Robust adaptive boundary control of a disk–beam–mass system under unknown distributed disturbance

This paper focuses on the boundary stabilization control of a rotating disk–beam–mass system (DBMS), comprised of a one-dimensional flexible beam perpendicularly affixed to a rotating rigid disk at its lower boundary and a payload, conceptualized as a tip mass at its opposite end. We posit that the boundary control, which includes an external torque acting on the disk and an external force acting on the tip mass, is subject to an undefined time-varying disturbance. Concurrently, the flexible beam experiences an undefined spatiotemporal-varying distributed disturbance. Firstly, we employ Hamilton’s principle to elaborate on the mathematical model that describes the motion of DBMS. Subsequently, an adaptive boundary control is designed to stabilize the beam’s transverse displacement and regulate the disk’s angular velocity to track a predetermined value asymptotically. Applying the theory of Lyapunov, we demonstrate that uniform and ultimate boundedness under distributed disturbance can be achieved. Finally, we conduct several numerical simulations to showcase the applicability and efficacy of our proposed adaptive boundary controller.