Smith Predictor Based ℋ∞ Control for Piezoelectric Nano Stages with Time Delays

Nano precision capacitive displacement sensors have been successfully employed to the servo control of piezoelectric nano stages. However the analog-to-digital (A/D) conversion of the ultra high precision signal results in major time delays for the nano control systems. Meanwhile, the behavior of the hysteresis of piezoactuators can be also approximated as a variable gain cascaded with a frequency varying time delay. The infinite dimensionality of the time delays in nano servo systems poses new challenges for the control of nano stages, where traditional control methods can not be applied directly. In this paper, a linear model with time delays and hysteresis approximation is discussed for piezoelectric nano stages, where the system parameters are further determined using an identification method by experimental data. Furthermore a Smith predictor based robust ℋ∞ controller is developed to achieve high performance and robust stability for the control of nano stages. Real time experiments with the proposed control design are conducted, where robustness against model uncertainties and accurate positioning performance are demonstrated, which outperforms the method without considering time delays.