Modeling and characterization of the shape memory alloy–based morphing wing behavior using proposed rate-dependent Prandtl-Ishlinskii models

Abstract

Unique features of shape memory alloys make them a proper actuation choice in various control systems. However, their nonlinear hysteresis behavior negatively affects wide utilization of such materials in structure actuation. In this study, the frequency effect on the hysteresis behavior of a shape memory alloy–actuated structure is experimentally investigated, and also two proposed versions of rate-dependent Prandtl-Ishlinskii (modified rate-dependent Prandtl-Ishlinskii and revised modified rate-dependent Prandtl-Ishlinskii) are presented, which are capable of characterizing this phenomenon. Experimental results show that increasing excitation frequency leads to bigger hysteresis loops. It is also proven that rate-dependency cannot be predicted by generalized Prandtl-Ishlinskii model. In addition, a comparison between the dead zone function-based rate-dependent Prandtl-Ishlinskii model as an only benchmark model and the proposed models have been done that proves the proposed models’ superiority. In addition, genetic algorithm is exploited to identify unknown parameters of all models. Trained models performance is also experimentally evaluated at different input frequencies. Comparison between simulation and experimental results indicates that the proposed models can reliably predict saturated, asymmetric, rate-dependent hysteresis behavior, and minor loops in shape memory alloy–embedded actuators.

Stress-dependent generalized Prandtl–Ishlinskii hysteresis model of a NiTi wire with superelastic behavior

“…To model the NiTi hysteresis effect, we adopted the generalized Prandtl-Ishlinskii (GPI) hysteresis model (Al Janaideh et al, 2008Basaeri et al, 2019;Falvo et al, 2007;Janaideh et al, 2008;Liu and Su, 2011;Shakiba et al, 2019;Sayyaadi et al, 2011;Sayyaadi and Zakerzadeh, 2012;Zakerzadeh and Sayyaadi, 2014). The envelop function g l and g r for the increase and decrease input-output relationship and the input v(t) 2 C m ½0, t E , where v(t) = ½T , s(t), provide input that comprises the temperature T and the applied stress s. The stress-dependent generalized play operator can be written as…”

Tracking control of an SMA-driven actuator with rate-dependent behavior using an inverse model of hysteresis

“…RDPI model is calculated by a summation of weighted rate-dependent play operators. The output of RDPI model y(t) is as follows [24]:…”

Modelling Hysteresis in Shape Memory Alloys Using LSTM Recurrent Neural Network

“…Hysteresis in SMAs refers to the phenomenon where the material exhibits different behaviors during loading and unloading cycles so the material's response is history-dependent, meaning it depends not only on the current input but also on its previous states. Hysteresis models can be classified into two main categories: operator-based models like Preisach [9], Krasnoselskii-Pokrovskii [10], and Prandtl-Ishlinskii [11] that use play operators and differential equation-based models [12,13]. Operator-based models can accurately predict hysteresis but require complex computations.…”