Analog Robust Repetitive Control for Nanopositioning Using Bucket Brigade Devices

Abstract

In many applications of nanopositioning, such as scanning probe microscopy, tracking fast periodic reference trajectories with high accuracy is highly desirable. Repetitive control is a simple and effective control scheme to obtain good tracking of such reference trajectories. In order to implement repetitive control, a method for introducing time-delay is necessary. This can easily be implemented using a memory buffer with digital signal processing equipment. To achieve fast, high accuracy, and low noise performance, fast microcontrollers or field-programmable gate array hardware with fast high-resolution analog-to-digital and digital-to-analog converters are needed. As an inexpensive alternative to digital signal processing, the use of an analog bucket brigade device to implement the time-delay is investigated in this paper. Bucket brigade devices use switching to carry the input voltage over an array of capacitors, achieving a specified time-delay. Low-noise bucket brigade devices can achieve a signal-to-noise ratio around 80 dB, comparable to the actual performance when using 16-bit analog-to-digital converters. In this paper, the proposed control scheme utilizes a modified integral control law in conjunction with the repetitive control law. The overall control scheme ensures robustness towards plant uncertainty. Experimental results demonstrate the effectiveness of the overall control scheme and the analog implementation.