A robust control method for electrostatic microbeam dynamic shaping with capacitive detection

Abstract

A robust closed-loop control and observation methodology for a microbeam electrostatic dynamic shaping using N small separate electrodes is described. After decomposing the displacements vector on the n eigenmodes using the modal analysis, n controllers are designed to control the dynamic coefficients of each mode and deliver the stresses that must be distributed throughout the beam. In a previous work, we considered direct access to non noisy displacement measurements. In this paper, we investigate the capacitive measurement of the local displacements done by each small electrode, which gives a noisy readout. Robust control methodology applied on extended standard model allows the design of n observers associated to n controllers and guarantees a precise shape tracking, free from noise and robust against parameters incertitude.