压电陶瓷驱动器迟滞建模方法研究

压电陶瓷驱动器是原子力显微镜(AFM)的关键组件。AFM在生物、材料及半导体等领域应用广泛,而利用AFM获得高精确的测试结果依然面临诸多挑战。其中,压电陶瓷驱动器具有迟滞、非线性等特点,在大范围高频工作状态下,对定位精度的影响更显著,这严重限制了AFM的进一步应用。本文围绕大范围压电陶瓷驱动器的迟滞性展开研究,设计一种基于改进型多项式拟合算法的迟滞建模方法,使得拟合模型可随输入信号频率的变化而变化,充分提高压电陶瓷迟滞模型的准确性。实验表明,该方法可为压电陶瓷驱动器建立准确的迟滞模型,建模过程简单,通过设计基于该迟滞逆模型的前馈控制算法,可使驱动范围在100μm的压电陶瓷驱动器的线性度提高至1.5%。     

动态迟滞Hammerstein系统的改进卡尔曼状态估计

迟滞特性具有非光滑、多值映射等复杂特性.而在实际的工程中,当输入电压变化频率超过一定的范围时,迟滞的特性是随着输入频率的改变发生变化,使得整个系统的状态估计工作更复杂.本文首先提出一种新的描述动态迟滞的方法,进而描述了动态迟滞Hammerstein系统的状态空间方程,根据此系统在传统卡尔曼滤波器的基础上进行改进得到一种新的非光滑卡尔曼滤波器.最后通过仿真和实验,比较了在输入信号变化频率比较大时,用动态迟滞Hammerstein系统来描述压电陶瓷和采用静态迟滞Hammerstein系统来描述压电陶瓷的特性,非光滑卡尔曼滤波器对这两种含有噪声的模型进行滤波,结果表明由于静态迟滞Hammerstein系统的建模不能很好的描述压电陶瓷的特性,模型存在着误差,因此对系统状态估计的结果也没有用动态Hammerstein系统的误差小,从而说明当输入电压频率变化比较大时研究动态的迟滞Hammerstein模型是很有意义的.     

压电作动器的动态迟滞建模与H∞鲁棒控制

压电作动器具有率相关动态迟滞非线性特性,给传统建模和控制技术提出了挑战.本文针对压电作动器,提出了一种基于Bouc-Wen的Hammerstein率相关迟滞非线性模型,其中Bouc-Wen模型和线性动态模块分别用于描述系统的静态迟滞非线性特性和率相关特性.同时,构造了一个基于Bouc-Wen模型的迟滞补偿器,将迟滞补偿器与被控对象串联使系统线性化;并建立了不确定性系统模型,提出了一种H∞鲁棒跟踪控制方案,可以实现给定频率范围内单频率和复合频率参考信号的良好跟踪.实验结果表明,所建动态模型具有良好的泛化能力,跟踪控制相对误差小于8%,证明了所提出方法的有效性.     

基于多项式拟合的压电陶瓷迟滞神经网络建模

在压电陶瓷致动器优化设计的研究中,针对压电陶瓷的迟滞非线性特性,提出了一种基于多项式拟合算法的神经网络建模方法.由于压电陶瓷驱动器的迟滞现象是一种多对多的映射关系,而传统的建模方法只能对一对一映射进行建模.为解决上述问题,在对压电陶瓷迟滞现象的形成原因和特点进行深入分析的基础上,采用多项式拟合和神经网络相结合的方法对压电陶瓷驱动器的迟滞现象进行建模.仿真结果表明,采用多项式拟合算法的神经网络建模克服了传统建模方法只能对迟滞曲线进行分段建模的局限性,且拟合精度比较高,神经网络正模型的拟合误差为1.45％,神经网络逆模型的拟合误差为1.16％.表明上述神经网络模型精确地反映了压电陶瓷的迟滞特性.     

微位移系统中压电陶瓷驱动器迟滞建模

针对超精密微位移系统中压电陶瓷驱动器的迟滞非线性问题,提出了一种基于遗传反向传播(BP)神经网络的压电陶瓷迟滞非线性建模方法.通过电涡流位移传感器获取压电陶瓷驱动器不同电压值下所对应的位移值;利用六次多项式拟合获得迟滞的数学模型,从而建立基于遗传BP神经网络的迟滞,模型.实验结果显示:该迟滞模型在神经网络测试下的最大误差为0.082 1 μm,平均绝对误差为0.0158 μm.表明,所建的迟滞模型能够较精确地反映出压电陶瓷驱动器的迟滞特性,同时为微位移控制系统设计提供了一定的理论基础.     

