Modeling, identification and compensation of hysteresis nonlinearity for a piezoelectric nano-manipulator

2016 ◽  
Vol 28 (7) ◽  
pp. 907-922 ◽  
Author(s):  
Yangming Zhang ◽  
Peng Yan
Keyword(s):  
Input Function ◽  
Rate Function ◽  
Hysteresis Model ◽  
Tracking Accuracy ◽  
Hysteresis Compensation ◽  
Rate Dependent ◽  
Hysteresis Nonlinearity ◽  
Tracking Motion ◽  
Play Operator ◽  
Compensation Approach

Hysteresis nonlinearity widely exists in piezoelectric actuated nano-positioning applications, which degrades their tracking accuracy and limits their precision positioning applications. This paper presents a novel hysteresis modeling and compensation approach to alleviate the adverse effect of the asymmetric and rate-dependent hysteresis nonlinearity for a piezoelectric transducer actuated servo stage. By integrating a generalized input function with the play operator of the classical Prandtl–Ishlinskii model, a novel polynomial-based rate-dependent Prandtl–Ishlinskii (PRPI) model is proposed to capture the hysteresis behavior of the piezoelectric positioning stage, where a polynomial function of input and a time rate function of input are introduced to formulate the generalized input function. Meanwhile, a new adaptive differential evolution optimization algorithm is developed to identify the parameters of the proposed PRPI hysteresis model. Based on the PRPI hysteresis model with the identified parameters, an inverse feedforward controller is constructed to achieve the accurate tracking motion. Furthermore, the hysteresis compensation error of the proposed PRPI model is theoretically analyzed. Finally, comparative experiments are conducted, and the experimental results provided in this paper demonstrate the effectiveness and superiority of the proposed inverse PRPI model compensation approach.

An Experimental Research on Generalized Prandtl-Ishlinskii Model for Modeling Asymmetric Hysteresis of a Piezoceramic Actuator

2015 ◽  
Vol 723 ◽  
pp. 793-798
Author(s):  
Shi Peng Feng ◽  
Dong Xu Li
Keyword(s):  
Input Voltage ◽  
Gain Factor ◽  
Preisach Model ◽  
Hysteresis Model ◽  
Exponential Functions ◽  
Modified Model ◽  
Piezoceramic Actuator ◽  
Hysteresis Nonlinearity ◽  
Play Operator ◽  
The Given

A piezoceramic actuator is widely employed in micropositioning and MEMS. However, the piezoceramic actuators are limited due to the natural hysteresis nonlinearity which affect the accuracy of the actuators in applications. In order to revise the hysteresis nonlinearity, lots of hysteresis models have been proposed such as the Preisach model, the classical Prandtl—Ishlinskii model and so on. While some drawbacks still exist with these models, a generalized hysteresis model for asymmetric hysteresis basing on the classical Prandtl—Ishlinskii model is devised. In the modified model, the exponential functions which contain the amplitude and the frequency of the input voltage and its gain factor are introduced into the NLPO (nonlinearity play operator). As a result, the generalized model in this paper applies to modeling asymmetric hysteresis. This model was identified and simulated using the experimental data by other researchers. At last, the validity and the accuracy of the given model were tested through the experiment of the piezoceramic control.

Tracking control of a 3-dimensional piezo-driven micro-positioning system using a dynamic Prandtl–Ishlinskii model

2021 ◽  
pp. 1045389X2110482
Author(s):  
Wei Zhu ◽  
Feifei Liu ◽  
Fufeng Yang ◽  
Xiaoting Rui
Keyword(s):  
Power Amplifier ◽  
Dynamic Characteristics ◽  
Tracking Control ◽  
Feedforward Control ◽  
Positioning System ◽  
Hysteresis Model ◽  
Tracking Accuracy ◽  
Simple Method ◽  
3 Dimensional ◽  
Rate Dependent

