Tracking of Triangular Reference Signals Using LQG Controllers for Lateral Positioning of an AFM Scanner Stage

• Published in: IEEE/ASME transactions on mechatronics 2014-08, Vol.19 (4), p.1105-1114
• Main Authors: Habibullah, H., Pota, H. R., Petersen, Ian R., Rana, M. S.
• Format: Article
• Language: English
• Subjects: Atomic force microscope (AFM); Atomic force microscopy; Compensators; Controllers; Creep; Design engineering; Electrodes; Electron tubes; Frequency control; Frequency measurement; linear quadratic Gaussian controller; Mathematical model; Mechatronics; Microscopes; Optimization; piezoelectric tube actuator (PTA); Reference signals; Simulation; system identification; Vibration; vibration compensator; Vibrations
• ISSN: 1083-4435; 1941-014X
• DOI: 10.1109/TMECH.2013.2270560

This paper presents the design of an internal reference model-based optimal linear quadratic Gaussian (LQG) controller for the lateral positioning of a piezoelectric tube actuator (PTA) used in an atomic force microscope (AFM). In this control design, internal modeling of the reference signal and system error are considered. As a result, the steady-state tracking error is minimized. In addition to the LQG controller, a vibration compensator is incorporated with the plant to suppress the vibration of the PTA at the resonance frequency. It achieves a high closed-loop bandwidth and significant damping of the resonant mode of the PTA, which enables a reference triangular signal to be tracked. Comparison of performance of the optimal LQG controller augmented with a vibration compensator and a PI controller demonstrates that the proposed controller shows significant improvements over the existing AFM PI controller.