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The present paper will describe an approach for the compensation of the hysteretic transfer characteristics of a piezoelectric stack transducer by an adaptive inverse hysteretic control. The basis of the inverse control is formed by a weighted superposition of elementary stop-type hysteresis operators which, in terms of mathematics, can be easily described and which reflect the qualitative properties of the inverse transfer characteristic of the transducer. Starting with a linear characteristic the weigths of an inverse hysteretic observer are identified during operation by a stable adaption law and transformed to the controller parameter. As a result the maximum linearity error caused by hysteresis is lowered about one order of magnitude.

Magnetic shape memory (MSM) alloys are comparatively new active materials which can be used for several industrial applications, ranging from precise positioning systems to advanced robotics. Beyond the material research, which deals with the basic thermo‐magneto‐mechanical properties of the crystals, the design as well as the control of the actuators displacement is an essential challenge. This paper addresses those two topics, trying to give to the reader a useful overview of existing results, but also presents new ideas. First, it introduces and discusses in details some possible designs, with a special emphasis on innovative actuator design concepts which are able to exploit the particular potentialities of MSM elements. The second focus of the paper is on the problem of designing a controller, i.e., an algorithm that allows to obtain a required performance from the actuator. The proposed control strategies try to take into account two main characteristics of MSM elements: the hysteresis and the temperature dependence. The effectiveness of the strategies is emphasized by experimental results performed on a commercially available MSM actuator demonstrator.

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