In this article, two models are used, namely rate-independent and rate-dependent generalized Prandtl–Ishlinskii, to characterize a magnetic shape memory alloy actuator. The results show that the rate-independent model cannot consider the effect of input excitation frequency, while the rate-dependent model omits this drawback by defining a time-dependent operator. For the first time, the effects of excitation frequency on the hysteretic behavior of magnetic shape memory alloy actuator are investigated. In this study, five excitation voltages with different frequencies in the range of 0.05–0.4 Hz are utilized as inputs to the magnetic shape memory alloy actuator and the displacement outputs are measured. Experimental results indicate that, with increasing the excitation frequency, the size of the hysteresis loops changes. Since the generalized rate-dependent Prandtl–Ishlinskii model cannot consider the asymmetric hysteresis loops, in the developed model, a tangent hyperbolic function is applied as an envelope function in order to improve the capability of the model in characterizing the asymmetric behavior of magnetic shape memory alloy actuator. The parameters of both rate-dependent and rate-independent models are identified by genetic algorithm optimization. The results reveal that the rate-independent form is not capable of accurately describing the hysteretic behavior of magnetic shape memory alloy actuator for different input frequencies. Simulation and experimental results also demonstrate the proficiency of the developed model for precise characterization of the saturated rate-dependent hysteresis loops of magnetic shape memory alloy actuator. In addition, the proposed model is utilized for determining a proper range for controller coefficients during controller design.
A simplified rate dependent model of forming and wrinkling of pre-impregnated woven composites