A generalized Prandtl–Ishlinskii model for characterizing the hysteresis and saturation nonlinearities of smart actuators

Abstract

Smart actuators, such as shape memory alloy (SMA) and magnetostrictive actuators, exhibit saturation nonlinearity and hysteresis that may be symmetric or asymmetric. The Prandtl–Ishlinskii model employing classical play operators has been used to describe the hysteresis properties of smart actuators that are symmetric in nature. In this study, the application of a generalized play operator capable of characterizing symmetric as well as asymmetric hysteresis properties with output saturation is explored in formulating a generalized Prandtl–Ishlinskii model. The generalized play operator employs different envelope functions under increasing and decreasing inputs to describe asymmetric and saturated output–input hysteresis loops. The validity of the proposed generalized model to characterize symmetric and asymmetric hysteresis properties is demonstrated by comparing the model responses with the measured major and minor hysteresis loops of three different types of actuator, namely SMA, magnetostrictive, and piezoceramic actuators. The simulation results suggest that the proposed generalized Prandtl–Ishlinskii model can be directly applied for modeling the hysteresis loops of different smart actuators together with the output saturation.

Hysteresis Modelling and Compensation of Pneumatic Artificial Muscles using the Generalized Prandtl-Ishlinskii Model

“…Due to the limitations of the conventional PI model, the GPI model [23] is employed to describe the length-pressure hysteresis behaviour of a PAM. The GPI model is expressed as a weighted superposition of generalized play operators.…”

“…According to [23], the threshold value r i and the weight of the i th operator p(r i ) are given as: (8) where α, ρ and τ are positive constants that need to be identified from experimental data.…”

Inverse Hysteresis Modeling for Piezoelectric Stack Actuators with Inverse Generalized Prandtl-Ishlinskii Model

“…하지만, 압전 액추에이터에서는 비선형적 히스테리시스(hysteresis) 현상이 발생되는 문제 점이 있으며, 이와 같은 히스테리시스는 압전 액추에이터를 사용한 시스템의 성능을 저하시키는 주요 원인으로 지적되 고 있다 [3]. 이러한 배경에서 많은 연구자들이 히스테리시스 를 수리적으로 모델링하고 [12], 이를 이용하여 시스템의 제 어성능을 향상시키기 위한 다양한 연구를 수행하고 있다 [3][4][5].…”

Three-Dimensional Hysteresis Modeling of Robotic Artificial Muscles with Application to Shape Memory Alloy Actuators

“…Since physics-based models are derived based on material properties [4], their utilization is more limited comparing to phenomenological models (e.g., Preisach model, Krasnoselskii-Pokrovskii model, Prandtl-Ishlinskii model, Maxwell-Slip model, Duhem model, and Bouc-Wen model), that are directly obtained by input and output data [1,15,18,24,28]. Among the phenomenological models, Preisach model has proven to be effective for various hysteresis behaviors [18,25,34,35].…”