复杂系统的智能建模与控制方法
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摘要
本文以白银铝厂阳极焙烧炉的温度控制系统为研究对象，针对复杂系统难建
模、难控制的特点，采用智能控制方法对系统进行了深入的研究。模糊神经网络
(FNN)是人工神经网络与模糊逻辑系统的有机结合，是一种能够处理抽象信息的
网络结构，具有强大的自学习和自整定功能，可以不依赖模型而映射出对象的输入
输出关系。FNN对于任意非线性对象的逼近和建模以及对不确定模型的控制均有很
好的效果，有很强的容错性和鲁棒性。因此文中对T-S型RBF神经网络的控制算法
进行了详细的理论分析和仿真研究，并与先进的控制方法--预测控制相结合，对
复杂系统进行预测建模控制。
在对T-S模糊模型与RBF神经网络进行深入研究的基础上，提出一种基于T-S
模糊模型的RBF神经网络的动态学习算法，改进了RBF网络的学习方法。此方法
可以动态地调节网络的隐节点个数、高斯径向基函数的数据中心及扩展常数，不仅
能有效地对T-S模型的参数进行训练，而且改进了FNN学习性能，加快了网络的
收敛速度，提高了算法的泛化能力和全局收敛能力。
鉴于T-S型模糊RBF神经网络对非线性系统具有很好逼近能力，本文将T-S
RBF模糊神经网络控制与预测控制相结合，提出一种能揉和模糊控制的逻辑推理能
力与神经网络的强学习能力的模糊神经网络预测控制模型。仿真结果表明，该控制
算法有较好的预测能力、自适应能力和较高的控制精度。
在理论研究和仿真的基础上，对现场采集到的阳极焙烧炉的温度控制系统的大
量的输入输出数据进行处理，建立了焙烧炉燃烧系统的预测模型，寻找出燃烧器的
控制输出(控制喷油的脉冲数)与火道温度分布之间的关系，从而保证炉内温度的
分布及升温速率满足工艺要求，从理论上为生产高质量炭阳极提供依据。
Intelligent control tactics are adopted to lucubrate with temperature control system of anode baking furnace of Baiyin aluminum plant for the traits of difficult modeling and control of complex system in this paper. Fuzzy neural network (FNN) is composed of neural network and fuzzy logic system, and it is the organic integration of the two parts. FNN is the network structure, which can deal with the abstract information and has strong self-learning function and self-tuning function. It can map the relationship of input and output of the object independing on the model. In addition, it has also good fault freedom and robustness. Making use of FNN, we may get very good effect of the approximation and modeling of the random nonlinear plants and good effect of the control of the uncertain models. So, in this paper we combine the T-S model RBF neural network with the advanced control method-predictive control to predict, model and control the complex systems through theoretically analyzing the control algorithm of T-S model RBF neural network in detail and doing a mass of simulation research.
A dynamic learning method of T-S fuzzy based RBF neural network is proposed on the basis of studying T-S fuzzy model and RBF neural network, by which the learning method of RBF NN is improved. The number of hidden layer nodes of T-S fuzzy RBF net is not only modified dynamically, but also the data centers and extended constants of gaussian radial basis function are changed adaptively during learning progress, moreover the algorithm can train effectively the parameters of T-S model. In addition, the algorithm also improve FNN learning performance, quicken convergence speed of the net, and generalization ability and convergence ability of the algorithm are enhanced.
Due to better approximation ability of T-S fuzzy RBF neural network for nonlinear systems, T-SFRBFNN control is combined with predictive control to develop a FNN predictive control model syncretized logical inference ability of fuzzy control with strong learning ability of NN. Simulation results show that the control method has better predictive ability, adaptive ability and higher control precision.
On the basis of the theory research and simulation, through processing a mass of collected input data and output data of temperature control system of anode baking furnace, we build the predictive model of baking furnace burning system and find out the relationship of control output of the firebox and temperature distributing in the fire way, which makes temperature distributing inside the furnace and calefactive velocity satisfy the technical need and offer theory foundation for producing anode of good quality.
