Improvements to Phenomenologically Modeled Behavior of Shape Memory Alloys

This paper presents improvements to phenomenological modeled behavior of Shape Memory Alloys (SMAs). The specific type of SMA analyzed is the two-way SMA wire that contracts upon heating and extends upon cooling due to an internal phase transformation. To optimally design controllers for SMAs, the proposed model accounts for varying conditions such as input supply voltages and wire diameters and at the same time exhibits attractive numerical features such as differentiability and numerical stability. The paper also analyzes some of the shortcomings of the conventional nonlinear model. For example, the conventional model is not fully able to describe the initial contraction behavior due to an artificial dead zone. The proposed improvements include a new method of approximating the phase transformation behavior, incorporating a dynamic internal resistance, and implementing a heat transfer model that accounts for changing diameter and latent heat. Nonlinear system identification is performed to show the effectiveness of the improved model.