Accounting for hysteresis in repetitive control design: Nanopositioning example

This paper deals with designing a repetitive controller (RC) for tracking periodic reference trajectories for systems that exhibit hysteresis, such as piezoelectric actuators used in nanopositioning systems. Hysteresis can drastically limit the performance of an RC designed around a linear dynamics model, and thus the effect of hysteresis on the closed-loop stability of RC is analyzed and the allowable size of the hysteresis nonlinearity for a stable RC is quantified. But when the hysteresis effect exceeds the maximum bound, an inverse-hysteresis feedforward controller based on the Prandtl–Ishlinskii hysteresis model is used to compensate for the nonlinearity. The control method is implemented on a custom-designed nanopositioning stage. Experimental results show that by incorporating hysteresis compensation the stability margin and the rate of error reduction improve. Likewise, the maximum tracking error reduces by 71%, from 13.7% (using industry-standard integral control) to 3.9% (using RC with hysteresis compensation), underscoring the benefits of RC with hysteresis compensation.     

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.     

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     

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.     

High-speed and precision control of a piezoelectric positioner with hysteresis,resonance and disturbance compensation

A novel composite control strategy is developed in this paper to compensate hysteresis, resonance and disturbances in a piezo-actuated nanopositioner. The control objective of the piezoelectric positioner is to achieve high tracking performance in terms of accuracy and speed. For this purpose, a Bouc–Wen model based hysteresis compensator is first applied to mitigate the hysteresis nonlinearity without the complex inverse hysteresis calculation. And then, the linear dynamic of the hysteresis compensated system is identified and inverted to account for the resonance. A model-based inversion feed-forward controller is designed to achieve high speed tracking. Afterwards, a high-gain feedback controller is designed based on a notch filter to handle the modeling inaccuracy and all kinds of disturbances. So, the feed-forward controller can be augmented to the feedback controller to realize high speed and precision tracking. The enhancement of tracking performance is demonstrated through several comparative experiments. The performance of 70 Hz bandwidth and 0.281 μm precision can be achieved, which validated the effectiveness of the proposed composite control scheme.     

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响,本文设计了一种单神经元自适应比例-积分-微分控制器,对压电驱动器进行跟踪控制,从而实现对期望信号的准确跟踪。实验结果验证了所建立模型的精度以及控制器的跟踪性能。     

Effect of Improved Tracking for Atomic Force Microscope on Piezo Nonlinear Behavior

Nanotechnology is an area of modern science which deals with the control of matter at dimensions of 100 nm or less. In recent years, of all the available microscopy techniques, atomic force microscopy (AFM) has proven to be extremely versatile as an investigative tool in this field. However the performance of AFM is significantly limited by the effects of hysteresis, creep, cross‐coupling, and vibration in its scanning unit, the piezoelectric tube scanner (PTS). This article presents the design and experimental implementation of a single‐input single‐output (SISO) model predictive control (MPC) scheme with a vibration compensator which is based on an identified model of the PTS. The proposed controller provides an AFM with the capability to achieve improved tracking and results in compensation of the nonlinear effects. The experimental results, which compare the tracking performances of the proposed controller for different reference signals, highlight the usefulness of the proposed control scheme.     

Pressure control of an electro-hydraulic actuated clutch via novel hysteresis model

This paper mainly focuses on the development of pressure tracking control logic of electro-hydraulic actuators for vehicle application. This is done to improve and ensure the performance of a precise lower-level controller for evolving modern shift control logic. The required performance is obtained by hysteresis model-based feed-forward control and additional feedback control. The hysteresis and the time delay, which adversely affect pressure control, are well known nonlinear behaviors in electro-hydraulic actuators. In order to cope with the hysteresis, a novel hysteresis model is proposed based on a physical phenomenon. A mathematical model based on a characteristic curve obtained in preliminary experiments is presented using only one tuning parameter, and this model can be inverted easily to construct a feed-forward controller. In addition, a feedback controller is designed considering the stability margin of a time delay system. The feedback control inputs ensure compensation of the feed-forward errors caused by model error and uncertainty. The proposed controller is designed to lower computational cost considering applicability for production vehicles. As a result, the developed pressure controller is applied to a transmission control unit of a production vehicle and verified experimentally for various driving scenarios.     

Simultaneous compensation of hysteresis and creep in a single piezoelectric actuator by open-loop control for quasi-static space active optics applications

Owing to their excellent properties piezoelectric actuators are studied as embedded elements for the quasi-statically active shape control of spatial optical mirrors. However, unwanted nonlinear effects in piezoelectric actuators, i.e., hysteresis and creep, severely limit their performance. This paper aims at developing a control methodology to compensate hysteresis and creep in a piezoelectric actuator simultaneously for quasi-static space active applications. In the methodology developed, hysteresis and creep behaviors are successively compensated by open-loop control. First, a derivative Preisach model is proposed to accurately portray the hysteresis while requiring relatively few measurements and describing the detachment between major and minor loops. The inverse derivative Preisach model is derived and inserted in open-loop to achieve hysteresis compensation. Then, the creep in the hysteresis compensated piezoelectric actuator is described by the use of a nonlinear viscoelastic model and a low pass filter is suggested to eliminate the effect of the inverse derivative Preisach model on the step reference input. To invert the creep model, the concept of “input relaxation” is implemented and an inverse multiplicative structure allows identifying the parameters of the inverse model while circumventing the difficulty of a mathematical computation. Finally, by cascading the low pass filter, the inverse model of creep and the inverse derivative Preisach model one after the other with the single piezoelectric actuator, the simultaneous compensation of hysteresis and creep is achieved. Experimental results show that in the case of step-like reference signals the hysteresis and the creep in a piezoelectric actuator can be significantly reduced at the same time. It implies that the developed methodology is effective and feasible in space active optics applications for which quasi-static distortions need to be compensated.     

