Experiment Verification and Stability Analysis of Iterative Learning Control for Shape Memory Alloy Wire

Abstract

To achieve the control of a small-sized robot manipulator, we focus on an actuator using a shape memory alloy (SMA). By providing an adjusted voltage, an SMA wire can itself generate heat, contract, and control its length. However, a strong hysteresis is generally known to be present in a given heat and deformation volume. Most of the control methods developed thus far have applied detailed modeling and model-based control. However, there are many cases in which it is difficult to determine the parameter settings required for modeling. By contrast, iterative learning control is a method that does not require detailed information on the dynamics and realizes the desired motion through iterative trials. Despite pioneering studies on the iterative learning control of SMA, convergence has yet to be proven in detail. This paper therefore describes a stability analysis of an iterative learning control to mathematically prove convergence at the desired length. This paper also details an experimental verification of the effect of convergence depending on the variation in gain.