A LYAPUNOV CONTROLLER FOR A VARYING LENGTH FLEXIBLE CABLE SYSTEMS TO SUPPRESS TRANSVERSE VIBRATION

摘要

Modeling and controller design for a flexible cable transporter system, with arbitrarily varying cable length is presented using Hamilton's principle and Lyapunov theory. The axial velocity of the system is assumed to be arbitrary in the model. This is different from existing literature where the axial velocity is assumed either constant or is prescribed. The governing equations are coupled non-linear partial differential equations (PDEs) and ordinary differential equations (ODEs), and boundary conditions. The interactions between the cables and the slider, pulleys, and motors are included in the model. Numerical solution of the governing equations is obtained using Galerkin's method. Based on the Lyapunov stability theory, we propose boundary controllers and the control law for an actuator within the domain to suppress the transverse vibration of the cables, while achieving the slider goal. The proposed controllers dissipate the vibratory energy and guarantee asymptotic stability of the closed-loop system. Simulation results demonstrate the effectiveness of the proposed controllers.