Robust estimation of spring stiffness in a Shape Memory Alloy actuator using Extended Kalman Filter

In this paper, at first a Shape Memory Alloy (SMA) actuator is modeled by Brinson model. Due to high efficiency of Brinson model in modeling SMA behavior, this model is studied in detail in all regions of temperature-stress plane. Then, an SMA actuator, that is composed of a SMA wire connected to a linear spring, is modeled. Since in many SMA actuators, some parameters, like spring stiffness in this case, cannot precisely determined or it is changed by the environment situations, an Extended Kalman Filter (EKF) is used to estimate these parameters. In this filter, an initial guess and its error covariance must be determined. But since this error covariance can’t be determined precisely, the effect of initial error covariance inaccuracy on the parameter estimation is analyzed. Also, since in actual cases the spring may have nonlinear behavior, a simulation is performed by using a nonlinear spring while the estimation is carried out by using linear spring model. These analyses show that EKF can estimate parameters of an SMA-actuated actuator quickly as well as accurately. Also these estimations are robust against the model and initial guess uncertainty.