Boundary control of a circular curved beam using active disturbance rejection control

ABSTRACT

In this paper, boundary stabilisation of vibration of a circular curved beam in the presence of exogenous disturbances using active disturbance rejection control is addressed. Based on the Euler–Bernoulli beam theory, the vibration of the inextensible curved beam including a tip mass is governed by a sixth-order partial differential equation (PDE) with dynamic boundary conditions. Based on the considered PDE, linear boundary control is introduced that exponentially stabilises the beam without disturbance. Furthermore, to control the beam under exogenous disturbances, the established linear control is enhanced by adding the estimates of disturbances. This is achieved by first designing an extended state observer that estimates the external disturbances using the beam vibration at the controlled end. The stability of the closed-loop system in the sense of Lyapunov is analysed based on the PDE model. Using the Faedo–Galerkin method combined with the compactness argument, it is shown the closed-loop system is well-posed. The efficacy of the suggested method is illustrated using simulation results.

KEYWORDS:

• Curved beam
• vibration
• boundary control
• ADRC
• ESO

Disclosure statement

No potential conflict of interest was reported by the author.