Modeling and L2-stability of a shape memory alloy position control system

Shape memory alloys (SMA's) are inherently nonlinear devices exhibiting significant hysteresis in their stress-strain-temperature characteristic, As a consequence most SMA actuator systems presented in the literature employ some form of proportional-integral-derivative (PID) or pulse-width modulated (PWM) control. Unfortunately, due to the hysteresis of the SMA, the theoretical stability of these systems has been largely ignored. This paper extends tl;e work of Ikuta el al. to arrive at a new model of an SMA actuator. The key feature of the model is its ability to model minor hysteresis loops. The model is suitable for computer simulation, even of closed-loop control systems, as well as control system analysis. Indeed, the model is used to prove the L-2-stability of a position control system.