H∞ Loop Shaping Controller for Shape Memory Alloy Actuators

This paper describes a Robust H∞Controller for a Shape Memory Alloy actuator. A formulation based on concepts from physics, has been used to model the Shape Memory Alloy (SMA). The modelling equations include Joules heating - convectional cooling to explain the dynamics of temperature, Fermi-Dirac statistics to explain the variation of mole fraction with temperature, and a stress-strain constitutive equation to relate changes in mole fraction and temperature to changes in stress and strain of the SMA. An H∞loop shaping controller using normalized coprime stabilization is designed such that the gains are high when the model describes the SMA accurately and low at higher frequencies when the model is inaccurate. Simulation and experimental results show fast and accurate control of the strain in the SMA actuator.