High bandwidth multi-variable combined resonant and integral resonant controller for fast image scanning of atomic force microscope

This paper presents the design and implementation of a multi-variable combined resonant and integral resonant controller for the piezoelectric tube scanner (PTS) of an atomic force microscope (AFM) to damp the resonant mode of the scanner, reduce the cross coupling effect 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 two-input two-output system and the system is identified using measured open-loop data. The value of each parameter of the proposed controller is determined by minimizing H₂ norm of the difference between the desired and the actual closed-loop transfer function. The performance improvement achieved by the proposed controller is presented by comparing scanned images obtained by implementing the proposed controller and the built-in proportional-integral (PI) controller of the AFM.