A hybrid dynamic model of shape memory alloy spring actuators

This paper presents the development of a hybrid model that describes the temperature, elongation and inner force relationships in a spring Shape Memory Alloy (SMA) actuator. The temperature-inner force relationship obeys a hybrid structure in which a sigmoid function correlates the variation of temperature for the SMA and the force executed by the spring actuator. The hybrid nature of the model describes the regular hysteresis behavior of the SMA. The switching law of the hybrid model depends on the time derivative of the temperature. A multivariable model depending on temperature, and inner and external forces was developed in order to characterize the Shape Memory Effect (SME). A set of experiments was carried out to obtain the parameters used to characterize the model. The application of the Levenberg-Marquardt method resulted in the parametric estimation procedure. An averaged correlation factor of 0.95 between the model response and experimental results justifies the proposed modeling approach.