Adaptive approximation-based control of hysteretic unconventional actuators

In this paper we develop an algorithm for adaptive control of unconventional actuators based on Prandtl-Ishlinskii models and Lyapunov design. The chosen family of models is general enough to capture the strongly variable shapes of the hysteresis exhibited by some electro-active materials and has an inverse model that can be computed analytically. The approach proposed in this paper adapts the parameters of the model with a learning law based on the minimization of the tracking error, and handles the parameters having a nonlinear influence on the output of the model by means of linearization. An outer position loop is then introduced to compensate the residual compensation error and further improve the tracking performance. The advantages and limitations of the approach are discussed and confirmed by experiments on a mechatronic position actuator based on magnetic shape memory alloys.