Modeling and experimental evaluations of a four-legged stepper rotary precision piezoelectric stage

A dynamic model of a stepper rotary stage composed of piezoelectric legs with sandwich structure is presented. The total model mainly consists of two components: the dynamic model of the four-legged piezoelectric actuator and the contact friction model between the legs and the output stage. The distributed parameter model theory is employed to develop the dynamic model of the piezoelectric legs based on the Timoshenko beam theory and the governing equations are derived by Lagrange’s equations. The two-dimensional dynamics contact theory is adopted to obtain the contact friction model. Experiment platform is set up to evaluate the developed model and output characteristics of the stage. The model is confirmed by experiments under different excitation signals, in which the maximum error of step distance between the simulation result and the experimental result is about 7.33%. The open-loop experimental results show that there is a linear relationship between the response step distance and the applied voltage and the maximum step distance of 60.68 μrad is obtained at no-load condition. The close-loop control experiments including the point-to-point positioning experiment and the sinusoidal trajectory tracking experiment are carried out to study the closed-loop performances, a relative steady state positioning error less below 0.057% and a sinusoidal tracking error of 19.51 μrad are achieved by the rotary stage, good positioning and tracking performances are obtained.