基于模糊PID的磁悬浮控制系统研究
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摘要
磁悬浮系统是学习和研究控制理论的重要平台之一。对磁悬浮系统的研究可以归结为对非线性系统和不稳定系统的研究,这类复杂控制对象难以用数学公式进行精确描述,采用经典控制方法也难取得好的控制效果。因此,对于磁悬浮系统,获取不依赖于数学模型的控制方法具有十分重要的意义。
本文基于德国Amira公司设计的MA401型磁悬浮实验设备,首先介绍单自由度磁悬浮系统的构成及工作原理,详细分析了系统的动态模型,在线性化基础上对系统进行定性分析,指出磁悬浮系统为本质不稳定对象,并应用奇异摄动法建立了磁悬浮系统的非线性数学模型。
其次,针对磁悬浮系统难以建立精确数学模型的特性,构造了一个二维模糊控制器,加入积分环节消除误差,实验结果表明系统具有很强的鲁棒性。
最后,在MATLAB环境下利用S-函数建立磁悬浮的非线性动态模型。针对系统的开环不稳定和强烈非线性的特性,在基本模糊控制和常规PID控制的基础上提出模糊自适应PID(FAPID)控制策略,虽然改善了系统的动态性能,却造成了稳态误差的增大。为此文中提出了一种改进的模糊自适应PID控制方法(IFAPID),将微分环节从模糊控制器中剥离出来,只对比例和积分参数进行模糊整定,并针对磁悬浮系统的强烈非线性,在模糊控制器中采用非线性模糊化。仿真结果表明,IFAPID控制系统的抗干扰和适应参数变化的能力都优于PID和FAPID控制方法,并具有更好的动态特性和稳定性。
The magnetic levitation system is one of the most important platforms to study and research control theory.The research on the magnetic levitation system can be attributed to the research on the nonlinear and unstable system. This kind of complicated control object is difficult to describe precisely with mathematic formula, and is very difficult to obtain the better effect using the classical control methods. Therefore, it’s great significant to obtain controlling means without depending on system mathematical model.
Based on the magnetic levitation equipment MA401 that is made in Germany Amira Company, firstly, the structure and working principle of the single degree freedom magnetic levitation system are introduced, and it's dynamic model is analyzed in detail. The qualitative analysis to the magnetic levitation system based on linearization is carried on, it can be concluded that the magnetic levitation system is an unstable object. And the nonlinear mathematical model of the magnetic levitation system is established, where the singular perturbation method is used.
Next, considering the difficulty of giving the exact mathematical model of magnetic levitation, a two-dimension fuzzy controller adding a integration element to avoid the error is constructed and the result shows the magnetic levitation has strong robustness.
Finally, the nonlinearity dynamic model of maglev system is programmed by S-function in MATLAB. Based on both the advantages of PID controller and fuzzy controller, a fuzzy adaptive PID controller(FAPID) is proposed for the characteristics of magnetic levitation system, such as open-loop instability and strong nonlinearity, which the FAPID controller aggrandize the error of stability by simulation, though it's dynamic property is improved. Therefore, the algorithm of the improved fuzzy adaptive PID controller(IFAPID) is advanced and designed that by parted D controller from PID controller, the problem of strong nonlinearity of magnetic levitation system are solved by using nonlinear fuzzy mapping in the fuzzy controller, and the PID controller's P and I parameters are adapted by fuzzy controller. The results showed that the IFAPID controller has the advantages of higher anti-interference ability and adaptability to parameters' changing than conventional PID controller and FAPID, and better dynamic property and stability.
