%0 Villanova Faculty Authorship
%A Elahinia, Mohammad H.
%E Ahmadian, Mehdi.
%E Ashrafiuon, Hashem.
%D 2004
%G English
%T Design of a Kalman Filter for Rotary Shape Memory Alloy Actuators.
%U http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:173873
%X 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.