In this paper, adaptive predictive control is proposed to control a Shape Memory Alloy (SMA) linear displacement actuator. A Black-Box (BB) model based on a Laguerre filter is used to identify the SMA actuator and the controller in closed loop. This identification is performed online using a recursive least squares (RLS) algorithm, thus providing a linear model which approximate the behaviour of whole system around a working point. Based on this model, a predictor is built and a simple control law is derived. This structure can be cast in the Model Reference Adaptive Control (MRAC) frame and understood as a modified Series-Parallel Model Reference Adaptive control (MRAC) scheme. Experimental results prove that the proposed method combined with an efficient online identification strategy is able to robustly handle both nonlinearities and input constraints.

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