Abstract-Piezocantilevers are commonly used for the actuation of micromechatronic systems. These systems are generally used to perform micromanipulation tasks which require high positioning accuracy. However, the nonlinearities, i.e. the hysteresis and the creep, of piezoelectric materials and the influence of the environment (vibrations, temperature change, etc.) create difficulties for such a performance to be achieved. Various models have been used to take into account the nonlinearities but they are often complex. In this paper, we study a one degree of freedom piezoelectric cantilever. For that, we propose a simple new model where the hysteresis curve is approximated by a quadrilateral and the creep is considered to be a disturbance. To facilitate the modelling, we first demonstrate that the dynamic hysteresis of the piezocantilever is equivalent to a static hysteresis, i.e. a varying gain, in series with a linear dynamic part. The obtained model is used to synthesize a linear robust controller, making it possible to achieve the performances required in micromanipulation tasks. The experimental results show the relevance of the combination of the developed model and the synthesized robust H∞ controller.Index Terms-Piezoelectric devices, hysteresis and creep, quadrilateral approximate model, robust control, micromanipulation.
The works presented in this article are motivated by the high performances required in micromanipulation/microassembly tasks. For that, this paper presents the developement, the modelling and the control of a 2 degrees of freedom (in linear and angular motion) micropositioning device. Based on the stick-slip motion principle, the device is characterized by unlimited strokes and submicrometric resolutions. First, experiments were carried out to characterize the performances of the micropositioning device in resolution and in speed. After that, a state-space model was developed for the sub-step functioning. Such functioning is interesting for a highly accurate task like nanopositioning. The model is validated experimentally. Finally, a controller was designed and applied to the micropositioning device. The results show good robustness margins and a response time of the closed-loop system.
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