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This study examines the concept of axisymmetric actuator based on the magnetorheological membrane, electromagnet and permanent magnet. The construction of the actuator enables its application in wide range of practical devices like pumping, loudspeaker or varying-stiffness button. This work will highlight its working principle especially the influence of permanent magnet. Furthermore, the model of devices will be defined relaying on the Hammerstein model. To show the properties of the actuator and to perform the model identification, the set of experiments was run taking into account static and dynamic working conditions.