Development of an Extended Kalman Filter for Self-Sensing Application of Shape Memory Alloy Wire Actuator Available to Purchase

This paper presents the development of an Extended Kalman Filter (EKF) for self-sensing application of Shape Memory Alloy (SMA) wire actuator. The EKF is used to estimate the end displacement of a SMA wire actuated compliant link using the electrical resistance variation of SMA. The model of the system is developed by coupling the stress-deformation relation of the link along the direction of the SMA actuator with the phenomenological model of the SMA wire. In EKF, the stress and temperature of SMA comprise the state vector and its electrical resistance is considered as output. The developed EKF is validated, by comparing the estimated system response with that of the model for a given input signal. The effects of the process and measurement noise on the estimation error have also been studied. An experimental setup is developed to measure the change in electrical resistance of the SMA wire, voltage drop across the same, and the associated end-displacement of the compliant link. Using the measured data, the end-displacement of the link is estimated using EKF and compared with the experimentally measured end-displacement. Significant qualitative agreement is observed. It is noted, that the convective heat transfer coefficient significantly affects the quantitative discrepancy. Thus the coefficient of convective heat transfer is determined, so as to minimize the gap between the two responses for a particular applied voltage. The coefficient is then used for different set of experiments, revealing the true potential of the EKF based approach to harness the self-sensing capability of SMA.