基于Levy算法的离子性聚合物金属复合材料分数阶模型辨识
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摘要
IPMC是一类被称为人工肌肉的电活性智能材料,在微机电系统、生物医学、仿生机构等领域都具有很好的应用前景。分数阶微积分中微分、积分的阶次可以是分数,能够更精准地描述实际系统的动态响应。为了说明分数阶模型比传统整数阶模型能够更精确的描述具有非整数阶动力学特性的IPMC驱动系统,首先根据IPMC驱动器输入信号与输出响应的实验数据得到实际频率响应伯德图;然后,结合实验数据应用Levy频域辨识算法分别建立了IPMC的整数阶模型和分数阶模型;最后,比较两类模型和实验数据的频域响应伯德图,可见分数阶模型和实验数据的伯德图拟合效果更精确,所以对于具有非整数阶动力学特性的IPMC驱动系统应该使用分数阶模型来描述和研究。
IPMC is a kind of electro- active intelligent material which is known as artificial muscle. It has good prospects in the fields of micro- electro- mechanical systems,biomedical,bionic institutions. The order of differentiation or integration can be a fraction in fractional calculus. It can describe the dynamic response of actual system more accurately. In order to illustrate the fractional model of IPMC can describe non- integer- order IPMC dynamics system more accurately than the traditional integer- order model of IPMC. First,the actual frequency response Bode diagram was obtained according to the experimental data of driver input signal and IPMC output response. Then,The integer order model and fractional order model of IPMC were established applying Levy frequency domain identification algorithms based on the measured data. Finally,the experimental data frequency response Bode diagram and two models Bode diagrams were compared. The Bode diagrams fitting results of fractional order model and the experimental data was more accurate. So that fractional model should be used to describe and research IPMC drive system with characteristics of non- integer order dynamics.
IPMC is a kind of electro- active intelligent material which is known as artificial muscle. It has good prospects in the fields of micro- electro- mechanical systems,biomedical,bionic institutions. The order of differentiation or integration can be a fraction in fractional calculus. It can describe the dynamic response of actual system more accurately. In order to illustrate the fractional model of IPMC can describe non- integer- order IPMC dynamics system more accurately than the traditional integer- order model of IPMC. First,the actual frequency response Bode diagram was obtained according to the experimental data of driver input signal and IPMC output response. Then,The integer order model and fractional order model of IPMC were established applying Levy frequency domain identification algorithms based on the measured data. Finally,the experimental data frequency response Bode diagram and two models Bode diagrams were compared. The Bode diagrams fitting results of fractional order model and the experimental data was more accurate. So that fractional model should be used to describe and research IPMC drive system with characteristics of non- integer order dynamics.
引文
1 Mohsen S,Kwang K J.Ionic polymer-metal composites:I.fundamentals.Smart Mater Struct,2001;10(8):19—833
2 Shahinpoor M,Bar-cohen Y,Simpson J O,et al.Ionic polymer-metal composites(IPMC)as biomimetic sensors,actuators and artificial muscle-a review.Smart Material and Structures,1998;7:15—30
3 Shahinpoor M,Kim K J.The effect of surface-electrode resistance on the performance of ionic polymer-matal composite artificial muscles.Smart Material and Structures,2000;9(4):543—551
4 Bar-Cohen Y,Leary S,Shahinpoor M,et al.Flexible low-mass device and mechanisms actuated by electroactive polymers.Proceeding of SPIE Conference Electroactive Polymer Actuators and Devices,Newport Beach,CA,1999:51—56
5 Bar-Cohen Y.Electroactive polymer(EAP)actuators as artificial muscles-capabilities,potentials and challenges.Robotics 2000 and Space2000;Albuquerque,NM,USA;2000:191—202
6 Bar-Cohen Y.world Wide electroactive polymers(EAP).Newsletter,2003;5(1):1—15
