Dynamic control of an Euler–Bernoulli equation with time-delay and disturbance in the boundary control

ABSTRACT

The boundary control problem of a cantilever Euler– Bernoulli is considered in this paper. If the control at the right end of the beam is of the form w _xxx (1, t) = u(t − τ) + r(t), where τ > 0 is the input time-delay and r(t) is an unknown external disturbance, a dynamic feedback control strategy based on the methods of partial state predictor and active disturbance rejection control is used to stabilise the system. Under some assumptions on r(t), it is proven that the state of the system exponentially converges to and stays in the compact set $\Omega =\left\{{(w,w_t)}^{\top }\right|\Vert {(w,w_t)}^{\top }{\Vert }_{\mathcal{H}}\le \epsilon \}$. The radius ϵ is determined by the time-delay τ and the properties of r(t). The simulations are provided to compare the influence of τ and r(t) on the radius ϵ.

KEYWORDS:

• Time-delay
• disturbance
• ADRC
• dynamic feedback control

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Science Natural Foundation in China (NSFC) [grant number 61503275], [grant number 61503276], [grant number 61174080]