Quasi-Repetitive Control for Fast and Accurate Atomic Force Microscopy

Repetitive controllers use delayed feedback for periodic operations to provide a feedforward-like control action capable of high bandwidth operation. However, the signal to be tracked/rejected must be perfectly periodic, with known time-period, to obtain asymptotic convergence. Any deviation from periodicity can severely degrade the tracking performance of the controller. This paper explores the idea of employing a variation of repetitive controller to expand the domain of signals that can be tracked with the repetitive framework. The signals intended to be tracked belong to a class of quasiperiodic signals that can be represented as an algebraic sum of periodic and polynomial signals. Many of the commonly occurring physiologic signals, speech, and vibration signals belong to this signal class. Moreover, periodic signals that drift can also be modeled as this type of quasiperiodic signals. The derived quasi-repetitive controller guarantees asymptotic convergence with a plug-in architecture that can be added to an existing feedback design. One practical application of this controller occurs in atomic force microscopy (AFM), where imaging a sloped or non-flat sample surface induces quasiperiodic disturbances in the control loop. Experimental results demonstrate accurate and high speed imaging can be performed using the prescribed controller.