A controller composed of a feed-forward loop based on a novel dynamic Prandtl–Ishlinskii (P-I) model and a PID feedback control loop is developed to support a 3-dimensional piezo-driven micro-positioning system for high-bandwidth tracking control. By considering the dynamic characteristics of the power amplifier, the dynamic P-I model can accurately describe the rate-dependent hysteresis of piezoelectric stack actuators (PSAs). To ensure that the hysteresis model is independent of system load, the P-I hysteresis operator in that model characterizes the relationship between the output force and the input voltage of PSAs. The dynamics equation of the mechanical is established by using the cutoff modal method. The feedforward control is designed based on the dynamic hysteresis model to reduce the rate-dependent hysteresis. The PID control is incorporated with the feedforward control to increase the tracking accuracy. Experimental results indicate that the controller can overcome the hysteresis efficiently and preserve good positioning accuracy in 1–100 Hz bandwidth. Just by introducing the dynamic characteristics of the power amplifier, which can be expressed as a first-order differential equation, the P-I model can accurately describe the rate-dependent hysteresis of the PSA, which provides a simple method to describe and control piezoelectric actuators and piezo-driven systems in a wide frequency.

Elman neural network–based identification of rate-dependent hysteresis in piezoelectric actuators

2020 ◽  
Vol 31 (7) ◽  
pp. 980-989
Author(s):  
Xinlong Zhao ◽  
Shuai Shen ◽  
Liangcai Su ◽  
Xiuxing Yin
Keyword(s):  
Neural Network ◽  
Dynamic Model ◽  
Dynamic Property ◽  
System Performance ◽  
Piezoelectric Actuators ◽  
Hysteresis Model ◽  
Elman Neural Network ◽  
Rate Dependent ◽  
Nanoscale System ◽  
Hysteresis Nonlinearity

Rate-dependent hysteresis nonlinearity in piezoelectric actuators severely limits micro- and nanoscale system performance. It is necessary to establish a dynamic model to describe the full behavior of rate-dependent hysteresis. In this article, the Elman neural network–based hysteresis model is developed for piezoelectric actuators. An improved dynamic hysteretic operator is proposed to transform the multi-valued mapping of hysteresis into one-to-one mapping on a newly constructed expanded input space. Then, Elman neural network incorporated with the improved dynamic hysteretic operator is utilized to approximate the behavior of rate-dependent hysteresis. The combination of Elman neural network and the improved dynamic hysteretic operator can dually embody the dynamic property and is capable of fully extracting the characteristics of rate-dependent hysteresis. The experimental results are presented to illustrate the potential of the proposed modeling technique.

Asymmetrically Dynamic Coupling Hysteresis in Piezoelectric Actuators: Modeling Identification and Experimental Assessments

2019 ◽  
Vol 11 (05) ◽  
pp. 1950051 ◽  
Author(s):  
Zijian Zhang ◽  
Yangyang Dong
Keyword(s):  
Piezoelectric Actuators ◽  
Dynamic Coupling ◽  
Threshold Functions ◽  
Saturation Nonlinearity ◽  
Dynamic Excitation ◽  
Rate Dependent ◽  
Hysteresis Nonlinearity ◽  
Play Operator ◽  
External Loads ◽  
Envelope Functions

An asymmetrically dynamic coupling hysteresis (ADCH) model is proposed as an extension of the Prandtl–Ishlinskii (PI) model to characterize the hysteretic nonlinearities in piezoelectric actuators (PEAs). When subject to two-input: dynamic excitation and external loads. In this model, the developed asymmetrically one-side play operator helps to represent the saturation, nonlinearity, and centrally asymmetric properties of PEAs employed inverse hyperbolic envelope functions. The dynamic threshold functions are put in place to characterize the width of rate-dependent hysteresis property. Introductions of continuously coupled density functions are beneficial to the cross-coupled hysteresis behaviors of external load/excitation voltage-to-expansion. Besides, the proposed ADCH model is verified to satisfy indeed the wiping-out property and equal vertical chords property, which means that it can be regarded as well-suited in modeling the complicated hysteresis nonlinearity of PEAs. Furthermore, this paper also tackles the identification issue of the proposed ADCH model by using a global research method, which possesses satisfactory accuracy without strict requirements for the initially iterative value.

