In this paper, the modified repetitive control (MRC) approach is developed to improve the tracking performance of piezoelectric tube scanner in Atomic Force Microscope for Lissajous trajectories, which has the capability to reject the periodic tracking errors induced by hysteresis nonlinearity and the cross-coupling effect. The fundamental of Lissajous trajectory and the MRC technique are presented initially. As the plug-in feature of MRC scheme, a proportional-integral (PI) controller is also designed in feedback loop for realizing the high-precision motion control. The tracking performance of the scanner with PI+MRC is compared with the conventional PI controller to show the effectiveness of the developed method for Lissajous trajectory tracking. The desired Lissajous trajectory and the actual scan trajectory are additionally demonstrated for the scanner with different control strategies. According to the experiment results, the MRC-based technique improves the tracking performance significantly, in which the root mean square tracking error is reduced from 4328nm to 63.3nm for the scanning frequency of 25-Hz.
This paper presents a comparative study of the proportional-integral (PI) control, sliding mode control (SMC), and robust adaptive control (RAC) for applications to piezo-actuated nanopositioning stages without the inverse hysteresis construction. For a fair comparison, the control parameters of the SMC and RAC are selected on the basis of the well-tuned parameters of the PI controller under same desired trajectories and sampling frequencies. The comparative results show that the RAC improves the tracking performance by 17 and 37 times than the PI controller in terms of the maximum tracking error em and the root mean tracking error erms, respectively, while the RAC improves the tracking performance by 7 and 9 times than the SMC in terms of em and erms, respectively.
This paper presents the design and analysis of a high-speed XYZ nanopositioning stage. The developed stage is composed of a parallel-kinematic XY stage and a Z stage which is nested within the end-effector of the XY stage. To achieve high resonance frequencies, four special flexure modules with large stiffness are employed for the XY stage. These modules are arranged symmetrically to reduce cross-coupling between X- and Y-axis. For the Z stage, a symmetrical leaf flexure parallelogram mechanism is adopted, which has high resonance frequencies and no cross-coupling. Static and dynamic analysis are performed respectively to establish analytical models for the developed XYZ stage. Based on these models, the dimensions of the stage are optimized to maximize the first resonance frequency of the X-and Y-axis. Then, finite-element analysis (FEA) is conducted to validate the performance of the developed XYZ nanopositioning stage. The FEA results reveal that the workspace of the stage is 9.2 μm × 9.2 μm × 3.1 pm and the first resonance frequencies of the stage in three axes are 7.3 kHz, 7.3 kHz and 46.2 kHz, respectively, which agrees with the analytical results.
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