Active disturbance rejection and Lyapunov redesign approaches for robust boundary control of plate vibration

In this paper, two approaches, namely active disturbance rejection control (ADRC) and Lyapunov redesign, are utilised to stabilise the vibration of a boundary-controlled flexible rectangular plate in the presence of exogenous disturbances. Based on ADRC, an estimation/cancellation strategy is applied where disturbance is estimated online by an extended state observer (ESO) and cancelled by injecting the output of ESO into the feedback loop. By the Lyapunov redesign, on the other hand, the control law intended for a nominal system is redesigned by adding a (discontinuous) control component that makes the system robust to large uncertainties. Both control algorithms are designed directly based on partial differential equation model of the plate so that spillover instabilities that are a result of model truncation are avoided. The established control schemes are able to stabilise the plate vibration by actuating and sensing only along the plate boundary while accounting for the dynamical effects of Gaussian curvature integral, in-plane membrane force and actuator mass. The stability of each control approach is proven using Lyapunov analysis. The efficacy of each proposed control is illustrated by simulation results.