Preisach Model

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  • Development of a combined Prandtl Ishlinskii–Preisach Model
    Sensors and Actuators A-physical, 2020
    Co-Authors: Zhi Li, Xiuyu Zhang, Lianwei Ma
    Abstract:

    Abstract The Prandtl-Ishlinskii (PI) Model and the Preisach Model are commonly used Models to predict the hysteretic behaviors in smart materials-based actuators. The advantages of the PI Model are that (1) the structure of the Model is simple, which facilitates the implementation of the Model; (2) the analytical inverse of the Model is available. The disadvantage of the PI Model is that it can only describe the symmetric hysteresis effects. For the Preisach Model, it is capable of describing various types of hysteretic behaviors, however, the Model is too complicated to implement numerically. To merge the advantages of both Models, a combined Prandtl Ishlinskii-Preisach (CPIP) Model is proposed in this paper. The CPIP is not a simple combination of the two Models. The discrete empirical interpolation method (DEIM) is applied to determine the structure of the CPIP Model by selecting the dominated elementary operators. The CPIP Model preserves the advantages of the PI Model and the Preisach Model, and is easy to implement numerically in the Matlab/Simulink environment. Experimental results validate the proposed CPIP Model.

  • Inverse Compensator for A Simplified Discrete Preisach Model Using Model-Order Reduction Approach
    IEEE Transactions on Industrial Electronics, 2019
    Co-Authors: Zhi Li, Jinjun Shan, Ulrich Gabbert
    Abstract:

    The classical Preisach Model, which is built by the superposition of a great number of relay operators, is one of the most popular Models to represent the hysteretic behaviors in various applications, such as the smart materials-based actuators. However, the construction of the inverse compensator for the classical Preisach Model is very challenging for some reasons, first, the analytical inverse of the classical Preisach Model is not available, and, second, due to a huge amount of the relay operators the implementation of the inverse compensator is troublesome and causes heavy computational burden. To overcome these drawbacks, a simplified discrete Preisach Model is developed in this paper. The simplified Model has an explicit expression with respect to the input of the Model, thus it is simple to construct its inverse compensator using the inverse multiplicative structure approach. To reduce the computational effort in implementing the inverse compensator, the Model-order reduction method is employed to reduce the complexity of the inverse compensator. Experimental tests are carried out to validate the effectiveness of the proposed approach.

  • Development of Reduced Preisach Model Using Discrete Empirical Interpolation Method
    IEEE Transactions on Industrial Electronics, 2018
    Co-Authors: Zhi Li, Jinjun Shan, Ulrich Gabbert
    Abstract:

    The Preisach Model, which is constructed by the superposition of relay operators, is one of the most popular hysteresis Models to describe the hysteresis nonlinearities in smart-materials-based actuators. The application of the Preisach Model suffers from the tradeoff between the Model accuracy and the number of the relay operators. With a large number of relay operators, the Preisach Model can predict the hysteretic effect very precisely; however, a large number of relay operators may lead to a heavy computation burden. To deal with this tradeoff, in this paper, a Model order reduction method, namely discrete empirical interpolation method, is applied to reduce the number of the relay operators and meanwhile to preserve the Model accuracy of the original Preisach Model. Simulations under different conditions (different input signals and different density functions) and experimental tests on a magnetostrictive-actuated platform are conducted to validate the effectiveness of the proposed reduced Preisach Model.

  • Compensation of Hysteresis Nonlinearity in Magnetostrictive Actuators With Inverse Multiplicative Structure for Preisach Model
    Automation Science and Engineering, IEEE Transactions on, 2014
    Co-Authors: Zhi Li, Chun-yi Su, Tianyou Chai
    Abstract:

    Compensation of hysteresis nonlinearities in smart material based actuators presents a challenging task for their applications. Many approaches have been proposed in the literature, including the inverse multiplicative scheme. The advantage for such a scheme is to avoid direct Model inversions. However, the approach is mainly developed for the Bouc-Wen Model. Focusing on the Preisach Model which is utilized to describe magnetostrictive actuators, in this paper an inverse compensation approach for Preisach Model using the inverse multiplicative structure is developed. Since the input signal is implicitly involved in the Preisach Model, it imposes a great challenge to construct the inverse function of the Model. To obtain an explicit expression of the input signal from its implicit form so that the inverse multiplicative technique can be applied, the Preisach Model is decomposed into a non-memory part and memory part. Using this separation, it only requires to solve the inverse of the non-memory part to obtain an explicit expression of the input signal, thus avoiding constructing the inverse for entire complex dual integral formulation of the Preisach Model. Experimental results for a magnetostrictive actuator demonstrate the effectiveness of the proposed approach.

  • ICIRA (2) - A Novel Analytical Inverse Compensation Approach for Preisach Model
    Intelligent Robotics and Applications, 2013
    Co-Authors: Zhi Li, Chun-yi Su
    Abstract:

    Hysteresis a non-smooth and non-differential phenomena. The inverse compensation for the purpose of removing the hysteresis effect is the most popular approach. Because the Preisach Model is the widespread used hysteresis Model, research on inverse compensation based on Preisach Model attracts much attention. In this paper, we develop a novel analytical inverse compensation method for the Preisach Model, in which we divided the Preisach Model into two parts: non-memory part and memory part. Due to this division, we only need to construct the inverse of the non-memory part, which is invertible through selection of the suitable density function, instead of the whole Preisach Model, which avoids to solve the inverse of the complex dual integral formulation of the Preisach Model. The simulation and experimental results demonstrate the effectiveness of the proposed method.

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