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

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.