SVD‐Based Accurate Identification and Compensation of the Coupling Hysteresis and Creep Dynamics in Piezoelectric Actuators

In this paper, the coupling hysteresis and creep in piezoelectric actuators are identified and compensated for accurate tracking. First, we present the coupling hysteresis and creep model in smart actuators. Next, a complete identification strategy is designed according to the properties of the Preisach model. Then, an approach for parameter updating of the coupling model is provided. With the identified hysteresis and creep, the model‐based inversion compensation is designed. Finally, we apply the model identification and compensation to a piezoelectric stage to demonstrate the effectiveness of the proposed approaches. Significant reduction of the tracking error is achieved with the model‐based inversion feedforward compensator in which the relative errors at 10 Hz and 50 Hz are reduced to 1.85% and 4.53%, respectively. In addition, the model‐based feedforward is augmented with an integral feedback controller. With the composite controller, the relative errors at 10 Hz and 50 Hz are reduced to 0.42% and 3.04%, respectively.     

A hysteresis compensation method of piezoelectric actuator: Model,identification and control

A major deficiency of piezoelectric actuators is that their open-loop control accuracy is seriously limited by hysteresis. In this paper, a novel mathematical model is proposed to describe hysteresis precisely. Based on the hysteresis model, an adaptive inverse control approach is presented for reducing hysteresis. The weights of the main hysteresis loop are identified by using least mean square (LMS) algorithm. The realization of an inverse feedforward controller for the linearization of a piezoelectric actuator is formulated. Experiments were performed on a micro-positioning system driven by piezoelectric actuators. The experimental results demonstrate that the positioning precision is noticeably improved in open-loop operation compared to the conventional open-loop control without any compensation.     

Modeling and control of hysteresis in magnetostrictive actuators

A novel dynamic model is proposed for the hysteresis in magnetostrictive actuators by coupling a Preisach operator to an ordinary differential equation, and a parameter identification method is described. An efficient inversion algorithm for a class of Preisach operators with piecewise uniform density functions is then introduced, based upon which an inverse control scheme for the dynamic hysteresis model is presented. Finally the inversion error is quantified and l₁ control theory is applied to improve the robustness of inverse compensation. Simulation and experimental results based on a Terfenol-D actuator are provided.     

Approximate inversion of the Preisach hysteresis operator with application to control of smart actuators

Hysteresis poses a challenge for control of smart actuators. A fundamental approach to hysteresis control is inverse compensation. For practical implementation, it is desirable for the input function generated via inversion to have regularity properties stronger than continuity. In this paper, we consider the problem of constructing right inverses for the Preisach model for hysteresis. Under mild conditions on the density function, we show the existence and weak-star continuity of the right-inverse, when the Preisach operator is considered to act on Holder continuous functions. Next, we introduce the concept of regularization to study the properties of approximate inverse schemes for the Preisach operator. Then, we present the fixed point and closest-match algorithms for approximately inverting the Preisach operator. The convergence and continuity properties of these two numerical schemes are studied. Finally, we present the results of an open-loop trajectory tracking experiment for a magnetostrictive actuator.     

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     

一种新的磁滞非线性前馈补偿算法

针对超磁致伸缩致动器磁滞非线性特征, 建立了描述其非线性行为的Preisach数学模型, 以F函数法求解了该模型的数值模型. 针对当前致动器非线性前馈补偿控制中迭代和执行效率低的缺点, 将磁滞非线性理解为系统干扰, 提出了一种新的非线性前馈补偿算法, 在求解Preisach逆模型过程中,引入稳态误差信号作为参考变量, 以Sigmoid函数变步长算法进行迭代步长自适应动态调整. 计算机仿真和实验研究均表明,与当前的磁滞模型求逆算法相比, 所提出的算法在保证控制精度的同时可以显著提高系统收敛速度, 大大提高了程序的执行效率.     

Adaptive identification and control of hysteresis in smart materials

Hysteresis hinders the effective use of smart materials in sensors and actuators. This paper addresses recursive identification and adaptive inverse control of hysteresis in smart material actuators, where hysteresis is modeled by a Preisach operator with a piecewise uniform density function. Two classes of identification schemes are proposed and compared, one based on the hysteresis output, the other based on the time-difference of the output. Conditions for parameter convergence are presented in terms of the input to the Preisach operator. An adaptive inverse control scheme is developed by updating the Preisach operator (and thus its inverse) with the output-based identification method. The asymptotic tracking property of this scheme is established, and for periodic reference trajectories, the parameter convergence behavior is characterized. Practical issues in the implementation of the adaptive identification and inverse control methods are also investigated. Simulation and experimental results based on a magnetostrictive actuator are provided to illustrate the proposed approach.     

