压电驱动器的免疫PID控制技术研究

针对压电驱动器的伺服控制问题,提出了一种基于生物免疫反馈调节规律的PID控制算法;对于具有非线性滞环特性的压电驱动器,采用线性PID控制器难以达到理想的控制效果;如果借助于生物免疫反馈调节规律来自动整定PID控制器的参数,就有可能使压电驱动器的阶跃响应无振荡现象发生并具有较好的鲁棒性;试验结果表明,与传统的压电驱动器PID控制系统比较,应用免疫PID控制算法可以使伺服系统获得更好的动态特性。     

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．     

Tuning PID control parameters for micro-piezo-stage by using grey relational analysis

The materials used in piezo-actuators, which ferroelectric, demonstrate inherent hysteresis behavior in an applied electric field. Unfortunately, this behavior typically results in control problems, with severe inaccuracy and degraded tracking performance. This work focuses on the control of the piezoelectric positioning stage. The hysteresis function is expressed as an external disturbance. Grey relational analysis is proposed to examine the sensitivity of the tuning of the PID parameters for such system, to achieve the desired performance. Accordingly, the PID parameters can be tuned to handle uncertain information. The experimental results of the proposed grey relational approach also indicate that developing a low-cost, reliable, automatic, less time-consuming controller than conventional PID control for a piezoelectric positioning stage is technically and economically feasible. Hence, the results obtained using this proposed methodology can be applied to various mechanical systems, such as positioning control subjected to external disturbances.     

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     

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,Fast Tool Servo)要求重复定位精度优于10nm,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。     

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.     

Adaptive Kalman filter and dynamic recurrent neural networks-based control design of macro-micro manipulator

In this paper,a composite control scheme for macro-micro dual-drive positioning stage with high acceleration and high precision is proposed.The objective of control is to improve the precision by reducing the influence of system vibration and external noise.The positioning stage is composed of voice coil motor(VCM) as macro driver and piezoelectric actuator(PEA) as micro driver.The precision of the macro drive positioning stage is improved by the combined PID control with adaptive Kalman filter(AKF).AKF is used to compensate VCM vibration(as the virtual noise) and the external noise.The control scheme of the micro drive positioning stage is presented as the integrated one with PID and intelligent adaptive inverse control approach to compensate the positioning error caused by macro drive positioning stage.A dynamic recurrent neural networks(DRNN) based inverse control approach is proposed to offset the hysteresis nonlinearity of PEA.Simulations show the positioning precision of macro-micro dual-drive stage is clearly improved via the proposed control scheme.     

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.     

Backstepping-based robust-adaptive control of a nonlinear 2-DOF piezoactuator

This paper deals with the control of a two degrees of freedom (2-DOF) piezoelectric actuator for precise positioning and which exhibits strong hysteresis nonlinearity and strong cross-couplings. To tackle the nonlinearity and the cross-couplings, we propose two decoupled models in which they are considered as (fictive) external disturbances which require proper characterization. Then, a backstepping technique is proposed to construct a robust controller that merges sliding-mode and adaptive schemes. Extensive experimental tests are finally carried out to prove the efficiency of the modeling and control technique proposed.     

模糊神经网络PID在电动舵机控制中的应用

研究电动舵机控制系统优化问题。针对传统控制器响应速度慢,由于系统本身是多变量非线性的复杂系统,存在时滞问题,系统参数不易整定,为了优化电动舵机控制系统的快速性性能,设计了一种改进的模糊神经网络PID控制器,提出了分离学习算法,利用自组织学习整定隶属度函数参数和误差反向传播学习整定加权系数。将算法用于电动舵机控制,实现对舵机以及导弹姿态的快速控制。仿真结果表明,改进控制器的响应时间达到4.8ms,优于传统的PID控制器和模糊PID控制器,为电动舵机控制系统快速性、高精度的设计提供了依据。     

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。     

Observability and Controllability Analysis for Micro‐Positioning Stage Described by Sandwich Model with Hysteresis

In this paper, an approach for analyzing the observability and controllability of micro‐positioning stage with piezoelectric actuator described by sandwich model with hysteresis is proposed. As hysteresis inherent in piezoelectric actuator is a non‐smooth nonlinear function with multi‐valued mapping, the positioning system is also a non‐smooth dynamic system. The Prandtl‐Ishlinksii (PI) submodel is employed to describe the characteristic of hysteresis embedded in the sandwich system. A linearization method based on non‐smooth optimization is proposed to derive a generalized linearized state‐space function to approximate the non‐smooth sandwich systems within a bounded region around the equilibrium points the system works at. Then, both observability and controllability matrices are constructed and the methods to analyze the observability as well as the controllability of sandwich system with hysteresis are derived. Finally, a simulation example and an application of the proposed method to a micro‐positioning stage with piezoactuator are presented to validate the proposed method.     

