A dual-loop tracking control approach to precise nanopositioning

Abstract

Nanopositioners are mechanical devices that can accurately move with a resolution in the nanometre scale. Due to their mechanical construction and the piezoelectric actuators popularly employed in nanopositioners, these devices have severe performance limitations due to resonance, hysteresis and creep. A number of techniques to control nanopositioners, both in open-loop and closed-loop, have been reported in literature. Closed-loop techniques clearly outperform open-loop techniques due to several desirable characteristics, such as robustness, high-bandwidth, absence of the need for tuning and high stability along with others. The most popular closed-loop control technique reported is one where a damping controller is first employed in an inner loop to damp the mechanical resonance of the nanopositioner, thereby increasing achievable bandwidth. Consequently, a tracking controller, typically an Integral controller or a Proportional-Integral controller, is implemented in the outer loop to enforce tracking of the reference signal, thereby reducing the positioning errors due to hysteresis and creep dynamics of the employed actuator. The most popular trajectory a nanopositioner is forced to track is a raster scan, which is generated by making one axis of the nanopositioner follow a triangular trajectory and the other follow a slow ramp or staircase. It is quite clear that a triangle wave (a finite velocity, zero acceleration signal) cannot be perfectly tracked by a first-order integrator and a double integrator is necessary to deliver error-free tracking. However, due to the phase profile of the damped closed-loop system, implementing a double integrator is difficult. This paper proposes a method by which to implement two integrators focused on the tracking performance.The criteria for gain selection, stability analysis, error analysis, simulations and experimental results are provided. These demonstrate a reduction in positioning error by 50%, when compared to the traditional damping plus first-order integral tracking approach.

Global fast non-singular terminal sliding-mode control for high-speed nanopositioning

“…Due to lack of robustness, high dependency on accurate modeling and low disturbance rejection characteristics, open-loop approaches were discarded in favour of closed-loop approaches [13]. Closed-loop approaches predominantly focussed on a two stage approach of implementing linear damping and tracking controllers in tandem to de-liver acceptable positioning performance [14]. However, most of the reported techniques are based on a simple second-order system model and do not explicitly model the hysteresis; rather depend on the high-gain tracking controller (typically an integrator) to minimize hysteresis-induced positioning errors.…”

Enhanced Positioning Bandwidth in Nanopositioners via Strategic Pole Placement of the Tracking Controller

“…After damping control, conventional Proportional Integral (PI) or Integral (I) control algorithms are able to achieve accurate tracking control in nanopositioning applications. There are numerous attempts in the literature to employ a double integral, as reported in [27,28]. However, these control methods increase the order of the system and introduce a phase shift in the tracking control.…”