Improvement of the nonlinear dynamic response of a Z-tilts lead zirconate titanate-based compensation stage using the capacitor insertion method

This paper presents a Z-tilts compensation stage with three piezoelectric actuators and three guided hinges, which are a combination of a two-dimensional rotational hinge and a spring-type hinge. In order to reduce the nonlinearity of the three piezoelectric actuators, the capacitor insertion method was applied on each piezoelectric actuator. The relationship between the improved nonlinearity and the decreased displacement with various inserted capacitors is discussed and suitable capacitors for the stage are determined. A three-dimensional feedback measuring system composed of a laser interferometer and a quadrant photodiode detector was used to directly measure the real working position of the platform of the Z-tilts compensation stage without measuring the individual displacement of the three piezoelectric actuators. The minimum displacement and angular displacement of the Z-tilt stage were ±10 nm and ±0.1 arc sec, respectively. The error of the dynamic response of z, θ_x, and θ_y with amplitudes of 3 μm of a sine wave at 30 Hz were ±70 nm, ±0.1 arc sec, and ±0.4 arc sec, respectively, with the capacitor insertion method and a simple proportional-integral controller.