Modeling and state estimation for the advanced control of a multimaterial shape memory based actuator

Shape Memory Alloys (SMAs) are a class of smart materials with interesting thermomechanical properties, such as the ability to recover very large deformations when heated. A peculiar application of SMA actuators is soft robotics, where a SMA wire can be embedded inside a soft material, such as a polymeric matrix [1]. In this work, we expand the SMA model proposed in the literature by Brinson [2] so as to develop a new thermomechanical multimaterial model of a SMA-based actuator made by a SMA wire coated by a silicone rubber layer. The system is highly nonlinear, time-varying and hysteretic, adding to the complexity of controlling actuation. We improved the controllability of the multi-material by implementing a new switched controller concept in the form of a Variable PID. Its parameters are tuned based on the changing SMA operating zone, which is determined via a state estimator and a logical block. Key to the switched controller implementation is the development of an Extended Kalman Filter (EKF) for state estimation. The EKF was tested and showed robustness in predicting the state. Preliminary simulations of the Variable PID show that the innovative strategy allows for faster heating and cooling in the reaching some reference position compared to a conventional PID. This control method could be used to reduce the requested electrical power and improve the overall material performance.