Microbeam dynamic shaping by closed-loop electrostatic actuation using modal control

A closed-loop control approach for the dynamic shaping of a microbeam by electrostatic actuation is described. Starting from a desired displacements reference vector of N small segments of the beam (representing the approximation of the continuous case), n controllers (n is the number of considered modes) output the stresses that must be distributed throughout the beam, on the N actuators. Because this reference may vary with time, the controllers are designed so that they accomplish good response dynamics, as well as performance and robustness specifications. The innovation in this method is that we control the dynamic coefficients associated to the modes of the microbeam and not directly the physical displacements in each small segment, which reduces the number of correctors from N to the number of n modes to control.