Application of the extended Kalman filter to control of a shape memory alloy arm

摘要

In some SMA-actuated systems the stress of the SMA element changes as a result of the motion of the actuator. Such complex thermomechanical loadings, for example, take place in rotary SMA actuators. For this and similar SMA actuators, the phase transformation temperatures, that define the actuation of the SMAs, vary due to the change in the stress. The control problem for such systems is challenging and therefore sophisticated control algorithms are needed. This paper presents two nonlinear algorithms for control of a single-degree-of-freedom rotary manipulator actuated by shape memory alloy ( SMA) wire. For this system the stress of the SMA wire changes as the arm moves upwards and the stress reaches its maximum at a certain angular position. Therefore, the transformation temperatures of the SMA wire, as the arm moves, increase, and after reaching the maximum stress position they decrease. The controllers designed in this study use the stress and temperature of the SMA wire while the only state variable that can be readily measured is the angular position of the arm. Due to measurement difficulties, the other three state variables, arm angular velocity and SMA wire stress and temperature, cannot be directly measured. Therefore, an extended Kalman filter (EKF) is used by the controllers to estimate the unmeasured state variables. As shown by simulations in this work, the controllers, which are also applicable for other SMA actuators under similar complex loadings, provide precise motion control for the SMA actuator.