LQG controller with sinusoidal reference signal modeling for spiral scanning of atomic force microscope

In this paper, we present a spiral scanning method using an atomic force microscope (AFM). Spiral motion is generated by applying slowly varying amplitude sine wave in the X-axis and cosine wave in the Y-axis of the piezoelectric tube (PZT) scanner of the AFM. An LQG controller also designed for damping the resonant mode of a PZT scanner for the lateral positioning of the AFM scanner stage. In this control design, an internal model of the reference sinusoidal signal is introduced with the plant model and an integrator with the system error is introduced. A vibration compensator is also designed and included in feedback loop with the plant to suppress the vibration of the PZT at the resonant frequency. Experimental results demonstrate the effectiveness of the proposed scheme.