Multi-variable double resonant controller for fast image scanning of atomic force microscope

This paper presents the design and implementation of a multi-variable double resonant controller with a multivariable integral controller on the piezoelectric tube scanner (PTS) of an atomic force microscope (AFM) to damp the resonant mode of the scanner, reduce the cross coupling between the axes of the scanner, increase the bandwidth of the overall closed-loop system, and improve the high speed imaging performance of the AFM. The lateral and longitudinal positioning system of the PTS is treated as a multi-input multi-output system and the system is identified by using the measured open-loop data. The controller parameters are obtained by minimizing the H2 norm of the difference between the desired and the actual closed-loop transfer function and the performance improvement achieved by the proposed controller is shown by comparing the scanned images obtained by implementing the proposed controller and the built-in proportional-integral (PI) controller of the AFM.