Intelligent Integral Backstepping Sliding-mode Control Using Recurrent Neural Network for Piezo-flexural Nanopositioning Stage

In this study, an intelligent integral backstepping sliding-mode control (IIBSMC) system using a recurrent neural network (RNN) is proposed for the three-dimensional motion control of a piezo-flexural nanopositioning stage (PFNS). First, the dynamic model of the PFNS is derived. Then, an integral backstepping sliding-mode control (IBSMC) system is proposed for the tracking of the reference contours. The steady-state response of the control system can be improved effectively due to the addition of the integrator in the IBSMC. Moreover, to relax the requirements of the bound and discard the switching function in the IBSMC, an IIBSMC system using an RNN estimator is proposed to improve the control performance and the robustness of the PFNS. The RNN estimator is proposed to estimate the lumped uncertainty, including the system parameters and external disturbance, online. Furthermore, the online tuning law for the training of the parameters of the RNN is derived using the Lyapunov stability theorem. In addition, a robust compensator is proposed to confront the minimum reconstructed error occurring in the IIBSMC system. Finally, some experimental results for the tracking of various contours are given to demonstrate the validity of the proposed IIBSMC system. From the performance measurements of the proportional-integral control, sliding mode control, IBSMC, and IIBSMC systems, the proposed IIBSMC system has the lowest maximum, average, and standard deviation of the position tracking errors for three-dimensional motion control of the PFNS.