L2-stability of a shape memory alloy position control system

In most shape memory alloy (SMA) actuator systems presented in the literature, some form of PID or pulse-width modulating controller is typically used. Unfortunately, due to the hysteresis inherent in any SMA actuator system, the theoretical stability of these systems has been largely ignored. This paper employs a model developed by the author and a general form of the passivity theorem of Vidyasagar (1993) to prove the L₂-stability of an SMA actuator system employing a form of proportional control. The complex nonlinear behaviour of the SMA actuator is taken into account, along with nonlinear effects such as saturation. Due to the flexibility of the model in specifying the shape and position of the hysteresis, the stability result may be applicable to other hysteretic systems