本文基于德国Amira公司设计的MA401型磁悬浮实验设备,首先介绍单自由度磁悬浮系统的构成及工作原理,详细分析了系统的动态模型,在线性化基础上对系统进行定性分析,指出磁悬浮系统为本质不稳定对象,并应用奇异摄动法建立了磁悬浮系统的非线性数学模型。
其次,针对磁悬浮系统难以建立精确数学模型的特性,构造了一个二维模糊控制器,加入积分环节消除误差,实验结果表明系统具有很强的鲁棒性。
最后,在MATLAB环境下利用S-函数建立磁悬浮的非线性动态模型。针对系统的开环不稳定和强烈非线性的特性,在基本模糊控制和常规PID控制的基础上提出模糊自适应PID(FAPID)控制策略,虽然改善了系统的动态性能,却造成了稳态误差的增大。为此文中提出了一种改进的模糊自适应PID控制方法(IFAPID),将微分环节从模糊控制器中剥离出来,只对比例和积分参数进行模糊整定,并针对磁悬浮系统的强烈非线性,在模糊控制器中采用非线性模糊化。仿真结果表明,IFAPID控制系统的抗干扰和适应参数变化的能力都优于PID和FAPID控制方法,并具有更好的动态特性和稳定性。
The magnetic levitation system is one of the most important platforms to study and research control theory.The research on the magnetic levitation system can be attributed to the research on the nonlinear and unstable system. This kind of complicated control object is difficult to describe precisely with mathematic formula, and is very difficult to obtain the better effect using the classical control methods. Therefore, it’s great significant to obtain controlling means without depending on system mathematical model.
Based on the magnetic levitation equipment MA401 that is made in Germany Amira Company, firstly, the structure and working principle of the single degree freedom magnetic levitation system are introduced, and it's dynamic model is analyzed in detail. The qualitative analysis to the magnetic levitation system based on linearization is carried on, it can be concluded that the magnetic levitation system is an unstable object. And the nonlinear mathematical model of the magnetic levitation system is established, where the singular perturbation method is used.
Next, considering the difficulty of giving the exact mathematical model of magnetic levitation, a two-dimension fuzzy controller adding a integration element to avoid the error is constructed and the result shows the magnetic levitation has strong robustness.
Finally, the nonlinearity dynamic model of maglev system is programmed by S-function in MATLAB. Based on both the advantages of PID controller and fuzzy controller, a fuzzy adaptive PID controller(FAPID) is proposed for the characteristics of magnetic levitation system, such as open-loop instability and strong nonlinearity, which the FAPID controller aggrandize the error of stability by simulation, though it's dynamic property is improved. Therefore, the algorithm of the improved fuzzy adaptive PID controller(IFAPID) is advanced and designed that by parted D controller from PID controller, the problem of strong nonlinearity of magnetic levitation system are solved by using nonlinear fuzzy mapping in the fuzzy controller, and the PID controller's P and I parameters are adapted by fuzzy controller. The results showed that the IFAPID controller has the advantages of higher anti-interference ability and adaptability to parameters' changing than conventional PID controller and FAPID, and better dynamic property and stability.
引文
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[2]徐安,李勇善.磁悬浮技术在德国的发展[J].城市轨道交通研究,2001,2:64-68.
[3]赵鸿宾.磁悬浮技术综述[J].国际学术动态,1992,5:43-47.
[4]林国斌,连级三.日本磁悬浮高速铁路发展情况及山梨试验线的技术与系统特点[J].机车电传动,1998,4:5-8.
[5]孙永福,李瑞绅,李中浩.德国磁浮系与轮轨系铁路考察及思考[J].中国铁路,1997,3:44-48.
[6]张瑞华,严陆光,徐善纲.几种典型的高速磁悬浮列车方案比较[J].电工电能新技术,2004,23(2):46-50.
[7] HARTAVI A E, USTUN O, TUNCAY R N, et al. The Design, Simulation and Experimental Study of Active Magnetic Bearing[J]. Electric Machines and Drives Conference, IEEE International, 2001: 492-495.
[8] MARTY HUMPHREY, EDGAR HILTON, PAUL ALLAIRE. Experiences Using RT-Linux to Implement a Controller for a High Speed Magnetic Bearing System[J]. IEEE Trans. Indust. Electr, 1999: 121-130.
[9]吴启迪.自动化学科的理论前沿和应用拓展[J].自动化学报,2002,28:157-164.
[10]朱熀秋，张伟霞，费德成.磁悬浮无轴承电动机发展、应用和前景[J].微特电机,2006,3:39-41.
