基于T-S模型的模糊预测控制在线优化算法研究
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摘要
针对复杂非线性系统难以建模从而难以控制以及约束预测控制的在线优化计算量大的问题,本文研究了基于T-S模糊模型的非线性系统辨识算法,并在此基础上研究非线性系统的模糊预测控制问题。对比研究了约束预测控制的在线优化几种求解算法,仿真表明本文所提算法的有效性。论文的主要研究工作内容有以下几个方面:
(1)针对复杂非线性动态系统的模糊建模问题,本文采用一种基于T-S模型在线自学习的模糊辨识算法。通过模糊聚类算法对T-S模糊模型的前提部分进行辨识;对于T-S模糊模型的后件参数采用在线学习的方法进行辨识。仿真研究表明该算法较好的辨识效果。
(2)有约束的预测控制滚动优化可以转化成一个标准的二次规划问题。对比研究投影最小二乘算法、有效集算法和Dantzig-Wolfe算法在预测控制在线优化中的求解效果,Shell塔仿真表明投影最小二乘算法在约束预测控制在线优化求解中有较好的效果。
(3)研究了基于T-S模糊模型的DMC和GPC两种模糊预测控制算法,并且与普通的PID的控制效果进行比较,pH中和过程表明基于T-S模型模糊预测控制较普通的PID有较好的效果。将非线性系统预测控制的目标函数转化为线性二次规划问题,避免了非线性规划巨大的计算量,同时利用投影最小二乘算法进行在线求解。
In this dissertation, for complex nonlinear system difficult modeling and the large online optimization calculation of constrained predictive control, the identification algorithm of nonlinear system based on T-S fuzzy model is researched. On the basis of these, the fuzzy predictive control based on T-S model is researched. Several algorithms of the online optimization of constrained predictive control are studied, the simulation results show that the new method are of effectiveness. The main contents are concluded as followings:
(1) In view of modeling problems of nonlinear and dynamic system, a self-learning fuzzy identification algorithm is presented based on T-S model in this paper. The premise parameter is identified by fuzzy clustering and the consequent parameter is identified by self-learning. The simulation result shows that the algorithm has high accuracy and can be used in online modeling.
(2) The online optimization of constrained model predictive control could be converted into quadratic programming. Projected least-squares algorithm, active set method and Dantzig-Wolfe algorithm are contrastively researched in the quadratic programming of model predictive control. The simulation of Shell tower predictive control shows the projected least-squares algorithm is effective to solve the online optimization problem.
(3) Two nonlinear fuzzy predictive control methods, namely fuzzy DMC and GPC based on T-S fuzzy model, are contrastively researched in the paper. And comparing the performance of fuzzy predictive control with the common PID control, the simulation result on pH neutralization demonstrates the performance of fuzzy predictive control performance is superior to conventional PID controller. Objective function is converted into linear programming and thus the huge computational burden is avoided. The projected least squares algorithm is also used in the online optimization of fuzzy predictive control.
(1)针对复杂非线性动态系统的模糊建模问题,本文采用一种基于T-S模型在线自学习的模糊辨识算法。通过模糊聚类算法对T-S模糊模型的前提部分进行辨识;对于T-S模糊模型的后件参数采用在线学习的方法进行辨识。仿真研究表明该算法较好的辨识效果。
(2)有约束的预测控制滚动优化可以转化成一个标准的二次规划问题。对比研究投影最小二乘算法、有效集算法和Dantzig-Wolfe算法在预测控制在线优化中的求解效果,Shell塔仿真表明投影最小二乘算法在约束预测控制在线优化求解中有较好的效果。
(3)研究了基于T-S模糊模型的DMC和GPC两种模糊预测控制算法,并且与普通的PID的控制效果进行比较,pH中和过程表明基于T-S模型模糊预测控制较普通的PID有较好的效果。将非线性系统预测控制的目标函数转化为线性二次规划问题,避免了非线性规划巨大的计算量,同时利用投影最小二乘算法进行在线求解。
In this dissertation, for complex nonlinear system difficult modeling and the large online optimization calculation of constrained predictive control, the identification algorithm of nonlinear system based on T-S fuzzy model is researched. On the basis of these, the fuzzy predictive control based on T-S model is researched. Several algorithms of the online optimization of constrained predictive control are studied, the simulation results show that the new method are of effectiveness. The main contents are concluded as followings:
(1) In view of modeling problems of nonlinear and dynamic system, a self-learning fuzzy identification algorithm is presented based on T-S model in this paper. The premise parameter is identified by fuzzy clustering and the consequent parameter is identified by self-learning. The simulation result shows that the algorithm has high accuracy and can be used in online modeling.
(2) The online optimization of constrained model predictive control could be converted into quadratic programming. Projected least-squares algorithm, active set method and Dantzig-Wolfe algorithm are contrastively researched in the quadratic programming of model predictive control. The simulation of Shell tower predictive control shows the projected least-squares algorithm is effective to solve the online optimization problem.
