Active Boundary Control of Elastic Cables

Cables are lightweight structural elements used in a variety of engineering applications. This paper introduces an active boundary control approach that damps undesirable vibrations in a cable. Using Hamilton’s principle, the governing nonlinear partial differential equations for an elastic cable are derived, including the natural boundary conditions associated with boundary force control. Based on Lyapunov theory, passive and active vibration controllers are developed. A Galerkin approach generates the linearized, closed loop, modal dynamics equations for out-of-plane vibration. Simulations demonstrate the improved damping provided by the passive and active controllers.