Design of a Kalman filter for rotary shape memory alloy actuators

Measuring the state variables of systems actuated by shape memory alloys (SMAs) is normally a difficult task because of the small diameter of the SMA wires. In such cases, as an alternative, observers are used to estimate the state vector. This paper presents an extended Kalman filter (EKF) for estimation of the state variables of a single-degree-of-freedom rotary manipulator actuated by an SMA wire. This model-based state estimator has been chosen because it works well with noisy measurements and model inaccuracies. The SMA phenomenological models, that are mostly used in engineering applications, have both model and parameter uncertainties; this makes the EKF a natural choice for SMA-actuated systems. A state space model for the SMA manipulator is presented. The model includes nonlinear dynamics of the manipulator, a thermomechanical model of the SMA, and the electrical and heat transfer behavior of the SMA wire. In an experimental set-up the angular position of the arm is the only state variable that is measured besides the voltage applied to the SMA wire. The other state variables of the system are the arm's angular velocity and the SMA wire's stress and temperature, which are not available experimentally due to difficulty in measuring them. Accurate estimation of the state variables enables design of a control system that provides better system performance. At each time step, the estimator uses the SMA wire's voltage measurement to predict the state vector which is corrected as necessary according to the measured angular position of the arm. The input and output of the model are used for the EKF simulations. The state variables collected through model simulations are also used to evaluate the performance of the EKF. Several EKF simulations presented in this paper show accurate and robust performance of the estimator, for different control inputs.