Hysteresis modeling in thermal shape memory alloy wire actuators: an irreversible port-Hamiltonian approach

In this paper we present an irreversible port-Hamiltonian model for describing the hysteresis in thermal shape memory alloy (SMA) wire actuators. In contrast to most mechatronic actuators which are operated under isothermal conditions, SMA wires must be heated with an electric current to generate a stroke. As a result of the non-isothermal activation, concepts such as energy dissipation no longer hold from a thermodynamic viewpoint, thus making it difficult to quantitatively analyze the relationship between SMA hysteresis and system stability. Starting from a physics-based model of the SMA based on the work of Muller-Achenbach-Seelecke, a candidate Helmholtz free-energy function is first proposed to describe the material under non-isothermal condition. Based on this result, the system internal energy is constructed and used as a storage function for an irreversible port-Hamiltonian representation. The developed model permits to quantify the energetic performance of SMA wires during non-isothermal actuation, as well as to assess the system thermodynamic consistency based on irreversible entropy production. In addition, the model represents the first step towards the design of energy-based control systems for hysteresis compensation.