Disturbance Observer-Based Sliding Mode Control of a Piezoelectric Nano-Manipulator

2017 ◽  
Author(s):  
Yangming Zhang ◽  
Peng Yan
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Disturbance Observer ◽  
Sliding Mode ◽  
Rate Function ◽  
Tracking Accuracy ◽  
Mode Control ◽  
Rate Dependent ◽  
Compensation Error ◽  
Control Methodology

This paper is concerned with the ultra high precision tracking control problem of a class of hysteretic systems with both external disturbances and model uncertainties. By integrating a time rate function of the input into the classical Prandtl-Ishlinskii operators, a rate-dependent Prandtl-Ishlinskii model is introduced to compensate the rate-dependent hysteresis of such systems. Furthermore, the resulting inverse compensation error is considered, and a finite-time convergent disturbance observer-based sliding mode control methodology is proposed to improve both the tracking accuracy and transient performance. In this control methodology, a finite-time convergent disturbance observer is employed to estimate various disturbances for accurate eliminations, where the inverse compensation error is regarded as a bounded disturbance. Meanwhile, a novel sliding mode controller is designed to achieve the finite-time stability of the closed-loop system. In particular, it can be proved that both the sliding variable and disturbance estimated error can converge to zero in a finite time. Finally, the proposed control architecture is applied to a PZT (piezoelectric transducer) actuated servo stage, where good hysteresis suppression capability and excellent tracking performance are demonstrated in the experimental results.

scholarly journals Hysteresis Modeling and Compensation of Fast Steering Mirrors with Hysteresis Operator Based Back Propagation Neural Networks

Micromachines ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 732
Author(s):  
Kairui Cao ◽  
Guanglu Hao ◽  
Qingfeng Liu ◽  
Liying Tan ◽  
Jing Ma
Keyword(s):  
Neural Network ◽  
Back Propagation ◽  
Hysteresis Model ◽  
Cooperative Movement ◽  
Hysteresis Operator ◽  
The Neural Network ◽  
Hysteresis Nonlinearity ◽  
Hysteresis Modeling ◽  
Hysteresis Characteristics ◽  
Inverse Hysteresis

Fast steering mirrors (FSMs), driven by piezoelectric ceramics, are usually used as actuators for high-precision beam control. A FSM generally contains four ceramics that are distributed in a crisscross pattern. The cooperative movement of the two ceramics along one radial direction generates the deflection of the FSM in the same orientation. Unlike the hysteresis nonlinearity of a single piezoelectric ceramic, which is symmetric or asymmetric, the FSM exhibits complex hysteresis characteristics. In this paper, a systematic way of modeling the hysteresis nonlinearity of FSMs is proposed using a Madelung’s rules based symmetric hysteresis operator with a cascaded neural network. The hysteresis operator provides a basic hysteresis motion for the FSM. The neural network modifies the basic hysteresis motion to accurately describe the hysteresis nonlinearity of FSMs. The wiping-out and congruency properties of the proposed method are also analyzed. Moreover, the inverse hysteresis model is constructed to reduce the hysteresis nonlinearity of FSMs. The effectiveness of the presented model is validated by experimental results.

Modeling Rate-Dependent Hysteresis for GMA Using Online Least Squares Support Vector Machines

2011 ◽  
Vol 48-49 ◽  
pp. 710-714
Author(s):  
Zhen Kai Guo ◽  
Zhao Qing Song ◽  
Xin Jiang Wei
Keyword(s):  
Support Vector Machines ◽  
Least Squares ◽  
Active Vibration Control ◽  
Support Vector ◽  
Nonlinear Phenomenon ◽  
Rate Dependent ◽  
Hysteresis Nonlinearity ◽  
Vector Machines ◽  
Active Vibration ◽  
And Control

Rate-dependent hysteresis is a strongly nonlinear phenomenon which exists in the giant magnetostrictive actuator (GMA); it has influence in the precision and stability of active vibration control. It is highly important in the control theory and control engineering that the influence of hysteresis is eliminated by the modeling of rate-dependent hysteresis for GMA. So an online intelligent modeling method, which is based on an improved online least squares support vector machines (IOLS-SVM), is presented for identifying rate-dependent hysteresis nonlinearity for GMA, and is used to online real-time training. The data measured in the experiment are used for modeling. The numerical simulation shows the effectiveness of the method.

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