Creep, hysteresis, and cross-coupling reduction in the high-precision positioning of the piezoelectric scanner stage of an atomic force microscope

This paper presents the high-precision lateral positioning of a piezoelectric tube scanner (PTS) used in an atomic force microscope (AFM). The operation of the PTS is affected by various nonlinearities depending upon its operating conditions. An internal reference model-based optimal linear quadratic Gaussian (LQG) controller with a vibration compensator is designed and implemented on the AFM to reduce creep, hysteresis, induced vibration, and cross coupling. This proposed controller has integral action on the error state which makes it possible to track the reference signal and the vibration compensator achieves significant damping of the resonant modes of the PTS in the X- and Y-axes. It also compensates the cross coupling between the X-Y axes dynamics of the AFM system, reducing the artifacts instigated by the system dynamic behavior at high scan rates. The closed-loop frequency responses for both the axes have a high bandwidth. The experimental results are presented which demonstrate the efficacy of the proposed method.