Dynamic Compensation of an Euler-Bernoulli beam with disturbances

This paper addresses the stabilization problem of an ODE system actuated through an Euler-Bernoulli beam dynamic subject to unknown sinusoidal disturbances. The ODE state is driven by one end of the beam and the controls act on the other end of the beam. We design an infinite-dimensional observer to estimate the beam state and the disturbance. An infinite-dimensional dynamic compensator is proposed to stabilize the ODE-Beam cascade system. The well-posedness and stability of the closed-loop system are proved by employing the semigroup theory. The numerical simulations are presented to illustrate the validity of the proposed controller.

I. Introduction

Many control systems with infinite dimensional actuator dynamics can be simulated as cascaded partial differential equation (PDE) and ordinary differential equation (ODE) systems. Due to the interaction and transmission between subsystems, the corresponding controller design and stability analysis of closed-loop systems will become complex. This stimulated many researchers, whose objective is to understand the mechanisms of instabilities and find ways to counteract them [1]–[3].