Modeling and control of longitudinal vibration on flexible hoisting systems with time-varying length

To evaluate longitudinal vibration of flexible hoisting systems with time-varying length, the governing equations are developed employing the extended Hamilton's principle considering mutual influence of the rigid motion and deformation of flexible hoisting systems. The Galerkin's method is used to discretize the governing equations. In the mean time, A Lyapunov controller which can dissipate the vibratory energy is derived. The motions of elevator hoisting systems were illustrated to evaluate the proposed mathematical models and controller. The results of simulation show that the modeling methods can represent the longitudinal vibration of flexible hoisting systems. The proposed controller can effectively dissipate vibratory energies of the flexible hoisting systems.