Abstract. Shape memory alloys (SMA) are more and more integrated in engineering applications. These materials with their shape memory effect permit to simplify mechanism and to reduce the size of actuators. SMA parts can easily be activated by Joule effect but their modelling and consequently their control remains difficult, it is principally due to their hysteretic thermomechanical behaviour. Another difficulty is that the characteristics of the material are timevarying, especially during cyclic loadings. So, most of successful control strategy applied to SMA actuator are particularly heavy and used the Preisach model or neural networks to model the hysteretic behaviour of these material but this kind of models are difficult to identify and to use in real time. That is why this study deals with an application of the new framework of model-free control and restricted model control applied to a SMA spring based actuator. This control strategy is based on new results on fast derivative s estimation of noisy signals, its main advantages are: its simplicity, its robustness and the fact that it is easy to compute. Experimental results and comparisons with PID control are exposed that demonstrate the efficiency of this new control strategy despite thermal perturbations.