Adaptive RBF-PIDSMC control method with estimated model parameters for a piezo-actuated stage

The aim of this work is to find an adaptive control scheme to realize precise position tracking for a piezo-actuated stage, which is usually very difficult to control due to the essential nonlinearity and unknown uncertainty. Firstly, a proportional-integral-derivative (PID) sliding mode controller is designed based on the established model and the estimated parameters. Then, in order to reduce the influence of model error, a radial basis function (RBF) neural network is integrated to the controller to improve the control performance. Eventually, an adaptive RBF based PID-type sliding mode controller (RBF-PIDSMC) is proposed and its stability is derived mathematically based on Lyapunov theory. Simulation results of the proposed controller are compared with the PID sliding mode controller to verify its tracking performance. Positioning tracking experiments with two different trajectories are also conducted to verify the correctness and effectiveness of the proposed controller. We can conclude that the proposed controller can be used to track commanded position trajectory for the piezoelectric stage.