基于改进CQPSO算法的压电陶瓷建模研究

压电精密定位技术在高精度定位与控制领域起着关键作用。针对压电陶瓷迟滞非线性特性进行建模与分析是当前研究的一大热点。传统智能算法对迟滞模型的辨识易陷入局部最优,因此,提出一种改进混沌量子粒子群算法(Improved chaotic quantum particle swarm optimiztaion, ICQPSO)。以量子粒子群算法(QPSO)结合基于早熟系数的混沌映射跳出局部收敛。引入变尺度法缩小可行解空间提升收敛效率和精度,采用Bouc-Wen微分方程模型对多频输入动态迟滞现象进行建模。经实验验证,该算法对Bouc-Wen模型的辨识精度明显高于GA、MFA算法。     

基于改进果蝇优化的压电精密定位平台迟滞Bouc-Wen模型辨识

提出一种基于改进果蝇优化算法（Improved Fruit fly Optimization Algorithm,IFOA）的压电精密定位平台迟滞特性的Bouc-Wen模型参数辨识方法。通过引入交叉因子和自适应搜索步长,IFOA可有效实现全局搜索与局部优化的动态平衡,并通过一种新的搜索策略提高整体搜索效率和优化精度。将IFOA应用于压电精密定位平台迟滞Bouc-Wen模型的参数辨识。实验辨识结果验证了该方法的有效性和潜力。     

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.     

基于差动电容传感器的微动定位系统设计

设计并加工了一种结构简单、小巧的微动定位系统,该系统精度较高、扫描范围大且成本低廉.采用簧片结构设计系统的机械结构,使用压电陶瓷作为执行器件,使用差动电容传感器作为位移反馈,实现闭环控制,从而有效克服了压电陶瓷执行器件的迟滞和蠕变效应.介绍了微动定位系统的机械组成和差动电容传感器信号检测电路的工作原理,并对系统进行了测试和标定实验.实验结果显示:该平台能够实现15 μm的扫描,精度约为15 nm,且动态性能良好.     

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。     

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.     

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.     

基于频率相关的压电作动器迟滞特性建模及参数辨识

为辨识压电作动器在应用过程中的率相关迟滞特性,采用基于最小二乘支持向量机理论对压电作动器进行建模,并引入粒子群算法对模型的参数进行优化,模型以当前及历史输入电压、历史输出位移组成的向量作为模型的输入,而以当前的输出位移作为模型的输出进行训练。最后,通过仿真结果和实验结果对比发现,本文建立的压电率相关迟滞模型平均误差为0.0208μｍ,最大误差为0.4290μｍ比Bouc-Wen模型精度高,验证了本文建模方法的可行性。     

基于加速度变化的步态识别方法

为辨识压电作动器在应用过程中的率相关迟滞特性,采用基于最小二乘支持向量机理论对压电作动器进行建模,并引入粒子群算法对模型的参数进行优化,模型以当前及历史输入电压、历史输出位移组成的向量作为模型的输入,而以当前的输出位移作为模型的输出进行训练。最后,通过仿真结果和实验结果对比发现,本文建立的压电率相关迟滞模型平均误差为0.0208μｍ,最大误差为0.4290μｍ比Bouc-Wen模型精度高,验证了本文建模方法的可行性。     

融合迭代学习与干扰观测器的压电微动平台精密运动控制

针对运动系统中常见的重复参考轨迹,尽管迭代学习控制（iterative learning control,ILC）可以通过迭代有效消除重复误差,但其对于非重复性干扰十分敏感．为实现在非重复干扰环境下压电微动平台的精密运动,提出了融合ILC与干扰观测器（disturbance observer,DOB）的控制策略．为避免复杂的迟滞建模,将迟滞非线性视为迭代过程中的重复性输入干扰．为保证控制策略的稳定性,推导其收敛条件并分析对非重复性干扰的抑制作用从而降低收敛误差．最后在压电微动平台进行了对比实验,结果表明：所提控制策略可以在无迟滞模型的前提下有效补偿迟滞非线性．针对理想环境下的5Hz、10Hz、20Hz三角波跟踪,其跟踪误差的均方根在行程的0.4%以内;而在非重复干扰环境下,跟踪误差的均方根为10.24nm,与内置的控制器、单独的反馈控制器、ILC相比,分别降低了98.73%、98.67%与88.24%．而且在干扰环境下,所提控制策略加快了ILC的收敛速度．实验结果充分验证了所提控制策略的有效性,实现了压电微动平台的精密运动．     

