Piezoelectric actuators (PEA) have been widely used in the ultra-precision manufacturing fields. However, the hysteresis nonlinearity between the input voltage and the output displacement, which possesses the properties of rate dependency and multivalued mapping, seriously impedes the positioning accuracy of the PEA. This paper investigates a control methodology without the hysteresis model for PEA actuated nanopositioning systems, in which the inherent drawback generated by the hysteresis nonlinearity aggregates the control accuracy of the PEA. To address this problem, a neural network self-tuning control approach is proposed to realize the high accuracy tracking with respect to the system uncertainties and hysteresis nonlinearity of the PEA. First, the PEA is described as a nonlinear equation with two variables, which are unknown. Then, using the capabilities of super approximation and adaptive parameter adjustment, the neural network identifiers are used to approximate the two unknown variables automatically updated without any off-line identification, respectively. To verify the validity and effectiveness of the proposed control methodology, a series of experiments is executed on a commercial PEA product. The experimental results illustrate that the established neural network self-tuning control method is efficient in damping the hysteresis nonlinearity and enhancing the trajectory tracking property.

The strong hysteresis nonlinearity extremely limits the positioning precision of piezoelectric actuators (PZAs). For the purpose of eliminating hysteresis effect and achieving high precise output displacement of PZAs, an adaptive sliding mode control method is proposed in this paper. The proposed hybrid control method is composed of an adaptive control method and a sliding mode control method. The simulations are conducted to validate the effectiveness of the proposed control method. The simulation results show that the proposed control method restrains hysteresis behaviour of PZAs efficiently and reduces maximum relative error to 0.57%. In contrast, the existing works lack efficient methods to deal with the uncertain parameters of the hysteresis model. The proposed control method in this paper can effectively solve the existing problems and improve the positioning precision of the control system of PZAs.