PID control for a distributed system with a smart actuator

The emergence of distributed architectures based on smart components and fieldbus networks is promoting changes in proportional-integral-derivative (PID) controller design issues. This paper explores how PID control can benefit from smart actuator and fieldbus technologies. Firstly, this paper discusses a smart actuator scheme to improve the efficiency of PID controller retuning, as well as an implementation using a low-cost stepper-motor. Then, the smart actuator is applied to on-line adaptation of PID parameters using a standard pole-placement design method. Finally, experimental validation of the proposed approach is conducted using a controller area network (CAN) bus-based distributed architecture demonstrator.     

Digital controller design for Bouc–Wen model with high-order hysteretic nonlinearities through approximated scalar sign function

In the models of piezoelectric actuator (PEA) systems, the hysteresis effects are often described by the concise Bouc–Wen models; however, these models are nonlinear and non-smooth because of the existence of terms which involve the absolute-value function. In particular, a challenging control problem is posed when, due to the properties of certain materials, such absolute-value terms are of high order. This control problem has been rarely studied. This article proposes the use of the approximated scalar sign function (ASSF), which is a numerically stable and differentiable nonlinear function, to represent the hysteresis function, with single-order or high-order absolute-value terms. This innovative step leads to a nonlinear but sufficiently smooth model. Then, a systematic digital design methodology is presented, which involves the following steps: (1) establish an optimal linear model based upon the resulting smooth model, (2) adopt a PI-based analogue controller and (3) apply the prediction-based digital redesign technique for digital implementation. A digital observer is also developed for state reconstruction, and to improve the input disturbance rejection. The positioning control of a PEA system with a high-order hysteretic Bouc–Wen model is implemented to demonstrate the effectiveness of the proposed ASSF based modelling and controller design approaches.     

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.     

On the robust PID adaptive controller for exoskeletons: A particle swarm optimization based approach

This article proposes a robust PID adaptive controller for nonlinear systems with one or more degrees of freedom (DoF). The adaptive controller aims at minimizing the errors in trajectory tracking without requiring a prior modeling of the targeted nonlinear system. Furthermore, the proposed controller requires only the inputs and outputs of the system. And it is based on modified particle swarm optimization algorithm whose goal is to find the best PID parameters that optimize the execution of desired task by minimizing an objective function. The adaptation by the controller addresses two critical problems: The first problem is the instability of the control signal provided by the convergence phase of the classical PSO algorithm. This behavior adversely affects the lifetime of any actuator and, therefore, is undesirable. The second problem is the stagnation of the classical PSO algorithm after convergence at the immediately found optimal solution. The proposed adaptive PID controller is initially tested in simulation on a dynamical model of a robot manipulator evolving in the vertical plan. Which is followed by experimental tests performed on an actuated joint orthosis worn by human subjects having different morphologies. A comparative study with two other algorithms has been also conducted. Based on the obtained results, we conclude the efficiency of the proposed approach.     

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.      

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.     

电压驱动与电流积分器相结合实现压电电荷控制

用电荷控制可以补偿压电执行器的位移迟滞，文中在分析几种电荷控制方案不足的基础上，提出了集电压驱动和电流积分器为一体的驱动方法，积分器能获得压电电荷，却不影响驱电压，为补偿压电漏电，给积分器增加了漏电流补偿电阻，基于此驱动电路可实现电荷控制，文章用于开环位移监测和闭环PID控制的线性位移跟踪，证实了该电荷控制方法的有效性。     

A hysteresis functional link artificial neural network for identification and model predictive control of SMA actuator

In this paper, a modified Hysteresis Functional Link Artificial Neural Network (HFLANN) is proposed to identify and control a Shape Memory Alloy (SMA) actuator, which has an inherent hysteresis phenomenon. In this structure, a hysteresis operator combined with the Functional Link Artificial Neural Network (FLANN) to employ the hysteresis phenomenon and the dynamic of the SMA actuator. The hysteresis operator is introduced to capture the SMA hysteresis. And the FLANN is employed to approximate the dynamic of the system. In identification problem, the FLANN parameters are trained by Particle Swarm Optimization technique. For control problem, a Model Predictive Controller based HFLANN is derived to control the system. The identification results show that the HFLANN can employ for the SMA dynamic. The simulation and experimental results demonstrated the effectiveness of the proposed algorithm. The SMA hysteresis phenomenon is compensated completely by proposed controller.