模、难控制的特点，采用智能控制方法对系统进行了深入的研究。模糊神经网络
(FNN)是人工神经网络与模糊逻辑系统的有机结合，是一种能够处理抽象信息的
网络结构，具有强大的自学习和自整定功能，可以不依赖模型而映射出对象的输入
输出关系。FNN对于任意非线性对象的逼近和建模以及对不确定模型的控制均有很
好的效果，有很强的容错性和鲁棒性。因此文中对T-S型RBF神经网络的控制算法
进行了详细的理论分析和仿真研究，并与先进的控制方法--预测控制相结合，对
复杂系统进行预测建模控制。
在对T-S模糊模型与RBF神经网络进行深入研究的基础上，提出一种基于T-S
模糊模型的RBF神经网络的动态学习算法，改进了RBF网络的学习方法。此方法
可以动态地调节网络的隐节点个数、高斯径向基函数的数据中心及扩展常数，不仅
能有效地对T-S模型的参数进行训练，而且改进了FNN学习性能，加快了网络的
收敛速度，提高了算法的泛化能力和全局收敛能力。
鉴于T-S型模糊RBF神经网络对非线性系统具有很好逼近能力，本文将T-S
RBF模糊神经网络控制与预测控制相结合，提出一种能揉和模糊控制的逻辑推理能
力与神经网络的强学习能力的模糊神经网络预测控制模型。仿真结果表明，该控制
算法有较好的预测能力、自适应能力和较高的控制精度。
在理论研究和仿真的基础上，对现场采集到的阳极焙烧炉的温度控制系统的大
量的输入输出数据进行处理，建立了焙烧炉燃烧系统的预测模型，寻找出燃烧器的
控制输出(控制喷油的脉冲数)与火道温度分布之间的关系，从而保证炉内温度的
分布及升温速率满足工艺要求，从理论上为生产高质量炭阳极提供依据。
Intelligent control tactics are adopted to lucubrate with temperature control system of anode baking furnace of Baiyin aluminum plant for the traits of difficult modeling and control of complex system in this paper. Fuzzy neural network (FNN) is composed of neural network and fuzzy logic system, and it is the organic integration of the two parts. FNN is the network structure, which can deal with the abstract information and has strong self-learning function and self-tuning function. It can map the relationship of input and output of the object independing on the model. In addition, it has also good fault freedom and robustness. Making use of FNN, we may get very good effect of the approximation and modeling of the random nonlinear plants and good effect of the control of the uncertain models. So, in this paper we combine the T-S model RBF neural network with the advanced control method-predictive control to predict, model and control the complex systems through theoretically analyzing the control algorithm of T-S model RBF neural network in detail and doing a mass of simulation research.
A dynamic learning method of T-S fuzzy based RBF neural network is proposed on the basis of studying T-S fuzzy model and RBF neural network, by which the learning method of RBF NN is improved. The number of hidden layer nodes of T-S fuzzy RBF net is not only modified dynamically, but also the data centers and extended constants of gaussian radial basis function are changed adaptively during learning progress, moreover the algorithm can train effectively the parameters of T-S model. In addition, the algorithm also improve FNN learning performance, quicken convergence speed of the net, and generalization ability and convergence ability of the algorithm are enhanced.
Due to better approximation ability of T-S fuzzy RBF neural network for nonlinear systems, T-SFRBFNN control is combined with predictive control to develop a FNN predictive control model syncretized logical inference ability of fuzzy control with strong learning ability of NN. Simulation results show that the control method has better predictive ability, adaptive ability and higher control precision.
On the basis of the theory research and simulation, through processing a mass of collected input data and output data of temperature control system of anode baking furnace, we build the predictive model of baking furnace burning system and find out the relationship of control output of the firebox and temperature distributing in the fire way, which makes temperature distributing inside the furnace and calefactive velocity satisfy the technical need and offer theory foundation for producing anode of good quality.
引文
[1] 李人厚．智能控制理论和方法[M]，西安：西安电子科技大学出版社，1999．
[2] 张乃尧，阎平凡．神经网络与模糊控制，清华大学出版社，1999，5
[3] Mag.. 'Seeking the essence of intelligent control', IEEE Controi Syst. June 1994
[4] Yaochu Jin, Jingping Jiang. 'Techniques in Neural Network Based Fuzzy System Identification and Their Application in Control of Complex System'.
