Active Control of an Elastic Beam Based on State and Input Constraints

This paper focuses on developing an active controller for an elastic beam with tip payload subject to state and input constraints. The dynamics of the elastic beam is expressed by partial differential equations. A novel hyperbolic barrier Lyapunov function (HBLF) is proposed to ensure Lyapunov asymptotic stability of the closed-loop system and enable the constraint of system states. Then, a HBLF-based controller is developed to track desired position of angle and rapidly suppress vibrations of the beam. The controller is developed by using smooth hyperbolic functions, and the issue of input constraint is also handled simultaneously. It is proven that the input and state constraints are both guaranteed. The favorable performance is shown by simulations which validate the effectiveness of control scheme.