基于PI模型的压电陶瓷执行器迟滞特性建模

PI模型是一种运算量小,容易求逆并可用于实时控制系统中的迟滞模型.它是与输入信号频率无关的静态模型.而压电陶瓷表现为与输入频率有关的动态迟滞特性.对PI模型进行改进,引入惯性环节,增加迟滞元的动态特性,提出了动态PI迟滞模型.实验结果表明,改进的PI动态模型能很好地逼近压电陶瓷的位移输出信号,并具有较高的模型预测精度.     

基于RBF神经网络的压电位移台迟滞非线性建模研究

针对压电陶瓷微位移台固有的率相关迟滞非线性特性,以基于play算子的改进PPI模型构建迟滞算子,结合径向基(Radial Basis Function,RBF)神经网络模型,建立描述压电陶瓷微位移台迟滞特性的率相关模型.研究结果表明,在输入信号频率在10 Hz～90 Hz范围内时,模型输出的最大位移误差为0.399 0 μm～0.932 1 μm,均方根误差为0.259 4 μm～0.565 2 μm,相对误差为0.95％～2.48％.验证了基于PI迟滞算子和RBF神经网络的仿真模型能够准确有效的描述压电微位移台的率相关动态迟滞特性,具有较高的频率泛化能力.该方法易于实现,工程适用性强,具有较好的实用价值.     

循环神经网络前馈补偿的压电驱动器跟踪控制

压电驱动器固有的迟滞特性,以及其他动态特性严重地影响其跟踪性能.循环神经网络能够准确拟合非线性系统,并且具有记忆存储能力,本文设计了一种循环神经网络对压电驱动器的迟滞特性进行建模,进而得到能够准确模拟输出位移和输入电压之间关系的逆模型,并据此对压电驱动器进行前馈补偿.此外,考虑到建模误差以及其他扰动对驱动器跟踪精度的影...     

基于C8051F120单片机的压电陶瓷特性测试平台设计

压电陶瓷固有的迟滞、蠕变和非线性特性,严重的影响了它的定位精度。提出了基于C8051F120单片机与DGS-6B数显电感测微仪的对于压电陶瓷微位移驱动器的迟滞、蠕变和非线性等特性研究的方法,实现了对压电陶瓷相关特性测试。     

压电陶瓷驱动器迟滞非线性误差的建模与分析

压电陶瓷驱动器的最大迟滞非线性误差可以超过输出行程的15%,而快刀伺服系统(FTS)要求重复定位精度优于10 nm,相对线性度误差优于0.5%,压电陶瓷驱动器的误差无法满足该精度要求;首先对压电陶瓷迟滞非线性误差进行实验分析,将迟滞非线性误差分为频率无关迟滞现象和频率相关迟滞现象;接着对Bouc-Wen(BW)和Prandtl-Ishlinskii(PI)的频率无关迟滞模型进行修正和对比,确定了采用PI模型描述本文的频率无关迟滞现象,PI模型对频率无关迟滞曲线的辨识精度为0.392%;然后设计基于Hammerstein模型的频率相关迟滞模型,Hammerstein模型对频率相关迟滞曲线的辨识误差相比PI模型时,其均方根值降低了88.068%;提出了压电陶瓷驱动器迟滞非线性误差的建模方法,并分析了其有效性和准确性,给FTS伺服控制提供了一种实用的前馈控制器。     

Modeling and H_∞ Robust Control of a Smart Structure with Rate-dependent Hysteresis Nonlinearity

The performance of smart structures in trajectory tracking under sub-micron level is hindered by the rate-dependent hysteresis nonlinearity.In this paper,a Hammerstein-like model based on the support vector machines(SVM)is proposed to capture the rate-dependent hysteresis nonlinearity.We show that it is possible to construct a unique dynamic model in a given frequency range for a rate-dependent hysteresis system using the sinusoidal scanning signals as the training set of signals for the linear dynamic subsystem of the Hammerstein-like model.Subsequently,a two-degree-of-freedom(2DOF)H∞robust control scheme for the ratedependent hysteresis nonlinearity is implemented on a smart structure with a piezoelectric actuator(PEA)for real-time precision trajectory tracking.Simulations and experiments on the structure verify both the efectiveness and the practicality of the proposed modeling and control methods.     

超磁致伸缩作动器的率相关Hammerstein模型与H∞鲁棒跟踪控制

利用Hammerstein模型对超磁致伸缩作动器（Giant magnetostrictive actuators,GMA）的率相关迟滞非线性进行建模,分别以改进的 Prandtl-Ishlinskii（Modified Prandtl-Ishlinskii）模型和外因输入自回归模型（Autoregressive model with exogenous input,ARX）代表Hammerstein模型中的静态非线性部分和线性动态部分,并给出了模型的辨识方法. 此模型能在1～100Hz频率范围内较好地描述GMA的率相关迟滞非线性. 提出了带有逆补偿器和H∞鲁棒控制器的二自由度跟踪控制策略,实时跟踪控制实验结果证明了所提策略的有效性.     