[5] Jang. S R. ANFIS: Adaptive-network-based fuzzy inference systems [J],IEEE Trans. On systems, Man&Cybernetics, 1993,23(3) ,665-685
[6] 王立新．自适应模糊系统与控制--设计与稳定性分析[M]，北京：国防工业出 版社，1985
[7] Mug.. 'Intelligence and learning', IEEE Control Sysr, June 1995
[8] UN, C.T., and LEE, C.S.G.: 'Reinforcement structure/parameter learning for neural nctwork based fuzzy logic control systems', ZEEE Trans. Fuzzy Syst., 1994, 2, (1) , pp. 46-63
[9] Hecht-Neilsen R. Counterpropagation network, Proc. of EEEE Firsh International Conference on Neural Networks, 1987,19-32
[10] TAKAGI, H..'Fusion techniques of fuzzy systems and neuralnetworks and fuzzy systems and genetic algorithms', Proc. SPIE Int. Sue. Opt. Eng., 1993, 2061, pp. 402413
[11] 王振雷，顾树生，基于实值遗传算法的模糊神经网络辨识器，东北大学学报(自 然科学版)，2000，21(4) ，354-356
[12] 王伟．广义预测控制理论及其应用[M]，北京：科学出版社，1998，9
[13] Wang Z L, Wang J H, Gu S S. New learning algorithm of neuro-fuzzy network, Proceedings of IFAC Conference on New Technologies for Computer Control, 2001,614-618．
[14] Kevin M．Passino，Stephen Yurkovich，‘fuzzy control’，北京：清华大学出版社，2001
[15] Simon Haykin，NEURAL NETWORKS---A Comprehensive Foundation(Second Edition)．北京：清华大学出版社，2001
[16] HORIKAWA, S., FURUHASHI, T., UCHIKAWA, Y., and TAGAWA, T.:'A study on fuzzy modelling using fuzzy neural networks'. Proceedings of international symposium on Fuzzy engineering, 1991
[17] Bianchini M, Frasconi P, Cori M. Learning Without Minima in Radial Basis Function Network . IEEE Trans. On Neural Network,1995(3) :749-756
[18] WANG, L.X., and MENDEL, J.M.: 'Fuzzy basis functions, universal approximation and orthogonal least squares', ZEEE Trans. Neural Neiw., 1992, pp. 807-814
[19] L'aszl'o T. K'oczy, Domonkos Tikk, and Tam'as D. Gedeon, 'On functional equivalence of certain fuzzy controllers and RBF type approximation schemes '
[20] Hunt K J. Extending the Functional Equivalence of Radial Basis Funetion Networks and Fuzzy Inference System . IEEE Trans. On Neural Network, 1996(3) :776-781
[21] Yaochu Jin,Werner Von Seelen, ' Extracting Interpretable Fuzzy Rules from RBF Neural Networks' Internai Report 2002-02
[22] 'Fuzzv Iomc in control svstems'. ZEEE Trans. 1990． LEE, C C , ,SMC-20, pp. 404143T
[23] Takagi T, Sugeno M. Fuzzy Identification of System and Its Application to
Modeling and Control. IEEE Trans. Syst. ,Man,Cyber. 1985,SMC-15:116-132
[24] D.A. Linkens ,H.O. Nyongesa," learning systems in intelligent control: an appraisal of fuzzy, neural and genetic algorithm control applications" IEE Porc.-Control Theory Appl. ,Vol. 143,No.4,July 1996
[25] 鲍鸿，黄心汉， “T-S型模糊RBF神经网络的结构研究”，华中理工大学学报， 1999，27(1)
[26] 魏海坤，丁维明，RBF网的动态设计方法，控制理论与应用，2002年10月
[27] Chen S, Cowan C F N, Grant P N. Orthogonal least squares learning algorithms for radial basis function networks[J]. Neural Computation,1995,7:606-623
[28] Orr M J L .Regularization in the Selection of Radial Basis Function Centers[J]. Neural Computation
[29] Nicolao B. Karayiannis, "Reformulated Radial Basis Neural Networks Trained by Gradient Descent" IEEE Trans. On Neural Networks,Vol.lO,No.3,May 1999
[30] 鲍鸿，黄心汉，李锡雄．T-S型模糊RBF神经网络快速学习算法[J]．华中理工 大学学报，1999，27(2) ：84-86．
[31] 邓秋琼，黄道平，基于神经网络的非线性预测控制的进一步研究，研究与开发， 1998
[32] Teo Lian Seng 'Adaptive Neuro-Fuzzy Control System by RBF and GRNN Neural Networks' Journal of Intelligent and Robotie System,Vol. 23,pp. 267-289,1998,Kluwer Academic.
