A Hybrid Dynamical Modeling Framework for Shape Memory Alloy Wire Actuated Structures

TL;DR

This paper introduces a hybrid dynamical modeling framework for SMA wire actuators that simplifies simulation while maintaining accuracy, enabling more efficient control of SMA-driven systems.

Contribution

The paper presents a novel hybrid reformulation of the MAS model, dividing SMA hysteresis into modes for improved simulation efficiency and control.

Findings

Achieves up to 80% reduction in simulation time

Maintains the accuracy of the original MAS model

Enables hybrid systems approach to SMA control

Abstract

In this paper, a hybrid model for single-crystal Shape Memory Alloy (SMA) wire actuators is presented. The result is based on a mathematical reformulation of the M\"uller-Achenbach-Seelecke (MAS) model, which provides an accurate and interconnection-oriented description of the SMA hysteretic response. The strong nonlinearity and high numerical stiffness of the MAS model, however, hinder its practical use for simulation and control of complex SMA-driven systems. The main idea behind the hybrid reformulation is based on dividing the mechanical hysteresis of the SMA into five operating modes, each one representing a different physical state of the material. By properly deriving the switching conditions among those modes in a physically-consistent way, the MAS model is effectively reformulated within a hybrid dynamical setting. The main advantage of the hybrid reformulation is the possibility of describing the material dynamics with a simplified set of state equations while maintaining all benefits of the physics-based description offered by the MAS model After describing the novel approach, simulation studies are conducted on a flexible robotic module actuated by protagonist-antagonist SMA wires. Through comparative numerical analysis, it is shown how the hybrid model provides the same accuracy as the MAS model while saving up to 80% of the simulation time. Moreover, the new modeling framework opens up the possibility of addressing SMA control from a hybrid systems perspective.