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Odd-harmonic repetitive control (ORC) has been successfully applied to improve the triangular trajectory tracking performance of nanopositioners. However, the conventional ORC tends to amplify the tracking errors at frequencies other than the odd-harmonic components, mainly the even harmonics of the fundamentals of the intended triangular trajectory to be tracked. Due to the influence from the hysteresis nonlinearity of the piezoelectric actuator, this would result in significant tracking errors. To overcome this limitation, this article proposes an enhanced odd-harmonic repetitive control (EORC) using the spectrum-selection filtering scheme to improve the loop-shaping property of the ORC. This effectively eliminates the problem of amplifying the tracking errors while preserving the advantages of the conventional ORC, such as fast convergence speed and low computation cost. The EORC is combined with a proportional–integral tracking controller to improve the tracking performance. The controller design, stability analysis, and performance evaluation are presented. The experimental results demonstrating the effectiveness of the proposed EORC-based control scheme are presented showing the excellent tracking of triangular trajectories with fundamental frequencies up to 1000 Hz. Moreover, a reduction in rms tracking errors by up to 52% is achieved. Note to Practitioners—The high-speed atomic force microscopy (AFM) plays an increasingly vital role in observing and manipulating objects at the nanoscale. In the raster scanning of AFMs, the most challenging issue is the triangular trajectory tracking of nanopositioning stages with high precision. Although the odd-harmonic repetitive control (ORC) has been successfully applied to improve the tracking performance, the conventional ORC would amplify the tracking errors distributed at the frequencies other than the odd harmonics, especially those at the even harmonics, resulting from the inherent complicated hysteresis nonlinearity. This problem of amplifying the tracking errors would lead to larger tracking errors, deteriorating the performance of AFM imaging. To address this issue, this article proposes an enhanced ORC using the spectrum-selection filtering scheme to improve the loop-shaping property of the ORC, so as to eliminate the problem of amplifying the tracking errors while preserving the advantages of the conventional ORC, such as fast convergence speed and low computation cost. The experimental results show that, with this simple modification, the positioning errors are reduced greatly, all-the-while preserving the benefits of the conventional ORC scheme– fast convergence speed and low computation cost. In terms of tracking accuracy and the simple structure, this development can be easily implemented to other systems that challenge from the tracking accuracy under ORC scheme. [ABSTRACT FROM AUTHOR]

The scanning speed of atomic force microscopes (AFMs) is typically limited by the frequency of the triangular trajectory used in generating the raster scan. This is because the higher harmonics of the triangular trajectory have a tendency to excite the mechanical resonances of the nanopositioners incorporated in the AFM; thereby, introducing significant positioning errors. To address this issue, this article proposes a novel scanning trajectory smoothing method to enable high-speed raster scanning. The proposed method utilizes the acceleration-continuous B-spline to replace the backward path of the triangular trajectory for the fast axis. As a result, the advantage of uniform sampling along the forward path is preserved. The trajectory generation process is described in detail. A hysteresis compensation method is employed to improve the tracking performance of the scanner. Experiments conducted on a commercial piezoelectric tube scanner are presented to demonstrate the performance improvement delivered by the proposed method when compared with the traditional raster scanning method. It is shown that the proposed method enables a five-fold improvement in achievable scanning rate, from 10 to 50 Hz. [ABSTRACT FROM AUTHOR]

In raster scanning applications of atomic force microscopies, precisely tracking periodic triangular trajectories is the major objective of nanopositioning stages. Considering the fact of periodic operations, the repetitive control technique becomes promising and has been recently developed to reduce tracking errors. In our new experiments, it is found that, with triangular reference input, the hysteresis nonlinearity mainly affects the system at the odd harmonics of the input signal. In this sense, an odd-harmonic repetitive control (ORC) strategy is proposed to handle the hysteresis nonlinearity, with the hysteresis treated as the odd-harmonic periodic disturbance. Therefore, it avoids the modeling and inverting of the complex hysteresis nonlinearity. Another benefit of the developed ORC strategy is that it can also account for the tracking errors caused by the linear dynamics effect. To verify the effectiveness of the ORC strategy, real-time experiments are performed on a custom-built piezo-actuated nanopositioning stage. Experimental results show that the developed ORC strategy achieves precise tracking of 1562.5-Hz triangular trajectory with the hysteresis nonlinearity mitigated to a negligible level, which demonstrates the feasibility and effectiveness of the developed ORC strategy on hysteresis compensation during high-speed raster scanning. [ABSTRACT FROM AUTHOR]

The image quality of an atomic force microscope highly depends on the tracking performance of the lateral X–Y axis scanner. To reduce the requirement for accurate system models, this article describes a method based on Model-free Repetitive Control (MFRC) for high performance control of fast triangular trajectories in the X-axis while simultaneously achieving coupling compensation from the X-axis to Y-axis. The design and stability analysis of the MFRC scheme are presented in detail. The tracking results are experimentally evaluated with a range of different load conditions, showing the efficacy of the method with large variations in plant dynamics. To address the coupling from the X-axis to the Y-axis while tracking the non-periodic staircase trajectories, a pre-learning step is used to generate the compensation signals, which are combined with the baseline Proportional–Integral (PI) control in a feedforward manner in real-time implementations. This approach is also applied to address the problem of longer convergence if needed. Experimental tracking control and coupling compensation are demonstrated on a commercially available piezo-actuated scanner. The proposed method reduces the root-mean-square coupled tracking errors in Y-axis from 191.4 nm in open-loop control or 194.6 nm with PI control, to 2.8 nm with PI+MFRC control at 100 Hz tracking frequency, which demonstrates the significant improvement achieved by the proposed method. • The Model-free Repetitive Control is proposed for rejecting periodic tracking errors. • This method handles the problem of model uncertainties met in practical applications. • The design and stability analysis of the proposed method are presented in detail. • Experimental tracking and coupling compensation of an AFM scanner are validated. [ABSTRACT FROM AUTHOR]