Damping Controller Design for Nanopositioners: A Mixed Passivity, Negative-Imaginary, and Small-Gain Approach

A design of a damping controller to damp the first resonant mode of a piezoelectric tube scanner (PTS) used in most commercial atomic force microscopes (AFMs) is proposed in this study. The design of the controller is carried out by proposing a novel analytical framework. The analytical framework examines the finite-gain stability for a positive feedback interconnection between two stable linear time-invariant systems, where one system has mixed passivity, negative-imaginary, and small-gain properties and the other system has mixed negative-imaginary, negative-passivity, and small-gain properties. Experimental results are presented to show the effectiveness of the proposed analytical framework to design the proposed controller.