LQG controller with a vibration compensator for the lateral positioning of an AFM scanner

This paper presents the design of an LQG controller for the lateral positioning of a piezoelectric tube actuator (PZT) used in an atomic force microscope (AFM). In the proposed control scheme, an internal model of the reference signal is included in the plant model and an integrator with the system error is introduced. As a result, it reduces the steady-state tracking error. A vibration compensator is also designed and included in a feed-back loop with the plant to suppress the vibration of the PZT at the resonance frequency. Consequently, the proposed controller achieves higher closed-loop bandwidth and significant damping of the resonant mode of the PZT, which enables the tracking of a reference triangular signal. Experimental results show the significant improvement of the scanned images as compared to the in-built PI controller of the AFM.