An output feedback LPV control strategy of a nonlinear electrostatic microgripper through a singular implicit modeling

Abstract

The aim of the paper is the design and the analysis of a gain scheduled controller for an accurate and fast positioning with nanometer resolution of a nonlinear electrostatic microgripper. The controller is designed to achieve a positioning of the gripping arm from few hundred nanometers to several tens of micrometers with some performance criteria. This very large operating range is crucial for a range of microrobotics applications and has never been addressed in existing control techniques of microgrippers. The controller is designed considering noises that are relevant at the nanometer scale and nonlinearities that become significant at the micrometer scale. Therefore, a nonlinear model of the system is proposed and is reformulated into a polynomial LPV (Linear Parameter Varying) model. The most relevant source of noise to be considered for the controller synthesis is defined taking into account results from previous works. Considering the particular polynomial parametric dependence of the LPV model, a multivariable controller is designed using an affine LPV descriptor representation of the system and specific linear matrix inequalities. The efficiency of the controller and the relevance of the theoretical approach is demonstrated through experimental implementation results.