A Green's Function-Based Design for Deformation Control of a Microbeam With In-Domain Actuation

Abstract

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 the test function that enables the solvability of a map between the original nonhomogeneous partial differential equation and a target system in standard boundary control form. Then a regularized Green's function is employed in motion planning, leading to a computationally tractable 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.