Deformation control of a 1-dimensional microbeam with in-domain actuation

This paper addresses the problem of asymptotic tracking control of a deformable microbeam described by an Euler-Bernoulli model with in-domain pointwise actuation. The motivation behind the consideration of such a system comes mainly from deformation control of micro-mirrors, in which the structure is steered to desired shapes by micro-actuators beneath it. The proposed solution for tackling this problem consists in first mapping the nonhomogeneous partial differential equation to a standard boundary control form. Then, a combination of the methods of energy multiplier and motion planning is used so that the closed-loop system is stabilized around reference trajectories. The simulation results demonstrate the viability and applicability of the proposed approach through a representative microbeam with in-domain actuation.