A Digitized Representation of the Modified Prandtl–Ishlinskii Hysteresis Model for Modeling and Compensating Piezoelectric Actuator Hysteresis

Abstract

Piezoelectric actuators are widely used in micromanipulation and miniature robots due to their rapid response and high repeatability. The piezoelectric actuators often have undesired hysteresis. The Prandtl–Ishlinskii (PI) hysteresis model is one of the most popular models for modeling and compensating the hysteresis behaviour. This paper presents an alternative digitized representation of the modified Prandtl–Ishlinskii with the dead-zone operators (MPI) hysteresis model to describe the asymmetric hysteresis behavior of piezoelectric actuators. Using a binary number with n digits to represent the classical Prandtl–Ishlinskii hysteresis model with n elementary operators, the inverse model can be easily constructed. A similar representation of the dead-zone operators is also described. With the proposed digitized representation, the model is more intuitive and the inversion calculation is avoided. An experiment with a piezoelectric stacked linear actuator is conducted to validate the proposed digitized MPI hysteresis model and it is shown that it has almost the same performance as compared to the classical representation.

Dynamic modeling and disturbance rejection compensation for hysteresis nonlinearity of high voltage piezoelectric stack actuators

“…According to equation (25), the actual output of the piezoelectric actuator after hysteresis compensation is consistent with the desired output strain, thereby eliminating the hysteresis nonlinearity of the HVPSA.…”

“…Several hysteresis models have been proposed in previous studies to predict the hysteresis nonlinearity of piezoelectric materials [20]. The first type of hysteresis model is obtained by multiplying large number of basic operators with their corresponding weight vectors and then superimposing them together, such as the classical Preisach model [21,22], the Krasnosel'skii-Pokrovskii model [23,24], and the Prandtl-Ishlinskii model [25][26][27], etc. The advantage of these kinds of models is that they can improve the prediction accuracy by increasing the number of basic operators.…”

Hysteresis Characteristics and MPI Compensation of Two-Dimensional Piezoelectric Positioning Stage

“…The constitutive model is deduced based on the inherent constitutive relationship of piezoelectric ceramics, but the establishment process is difficult due to the complex internal characteristics of the hysteresis phenomenon [1,15]. The phenomenological method approximates the measured hysteresis curve by directly establishing mathematical models [16][17][18][19][20], such as Bouc-Wen (B-W) model [21], KP model [22], Preisach model [23], Prandtl-Ishlinskii (PI) model [24][25][26][27][28][29][30][31], etc. Among them, the PI model has attracted extensive attention because it is easy to implement the inverse model [24].…”

Imaging-Guided Micromachines: Towards Intelligent Systems

“…To tackle this challenge, Zhou et al, present an alternative digitized representation of the modified Prandtl-Ishlinskii hysteresis model. The asymmetric hysteresis behavior of piezoelectric actuators is analyzed by a dead-zone operator hysteresis model [3]. The digitized representation also avoids inversion calculations.…”