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

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.

Download Full-text

Piezo Actuator Hybrid Modeling for Nonlinear Inverse Control in Diamond Turning

10.1115/imece1999-0722 ◽

1999 ◽

Author(s):

Dongwoo Song ◽

C. James Li

Keyword(s):

Pid Control ◽

Inverse Dynamics ◽

Feedforward Control ◽

Diamond Turning ◽

Piezo Actuator ◽

Positioning System ◽

Preisach Model ◽

Hysteresis Model ◽

Inverse Control ◽

Spring Mechanism

Abstract This paper describes a micro-positioning system based on piezo actuators and a spring mechanism, and a hybrid hysteresis model integrating a neural network and Preisach model to identify the inverse dynamics of the micro-positioning system. To improve the workpiece form accuracy in diamond turning, feedforward control using the hybrid inverse model and feedback PID control were applied individually and in combination. The performance of these controllers are compared in actual cutting tests.

Download Full-text

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

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x16666174 ◽

2016 ◽

Vol 28 (7) ◽

pp. 907-922 ◽

Cited By ~ 11

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.

Download Full-text

Rate-Dependent Modeling of Piezoelectric Actuators for Nano Manipulation Based on Fractional Hammerstein Model

Micromachines ◽

10.3390/mi13010042 ◽

2021 ◽

Vol 13 (1) ◽

pp. 42

Author(s):

Liu Yang ◽

Zhongyang Zhao ◽

Yi Zhang ◽

Dongjie Li

Keyword(s):

Fractional Order ◽

Dynamic Characteristics ◽

Autoregressive Model ◽

Tracking Control ◽

Piezoelectric Actuators ◽

Hammerstein Model ◽

Order Model ◽

Integer Order ◽

Rate Dependent ◽

Rate Correlation

Piezoelectric actuators (PEAs), as a smart material with excellent characteristics, are increasingly used in high-precision and high-speed nano-positioning systems. Different from the usual positioning control or fixed frequency tracking control, the more accurate rate-dependent PEA nonlinear model is needed in random signal dynamic tracking control systems such as active vibration control. In response to this problem, this paper proposes a Hammerstein model based on fractional order rate correlation. The improved Bouc-Wen model is used to describe the asymmetric hysteresis characteristics of PEA, and the fractional order model is used to describe the dynamic characteristics of PEA. The nonlinear rate-dependent hysteresis model can be used to accurately describe the dynamic characteristics of PEA. Compared with the integer order model or linear autoregressive model to describe the dynamic characteristics of the PEA Hammerstein model, the modeling accuracy is higher. Moreover, an artificial bee colony algorithm (DE-ABC) based on differential evolution was proposed to identify model parameters. By adding the mutation strategy and chaos search of the genetic algorithm into the previous ABC, the convergence speed of the algorithm is faster and the identification accuracy is higher, and the simultaneous identification of order and coefficient of the fractional model is realized. Finally, by comparing the simulation and experimental data of multiple sets of sinusoidal excitation with different frequencies, the effectiveness of the proposed modeling method and the accuracy and rapidity of the identification algorithm are verified. The results show that, in the wide frequency range of 1–100 Hz, the proposed method can obtain more accurate rate-correlation models than the Bouc-Wen model, the Hammerstein model based on integer order or the linear autoregressive model to describe dynamic characteristics. The maximum error (Max error) is 0.0915 μm, and the maximum mean square error (RMSE) is 0.0244.

Download Full-text

Modeling and Control for GMA Based on Hammerstein Model Structure

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.668.406 ◽

2013 ◽

Vol 668 ◽

pp. 406-409

Author(s):

Qing Song Liu ◽

Zhen Zhang ◽

J.Q. Mao

Keyword(s):

Tracking Control ◽

Hammerstein Model ◽

Model Structure ◽

Hysteresis Model ◽

Modeling And Control ◽

Feedforward Loop ◽

Rate Dependent ◽

Proposed Model ◽

Magnetostrictive Actuator ◽

And Control

A rate-dependent hysteresis model for Giant Magnetostrictive Actuator (GMA) is proposed based on Hammerstein model structure. The Generalized Prandtl-Ishlinskii (GPI) model is used to represent nonlinear block in Hammerstein model. The validity of model is examined by comparsion between simulation results and experimental data. Based on the proposed model, a PID feedback controller combined with an inverse compensation in the feedforward loop is used for tracking control. Experimental results show that the control strategy is effective.

Download Full-text

Tracking Control of a Galfenol-Actuated Nanopositioning Stage Using Feedforward Control with a Disturbance Observer

Advances in Materials Science and Engineering ◽

10.1155/2019/3025871 ◽

2019 ◽

Vol 2019 ◽

pp. 1-9

Author(s):

Shiping Jiang ◽

Bin Xu ◽

Shuxin Liu ◽

Wei Zhu

Keyword(s):

Tracking Control ◽

Disturbance Observer ◽

Control Method ◽

Feedforward Control ◽

Unmodeled Dynamics ◽

Output Displacement ◽

Hysteresis Compensation ◽

Rate Dependent ◽

Main Challenge ◽

Compensation Error

The main challenge of the galfenol actuator for high-precision positioning is the inherent nonsmooth hysteresis, which may lead to undesirable inaccuracies or oscillations and even instability. The primary aim of this study is to develop a tracking control method to precisely control the output displacement of a galfenol-actuated nanopositioning stage using feedforward control with a disturbance observer. In order to accurately describe the rate-dependent hysteresis, considering the dynamic behavior of the power amplifier, a novel dynamic model is put forward. Then, a developed controller is designed. In this controller, a feedforward control is developed to compensate the rate-dependent hysteresis, and a disturbance observer is employed to restrain disturbances, high-order unmodeled dynamics, and hysteresis compensation error. The comparative experimental results show that the proposed control method can significantly improve the positioning accuracy and suppress disturbances. This research can be applied in various micro and nanopositioning and vibration control fields.