An integrated physical model that characterizes creep and hysteresis in piezoelectric actuators

In this paper, a model that can precisely portray hysteresis and creep in piezoelectric actuators is proposed. The model, which is originally constructed using bond-graph representation, describes the actuator’s various physical effects and energy interaction between physical domains. Specifically, the model utilizes a parallel connection of Maxwell-slip elements and a nonlinear spring to describe hysteresis, and a series connection of Kelvin–Voigt units to describe creep. Using the experimental data, the constitutive relation of the nonlinear spring and the parameters of linear, physical elements in the model can be systematically identified via the linear programming method. To further account for the frequency-dependent hysteresis behavior, a dynamic damper is incorporated. By analyzing the model, the influence of initial strain/charges on the creep response is revealed and an initialization procedure is devised to eliminate such an influence. An inverse model control, in the sense of feedback linearization, is constructed based on the identified model to make the actuator track reference trajectories. Experiments show that both creep and hysteresis are effectively cancelled and accurate tracking of selected reference trajectories is achieved.     

On superposition of Hammerstein systems: Application to simultaneous hysteresis‐dynamics compensation

Superposition principle (SP)—the response (output) of a linear system to a weighted combination of inputs equals to the combination of the outputs with the same weights and each corresponding to the individual input, respectively—is one of the most fundamental properties of linear systems, and has been exploited for controls, for example, in the development of model predictive control. Extension of the superposition principle beyond linear systems, however, is largely limited. In this paper, the almost superposition of Hammerstein systems (ASHS) and its application to precision control of hysteresis‐Hammerstein systems is studied. We first show, under some minor conditions, the existence of a nonstrict form ASHS, and under one further condition, the strict‐form ASHS. We then present one application of the ASHS—simultaneous hysteresis and dynamics compensation in output tracking of hysteresis‐Hammerstein systems, where offline iterative learning control to track the output elements is integrated with online synthesis of the control input via an inverse Preisach modeling. The proposed ASHS‐based technique is further enhanced through two online optimization schemes, and then illustrated through a simulation example on piezoelectric actuators model.     

Two-Axial Piezoelectric Actuator Controller Using a Multi-Layer Artificial Neural Network Featuring Feedback Connection for Tactile Displays

Although some compensation method is required when using a piezoelectric actuator because of hysteresis, a sensor feedback method is not suitable for an actuator array. In this study, we design a controller using a neural network to apply it to a tactile display composed of two-axial miniature actuators. This paper describes the two-axial miniature actuator, which is composed of two bimorph piezoelectric elements and two small links connected by three joints. A control system for the two-axial miniature actuator is designed based on a multi-layered artificial neural network to compensate for the hysteresis of piezoelectric elements. The output neuron emits the time derivative of voltage, a two-bit signal expressing increment or decrement condition is generated by two input neurons, and two input neurons calculate current values of voltage and displacement, respectively. The neural network is outfitted with a feedback loop including an integral element to reduce the number of neurons. In the experiment, if the result of the left piezoelectric element is compared to that of the right element, the displacement amplitudes and the inclinations coincide on the right and left piezoelectric elements. Although precise hysteresis characteristics such as loop width are considerably different, the present neural system can follow the difference.     

Control of hysteresis in smart actuators with application to micro-positioning

Hysteresis in smart material actuators makes the effective use of these actuators quite challenging. The Preisach operator has been widely used to model smart material hysteresis. Motivated by positioning applications of smart actuators, this paper addresses the value inversion problem for a class of discretized Preisach operators, i.e., to find an optimal input trajectory given a desired output value. This problem is solved through optimal state transition of a finite state machine (FSM) that corresponds to the discretized Preisach operator. A state-space reduction scheme for the FSM is developed, which significantly saves the memory and the computation time. Experimental results on micro-positioning control of a magnetostrictive actuator are presented to demonstrate the effectiveness of the proposed approach.     

弯曲型导电聚合物驱动器逆模型控制

针对三层弯曲型导电聚合物驱动器,研究了一种无需外部传感反馈装置的逆模型控制方法。通过实验辨识获得驱动器系统传递函数准确,以驱动器系统的4阶传递函数建立的逆模型控制系统结构简单、易于实现。通过补偿驱动器位移漂移特性提高位移控制精度。实验结果表明：其所提出的具有位移漂移补偿的逆模型控制位移输出能够快速有效地跟踪驱动器的实际位移响应,同时精度符合控制要求。     

Decoupling and control of micromotion stage based on hysteresis of piezoelectric actuation

