Estimation of shape memory alloy actuator dynamics to design reduced-order position controller with input saturation

Abstract

This study focuses on the precise model estimation for a position control problem actuated by a shape memory alloy (SMA) wire. Because the hysteresis characteristic of SMA introduces complexities in system modelling and adds degrees of freedom, a model with reduced order is implemented for controller design. This model is online updated by calculating a complementary term from the measured data to compensate for the SMA actuator dynamics and other parametric uncertainties. The position controller, derived from the formulated reduced-order model, adapts itself to real conditions and is cost-effective due to the use of only displacement sensor. The saturation of the control input is modelled within the structure of a constrained optimization problem solved by Karush–Kuhn–Tucker theorem. The boundedness of mean and covariance of tracking error and its derivative is demonstrated by stochastic analysis. The experimental results conducted on a platform incorporating a SMA wire show the efficiency of the proposed system in precisely controlling the position by admissible voltage range. The comparative results with a sliding mode controller indicate higher accuracy for the proposed controller to reduce the effect of uncertainties.