Multidimensional Hysteresis Modeling and Analysis of Rate-Dependence and Creep Phenomena in Magnetorheological Actuator

Magnetorheological actuator (MRA) exhibits complex nonlinear behaviors, including rate-dependence and creep, which pose challenges for accurate modeling. Existing differential-equation-based hysteresis models fail to accurately capture the complex characteristics of the MRA due to their single-dimensional approach. Therefore, this article proposes a novel multidimensional differential-equation-based hysteresis model to address this limitation. By adopting the multidimensional model structure, the proposed model significantly enhances performance. To effectively capture both rate-dependence and creep phenomena, a rate-dependent operator is introduced, and fractional calculus is employed to describe the creep compactly. Unlike existing models, the rate-dependence in the proposed operator originates from the differential equation’s structure rather than from adding dynamic factors or cascading functions. Furthermore, considering the numerical solution convergence of the differential-equation-based models, the parameter constraints are analyzed and incorporated into the parameter identification algorithm, which is neglected in the existing studies. The model’s effectiveness is validated through the theoretical analyses, the simulations, and the experimental verifications, demonstrating its capability to accurately capture both rate-dependence and creep phenomena in the MRA.