A numerically optimized vector hysteresis model using play operator

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.

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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.

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Optimal Compression of a Generalized Prandtl-Ishlinskii Operator in Hysteresis Modeling

Volume 3: Nonlinear Estimation and Control; Optimization and Optimal Control; Piezoelectric Actuation and Nanoscale Control; Robotics and Manipulators; Sensing; System Identification (Estimation for Automotive Applications, Modeling, Therapeutic Control in Bio-Systems); Variable Structure/Sliding-Mode Control; Vehicles and Human Robotics; Vehicle Dynamics and Control; Vehicle Path Planning and Collision Avoidance; Vibrational and Mechanical Systems; Wind Energy Systems and Control ◽

10.1115/dscc2013-3969 ◽

2013 ◽

Cited By ~ 3

Author(s):

Jun Zhang ◽

Emmanuelle Merced ◽

Nelson Sepúlveda ◽

Xiaobo Tan

Keyword(s):

Smart Materials ◽

Model Verification ◽

Hysteresis Model ◽

Compression Scheme ◽

Uniform Compression ◽

Compression Performance ◽

Leibler Divergence ◽

Modeling Errors ◽

Play Operator ◽

Model Subject

The Prandtl-Ishlinskii (PI) model is a popular hysteresis model that has been widely applied in smart materials-based systems. Recently, a generalized PI model is formulated that is capable of characterizing asymmetric, saturated hysteresis. The fidelity of the model hinges on accurate representation of envelope functions, play operator radii, and corresponding weights. For a given number of play operators, existing work has typically adopted some predefined play radii, the performance of which could be far from optimal. In this paper, novel schemes based on entropy and relative entropy (Kullback-Leibler divergence) for optimal compression of a generalized PI model are proposed to best represent the original hysteresis model subject to a given complexity constraint, i.e., the number of play operators. The overall compression performance is expressed as a cost function, and is optimized using dynamic programming. The proposed compression schemes are applied to the modeling of the asymmetric hysteresis between resistance and temperature of a vanadium dioxide (VO2) film, and the effectiveness is further demonstrated in a model verification experiment. In particular, under the same complexity constraint, an entropy-based compression scheme and a Kullback-Leibler divergence-based compression scheme result in modeling errors around 37% and 48%, respectively, of that under a uniform compression scheme.

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Stress-dependent generalized Prandtl–Ishlinskii hysteresis model of a NiTi wire with superelastic behavior

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x20983888 ◽

2021 ◽

pp. 1045389X2098388

Author(s):

HouPin Yoong ◽

ChunYi Su ◽

KiamBeng Yeo

Keyword(s):

Applied Stress ◽

Phenomenological Model ◽

Hysteretic Behavior ◽

Quadratic Functions ◽

Hysteresis Model ◽

Niti Wire ◽

Stress Variation ◽

Superelastic Behavior ◽

Play Operator ◽

Stress Dependent

The extremely useful superelastic behavior of NiTi has been poorly explored because of the limited number of models that can describe the complete hysteretic behavior of NiTi, including a superelastic condition that strongly depends on the applied stress. This paper presents the development of a stress-dependent phenomenological model of NiTi by modifying the existing generalized Prandtl–Ishlinskii (GPI) model. The parameters of the envelop function of the GPI model’s play operator are reformulated as quadratic functions of the applied stress. The stress-dependent GPI model can satisfactorily predict the output strain of a NiTi #6 wire under temperature and stress variation.

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Modeling and Compensation for Asymmetrical and Dynamic Hysteresis of Piezoelectric Actuators Using a Dynamic Delay Prandtl–Ishlinskii Model

Micromachines ◽

10.3390/mi12010092 ◽

2021 ◽

Vol 12 (1) ◽

pp. 92

Author(s):

Wen Wang ◽

Fuming Han ◽

Zhanfeng Chen ◽

Ruijin Wang ◽

Chuanyong Wang ◽

...

Keyword(s):

High Frequency ◽

Piezoelectric Actuators ◽

Superior Performance ◽

Precision Machining ◽

Nonlinear Phenomena ◽

Input Frequency ◽

Hysteresis Model ◽

Inverse Dynamic ◽

Dynamic Hysteresis ◽

Play Operator

Piezoelectric actuators are widely used in micro- and nano-manufacturing and precision machining due to their superior performance. However, there are complex hysteresis nonlinear phenomena in piezoelectric actuators. In particular, the inherent hysteresis can be affected by the input frequency, and it sometimes exhibits asymmetrical characteristic. The existing dynamic hysteresis model is inaccurate in describing hysteresis of piezoelectric actuators at high frequency. In this paper, a Dynamic Delay Prandtl–Ishlinskii (DDPI) model is proposed to describe the asymmetrical and dynamic characteristics of piezoelectric actuators. First, the shape of the Delay Play operator is discussed under two delay coefficients. Then, the accuracy of the DDPI model is verified by experiments. Next, to compensate the asymmetrical and dynamic hysteresis, the compensator is designed based on the Inverse Dynamic Delay Prandtl–Ishlinskii (IDDPI) model. The effectiveness of the inverse compensator was verified by experiments. The results show that the DDPI model can accurately describe the asymmetrical and dynamic hysteresis, and the compensator can effectively suppress the hysteresis of the piezoelectric actuator. This research will be beneficial to extend the application of piezoelectric actuators.

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