Stability analysis and control of overhead crane with time-dependent flexible cable

A mathematical model of an overhead crane system with load hoisting and a flexible cable is presented. The model consists of a hyperbolic partial differential equation describing the dynamics of the moving flexible cable and ordinary differential equations describing the trolley and payload dynamics. Lyapunov direct method is used to design a model-based boundary control law that achieves trolley and payload desired positions and ensures vibration reduction of the flexible cable. The proposed control law is based on measurable variables for the trolley and the cable. The stability of the closed loop system under this boundary control scheme is proved through the use of inequality and metric analysis