Tracking Control of Nanopositioning Stages Using Parallel Resonant Controllers for High-Speed Nonraster Sequential Scanning

Abstract

The resonant controller (RC), as a promising candidate for high-speed nonraster nanopositioning applications, can track the sinusoidal reference with zero steady-state error. This article presents a controller composed of several RCs in parallel for tracking nonraster sequential scanning trajectories. The selection for each RC in the parallel array is based on two considerations: one is the spectrum of the reference signal and the other is the harmonics caused by the nonlinearities of the nanopositioning stage. The performance of RC is highly dependent on the accurate placement of the resonant poles, but unfortunately, many existing digital implementation methods could cause a deviation of the resonant poles from their initial locations. To address this problem, a modified Tustin (MTus) method is proposed in this article to implement the controller with better accuracy. Furthermore, the fractional-order (FO) calculus is introduced to improve the transient performance of the RCs. To validate the proposed methods, a comprehensive examination of several types of the nonraster sequential scanning trajectories with a wide frequency range has been carried out on a nanopositioning stage. The results have been compared with other methods, showing that the tracking errors are reduced significantly under the controller implemented by the MTus method especially in high-frequency conditions and that the application of the FO calculus reduces the settling time of the controller by more than 30% in most cases. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The demand for high-speed atomic force microscope (AFM) increases rapidly. However, the commonly used raster trajectory limits the achievable scan speed of the AFM. An effective way to improve the scanning and imaging speed of the AFM is the application of the sequential nonraster scanning methods. The trajectories of sequential nonraster scanning patterns mainly composed of few sinusoid signals with different frequencies. Therefore, the resonant controller (RC) is introduced in this article as it is capable to track the sinusoidal reference with zero steady-state error. Several RCs are selected first based on the spectrum analysis of the reference and the consideration of the harmonics caused by the system nonlinearities, and then, they are connected in parallel to form the controller for precise tracking of the reference. In order to realize the digital implementation of the designed controller, a modified Tustin discretization method is proposed, which ensures the accurate resonant pole placement of the RC and thus maintains the tracking performance of the RC. In addition, the fractional-order (FO) calculus is introduced to speed up the convergence of the designed controller while preserving the tracking accuracy, and this parallel-structure FO RC (PSFORC) design can be implemented to other systems that require high-speed and high-accuracy tracking of the periodic signals.