Vibration and Position Control of Overhead Crane With Three-Dimensional Variable Length Cable Subject to Input Amplitude and Rate Constraints

In this paper, the modeling and control problem of an overhead crane equipped with a three-dimensional (3-D) variable length flexible cable is discussed. In order to achieve high control performance, a partial differential equation (PDE) model is deduced with exactly preserving high frequency modes of the original system. For the sake of dealing with the effect of input amplitude and rate constraints, a boundary control scheme is carried out to drive the payload to a desired position with the 3-D vibration reduction of the variable length cable by applying the backstepping technology. The exponential stability of the closed-loop system is demonstrated based on the Lyapunov's direct method. The simulation results verify the effectiveness of the proposed control strategy.