LMI-based boundary and distributed control design for a flexible string subject to disturbance

摘要

In this paper, boundary and distributed controllers are proposed to reduce the vibration of a flexible string with external disturbance. To accurately represent the flexible string's behaviour, partial differential equations are introduced for the flexible string modelling. Boundary and distributed disturbance observers, which are proved exponentially stable, are designed to compensate unknown disturbance. Based on the proposed disturbance observers, the boundary and distributed controllers are developed by linear matrix inequality and the asymptotic stability of the system with controllers is demonstrated by Lyapunov's direct method. Extensive numerical simulations are presented to validate the good performance of the proposed control laws.