A Negative Imaginary Theory-based Controller Synthesis for Vibration Control of a Piezoelectric Tube Scanner

Abstract In this paper, a data-driven controller is synthesised for systems with negative imaginary (NI) properties such as the piezoelectric tube scanner (PTS) of an atomic force microscopy (AFM). The scanning speed of an AFM is limited by the dynamic behaviours of its scanning unit. The controller aims to damp vibrations, increase the closed-loop bandwidth and track reference signals with high accuracy. The measured frequency response of the PTS is used to calculate the controller frequency response at each frequency by minimising a cost function. The data-driven control optimisation problem is constrained by NI properties to guarantee that the controller is stable and identifiable. The designed controller is implemented on the AFM using a dSPACE ds1103 real-time prototyping system. Experimental results show that the controller is able to significantly damp the resonances in the scanner’s lateral axes, provide a high-bandwidth closed-loop system and allow reference signal tracking.

[1]  D. Croft,et al.  Creep, Hysteresis, and Vibration Compensation for Piezoactuators: Atomic Force Microscopy Application , 2001 .

[2]  Ian R. Petersen,et al.  Creep, Hysteresis, and Cross-Coupling Reduction in the High-Precision Positioning of the Piezoelectric Scanner Stage of an Atomic Force Microscope , 2013, IEEE Transactions on Nanotechnology.

[3]  Ian R. Petersen,et al.  Stability Robustness of a Feedback Interconnection of Systems With Negative Imaginary Frequency Response , 2008, IEEE Transactions on Automatic Control.

[4]  Xin Zhang,et al.  Data-Driven Robust Approximate Optimal Tracking Control for Unknown General Nonlinear Systems Using Adaptive Dynamic Programming Method , 2011, IEEE Transactions on Neural Networks.

[5]  H. R. Pota,et al.  High-speed spiral imaging technique for an atomic force microscope using a linear quadratic Gaussian controller. , 2014, The Review of scientific instruments.

[6]  Ian R. Petersen,et al.  Tracking of Triangular Reference Signals Using LQG Controllers for Lateral Positioning of an AFM Scanner Stage , 2014, IEEE/ASME Transactions on Mechatronics.

[7]  Alexander Lanzon,et al.  Feedback Control of Negative-Imaginary Systems , 2010, IEEE Control Systems.

[8]  Ian R. Petersen,et al.  Damping Controller Design for Nanopositioners: A Mixed Passivity, Negative-Imaginary, and Small-Gain Approach , 2015, IEEE/ASME Transactions on Mechatronics.

[9]  I. Petersen,et al.  Phase-locked loop-based proportional integral control for spiral scanning in an atomic force microscope , 2014 .