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

Abstract

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, theta(x), and theta(y) with amplitudes of 3 microm 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.

Optimal Design and Control of a z-Tilt Piezoelectric Based Nano-Scale Compensation Stage with Circular Flexure Hinges

“…Step 6. To compute the S/N ratio: According to Equations (1) and (2) and Table 3, the S/N ratio for each trial can be computed as shown in Table 5. The average S/N ratio denoted of η, for example, for A1 and B2 are: η for A 1 : η A1 = (56.377)+(55.891)+(55.394)…”

“…The two most common kinds of nano-scale compensation stage are x-y-yaw and z-tilt. The x-y-yaw stage is like that proposed by Lee et al [1], and the z-tilt stage is like another proposed by Liu et al [2]. The structure of z-tilt stages is usually simpler than that of x-y-yaw stages.…”

“…Thus, some studies using a compensator with a PID (proportional-integral-derivative) controller to improve the steady state error and dynamic tracking performance like Ru et al proposed [19]. Beside mathematical compensation methods (e.g., feed-forward compensator), Liu et al employed a capacitor in the piezoelectric driving circuit for hysteresis reduction and the method is called capacitor insertion method [2]. This study was concerned with positioning accuracy.…”

“…Estimating of the static performance of a z-tilt stage, such as coupling displacement and stage stiffness, can be made using simulation and stepwise displacement experiments. The dynamic performance of a z-tilt stage can be tested by a tracking experiment [2,20]. The first part of this study describes the use of the Taguchi method to optimize design of the circular flexure hinges.…”

“…Table 7 were constructed and ranking was made according to the degree of influence. In Equations (1) and (2), yi represents the simulation output value, for example, the natural frequency (units can be ignored); n represents the number of output response (n = 1 for η1; n = 1 for η2).…”