A Green´s function-based design for deformation control of a microbeam with in-domain actuation

This paper presents a Green´s function-based design for deformation control of a microbeam described by an Euler-Bernoulli equation with in-domain pointwise actuation. The Green´s function is first used in control design to construct a test function that guarantees the solvability of a map between the original nonhomogeneous partial differential equation and a target system in a standard boundary control form. Then the regularized Green´s function is employed in motion planning, leading to a computationally traceable implementation of the control scheme combined by a single feedback stabilizing loop and feedforward controls. The viability and the applicability of the proposed approach are demonstrated through numerical simulations of a representative microbeam.