[33] 赖兴余，李春雄．基于神经网络的自适应模糊控制器．江西农业大学学报，1998， 20(1) 100-115．
[34] 李卓，萧德云，何世忠．基于神经网络的模糊自适应PID控制方法．控制与决策， 1996，11(3) ，340-345．
[35] XU Xiangyuan, MAO Zongyuan . The Neural Network Predictive Control of Time-Delay Systems. CONTROL THEORY AND APPLICATIONS,2001． 12
[36] 王守唐，高东杰．基于T-S模糊模型的辨识算法[J]，控制与决策，2001，9， 16(5) ：630-633．
[37] 高靖，杨智，预测型智能自整定PID控制器，甘肃工业大学学报，1999，6， 25(2) ，56-61．
[38] 郭力，炭素阳极环式焙烧炉自动化燃烧技术研究，炭素技术学报，2002． 2
[39] 李正伟，张家鸿，马正清， 阳极焙烧工艺技术的改进和升温曲线的选择，炭 素技术学报，2000． 6
[40] 崔东生，“提高预焙阳极质量的途径”，轻金属学报，1999年第五期
[41] 边渭平，焙烧烧炉燃料燃烧控制技术的应用与研究．轻金属学报，2000． 6
[42] 陈喜平，刘凤琴“生产优质预焙炭阳极的探讨”，郑州轻金属研究院，2001． 4
[43] 张新建，“碳素制品焙烧炉的技术进展”，轻金属学报，1994年NO．10
[44] 杨智，高靖，神经元自适应预测PID控制器及实现，信息与控制1999，10， 28(5) ，345-349
[2] 张乃尧，阎平凡．神经网络与模糊控制，清华大学出版社，1999，5
[3] Mag.. 'Seeking the essence of intelligent control', IEEE Controi Syst. June 1994
[4] Yaochu Jin, Jingping Jiang. 'Techniques in Neural Network Based Fuzzy System Identification and Their Application in Control of Complex System'.
[5] Jang. S R. ANFIS: Adaptive-network-based fuzzy inference systems [J],IEEE Trans. On systems, Man&Cybernetics, 1993,23(3) ,665-685
[6] 王立新．自适应模糊系统与控制--设计与稳定性分析[M]，北京：国防工业出 版社，1985
[7] Mug.. 'Intelligence and learning', IEEE Control Sysr, June 1995
[8] UN, C.T., and LEE, C.S.G.: 'Reinforcement structure/parameter learning for neural nctwork based fuzzy logic control systems', ZEEE Trans. Fuzzy Syst., 1994, 2, (1) , pp. 46-63
[9] Hecht-Neilsen R. Counterpropagation network, Proc. of EEEE Firsh International Conference on Neural Networks, 1987,19-32
[10] TAKAGI, H..'Fusion techniques of fuzzy systems and neuralnetworks and fuzzy systems and genetic algorithms', Proc. SPIE Int. Sue. Opt. Eng., 1993, 2061, pp. 402413
[11] 王振雷，顾树生，基于实值遗传算法的模糊神经网络辨识器，东北大学学报(自 然科学版)，2000，21(4) ，354-356
[12] 王伟．广义预测控制理论及其应用[M]，北京：科学出版社，1998，9
[13] Wang Z L, Wang J H, Gu S S. New learning algorithm of neuro-fuzzy network, Proceedings of IFAC Conference on New Technologies for Computer Control, 2001,614-618．
[14] Kevin M．Passino，Stephen Yurkovich，‘fuzzy control’，北京：清华大学出版社，2001
[15] Simon Haykin，NEURAL NETWORKS---A Comprehensive Foundation(Second Edition)．北京：清华大学出版社，2001
[16] HORIKAWA, S., FURUHASHI, T., UCHIKAWA, Y., and TAGAWA, T.:'A study on fuzzy modelling using fuzzy neural networks'. Proceedings of international symposium on Fuzzy engineering, 1991
[17] Bianchini M, Frasconi P, Cori M. Learning Without Minima in Radial Basis Function Network . IEEE Trans. On Neural Network,1995(3) :749-756
