Precise tracking of a piezoelectric positioning stage via a filtering-type sliding-surface control with chattering alleviation

A filtering-type sliding-surface control (FTSSC) design with chattering alleviation compared to the traditional sliding-mode control (SMC) is proposed for precise trajectory tracking of a piezoelectric positioning stage (abbreviated by `piezo-stage´). First, considering the dynamics of motion of a mass-spring mechanical system, the differential equations of motion system which contains the parameters of a linear viscous friction, spring-coefficient, and a nonlinear hysteresis function - are proposed to describe the dynamics of motion of the piezo-stage. Then, the frequency-dependent hysteresis responses from both the proposed equations and the practical piezo-stage are illustrated to validate the equations. Based on the equations proposed, a state-space model is developed in which the applied voltage to the stage is defined as an output of a new control variable. According to the state-space model, the FTSSC design is proposed to provide not only the advantages of the traditional SMC, but also chattering improvement. Using the proposed control approach to the trajectory tracking of the piezo-stage, we can obtain that (a) high-performance tracking response, (b) robustness to system uncertainties and (c) chattering alleviation compared with the traditional SMC. Experimental results are illustrated to validate the proposed control approach for practical applications in trajectory tracking