Application of the Extended Kalman Filter to Control of a Shape Memory Alloy Arm

Abstract

This paper presents a robust nonlinear control that uses a state variable estimator for control of a single degree of freedom rotary manipulator actuated by Shape Memory Alloy (SMA) wire. A model for SMA actuated manipulator is presented. The model includes nonlinear dynamics of the manipulator, a constitutive model of the Shape Memory Alloy, and the electrical and heat transfer behavior of SMA wire. The current experimental setup allows for the measurement of only one state variable which 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. A model-based state estimator that works with noisy measurements is presented based on the Extended Kalman Filter (EKF). This estimator predicts the state vector at each time step and corrects its prediction based on the angular position measurements. The estimator is then used in a nonlinear and robust control algorithm based on Variable Structure Control (VSC). The VSC algorithm is a control gain switching technique based on the arm angular position (and velocity) feedback and EKF estimated SMA wire stress and temperature. The state vector estimates help reduce or avoid the undesirable and inefficient overshoot problem in SMA one-way actuation control.