[18] WANG, L.X., and MENDEL, J.M.: 'Fuzzy basis functions, universal approximation and orthogonal least squares', ZEEE Trans. Neural Neiw., 1992, pp. 807-814
[19] L'aszl'o T. K'oczy, Domonkos Tikk, and Tam'as D. Gedeon, 'On functional equivalence of certain fuzzy controllers and RBF type approximation schemes '
[20] Hunt K J. Extending the Functional Equivalence of Radial Basis Funetion Networks and Fuzzy Inference System . IEEE Trans. On Neural Network, 1996(3) :776-781
[21] Yaochu Jin,Werner Von Seelen, ' Extracting Interpretable Fuzzy Rules from RBF Neural Networks' Internai Report 2002-02
[22] 'Fuzzv Iomc in control svstems'. ZEEE Trans. 1990． LEE, C C , ,SMC-20, pp. 404143T
[23] Takagi T, Sugeno M. Fuzzy Identification of System and Its Application to
Modeling and Control. IEEE Trans. Syst. ,Man,Cyber. 1985,SMC-15:116-132
[24] D.A. Linkens ,H.O. Nyongesa," learning systems in intelligent control: an appraisal of fuzzy, neural and genetic algorithm control applications" IEE Porc.-Control Theory Appl. ,Vol. 143,No.4,July 1996
[25] 鲍鸿，黄心汉， “T-S型模糊RBF神经网络的结构研究”，华中理工大学学报， 1999，27(1)
[26] 魏海坤，丁维明，RBF网的动态设计方法，控制理论与应用，2002年10月
[27] Chen S, Cowan C F N, Grant P N. Orthogonal least squares learning algorithms for radial basis function networks[J]. Neural Computation,1995,7:606-623
[28] Orr M J L .Regularization in the Selection of Radial Basis Function Centers[J]. Neural Computation
[29] Nicolao B. Karayiannis, "Reformulated Radial Basis Neural Networks Trained by Gradient Descent" IEEE Trans. On Neural Networks,Vol.lO,No.3,May 1999
[30] 鲍鸿，黄心汉，李锡雄．T-S型模糊RBF神经网络快速学习算法[J]．华中理工 大学学报，1999，27(2) ：84-86．
[31] 邓秋琼，黄道平，基于神经网络的非线性预测控制的进一步研究，研究与开发， 1998
[32] Teo Lian Seng 'Adaptive Neuro-Fuzzy Control System by RBF and GRNN Neural Networks' Journal of Intelligent and Robotie System,Vol. 23,pp. 267-289,1998,Kluwer Academic.
[33] 赖兴余，李春雄．基于神经网络的自适应模糊控制器．江西农业大学学报，1998， 20(1) 100-115．
[34] 李卓，萧德云，何世忠．基于神经网络的模糊自适应PID控制方法．控制与决策， 1996，11(3) ，340-345．
[35] XU Xiangyuan, MAO Zongyuan . The Neural Network Predictive Control of Time-Delay Systems. CONTROL THEORY AND APPLICATIONS,2001． 12
[36] 王守唐，高东杰．基于T-S模糊模型的辨识算法[J]，控制与决策，2001，9， 16(5) ：630-633．
[37] 高靖，杨智，预测型智能自整定PID控制器，甘肃工业大学学报，1999，6， 25(2) ，56-61．
[38] 郭力，炭素阳极环式焙烧炉自动化燃烧技术研究，炭素技术学报，2002． 2
[39] 李正伟，张家鸿，马正清， 阳极焙烧工艺技术的改进和升温曲线的选择，炭 素技术学报，2000． 6
[40] 崔东生，“提高预焙阳极质量的途径”，轻金属学报，1999年第五期
[41] 边渭平，焙烧烧炉燃料燃烧控制技术的应用与研究．轻金属学报，2000． 6
[42] 陈喜平，刘凤琴“生产优质预焙炭阳极的探讨”，郑州轻金属研究院，2001． 4
[43] 张新建，“碳素制品焙烧炉的技术进展”，轻金属学报，1994年NO．10
[44] 杨智，高靖，神经元自适应预测PID控制器及实现，信息与控制1999，10， 28(5) ，345-349