Robust H^∞ Control in Fast Atomic Force Microscopy

Abstract

This paper develops a robust H ∞ method for fast tracking position control problems arising in an atomic force microscope (AFM). A commercial type NT‐MDT AFM is used to generate 3D images of scanned material surfaces at high speeds and accuracies. A major component of this AFM is a piezoelectric tube actuator used for position control in three directions. Due to the nature of the piezoelectric actuator, there is nonlinear hysteresis present which affects the AFM scanning qualities. The original commercial AFM uses traditional proportional‐integral‐derivative position control and can only obtain good quality images for scanning rates under about 20 Hz in both the x and y directions. In this paper, a robust H ∞ controller is designed based on a physical model of the AFM piezoelectric tube positioner in the x and y directions. On the electrical side of the positioning system, external capacitors are connected in series with the x and y contacts of the piezoelectric tube to provide measured voltages which are proportional to the charge on the actuator. The parameters for a nonlinear model are obtained from measurements of the system frequency response and time domain response. This model also takes into account the time delay resulting from the sensor electronics. This nonlinear model is represented as a linear uncertain system model with norm bounded uncertainty. The uncertain system model is used to design a robust H ∞ tracking controller for the AFM scanning system. Experimental results show that the robust H ∞ controller can improve the AFM scanning quality and increase the scanning speed significantly. The controller performs well in tracking a given reference scanning signal with frequencies up to 125 Hz.

Advanced Control of Atomic Force Microscope for Faster Image Scanning

“…Feedback control schemes have been used to compensate for hysteresis in [14][15][16][17]. A sector-bounded H ∞ controller is implemented in [16] to improve the scanning speed and image quality, and this achieves a scan rate of 125 Hz, but it has distortions at the edges of the images at high-frequency scanning, because it cannot achieve much damping of the resonant modes.…”

High-precision spiral positioning control of a piezoelectric tube scanner used in an atomic force microscope

“…The system error is defined as the difference between the reference input and plant output as: e = y r − y; (12) where y r is the sinusoidal reference input to the plant and assumed to satisfy the differential equation:…”

“…A signal transformation method is implemented to track the reference triangular signal in an AFM in [11]. A H ∞ controller is implemented to improve the scanning speed and image quality, which achieved a scanning rate of 125 Hz, as reported in [12]. Creep, hysteresis, and vibration effects have been minimized by implementing a proportional plus derivative high-gain feedback controller and feed-forward controller in [8].…”

Model predictive control of atomic force microscope for fast image scanning

“…On the other hand at low-range scans (i.e., when actuating a PZT with voltage signals of low amplitude), hysteresis can be ignored [9]. Feedback control schemes have been used to compensate for hysteresis in [10], [11], [12].…”