Quantification of parameter uncertainty for robust control of shape memory alloy bending actuators

Abstract

In this paper, we employ Bayesian parameter estimation techniques to derive gains for robust control of smart materials. Specifically, we demonstrate the feasibility of utilizing parameter uncertainty estimation provided by Markov chain Monte Carlo (MCMC) methods to determine controller gains for a shape memory alloy bending actuator. We treat the parameters in the equations governing the actuator's temperature dynamics as uncertain and use the MCMC method to construct the probability densities for these parameters. The densities are then used to derive parameter bounds for robust control algorithms. For illustrative purposes, we construct a sliding mode controller based on the homogenized energy model and experimentally compare its performance to a proportional-integral controller. While sliding mode control is used here, the techniques described in this paper provide a useful starting point for many robust control algorithms.