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This paper presents theoretical and experimental results concerning a feedback control system employing a Terfenol-D-based smart actuator. Such magnetostrictive devices exhibit significant hysteresis, which, under some conditions, can generate self-sustained periodic oscillations in the control loop. The paper proposes a general procedure to find these conditions and to compute this periodic solution by exploiting some classical results about describing function analysis and the well-known Preisach operator theory. The theoretical findings are supported by a rigorous mathematical analysis resorting to fixed-point theorems.