Flatness-based Deformation Control of an Euler-Bernoulli Beam with In-domain Actuation

TL;DR

This paper introduces a flatness-based control method for deforming an Euler-Bernoulli beam with in-domain actuation, combining feedback control and motion planning to achieve stabilization.

Contribution

It presents a novel approach linking PDE system modeling to flatness-based control for in-domain actuated beams, with stability analysis and numerical validation.

Findings

The control scheme stabilizes the beam around reference trajectories.

Numerical simulations demonstrate effective deformation control.

The method ensures well-posedness and stability of the controlled system.

Abstract

This paper addresses the problem of deformation control of an Euler-Bernoulli beam with in-domain actuation. The proposed control scheme consists in first relating the system model described by an inhomogeneous partial differential equation to a target system under a standard boundary control form. Then, a combination of closed-loop feedback control and flatness-based motion planning is used for stabilizing the closed-loop system around reference trajectories. The validity of the proposed method is assessed through well-posedness and stability analysis of the considered systems. The performance of the developed control scheme is demonstrated through numerical simulations of a representative micro-beam.