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The work carried out in this article essentially relates to the application of a synergetic control to the piezoelectric positioning mechanism or piezoelectric actuator (PEA). A LuGre model has been followed, capturing the most physical phenomena, in order to be able to follow the most realistic and representative model possible. From this model, which is then identified by particle swarm optimization (PSO), we apply the synergetic control technique, which is a very efficient control method that allows demonstrating the good functioning of the stability of nonlinear system in closed loop. The simulation results have been compared to those obtained when using sliding mode to confer the best performance in terms of tracking error and minimization of oscillations.

In this paper, a dynamic model of a piezo-actuator based on Coleman-Hodgdon (C-H) hysteresis model is considered. The hysteresis model is established by identification considering the particle swarm optimization (PSO) technique. The identified model is tested considering a classical PID controller in order to achieve a tracking control of nano-positioning system driven by piezoelectric actuator. Experimental results through real-time implementation are presented and discussed. A good system performance was obtained with a tracking error less than 100 nm.

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<p>The structure of the model may either be inferred via an experimental study or just by looking at the input and output data. A novel nonlinear autoregressive with exogenous inputs (NARMAX) method for identifying PEA piezoelectric positioning mechanisms is put forward in this study. The developed model enables accurate prediction of the hysteresis of the PEAs. The accuracy of the model built from the input and output data will be assessed by comparison with a LuGre model. The results of the identification show that the recommended approach is successful and that it has a high degree of identification precision within an absolute error range of one micron. The findings demonstrated the potential of the suggested method for classifying nonlinear PEAs.</p>