A hybrid model for rate-dependent hysteresis in piezoelectric actuators

A hybrid model is proposed in this paper to describe the static nonlinear and dynamic characteristics of rate-dependent hysteresis in piezoelectric actuators. In this model, a neural network based submodel is implemented to approximate the static nonlinear characteristic of the hysteresis while a submodel with the first-order differential operators is constructed to describe the dynamic behavior of the hysteresis. In this paper, a special hysteretic operator is proposed to extract the hysteretic feature of the hysteresis. Then, an expanded input space with such special hysteretic operator is constructed. Based on the constructed expanded input space, the neural network can be implemented to approximate the hysteresis phenomenon. The submodel to describe the dynamics is a sum of the weighted first-order differential operators. Finally, the experimental results of applying the proposed method to the modeling of hysteresis in a piezoelectric actuator are also presented.     

Modeling of rate-dependent hysteresis in piezoelectric actuators using a family of ellipses

In this paper, a new ellipse-like mathematic model is proposed to describe the rate-dependent hysteresis in piezoelectric actuators. Since the expressions of the model are completely analytical and can be determined only by a set of parameters, this method simplifies the modeling of complicated hysteresis behaviors. To represent the hysteresis effects, experiments are performed with designed sinusoidal excitations under different frequencies in the range 0.5–300 Hz. The rate-dependent hysteresis is characterized as increasing maximum hysteresis error (MHE) and decreasing peak-to-peak output amplitude (PPOA) phenomenons with the increase of input frequencies. Then, the parameters of the developed model are extracted from the experimental data using the direct least square method through MATLAB offline. The simulation results well correspond to the measured data and demonstrate that the developed model can precisely predict the rate-dependent hysteresis. We also investigate the parameters’ properties with hysteresis characteristics. In the developed model, the length of the minor radius describes the MHE varying with the input frequencies and amplitudes, while the length of major radius and the orientation of the ellipses represent the decreasing PPOA phenomenon. Finally, a real-time feedforward controller with an inverse model is designed to compensate for the rate-dependent hysteresis under different input frequencies. The experimental results show that the hysteresis effects are obviously reduced at both the lower and higher frequencies.     

Hysteresis Compensation and Adaptive Controller Design for a Piezoceramic Actuator System in Atomic Force Microscopy

This paper presents an indirect adaptive controller combined with hysteresis compensation to achieve high accuracy positioning control of piezoceramic actuators and illustrates the results with an atomic force microscope (AFM) application. A dynamic model of a piezoceramic actuator system in AFM is derived and analyzed. A feedforward controller based on the Preisach model is proposed to compensate for the nonlinear hysteresis effects. Then an indirect adaptive controller is designed to achieve desired tracking performance as well as deal with the uncompensated nonlinearity from hysteresis and the system parameter variation due to creep. Experimental results indicate that the proposed controller can significantly improve the positioning control accuracy of the piezoceramic actuator as well as achieve high image quality of the AFM system. The maximum scanning error was reduced from 2µm to 0.3µm in comparison with a proportional‐integral‐derivative (PID) controller. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于径向基神经网络的压电作动器建模与控制

针对压电作动器(piezoelectric actuator,PEA)的率相关迟滞非线性特性,构建了Hammerstein模型对压电作动器建模.采用径向基(radial basis function,RBF)神经网络模型表征迟滞非线性,利用自回归历遍模型(auto-regressive exogenous,ARX)表征频率的影响,并对模型参数进行了辨识.此模型可以在信号频率在1～300 Hz范围内时,较好地描述压电作动器的迟滞特性,建模相对误差为1.99%～4.08%.采用RBF神经网络前馈逆补偿控制,结合PI反馈的复合控制策略实现跟踪控制,控制误差小于2.98%,证明了控制策略的有效性.     

Tracking control of a piezo‐actuated stage based on a frictional model

The tracking control accuracy of a piezoelectric actuator (PEA) is limited due to the actuator's inherent hysteretic nonlinearity. Direct drive of PEA on a positioning stage with friction force will cause control problems. An approximated dynamic model of PEA with consideration of friction force is novel synthesized for control. This model is based on a second‐order transfer function with two parameterization terms. The first time delay term consists of the hysteresis of piezo effect combined with frictional force lag with varying velocity. The second term is comprised of both presliding and sliding regimes. The H‐infinite tracking controller is designed to compensate for the structural uncertainty associated with time delay and the unstructured frictional force in the PEA stage. Iterative Learning Control is implemented to reduce the unmodeled repetitive error by a factor of 20. Numerical simulations and experimental tests consolidate the root mean square (RMS), positioning error close to the hardware reproducibility and accuracy level. Experimental results show the controlled stage can be potentially used for precise positioning. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society