7 Yamakita M,Kamamichi N,Kozuki T,et al.A snake-like swimming pobot using IPMC actuator and verification of doping effect.Proc of the IEEE/RSJ Int Conf on Intelligent Robots and Systems,2005:3333—3338
8 陈震.压电智能材料IPMC的建模与控制研究.沈阳:东北大学,2013Chen Z.Study on modeling and control of electro-active smare material IPMC.Shenyang:Northeastern University,2013
9 Podlubny I.Fractional differential equations,New York:Academic Press,1999:1—340
10 薛定宇、陈阳泉.高等应用数学问题的MATLAB求解.北京:清华大学出版社,2008:435—442Xue D Y,Chen Y Q.MATLAB to solve advanced applied mathematics problem.Beijing:Tsinghua University Press,2008:435 —442
11 王福兴,蒲亦非,周激流.分数阶微积分的应用研究.无线互联科技,2011;8:12—14Wang F X,Pu Y F,Zhou J L.Research on application of fractional calculus.Wireless Internet Technology,2011;8:12—14
12 薛定宇,赵春娜.分数阶系统的分数阶PID控制器设计.控制理论与应用,2007;24(5):771—776Xue D Y,Zhao C N.Fractional order PID controller design for fractional order system.Control Theory&Applications,2007;24(5):771 —776
13 Torvik P J,Bagley R L.On the appearance of the fractional derivative in the behavior of real material.Transactions of the ASME,Journal of Applied Mechanics,1984;51(2):294—298
14 Valério Duarte SD A Costa Jé.Levy’s identification method extended to fractional order transfer functions.The Fifth Euromech Nonlinear Dynamics Conference,Eindhoven:Euromech,2005:1—10
15 Valério D.Fractional robust system control.Lisboa:Instituto Superior Técnico da Universidade Técnica de Lisboa,2005
2 Shahinpoor M,Bar-cohen Y,Simpson J O,et al.Ionic polymer-metal composites(IPMC)as biomimetic sensors,actuators and artificial muscle-a review.Smart Material and Structures,1998;7:15—30
3 Shahinpoor M,Kim K J.The effect of surface-electrode resistance on the performance of ionic polymer-matal composite artificial muscles.Smart Material and Structures,2000;9(4):543—551
4 Bar-Cohen Y,Leary S,Shahinpoor M,et al.Flexible low-mass device and mechanisms actuated by electroactive polymers.Proceeding of SPIE Conference Electroactive Polymer Actuators and Devices,Newport Beach,CA,1999:51—56
5 Bar-Cohen Y.Electroactive polymer(EAP)actuators as artificial muscles-capabilities,potentials and challenges.Robotics 2000 and Space2000;Albuquerque,NM,USA;2000:191—202
6 Bar-Cohen Y.world Wide electroactive polymers(EAP).Newsletter,2003;5(1):1—15
7 Yamakita M,Kamamichi N,Kozuki T,et al.A snake-like swimming pobot using IPMC actuator and verification of doping effect.Proc of the IEEE/RSJ Int Conf on Intelligent Robots and Systems,2005:3333—3338
8 陈震.压电智能材料IPMC的建模与控制研究.沈阳:东北大学,2013Chen Z.Study on modeling and control of electro-active smare material IPMC.Shenyang:Northeastern University,2013
9 Podlubny I.Fractional differential equations,New York:Academic Press,1999:1—340
10 薛定宇、陈阳泉.高等应用数学问题的MATLAB求解.北京:清华大学出版社,2008:435—442Xue D Y,Chen Y Q.MATLAB to solve advanced applied mathematics problem.Beijing:Tsinghua University Press,2008:435 —442
11 王福兴,蒲亦非,周激流.分数阶微积分的应用研究.无线互联科技,2011;8:12—14Wang F X,Pu Y F,Zhou J L.Research on application of fractional calculus.Wireless Internet Technology,2011;8:12—14
12 薛定宇,赵春娜.分数阶系统的分数阶PID控制器设计.控制理论与应用,2007;24(5):771—776Xue D Y,Zhao C N.Fractional order PID controller design for fractional order system.Control Theory&Applications,2007;24(5):771 —776
13 Torvik P J,Bagley R L.On the appearance of the fractional derivative in the behavior of real material.Transactions of the ASME,Journal of Applied Mechanics,1984;51(2):294—298
14 Valério Duarte SD A Costa Jé.Levy’s identification method extended to fractional order transfer functions.The Fifth Euromech Nonlinear Dynamics Conference,Eindhoven:Euromech,2005:1—10
15 Valério D.Fractional robust system control.Lisboa:Instituto Superior Técnico da Universidade Técnica de Lisboa,2005