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

Shape memory alloys (SMAs) 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. However, due to the hysteresis of the SMA, the theoretical stability of these systems has been largely ignored. This paper extends the work of Ikuta et al. (1991) 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 L₂-stability of a position control system