ULTRA‐FINE TRACKING CONTROL ON PIEZOELECTRIC ACTUATED MOTION STAGE USING PIEZOELECTRIC HYSTERETIC MODEL

The tracking control accuracy of the piezoelectric actuator (PEA) is limited due to its inherent hysteresis nonlinearity. A new piezoelectric‐actuator model is synthesized based on two first‐order transfer systems in parallel with two tuned parameters determined from one experiment. Two open‐loop tracking controllers are implemented with the proposed model to compensate the hysteresis of linear positioning. Numerical simulations and experimental tests on the tracking of sinusoidal and triangular waveforms with signal frequencies ranging from 1Hz to 30 Hz are revisited and compared with the conventional Bouc‐Wen and Duhem models. Experimental results reveal that the RMS tracking error can be reduced to less than 2% of the maximum traveling distance without any feedback sensor. When a piezoelectric actuated on a two Degree‐Of‐Freedom (DOF) monolithic motion stage was employed, the RMS tracking error was 50 nm within the measured sensor accuracy.     

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.     

Modeling and Tracking Control for Piezoelectric Actuator Based on a New Asymmetric Hysteresis Model

This paper presents a new asymmetric hysteresis model and its application in the tracking control of piezoelectric actuators. The proposed model is based on a coupled-play operator which can avoid the conventional Prandtl-Ishlinskii (CPI) model's defects, i.e., the symmetric property. The high accuracy for modeling asymmetric hysteresis is validated by comparing simulation results with experimental measurements. In order to further evaluate the performance of the proposed model in closed-loop tracking application, two different hybrid control methods which experimentally demonstrate their performance under the same operating conditions, are compared to validate that the hybrid control strategy with proposed hysteresis model can mitigate the hysteresis more effectively and achieve better tracking precision. The experimental results demonstrate that the proposed modeling and tracking control strategy can realize efficient control of piezoelectric actuator.      

Design and control of a 6-degree-of-freedom precision positioning system

This paper presents the design and test of a 6-degree-of-freedom(DOF) precision positioning system, which is assembled by two different 3-DOF precision positioning stages each driven by three piezoelectric actuators (PEAs). Based on the precision PEAs and flexure hinge mechanisms, high precision motion is obtained. The design methodology and kinematic characteristics of the 6-DOF positioning system are investigated. According to an effective kinematic model, the transformation matrices are obtained, which is used to predict the relationship between the output displacement from the system arrangement and the amount of PEAs expansion. In addition, the static and dynamic characteristics of the 6-DOF system have been evaluated by finite element method (FEM) simulation and experiments. The design structure provides a high dynamic bandwidth with the first natural frequency of 586.3 Hz. Decoupling control is proposed to solve the existing coupling motion of the 6-DOF system. Meanwhile, in order to compensate for the hysteresis of PEAs, the inverse Bouc-Wen model was applied as a feedforward hysteresis compensator in the feedforward/feedback hybrid control method. Finally, extensive experiments were performed to verify the tracking performance of the developed mechanism.     

结合误差变换的Bouc-Wen迟滞非线性系统反步控制器设计

针对智能材料执行器中非平滑、多映射的迟滞非线性,采用Bouc-Wen模型描述迟滞,并提出了一种基于误差变换的反步控制器设计方案.首先利用Bouc-Wen模型中的变量特性,通过预设性能函数,将误差约束在预设范围内.然后通过误差变换,将一个对输出误差存在约束的跟踪问题转化为一个无约束的镇定问题.最后利用反步控制法设计迟滞系统的控制器,该控制方法保证期望的跟踪精度,并能将误差限定在设定范围内且满足预设性能,提高了系统的暂态和稳态性能.仿真结果表明设计方法的有效性.     

Adaptation‐Enhanced Model‐Based Control with Charge Feedback for Piezo‐Actuated Stage

This paper proposes a new control design to compensate for the residual control error from charge feedback control. A part of the applied voltage is consumed by the hysteresis effect because of the nature of the piezoelectric material; moreover, this effect is difficult to overcome because it is rate dependent. This work utilizes a piezoelectric electromechanical model to propose a precompensation algorithm for a piezoelectric actuator. A nonlinear compensator can be used to treat both the hysteresis nonlinearity and the rate dependency of the system, and the adjustable parameters are specified through adaptive identification with only basic system information. The proposed design can position a piezoelectric stage with a magnifying mechanism within a few nanometers of a target, and the leftover hysteresis phenomenon is negligible.