Command Shaping for Vibration Reduction in Nonlinear Cabled Systems

Abstract

Cables are an integral part of many engineering systems; thus, the control of cables and systems containing cables is an important problem to address. This thesis proposes to use command shaping techniques to reduce command-induced vibration in two cabled systems, a tower crane and an electrodynamic tethered satellite system in low Earth orbit. Systems containing cables often exhibit important nonlinear dynamics, which complicates the application of command shaping. As a first step to demonstrate the effectiveness of command shaping techniques for nonlinear cabled systems, nonlinear tower crane dynamics are investigated. A novel command generation technique for the slewing of tower cranes is presented, and experimental results demonstrate its increased effectiveness. Once improvement of tower crane dynamics has been demonstrated, space tether dynamics are considered. Electrodynamic tethers have the promise to become invaluable propulsive actuators for orbit boost and station keeping. Using electrodynamic tethers, it is possible to boost orbits without the use of propellant because electrical energy is used to produce a Lorentz force that creates orbit boost. Furthermore, electrodynamic tether deboost makes it possible to accelerate the deorbiting of spent rocket stages and other space debris to reduce clutter in the space environment. Unfortunately, the Lorentz force pushes transversely on the cable tether, thereby producing a significant amount of vibration and libration. This thesis proposes to use command shaping techniques to reduce the command-induced vibration from a boosting operation. Intelligent command generation will significantly reduce the amount of tether libration and string vibration. First, flexible tether dynamics in a constant, circular orbit are investigated. The work is then expanded to include the effects of orbit boosting. The robustness of the command generation techniques is established through numerical simulation.