Robust tracking of nanopositioning stages using sliding mode control with a PID sliding surface

This paper presents a novel sliding mode control scheme for robust tracking control of a nanopositioning stage composed of piezoceramic stack actuators (PSAs) and compliant flexure mechanisms. The developed controller is distinguished by using a proportional-integral-derivative (PID) type sliding surface rather than the traditional proportionalderivative (PD) type sliding surface, which is more effective to reduce the tracking error. The stability of the developed control law is proved by Lyapnuov analysis. Finally, comparative studies are performed on a custom-built PSA-actuated stage to demonstrate the effectiveness of the developed controller. The major advantages of the developed control scheme lie in that: i) both the nominal system model and hysteresis model are not required in the control law; ii) it is ease of real-time implementation just like the PID control but with the improved tracking performance.