Damping and Tracking Control Schemes for Nanopositioning

Abstract

Fast and accurate tracking of periodic reference trajectories is highly desirable in many nanopositioning applications, including scanning probe microscopy. Performance in common positioning stage designs is limited by the presence of lightly damped resonances, and actuator nonlinearities such as hysteresis and creep. To improve the tracking performance in such systems, several damping and tracking control schemes have been presented in the literature. In this paper, five different control schemes are presented and applied to a nanopositioning system for experimental comparison. They include schemes applying damping control in the form of positive position feedback, integral resonant control, integral force feedback, and passive shunt-damping. Also, a control scheme requiring only a combination of a low-pass filter and an integrator is presented. The control schemes are fixed-structure, low-order control laws, for which few results exist in the literature with regards to optimal tuning. A practical tuning procedure for obtaining good tracking performance for all of the presented control schemes is therefore presented. The schemes provide similar performance, and the main differences are due to the specific implementation of each scheme.

Analog Robust Repetitive Control for Nanopositioning Using Bucket Brigade Devices

“…A simple, effective, and robust damping and tracking control law for a lightly damped structure can be obtained by modifying and optimally tuning an integral control law (Eielsen et al, 2014). Since the BBD is a sampled device, reconstruction and anti-aliasing filters must be present in order to mitigate aliasing effects.…”

“…As discussed in (Eielsen et al, 2014), the optimal values for the cut-off frequency and the integral gain can be found by minimizing…”

Butterworth Pattern-based Simultaneous Damping and Tracking Controller Designs for Nanopositioning Systems

“…However, numerous works have shown, experimentally, that integral tracking control reduces the effects of hysteresis on positioning error (Bhikkaji et al, 2007;Aphale et al, 2008a;Fleming, 2010). Eielsen et al (2014) showed that using Model Reference Control to obtain a closed-loop Butterworth filter pattern provides increased performance over traditional damping and tracking controllers, in terms of bandwidth and positioning error. The aim of this work is to provide a quick and simple method of deriving controllers to obtain a closed-loop Butterworth filter pattern.…”

H ∞ Reduced Order Control for Nanopositioning: Numerical Implementability

“…Some of these effects can be effectively compensated for such as hysteresis (Eielsen et al, 2012;Kaizuka and Siu, 1988;Croft et al, 2001). To handle the resonant peaks of the lightly-damped vibration dynamics, simpler control schemes such as damping and tracking control can be employed (Eielsen et al, 2013;Aphale et al, 2008;Fleming, 2010;Fleming et al, 2010). However, higher order model-matching based techniques, such as model reference control (MRC), linear quadratic control (LQR) and H ∞ -control, can in principle allow for higher bandwidth, and can therefore lead to better tracking performance.…”