Second-order terminal sliding mode control based on perturbation estimation for nanopositioning stage

This study proposes a robust second-order terminal sliding mode control with perturbation estimation (2OTSMCPE) strategy with application to trajectory tracking control of the flexure-based nanopositioning system. The proposed controller advantages not only lie on its finite-time convergence but also can provide a high tracking precision with a chattering alleviation which is attend by employing a second-order sliding surface with the switching function. The model of the piezo-driven nanopositioning system is presented first. Second, the sliding variable is designed such as proportional-integral-derivative form to enhance the dynamic response of the control system. Then, a non-singular terminal sliding function (NTSM) is used to achieve the finite-time convergence of the linear sliding variable. Next, a perturbation estimation technique is integrated with the control structure for online estimation of the system uncertainties, thus the prior knowledge of the bounds of system uncertainties are not needed in the proposed control design. Afterwards, the theoretical analysis of the 2OTSMCPE with stability proof is investigated herein. Finally, the system performance with the proposed controller is experimentally verified. The results reveal that the 2OTSMCPE has stronger robustness and also has smoother control signals in comparison with both conventional sliding mode control and the NTSM controller.