Design and Analysis of Discrete-Time Repetitive Control for Scanning Probe Microscopes

Abstract

This paper studies repetitive control (RC) with linear phase lead compensation to precisely track periodic trajectories in piezo-based scanning probe microscopes (SPMs). Quite often, the lateral scanning motion in SPMs during imaging or nanofabrication is periodic. Dynamic and hysteresis effects in the piezoactuator cause significant tracking error. To minimize the tracking error, commercial SPMs commonly use proportional-integral-derivative (PID) feedback controllers; however, the residual error of PID control can be excessively large, especially at high scan rates. In addition, the error repeats from one operating cycle to the next. To account for the periodic tracking error, a discrete-time RC is designed, analyzed, and implemented on an atomic force microscope (AFM). The advantages of RC include straightforward digital implementation and it can be plugged into an existing feedback control loop, such as PID, to enhance performance. The proposed RC incorporates two phase lead compensators to ensure robustness and minimize the steady-state tracking error. Simulation and experimental results from an AFM system compare the performance among (1) PID, (2) standard RC, and (3) the modified RC with phase lead compensation. The results show that the latter reduces the steady-state tracking error to less than 2% at 25 Hz scan rate, an over 80% improvement compared with PID control.

Low-order continuous-time robust repetitive control: Application in nanopositioning

“…Recently, RC has been introduced for nanopositioning systems [16,17,18,19]. For periodic references, due to the invariance to changes in plant dynamics, RC can address the challenges posed by state-of-the-art mechanically stiff nanopositioner-designs.…”

“…Compared to ILC, RC does not require resetting the initial conditions at the start of each iteration step, and can be implemented using analog devices. For convenience, RC can be plugged into an existing feedback loop to enhance performance with minimal changes to the existing control system [16].…”

Tracking of Triangular References Using Signal Transformation for Control of a Novel AFM Scanner Stage

“…Feedback control methods such as repetitive control (RC) for tracking of periodic references introduce large closed-loop bandwidths, which may not be acceptable in the presence of measurement noise. Moreover, the tradeoff between the tracking error and rejection of non-periodic disturbances in RC systems can cause problems when excessive cross coupling exist between the scanner axes [46], [47].…”

Analog Robust Repetitive Control for Nanopositioning Using Bucket Brigade Devices

“…Periodic reference trajectories occur in both imaging and manipulation applications of SPM equipment. Recently, repetitive control (RC) has been introduced for nanopositioning systems (Aridogan et al, 2009;Merry et al, 2011;Shan and Leang, 2012b). The RC scheme is based on the internal model principle (Francis and Wonham, 1976) and it is specifically tailored to track periodic reference trajectories.…”