(3) Two nonlinear fuzzy predictive control methods, namely fuzzy DMC and GPC based on T-S fuzzy model, are contrastively researched in the paper. And comparing the performance of fuzzy predictive control with the common PID control, the simulation result on pH neutralization demonstrates the performance of fuzzy predictive control performance is superior to conventional PID controller. Objective function is converted into linear programming and thus the huge computational burden is avoided. The projected least squares algorithm is also used in the online optimization of fuzzy predictive control.
引文
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[8] Oliver Hacker,Oliver Nelles,Olaf Moseler.Nonlinear system identifica- tion an d predictive control of a heat exchanger based on local fuzzy mode1.In:proceedings of the ACC.1997:3294—3298
[9]苏佰丽,陈增强,袁著祉.多变量非线性系统的有约束模糊预测控制.哈尔滨上业大学学报,2006,38(10):1700—1704
[10]梅华,孙建平.模糊预测控制原理及其实现方法.上海大学学报,2001,7(5):448—458
[11]雎刚,陈来九.多变量模糊预测控制及其应用研究.控制与决策,1997,12(1):83-87
[12]李少远,席裕庚.模糊动态环境下复杂系统的满意优化控制.自动化学报,2002,28(3):408-411
[13]冯晓云,赵冬梅,李治.基于满意优化的模糊多目标预测控制算法研究.西南交通大学学报, 2002,37(1):99-102
[14]阳盛明,罗长童编著.最优化原理、方法及求解软件.科学出版社,2006
[15]李静如,等.模糊预测控制及应用研究,控制理论与应用1992,9(3):283-287
[16]刘忠信,孙青林,陈增强,袁著祉,杨小军,唐共民,巴鲁军,???.基于T-S模型的钻杆对中自适应预测控制.控制与决策, 2002年5月第17卷第3期
[17]王树青,等编著.工业过程控制工程.化学工业出版社,2002
[18]刘斌.非线性系统建模及预测控制若干问题研究.博士学位论文,浙江大学,20041201
[19]李奇安.广义预测控制算法简化实现方法研究.博士学位论文,浙江大学,20050501
[20]陈虹,刘志远,解小华非线性模型预测控制的现状与问题控制与决策第16卷第4期2001.
[21]陈希平,梁敏非线性模型预测控制的理论及应用综述控制工程2003, 10增刊.
[22] Roubos J A F, Mollov S, Babuska Bet al. Fuzzy model-based predictive control using Takagi-Sngeno models[J].Int J Approx Reas,1999,22:3-30.
[23]王殿辉,柴天佑.基于ANN模型的非线性自校正预测控制器[J].自动化学报,1997,23(3):396-399
[24]席裕庚,耿晓军陈虹预测控制性能研究的新进展控制理论与应用第17卷第4期2000.
[25]邢宗义,胡维礼,贾利民基于T-S模型的模糊预测控制研究控制与决策2005年5月第20卷第5期
[26]梁敏.模糊预测控制理论及设计方法研究.硕士学位论文.兰州理工大学, 20040501
[27]白圣建,黄新生.基于T-S模型的一类挠性航天器模糊控制.中国科技论文在线
[28]安树.基于T-S模糊模型的广义预测控制方法研究硕士学位论文燕山大学20061010
[29] Gustafson D ,Kessel W. Fuzzy clustering with a fuzzy covariance matrix [A. Proc of IEEE Conf on Decision and control] C. San Diego,1979:761-766
[30] Ning Lia,b,*, Shao-Yuan Lia, Yu-Geng Xia. Multi-model predictive control based on the Takagi-Sugeno fuzzy models: a case study.ELSEVIER, Information Sciences 165 (2004) 247-263
[31]陈柔伊,张尧,武志刚,陈泽淮.改进的模糊聚类算法在负荷预测中的应用.电力系统及其自动化学报,2005年6月第17卷第3期
[32]张枸,邓辉文.基于减法聚类与聚类有效性评判的FCM聚类.重庆工学院学报, 2006年5月第20卷第5期
[33] Takagi, T. and Sugeno, M.Fuzzy identification of systems and its applications tomodeling and control[J]IEEE Trans. System,Man,and Cybern,1985,15:116-132.
[34]赵建军.模糊预测控制在火电厂的应用研究.硕士学位论文,华北电力大学(保定),20051227
[35]邹健.智能预测控制及其应用研究.博士学位论文,浙江大学,2002.6.1
[36]翟春艳,李书臣.基于满意优化的非线性预测控制.计算机仿真,第23卷第2期
[37]席裕庚.预测控制.北京:国防工业出版社,1993
[38]邹涛,李少远.带有可变约束条件的预测控制算法中国自动化学会华东地区第十七届学术年会会议论文.
[39]胡玉娥.基于满意优化的多约束非线性预测控制.自动化理论技术与应用2004.
[40] Goldfarb D.& A.Idnani. Dual and primal-dual methods for solving strictly convex quadratic programs,1987
[41] Nie Y.Y.&S.O.Magundho. A quasi-simplex methods for solving strictly convex quadratic programming, Mini-Micro System,22(1-6),2001
[42]贺立群不等式约束的凸二次规划问题的新算法北京理工大学学报,18(541一547).1998
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