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.

[1]  B. Bhikkaji,et al.  Integral Resonant Control of a Piezoelectric Tube Actuator for Fast Nanoscale Positioning , 2008, IEEE/ASME Transactions on Mechatronics.

[2]  I. Petersen,et al.  Robust H ∞ Control in Fast Atomic Force Microscopy , 2013 .

[3]  Santosh Devasia,et al.  Feedback-Linearized Inverse Feedforward for Creep, Hysteresis, and Vibration Compensation in AFM Piezoactuators , 2007, IEEE Transactions on Control Systems Technology.

[4]  S. O. Reza Moheimani,et al.  Tracking of Triangular References Using Signal Transformation for Control of a Novel AFM Scanner Stage , 2012, IEEE Transactions on Control Systems Technology.

[5]  Wook Hyun Kwon,et al.  Empirical frequency-domain optimal parameter estimate for black-box processes , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  Mohamed Soliman,et al.  Subspace identification with prior steady-state information , 2010, The 2010 International Conference on Computer Engineering & Systems.

[7]  Murti V. Salapaka,et al.  High bandwidth nano-positioner: A robust control approach , 2002 .

[8]  二瓶 亜三子,et al.  Scanning probe microscopes and scanning method , 2004 .

[9]  Bernard Friedland,et al.  Control System Design: An Introduction to State-Space Methods , 1987 .

[10]  S O Reza Moheimani,et al.  Making a commercial atomic force microscope more accurate and faster using positive position feedback control. , 2009, The Review of scientific instruments.

[11]  Chen Youping,et al.  A linear drive system for the dynamic focus module of SLS machines , 2007 .

[12]  Gerber,et al.  Atomic Force Microscope , 2020, Definitions.

[13]  Santosh Devasia,et al.  A Survey of Control Issues in Nanopositioning , 2007, IEEE Transactions on Control Systems Technology.

[14]  Hemanshu R. Pota,et al.  Resonant controllers for smart structures , 2002 .

[15]  Srinivasa M. Salapaka,et al.  Design methodologies for robust nano-positioning , 2005, IEEE Transactions on Control Systems Technology.

[16]  M Grossard,et al.  Modeling and Robust Control Strategy for a Control-Optimized Piezoelectric Microgripper , 2011, IEEE/ASME Transactions on Mechatronics.