Multivariable Control Designs for Piezoelectric tubes

Abstract

Most AFMs use piezoelectric tube nanopositioners for scanning. Fast actuation of piezoelectric tubes are restricted due to the presence of low mechanical resonant modes. These resonances, when excited, set off vibrations that cause loss of precision and repeatability of the scans. Thereby restricting the scanning frequencies to less than 1% of the first resonance frequency. Here, an innovative multivariable control design methodology for damping the resonant modes of the tube is presented. This methodology exploits the symmetry present in transfer-functions relating the input and output, and converts the multivariable control design problem into independent SISO designs. This methodology in conjunction with Integral Resonant control is used for damping the first resonant mode of the tube, and enables scans upto 10% of the first resonant mode. The proposed methodology can be applied to a large class of parallel kinematics nanopositioners used in scanning probe microscopes and probe-based data storage systems.