Development of Hybrid Prandtl–Ishlinskii and Constitutive Models for Hysteresis of Shape-Memory-Alloy-Driven Actuators

Abstract

SUMMARY Prandtl–Ishlinskii (PI) model has an excellent compromise to characterize an asymmetric saturated hysteresis behavior of shape-memory-alloy (SMA)-driven systems, but it cannot consider thermomechanical relations between components of SMA-driven systems. On the other hand, constitutive models are composed of these relations, but their precision needs to be improved. In this paper, PI model is proposed to boost constitutive models in two cases. In the first case, PI model is used to characterize martensite volume fraction (MVF) called hybrid model. In the second case, the model is applied as a regulator in the output of a constitutive model called PI-based output (PIO) regulator. Due to simplicity and ability of Liang–Rogers (LR) model in transformation phases, it is considered as an MVF in the original constitutive model. The performance of both proposed models is compared with the original LR-based constitutive model. Unknown parameters of all three models are identified using genetic algorithm in MATLAB Toolbox. The performance of the three models is investigated at three different frequencies of \[\frac{{2\pi }}{8}\] , \[\frac{{2\pi }}{{15}}\] , and \[\frac{{2\pi }}{{30}}\] Hz because the excitation frequency changes the hysteresis behavior. Results show that the proposed hybrid model keeps the precision of the original constitutive model at different frequencies. In addition, the proposed PIO model shows the best performance to predict hysteresis behavior at different frequencies.

Modeling and Position Control Simulation Research on Shape Memory Alloy Spring Actuator

“…If the driving current of the SMA spring is known, the temperature of SMA at any time in the heating process can be determined according to Equation (23), and then the temperature can be substituted into the phase transformation kinetics model of SMA to obtain the martensite content of the SMA material at the current temperature, and the shear modulus of the SMA spring at this time can be obtained. Substituting the current temperature T, martensite content ξ and shear modulus Gsma of the SMA spring into Equation ( 26) and combining it with Equation ( 24), the deformation ∆l h s and ∆l i b of the SMA spring and the bias spring during heating and cooling can be obtained.…”

“…In order to solve the position output of the differential shape memory alloy spring drive, firstly, the temperature of the SMA spring under a certain driving current is calculated according to Equation (23). Then, the martensite content in the SMA material at the current temperature is calculated according to the transformation kinetics model of the SMA material.…”

“…The macroscopic phenomenological model is the most widely used in engineering [23]. In 1986, Tanaka established the incremental constitutive relationship of SMA material based on the Helmholtz free energy by using Clausius Duhem inequality [24], and then Liang and Rogers replaced Tanka's exponential phase transformation evolution equation with a cosine phase transformation evolution equation, and assumed that the elastic modulus, phase transformation modulus and thermoelastic modulus of SMA material were constants to obtain a full-quantity unique constitutive equation [25].…”

A novel soft-rigid wheeled crawling robot with high payload and passing capability

“…Qin et al [19] designed a versatile soft crawling robot actuated by soft pneumatic actuators (SPAs), which can achieve rapid locomotion. Other smart actuators have also been used to develop soft crawling robots, such as shape memory alloys (SMAs), [20] ionic polymer metal composites, [21] magnetorheological fluid, [22] soft electrostatic actuators, [19,23] as well as dielectric elastomer actuators. [23,24,25] However, due to the intrinsic properties of soft materials with low stiffness, the soft bodies of these crawling robots result in low loads, which also limits the payload capacity of these crawling robots.…”