神经网络NARX压电陶瓷执行器迟滞建模
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摘要
为了准确描述压电陶瓷执行器中存在的速率依赖性迟滞,给出了一种由迟滞环节和动态环节构成的串联块模型。迟滞环节的数学模型通过引入描述梯度变化的迟滞算子,将多值映射转化为扩展输入空间上的一一映射,使用前向神经网络来逼近。基于迟滞模型,引入线性动态模型描述压电陶瓷迟滞输出的速率依赖性,构造神经网络NARX(nonlinear autoregressive model with exogenous inputs)模型。进一步,给出了模型参数优化的递推随机牛顿算法。实验结果验证了所提出的模型和估计算法的有效性。
To describe the rate-dependent hysteresis behavior of the piezoelectric actuators, a cascade block-based model is proposed in this paper, i.e., a rate-independent hysteresis block cascading with a rate-dependent block. For the approximation of the hysteresis block, a hysteresis operator is introduced into the input space to represent the changing tendency of the gradient with the hysteresis. Then a neural hysteresis sub-model is constructed based on a one-to-one mapping. Meanwhile, to describe the rate-dependent characteristics of the dynamic hysteresis, a NARX(nonlinear autoregressive model with exogenous inputs)model is adopted. And a recursive stochastic Newton approximation algorithm is derived for the optimization of the model. The validation results have shown the effectiveness of the proposed model for characterizing the dynamic hysteresis.
To describe the rate-dependent hysteresis behavior of the piezoelectric actuators, a cascade block-based model is proposed in this paper, i.e., a rate-independent hysteresis block cascading with a rate-dependent block. For the approximation of the hysteresis block, a hysteresis operator is introduced into the input space to represent the changing tendency of the gradient with the hysteresis. Then a neural hysteresis sub-model is constructed based on a one-to-one mapping. Meanwhile, to describe the rate-dependent characteristics of the dynamic hysteresis, a NARX(nonlinear autoregressive model with exogenous inputs)model is adopted. And a recursive stochastic Newton approximation algorithm is derived for the optimization of the model. The validation results have shown the effectiveness of the proposed model for characterizing the dynamic hysteresis.
引文
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[15]萧德云.系统辨识理论及应用[M].清华大学出版社,2015:190-194.Xiao D Y.Theory of System Identification with Applications[M].Tsinghua University Press,2015:190-194.
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[3]Wang X,Pommier-Budinger V,Reysset A,et al.Simultaneous Compensation of Hysteresis and Creep in a Single Piezoelectric Actuator by Open-loop Control for Quasi-static Space Active Optics Applications[J].Control Engineering Practice,2014,33:48-62.
[4]Xiao S,Li Y.Modeling and High Dynamic Compensating the Rate-dependent Hysteresis of Piezoelectric Actuators via a Novel Modified in Verse Preisach Model[J].IEEE Transactions on Control Systems Technology,2013,21(5):1549-1557.
[5]Zhang J,Merced E,Sepúlveda N,et al.Optimal Compression of Generalized Prandtl-Ishlinskii Hysteresis Models[J].Automatica,2015,57:170-179.
[6]Kuhnen K,Krejci P.Compensation of Complex Hysteresis and Creep Effects in Piezoelectrically Actuated Systems-A New Preisach Modeling Approach[J].IEEE Transactions on Automatic Control,2009,54(3):537-550.
[7]孟爱华,祝甲明,刘成龙,等.基于改进PSO算法的GMA迟滞模型参数辨识[J].控制工程,2014,21(5):735-739.Meng A H,Zhu J M,Liu C L,et al.Parameter Identification of Hysteretsis Model for GMA Based on Improved PSO Algorithm[J].Control Engineering of China,2014,21(5):735-739.
[8]Aljanaideh O,Habineza D,Rakotondrabe M,et al.Experimental Comparison of Rate-dependent Hysteresis Models in Characterizing and Compensating Hysteresis of Piezoelectric Tube Actuators[J].Physica B:Condensed Matter,2016,486:64-68.
[9]Lien J,York A,Fang T,et al.Modeling Piezoelectric Actuators with Hysteretic Recurrent Neural Networks[J].Sensors and Actuators,A:Physical,2010,163(2):516-525.
[10]N,Ahn K A Hysteresis Functional Link Artificial Neural Network for Identification and Model Predictive Control of SMA Actuator[J].Journal of Process Control,2012,22(4):766-777.
[11]张新良,谭永红.基于输入空间扩张的动态迟滞神经网络模型[J].自动化学报,2009,35(3):319-323.Zhang X L,Tan Y H.Neural Network Model for the Dynamic Hysteresis based on the Expanded Input Space,Acta Automatica Sinica,2009,35(3):319-323.
[12]赵新龙,谭永红,董建萍.基于扩展输入空间法的压电执行器迟滞特性动态建模[J].机械工程学报,2010,46(20):169-174.Zhao X L,Tan Y H,Dong J P.Dynamic Modeling of Rate-dependent Hysteresis in Piezoelectric Actuators Based on Expanded Input Space method[J].Journal of Mechanical Engineering,2010,46(20):169-174.
[13]Gao X,Ren X,Zhu C,et al.Identification and Control for Hammerstein Systems with Hysteresis Non-linearity[J].IET Control Theory and Applications,2015,9(13):1935-1947.
[14]Zhang X,Tan Y.A Hybrid Model for Rate-dependent Hysteresis in Piezoelectric Actuators,Sensors and Actuators A:Physical,January2010,157(1):54-60.
[15]萧德云.系统辨识理论及应用[M].清华大学出版社,2015:190-194.Xiao D Y.Theory of System Identification with Applications[M].Tsinghua University Press,2015:190-194.