We demonstrate the application of the internal model principle in tracking a sequential cycloid trajectory to achieve video-rate atomic force microscope (AFM) imaging. To generate a sequential cycloid pattern, one axis of the nanopositioner traces a sinusoidal signal superimposed on a slow triangular wave. Discontinuities at turning points induce large peaks in the steady-state tracking error. To address this issue, a smooth trajectory is designed to reduce the magnitude of error by 60 nm compared with the triangular wave. This trajectory reduces the magnitude of error 10 times. The tracking controller includes the dynamics of the harmonic waveforms and the ramp signal as well as higher order harmonics of the scanning frequency, and an integrator to cope with the system nonlinearities at low frequencies. We perform experiments on a two degree of freedom microelectromechanical system nanopositioner at various scanning frequencies ranging from 500 to 2580 Hz within a scan area of $5\,\,\mu \text {m} \times 10\,\,\mu \text {m}$ . The root-mean-square value of tracking error remains below 6.1 nm with a pitch size of 44.2 nm. We acquire time-lapse AFM images in contact mode at scan rates as high as 20 frames per second.

中文翻译：

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带摆线轨迹的视频速率非光栅AFM成像

我们演示了内部模型原理在跟踪连续摆线轨迹以实现视频速率原子力显微镜（AFM）成像中的应用。为了产生连续的摆线图案，纳米定位器的一个轴跟踪叠加在慢三角波上的正弦信号。转折点的不连续性会在稳态跟踪误差中引起较大的峰值。为了解决这个问题，设计了平滑的轨迹，与三角波相比，可将误差幅度降低60 nm。该轨迹将误差幅度降低了10倍。跟踪控制器包括谐波波形和斜坡信号的动态特性以及扫描频率的高次谐波，以及一个用于应对低频系统非线性的积分器。我们在$ 5 \，\，\ mu \ text {m} \ times 10 \，\，\ mu \ text的扫描区域内，在500至2580 Hz范围内的各种扫描频率下，在两自由度微机电系统纳米定位器上进行实验{m} $。跟踪误差的均方根值保持在6.1 nm以下，间距尺寸为44.2 nm。我们以接触模式以每秒20帧的高速率获取延时AFM图像。