Exponential Stabilization of a Rotating Body-Beam System With Boundary Output Constraint Under Unknown Time-Varying Disturbance

In this brief, we study the boundary stabilization problem of a rotating body-beam system (RBBS). The system consists of a flexible Euler-Bernoulli beam connected at its upper end to a payload and at its lower boundary to a rigid disk. The control action of the system is composed of an external force acting on the payload and a torque exerted on the disk. Furthermore, the unknown disturbances affecting the motion of both the payload and the disk are considered. We design an integral barrier Lyapunov function (IBLF)-based boundary controller for such an RBBS to stabilize the movement of the flexible beam while regulating the system’s angular velocity to track a predefined desired value exponentially. By applying Lyapunov’s second method, we prove that our designed controller achieves exponential stabilization of the infinite-dimensional flexible beam’s vibration, exponential convergence of the angular velocity towards the desired value, and satisfies a specific constraint condition on the boundary displacement output.