Proxy-Based Sliding-Mode Tracking Control of Piezoelectric-Actuated Nanopositioning Stages

In this paper, a proxy-based sliding-mode control (PBSMC) approach is proposed for robust tracking control of a piezoelectric-actuated nanopositioning stage composed of piezoelectric stack actuators and compliant flexure mechanisms. The essential feature of the PBSMC approach is the introduction of a virtual coupling proxy, which is controlled by the sliding-mode controller (SMC) to track the desired position. Simultaneously, due to the virtual coupling, a proportional-integral-derivative (PID) controller on the other side of the proxy ensures the position of the end-effector of the stage to follow the position of the proxy. Therefore, the PBSMC guarantees the end-effector to track the desired trajectory. The advantages of the developed PBSMC lie in the facts that 1) the discontinuous signum function in the traditional SMC is omitted without any approximation. Hence, the output of the PBSMC is continuous, which does not suffer from the chattering phenomenon; and 2) the PBSMC laws are developed without having the necessity to include the nominal system model, hysteresis model or the state observer. Hence, the PBSMC provides a novel effective yet simple control method, which permits to avoid the lack of performances from PID and the chattering from SMC, and permits to combine the advantages from them. The stability of the closed-loop control system is proved through Lyapunov analysis. Finally, comparative studies are performed on a custom-built piezo-actuated stage. Experimental results show that the tracking errors of the PBCM are reduced by 74.22%, as compared to the traditional PID controller, with the desired sinusoidal trajectory under the 50-Hz input frequency, which clearly demonstrates the superior tracking performance of the PBSMC.