This paper presents the mechanism and control design of a micro-motion stage, which employs the right-angle flexure hinges and piezoelectric actuators (PZT). Aiming at the mechanism with the characteristics of a large stroke and three degrees of freedom, analytical models of statics and dynamics are established; especially the coupling motions of stage are investigated, which are verified by finite element analysis simulation. Via open-loop experiment, the decoupling property is well certified. Owing to the hysteresis of PZT, the dynamic equation of system with Bouc–Wen hysteresis model is proposed, which is identified through the Least squares. Moreover, a closed-loop controller of proportion integral derivative combined with the inverse hysteresis model-based feedforward is developed to reduce the nonlinearity and uncertainty, which can improve the positioning accuracy. Besides, the single-axis and multi-axis motions are tested. Experimental results reveal that the stage has a well-decoupling performance, and the effectiveness of proposed Bouc–Wen model is validated under open-loop control. Furthermore, the micro-motion performance in single- and multi-axis motions can be achieved as well.

     

压电定位系统的自抗扰控制设计

纳米定位系统中广泛采用的压电驱动器因存在非线性、多映射的迟滞特性而严重影响了纳米定位系统的定位精度.为消除迟滞对定位精度的影响,将其视为干扰,设计不基于迟滞及定位系统精确数学模型的自抗扰控制算法,利用扩张状态观测器实时估计迟滞,进而补偿其对定位精度的影响,获得了良好的定化系统控制仿真效果.仿真结果表明,自抗扰控制器能够仃效消除迟滞、提高纳米定位系统的定位精度.     

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.     

Modeling of a three-layer piezoelectric bimorph beam withhysteresis

Piezoelectric actuators are usually stacked or bimorph in configuration. In this paper the mechanics of a three-layer piezoelectric bimorph is discussed and its dynamic model with hysteresis is presented. The results can be used to analyze piezoelectric actuators constructed with three-layer piezoelectric bimorphs. A piezoelectric bimorph actuator has been fabricated and experiments have been carried out to verify the model. The calculated results of this model closely matched the tested results. This model can also be used with other types of piezoelectric actuators with a slight modification     

具有Preisach类型磁滞输入的不确定非线性系统 自适应神经网络控制

本文针对一类执行器受Preisach磁滞约束的不确定非线性系统, 提出一种基于神经网络的直接自适应控制 方案, 旨在解决系统的预定精度轨迹跟踪问题. 由于Preisach算子与系统动态发生耦合, 导致算子输出信号不可测 量, 给磁滞的逆补偿造成了困难. 为解决此问题, 本文首先将Preisach模型进行分解, 以提取出控制命令信号用于 Backstepping递归设计, 并在此基础上融合一类降阶光滑函数与直接自适应神经网络控制策略, 形成对磁滞非线性 和被控对象非线性的强鲁棒性能, 且所设计方案仅包含一个需要在线更新的自适应参数, 同时可保证Lyapunov函数 时间导数的半负定性. 通过严格数学分析, 已证明该方案不仅保证闭环系统所有信号均有界, 而且输出跟踪误差随 时间渐近收敛到用户预定区间. 基于压电定位平台的半物理仿真实验进一步验证了所提出控制方案的有效性.     

基于单神经元PID控制器的压电陶瓷控制方法

卫星地面综合测试是卫星研制过程中的重要环节,对系统功能验证及性能评估具有重要作用。传统的卫星地面综合测试系统存在研制周期长、投入较大、自动化流程不够完整、可重用性较差等不足。而北斗导航卫星地面综合测试系统采用分布式、高实时性、可配置、多主机的集成体系结构,是集计算机通讯、实时控制、实时数据处理、事后分析等功能于一体的测试系统,适用于从卫星总装集成到发射各个阶段的电气测试。通过卫星系统级的各项接口、功能、性能指标测试,表明该系统满足支持系统论证、状态确认、问题排查等测试需求,有力支撑了北斗导航卫星的成功发射和在轨运行。     

Compensation of Scanner Creep and Hysteresis for AFM Nanomanipulation

Nanomanipulation with atomic force microscopes (AFMs) for nanoparticles with overall sizes on the order of 10 nm has been hampered in the past by the large spatial uncertainties encountered in tip positioning. This paper addresses the compensation of nonlinear effects of creep and hysteresis on the piezo scanners which drive most AFMs. Creep and hysteresis are modeled as the superposition of fundamental operators, and their inverse model is obtained by using the inversion properties of the Prandtl-Ishlinskii operator. Identification of the parameters in the forward model is achieved by a novel method that uses the topography of the sample and does not require position sensors. The identified parameters are used to compute the inverse model, which in turn serves to drive the AFM in an open-loop, feedforward scheme. Experimental results show that this approach effectively reduces the spatial uncertainties associated with creep and hysteresis, and supports automated, computer-controlled manipulation operations that otherwise would fail.     

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.