[11]曹建荣,虞烈,谢友柏.感应型磁悬浮电动机的解耦控制[J].电工技术学,2000,15(5):1-5.
[12]汤洁,李训铭.单自由度磁悬浮系统的状态反馈控制[J].计算机测量与控制,2005,13(5):472-474.
[13]沈建强,李平.神经模糊技术的研究现状与展望[J].控制与决策,1996,11(5):527-532.
[14]丁永生,应浩,任立红.解析模糊控制理论:模糊控制系统的结构和稳定性分析[J].控制与决策,2000, 15:129-135.
[15]李士勇.模糊控制、神经控制和智能控制论[M].哈尔滨:哈尔滨工业大学出版社,1998:108-147.
[16] SHAMELI E, KHAMESEE M B, HUISSOON J P. Nonlinear Controller Design for a Magnetic Levitation Device [J]. Microsystem Technologies, 2007, 13(5): 831-835.
[17] KUO CHAOLIN, LI TZUUHSENG, GUO NAIR. Design of a Novel Fuzzy Sliding-Mode Control for Magnetic Ball Levitation System[J]. Journal of Intelligent and Robotic Systems, 2005, 42(3): 295-316.
[18] WANG H O, K TANAKA, M F Griffin. An Approach to Fuzzy Control of Nonlinear Systems Stability and Design Issues[J]. IEEE Trans. Fuzzy Syst, 1996, 4(1): 14-23.
[19] S K Hong, R LANGARI. Fuzzy Modeling and Control of a Nonlinear Magnetic Bearing System[J]. Intelligent & Fuzzy Syst, 1999, 7: 335-346.
[20] CHEN T T, LI T H. Integragted Fuzzy GA-based Simplex Sliding-mode Control[J]. Internat. J. Fuzzy system, 2000, 2(4): 267-277.
[21] LI J H, LI T H. Multiloop Control of Thyristordriven Magnetic Levitation System[J]. Mechatronics, 2005, 5(5): 469-481.
[22] CHIN E LIN, HUEI L JOU. Force Model Identification for Magnetic Suspension System via Magnetic Field Measurement[J]. IEEE Trans. on Instrument and Measurement, 1993, 42(3): 767-771.
[23] HAJJAJI E H, OULADSINE M. Modeling and Nonlinear Control of Magnetic Levitation System[J]. IEEE Trans. Indust. Electr, 2001, 48(8): 831-838.
[24]肖经伟,尹力明.非线性控制在磁悬浮系统中的应用[J].国防科技大学学报,1999,21(6):106-108.
[25]何朕,王毅,孟范伟,等.磁悬浮系统Bode定理的应用[J].电机与控制,2007,11(3):253-256.
[26]张占军,林小玲.磁悬浮球系统控制器的分析设计[J].机电工程,2007,24(1):19-21.
[27]刘金琨.先进PID控制及其Matlab仿真[M].北京:电子工业出版社,2003:45-67.
[28] ZADEH L A. Fuzzy Sets Information and Control[J]. 1965, 8: 338-353.
[29] MAMDANI E H. Application of Fuzzy Algorithms for Control of Simple Dynamic Plant[J]. Proceedings IEEE, 1974, 12(12): 1585-1588.
[30] PROCYK T J. A Linguistic Self-Organizing Process Controller[J]. Automatic,1979, 15(1): 15-30.
[31] WANG L, MENDEL J M. Generating Fuzzy Rules by Learning From Examples[J]. IEEE Tran SMC, 1992, 22(6): 1414-1427.
[32] YING H. Suffieient Conditions on General Fuzzy Systems as Function Approximators[J]. Automatica, 1994, 30(3): 521-525.
[33] Wang L X. Adaptive Fizzy Systems and Control, Design and Stability Analysis[M]. New Jersey: PTR Prentice-Hall, 1994: 109-135.
[34]王永富,柴天佑.自适应模糊控制理论的研究综述[J].控制工程,2006,13(3):193-198.
[35]章卫国,杨向忠.模糊控制理论与应用[M].西安:西北工业大学出版社,1999:14-30.
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