID Controller in Pulp Concentration Control,” supported by the Doc-toral Research Foundation of Shaanxi University of Science & Technology, pp. 1204-1207, 2010.
[55]C.-G. Li and R.-Q. Hu, “Fuzzy PID Control for the Regulation of Blood Glucose in Diabetes,” IEEE computer society, pp. 170-174, 2009.
[56]Y,-T. Juang, Y.-T. Chang, and C.-P. Huang, “Design of fuzzy PID controllers using modified,” Information Sciences, vol. 178, pp. 1325-1333, 2008.
[57]Z,- Q. Wu and M. Mizumoto, “PID type fuzzy controller and pa-rameters adaptive method, ” Fuzzy Sets and Systems, vol. 78, pp. 23-35, 1996.
[58]亢海偉，楊慶芬，王碩禾，「基於MATLAB模糊邏輯工具箱的模糊控制系統仿真」，自動化與儀器儀表，15卷，2期，43頁-44頁， 2000。
[59]K. Mehran, Takagi-Sugeno Fuzzy Modeling for Process Control, Industrial Automation, Robotics and Artificial Intelligence, 2008.
[60]H. Li and Q. Ma, “Application of an Improved Genetic Algorithm to Fuzzy Controller Optimization, Control Engineering of China, vol. 15, no. 6, pp. 682-684, November 2008.
[61]付華，杜雛，「利用遺傳演算法優化模糊控制器綜述」，石油化工自動化，01期，24頁-26頁，2001。
[62]Z.-H. Chen and H.-H. Xiao, “Optimal Design of Fuzzy Logic Con-troller Based on Adaptive Genetic Algorithm,” Natural science edition, vol. 12, no. 01, pp. 140-143, February 2010.
[63]X. Yang, “Optimization of fuzzy controller rules based on genetic algorithm,” Electric drive automation, vol. 32, no. 5, pp. 41-44, 2010.
[64]R.-Y. Guo and S.-E. Shi, “A study on optimization of fuzzy con-troller parameters based on genetic algorithm,” Electronic Design Engineering, vol. 19, no. 12, pp. 79-81, June 2011.
[65]N.-Y. Zhang, “Use Genetic Algorithm to Optimize Membership Function Parameters of fuzzy Controller,” Electrical Automation, vol. 18, no. 1, pp. 4-7, January 1996.
[66]史峰，王輝，胡斐，郁磊，「MATLAB智能算法30個案例分析」， 北京航空航天大學出版社，17頁-26頁，July 2011。
[67]D.-P. Tian, “Improved fuzzy adaptive genetic algorithm Computer Engineering and Applications,” Computer Engineering and Appli-cation, no. 31, pp. 60-63, 2008
[68]L. Chen, T.-C. Tsai, and K.-C. Po, “A Research of Optimization of Reservoir Flood Control Using Fuzzy Theory and Genetic Algo-rithms,” Journal of Chinese Agricultural Engineering, vol. 48, no. 1, pp. 82-94, March 2002.
[69]畢雲峰，「遺傳演算法在模糊控制器設計中的應用」，微電腦資訊，自動化信，7頁-9頁，April 2001。
[70]王淑青，劉素一，張子蓬，袁曉輝，「基於遺傳演算法的模糊PID 控制在水輪發電機組中應用研究」，微電腦資訊，2卷，2-1期，62頁-63頁，2006。
[71]B.-Y. Jin, J.-J. Nie, and G.-B. Guo, “Research on GA optimized fuzzy control strategy for electric power steering system,” Machin-ery Design & Manufacture, no. 5, pp. 91-93, March 2010.
[72]盧奕南，張弘，「遺傳模糊系統的研究概述」，儀器儀表學報，25卷，4期，587頁-690頁，August 2004。
[73]M.-L. Qiao, J.-Y. Zhang, and Y.-Y. Wen, “Optimizing Approach for Fuzzy Control Rule Based on Genetic Algorithm,” Computer Measurement & Control, no. 10, pp. 1349-1351, 2006.
[74]吳瑞，「基於遺傳演算法的模糊神經網路控制器的優化以及MATLAB與VC數據交換的研究」，西安理工大學，2007。
[75]C.-H. Ma, S.H. Yu, and W.-X. Zhu, “Research on Optimization of Fuzzy Control Rules Based on Genetic Algorithms,” Journal of Ji-angsu University (Natural Science Edition), vol. 24, no. 4, pp. 69-73, July 2003.