ℒ1 adaptive control of a shape memory alloy actuated flexible beam

Abstract

This paper details the synthesis of an L1 adaptive controller for a shape memory alloy (SMA) actuated flexible beam. The controller manipulates applied voltage, which alters SMA tendon temperature to track reference bending angles. Simulated and experimental results show that the L1 adaptive controller provides precise tracking of the reference trajectories and effectively compensates for the nonlinear hysteretic relationship between SMA Joule heating and bending angle without explicitly modelling these characteristics. A simulation model whose results closely resemble the experimental performance results is presented. As a first step towards the development of L1 adaptive control implementation guidelines, a complete description of the L1 control parameters and their correlation to tracking performance is presented.