A dissipativity approach to stability of a shape memory alloy position control system

This paper deals with the L-2 stability of a shape memory alloy (SMA) actuated position control system, based on a single SMA wire under constant axial load. It is shown that system stability can be guaranteed for a large class of controllers having certain dissipativity characteristics. In particular, the results can be used to show stability under approximated proportional integral derivative (PID), PI, and PD control. Experimental step responses are given for two different PI controllers. The first controller guarantees a stable response, based on the work presented. While the second system displays superior performance and seems stable, it does not satisfy the stability criterion of the paper. This comparison underscores the conservative nature of the stability result.