Sliding‐mode control of a three‐degrees‐of‐freedom nanopositioner

This paper presents the sliding‐mode control of a three‐degrees‐of‐freedom nanopositioner (Z, θ_x, θ_y). This nanopositioner is actuated by piezoelectric actuators. Capacitive gap sensors are used for position feedback. In order to design the feedback controller, the open‐loop characteristics of this nanopositioner are investigated. Based on the results of the investigation, each pair of piezoelectric actuators and corresponding gap sensors is treated as an independent system and modeled as a first‐order linear model coupled with hysteresis. When the model is identified and the hysteresis nonlinearity is linearized, a linear system model with uncertainty is used to design the controller. When designing the controller, the sliding‐mode disturbance (uncertainty) estimation and compensation scheme is used. The structure of the proposed controller is similar to that of a proportional integral derivative controller. Thus, it can be easily implemented. Experimental results show that 3‐nm tracking resolution can be obtained. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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。     

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．     

自调式类神经PID控制器于压电微动平台之追迹控制(英文)

主要针对压电微动平台设计追迹控制器。压电致动器的非线性现象主要是受磁滞现象所影响,首先采用Prandtl-Ishlinskii(PI)模型来描述压电致动器的磁滞现象,利用最小平方算法识别出磁滞模型的权重值,再利用此模型求出其逆模型以前馈控制器来补偿,最后利用自调式类神经PID控制器来消除建模误差。实验验证方面,在PC-based压电控制平台架构下,利用前馈控制器与闭回路结合自调式类神经PID控制器进行定位控制。     

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.     

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.     

基于参数自学习的无人车越野环境跟踪控制方法

针对无人车在越野环境下难以高速、高精度地跟踪复杂路况的问题,设计了一种参数自学习的前馈补偿控制器,与模型预测控制方法构成前馈-反馈的控制结构。在该控制结构中,前馈控制根据实时状态的跟踪误差在线更新学习系数,有效考虑车辆高速运动过程中无法精确建模的非线性动力学特性以及复杂路况不断变化的曲率和路面条件等的影响,在保证稳定性的同时快速减小跟踪误差。在越野场景进行了高速的S型与直角弯路径跟踪实车实验来验证参数自学习控制器的有效性,结果表明,所设计的参数自学习控制器相比传统的模型预测控制器跟踪误差和横摆都较小,在跟踪精度和车辆稳定性上都有较大改善。     

Aggressive Longitudinal Aircraft Path Tracking Using Nonlinear Control

We study the problem of converting a trajectory tracking controller to a path tracking controller for a nonlinear non-minimum phase longitudinal aircraft model. The solution of the trajectory tracking problem is based on the requirement that the aircraft follows a given time parameterized trajectory in inertial frame. In this paper we introduce an alternative nonlinear control design approach called path tracking control. The path tracking approach is based on designing a nonlinear state feedback controller that maintains a desired speed along a desired path with closed loop stability. This design approach is different from the trajectory tracking approach where aircraft speed and position are regulated along the desired path. The path tracking controller regulates the position errors transverse to the desired path but it does not regulate the position error along the desired path. First, a trajectory tracking controller, consisting of feedforward and static state feedback, is designed to guarantee uniform asymptotic trajectory tracking. The feedforward is determined by solving a stable noncausal inversion problem. Constant feedback gains are determined based on LQR with singular perturbation approach. A path tracking controller is then obtained from the trajectory tracking controller by introducing a suitable state projection.     

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.     

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.     

Contouring accuracy improvement of a piezo-actuated micro motion stage based on fuzzy cerebellar model articulation controller

The motion accuracy and performance of piezoelectric actuators (PEA) are hampered by their inherent hysteresis nonlinearity and time-varying parameters. In order to overcome these drawbacks, an integrated motion control scheme is developed in this paper. In the proposed controller scheme, for each axis of the micro motion stage, a fuzzy CMAC feedforward controller combined with a conventional proportional-integral (PI) feedback controller and a critic-based learning mechanism (FCMAC-CLM) is used to improve the tracking performance and deal with the adverse effects due to hysteresis nonlinearity and external disturbance. In addition, one of the most important issues in the contour following tasks performed by a dual-axis micro motion stage is the contour error reduction. In order to improve the contouring accuracy, a fuzzy CMAC that is capable of real-time learning and self-adjusting is exploited to develop a fuzzy CMAC cross-coupled controller (FCMAC-CCC). Several experiments have been conducted to evaluate the tracking performance and contour accuracy of the proposed approach.