Periodic-Disturbance Observer Using Spectrum-Selection Filtering Scheme for Cross-Coupling Suppression in Atomic Force Microscopy

Abstract

Repetitive disturbances exist widely within the automation systems, which is one of the major issues that hinder the achievement of precision operations. Dedicated to mitigating these disturbances, a generalized periodic-disturbance observer (PDOB) using spectrum-selection filtering scheme is proposed in this paper with an application to a non-minimum phase system. The design process of the spectrum-selection filter that derives from the comb-like notch filter for the proposed PDOB is presented in detail. The variants of the proposed PDOB are also presented for the disturbances distributed only in odd-and even-harmonics. To achieve tracking of the desired trajectories, the proposed PDOB is combined in parallel with a baseline Proportional-Integral (PI) controller. The stability condition of the closed-loop system is derived to provide criteria for parameters selection. The experimental validation of the generalized PI+PDOB is conducted via real-time cross-coupling suppression in raster scanning of atomic force microscope (AFM), where the coupling induced root-mean-square tracking errors are reduced from 141.8 <inline-formula> <tex-math notation="LaTeX">$nm$</tex-math> </inline-formula> to 2.4 <inline-formula> <tex-math notation="LaTeX">$nm$</tex-math> </inline-formula> by employing the proposed PDOB for the scanning rate of 100 Hz. The results of convergence testing, raster scanning and AFM imaging are compared to illustrate the significant improvements achieved with the proposed PDOB. In addition, experimental results show that the tracking performance using PI+PDOB in the case of existing periodic disturbances resembles with that using PI control without periodic disturbances, which implies that the employment of the proposed PDOB does not interfere with the tracking-based control schemes for staircase trajectories, showing the advantages of the proposed PDOB. <i>Note to Practitioners</i>&#x2014;Repetitive motions facilitate diverse advanced functions within the automation systems, including the scanning electron microscope, atomic force microscope, manipulators, and robotic systems. These operations would unavoidably introduce repetitive disturbances, hindering its achievable precision. One particular issue is the widely existent cross-coupling effect that results in these repetitive disturbances. In this paper, a generalized periodic-disturbance observer (PDOB) based on the spectrum-selection filtering scheme is developed to address the repetitive disturbances for real-time coupling suppression in raster scanning of Atomic Force Microscopy. Consequently, the offline learning procedures required for other learning based schemes can be avoided. Without loss of generalization, the design of PDOB is demonstrated with an application to non-minimum phase systems. A scheme of the varying parameter is also developed to achieve both fast convergence and better performance at rejecting the periodic disturbances. The detailed variations to handle the disturbances distributed only in odd-and even-harmonics are also demonstrated. Different from other disturbance observers, the inclusion of the spectrum-selection filtering scheme provides more flexibility in rejecting specific repetitive disturbances. In terms of tracking accuracy and the simple structure, this development can also be easily implemented to other systems that suffer from repetitive disturbances.