Download Full-text

Tracking Control of Piezoelectric Stack Actuator Using Modified Prandtl–Ishlinskii Model

ASME 2011 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, Volume 2 ◽

10.1115/smasis2011-4939 ◽

2011 ◽

Author(s):

Yuansheng Chen ◽

Jose Palacios ◽

Edward C. Smith ◽

Jinhao Qiu

Keyword(s):

Tracking Control ◽

Hysteresis Model ◽

Tracking Accuracy ◽

Feedback Controllers ◽

Modified Model ◽

Control Scheme ◽

Different Types ◽

Feedforward Controller ◽

Hysteresis Control ◽

Piezoelectric Stack Actuator

This paper presents the development of Prandtl–Ishlinskii hysteresis model and tracking control of piezoelectric stack actuator with severe hysteresis. Classic Prandtl–Ishlinskii model which is a linearly weighted superposition of many backlash operators with different threshold and weight values, inherits the symmetry property of the backlash operator at about the center point of the loop formed by the operator. To describe the asymmetric hysteresis of piezoelectric stack actuators, two sets of weighting parameters are proposed to modify the weight values of backlash operators in the ascending and descending branches. Hence, two weight values correspond to one operator. Each pair of the weight values slides smoothly from one to another when the output of their corresponding operator is at a desired threshold. A feedforward controller was designed based on the modified model, which can precisely describe the inverse of the hysteresis. Then the modified model and the hysteresis of the piezoelectric stack actuator cancelled each other. A feedback controller was design to compensate for actuator creep. Different types of signal are used to test the feedforward and feedback controllers. The results show that the proposed hysteresis control scheme which combines feedforward and feedback controllers greatly improves the tracking accuracy of the piezoelectric actuator and the error is less than 0.15 μm.

Download Full-text

Novel multirate control strategy for piezoelectric actuators

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1243/09596518jsce695 ◽

2009 ◽

Vol 223 (5) ◽

pp. 673-682 ◽

Cited By ~ 2

Author(s):

M Zareinejad ◽

S M Rezaei ◽

H H Najafabadi ◽

S S Ghidary ◽

A Abdullah ◽

...

Keyword(s):

Tracking Control ◽

Control Method ◽

Feedforward Control ◽

Piezoelectric Materials ◽

Positioning System ◽

Electrical Field ◽

Fundamental Study ◽

Non Linear ◽

Multirate Control ◽

Hysteresis Behaviour

In this article, a novel control method is proposed for feedforward compensation of hysteresis non-linearity in various frequency ranges. By integrating a multirate hysteresis compensator controller with PID feedback control, a combined controller is developed and experimentally validated for a piezoelectric micro-positioning system. Piezoelectric materials show non-linear hysteresis behaviour when they experience an electrical field. A fundamental study of a piezoelectric actuator (PEA) shows that the hysteresis effect deteriorates the tracking performance of the PEA. This paper presents a non-linear model which quantifies the hysteresis non-linearity generated in PEAs in response to the applied driving voltages. The tracking control method is based on multirate feedforward control. The proposed multirate control method uses an inverse modified Prandtl-Ishlinskii operator to cancel out hysteresis non-linearity. The controller structure has a simple design and can be quickly identified. The control system is capable of achieving suitable tracking control and it is convenient to use and can be quickly applied to practical PEA applications. Experimental results are provided to verify the efficiency of the proposed method.

Download Full-text

Dynamic and Positioning Performances of Linear Electromechanical Actuator

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.809-810.682 ◽

2015 ◽

Vol 809-810 ◽

pp. 682-687

Author(s):

Vasile Nasui ◽

Mihai Banica ◽

Dinu Darabă

Keyword(s):

Dynamic Characteristics ◽

Practical Importance ◽

Correct Identification ◽

Positioning System ◽

Positioning Error ◽

Servo Motor ◽

Positioning Accuracy ◽

Electromechanical Actuator ◽

Initial Errors ◽

Selection For

This paper presents the dynamic characteristics and the proposed positioning performance of the system to them investigated experimentally. In this research, we developed the positioning system and we evaluated positioning accuracy. The developed system uses a servo motor for motion actuation. In this paper, we focused on studying the dependency of the positioning error – elementary errors – the position of the conducting element for the mechanism of the transformation of the rotation translation movement, representatively the mechanism screw – screwdriver and on emphasizing the practical consequences in the field of design, regulation and exploitation of the correct identification of all the initial errors in the structure of the mechanism, their character and the selection for an ultimate calculus of these which are of a real practical importance.

Download Full-text