Boundary output tracking for an Euler–Bernoulli beam equation with unmatched perturbations from a known exosystem

Abstract

In this paper, we consider boundary output regulation for an Euler–Bernoulli beam equation which can describe typically the flexible arm of robots. The reference signal and disturbance are generated by a finite-dimensional exosystem. The measurements are angular and angular velocity of the right end where the control is imposed. However, the performance output is on the left end which is non-collocated with control, a difficult case in practice where the control takes time to perform its force from the right end to the left. The objective is to design an output feedback controller to regulate the displacement of the left end to track the reference signal. We first design a state feedback regulator to make the performance output track the reference signal exponentially. An observer is then constructed to recover the state, with which, an output feedback regulator is designed by replacing state feedback with its estimation. The closed-loop system is shown to admit a unique bounded solution and the tracking error converges to zero exponentially. Some numerical simulations are presented to illustrate the effectiveness of the proposed output feedback regulator.