A dual-loop tracking control approach to precise nanopositioning

Nanopositioners are mechanical devices that can accurately move with a resolution in the nanometer 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 the 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. 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.