压电作动器的支持向量机迟滞模型  

Support vector machine-based hysteresis model of piezoelectric actuator

作　　者：严秀权 吴洪涛[1] 李耀[1] 杨小龙[1] 康升征 Yah Xiuquan;Wu Hongtao;Li Yao;Yang Xiaolong;Kang Shengzheng(College of Mechanical and Electrical Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)

机构地区：[1]南京航空航天大学机电学院

出　　处：《仪器仪表学报》2018年第9期228-235,共8页Chinese Journal of Scientific Instrument

摘　　要：压电作动器被广泛应用于高精度定位领域,但是其固有的迟滞非线性会严重影响定位精度。为了准确地描述压电作动器的迟滞特性,提出了一种基于非线性自回归移动平均（NARMAX）的支持向量机（SVM）迟滞模型。为了建立SVM迟滞模型,首先需要将压电作动器的输入输出关系从一个多值映射问题转化为单值映射问题,对比了不同的单值映射对SVM迟滞模型精度及泛化能力的影响,提出了一种基于NARMAX构建单值映射的方法,建立了在全局上具有更高精度的压电作动器SVM迟滞模型。通过减小训练集中所包含输入信号频率的间隔,提高了模型在测试集上的精度。采用交叉验证的方法确定SVM模型中的参数,提高了迟滞模型在全局上的精度和泛化能力。结果表明,相比传统Bouc-Wen模型,所提出的模型在1 Hz处精度提高了8倍,在50 Hz处精度提高了60倍。通过位移跟踪实验,证明了基于SVM迟滞逆模型的前馈＋反馈（FF＋FB）控制能够有效提高跟踪精度,相较于PID反馈控制,其跟踪误差最多可降低73.9%。Piezoelectric actuator has been widely adopted in the field of high-precision positioning applications. However, its inherent hysteresis nonlinearity seriously deteriorates the positioning accuracy of PEAs. In order to accurately describe the hysteresis characteristic of PEAs, a support vector machine（SVM） hysteresis model is proposed in this paper based on nonlinear autoregressive-moving-average with exogenous inputs（NARMAX）. To establish the SVM hysteresis model, first of all, it is necessary to convert the input output relationship of the PEA from a multivalued mapping problem into single-valued one. In this paper, the effects of different input variable single-valued mapping methods on the accuracy and generalization ability of the SVM hysteresis model are compared, a single-valued mapping method based on NARMAX is proposed, and a globally higher accuracy SVM hysteresis model for PEAs is established. By reducing the interval of the input signal frequency contained in the training set, the accuracy of the model on the test set is improved. The cross verification method is adopted to determine the parameters of the SVM model, which improves the global accuracy and generalization ability of the hysteresis model. The results show that compared with traditional B-W model, the model proposed in this paper more accurately describes the rate-dependent hysteresis of piezoelectric actuators, the accuracy is improved by 8 times at 1 Hz, by 60 times at 50 Hz and more at higher frequency. Through displacement tracking experiment, it is proved that the feedforward plus feedback（FF＋FB） control based on SVM hysteresis inverse model can effectively improve the tracking accuracy. Compared with PID feedback control, the tracking error can be reduced by 73.9% at most.

关 键 词：压电作动器 支持向量机 率相关迟滞建模 外部输入非线性自回归移动平均 

分 类 号：TP271[自动化与计算机技术—检测技术与自动化装置] TN384[自动化与计算机技术—控制科学与工程]