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

Shape memory alloys (SMAs) are inherently non-linear 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 PID or PWM controller. Unfortunately, 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 model is then used to prove the L₂-stability of a position control system. The key feature of the model is its ability to model minor hysteresis loops. The model is suitable for computer simulation and control system analysis. The stability result accounts for the complex non-linear behaviour of the SMA actuator, along with non-linear effects such as saturation