Journal of Sound and Vibration (1996) 198(1), 17–26 ACTIVE BOUNDARY CONTROL OF ELASTIC CABLES: THEORY AND EXPERIMENT C. F. B, C. D. R  B. D. N Center for Advanced Manufacturing, Department of Mechanical Engineering, Clemson University, Clemson 29634, U.S.A. (Received 12 September 1995, and in final form 5 April 1996) Cables are lightweight structural elements used in a variety of engineering applications. In this paper an active boundary control system is introduced that damps undesirable vibrations in a cable. Using Hamilton’s principle, the governing non-linear 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 and experiments demonstrate the improved damping provided by the active boundary controller.  1996 Academic Press Limited 1. INTRODUCTION Cables support structures, transport material, distribute power and tow vehicles. Due to their light weight and limited support, cables tend to vibrate, degrading their performance. Disturbances from boundary motion or fluid interaction intensify this vibration. Researcher have studied the modelling and vibration analysis of cable structures for many years. Irvine [1] summarized many of the contributions to this field. More recently, Perkins and Mote [2] studied the vibration of travelling elastic cables. Perkins [3] also investigated the non-linear response of elastic cables. While much of the results of the previous vibration research can be applied to passive control of cable structures, there has been relatively little research into active vibration control. Active modal control and distributed control have been applied to many vibratory systems, however, including space structures [4], flexible robot arms [5] and axially moving material systems [6]. Fujino et al . [7] theoretically and experimentally studied the active modal control of a cable. Rahn and Joshi [8] developed a distributed model controller for a flexible cable gantry crane. In this paper the non-linear equations of motion of a cable with boundary control forces are developed. Based on Lyapunov theory for the distributed model [9], two controllers are developed that stabilize all modes of the cable structure. The first controller provides passive boundary damping. The second controller uses active boundary position and angle feedback to increase vibration damping. Using a linearized model and a single out-of-plane control force, it is shown that these controllers provide an asymptotically decaying response of a modal model of the cable. Experimental results confirm the numerical simulation predictions, and demonstrate the effectiveness of the active boundary controller. 17 0022–460X/96/460017 + 10 $25.00/0  1996 Academic Press Limited