Time delay recursive neural network-based direct adaptive control for a piezo-actuated stage

Piezo-actuated stage is a core component in micro-nano manufacturing field. However, the inherent nonlinearity, such as rate-dependent hysteresis, in the piezo-actuated stage severely impacts its tracking accuracy. This study proposes a direct adaptive control (DAC) method to realize high precision tracking. The proposed controller is designed by a time delay recursive neural network. Compared with those existing DAC methods designed under the general Lipschitz condition, the proposed control method can be easily generalized to the actual systems, which have hysteresis behavior. Then, a hopfield neural network (HNN) estimator is proposed to adjust the parameters of the proposed controller online. Meanwhile, a modular model consisting of linear submodel, hysteresis submodel, and lumped uncertainties is established based on the HNN estimator to describe the piezo-actuated stage in this study. Thus, the performance of the HNN estimator can be exhibited visually through the modeling results. The proposed control method eradicates the adverse effects on the control performance arising from the inaccuracy in establishing the offline model and improves the capability to suppress the influence of hysteresis on the tracking accuracy of piezo-actuated stage in comparison with the conventional DAC methods. The stability of the control system is studied. Finally, a series of comparison experiments with a dual neural networks-based data driven adaptive controller are carried out to demonstrate the superiority of the proposed controller.