April 21, 2005
Flexible cable systems are widely used in many industrial applications, such as high-rise elevators, tethered satellite systems/submarines, cable suspended robots, and construction cranes. Under external disturbances, flexible cables tend to vibrate, thus degrading the performances of the overall system. Modeling and vibration control of such cable systems are the topic of this talk. The governing equations of motion for a cable system are developed using both Newtonís law and Hamiltonís principle. Calculus of variations is applied when using Hamiltonís principle. The theory of differential flatness and H∞ robust control theory are applied to modulate the residual vibration when the cable lengths are constant. The H∞ robust controller can compensate the bounded external disturbances. Subspace system identification theory is utilized to obtain an approximate state-space model from the experimental frequency response data for controller design. The minimax Linear Quadratic Gaussian (LQG) method is used to minimize the cost functional for multiplicative nonparametric bounded uncertainties. The controller design involves solutions of two simultaneous Riccati equations. The experimental results show that there are about 9 dB peak resonance reductions when implementing the proposed controller on a real time dSPACE CP1103 system. Modeling and control of cable systems with varying lengths is still an open question. In this work, we assume that the axial velocity of the cable system is unspecified, which has been usually assumed to be constant or prescribed in existing literature. The derived general motion equations complement the existing literature. Lyapunov-based controllers are proposed, which suppress the vibrations effectively, and assure the attainment of the slider goal, simultaneously. Closed-loop stability is guaranteed by the Lyapunov stability theory. An approximate numerical solution of the system is provided using a modified Galerkinís method. Simulation results have verified the effectiveness of the proposed Lyapunov controller.