A hybrid command-shaper for double-pendulum overhead cranes

A crane is generally modeled as a simple pendulum with a point mass attached to the end of a massless rigid link. Numerous control systems have been developed to reduce payload oscillations in order to improve safety and positioning accuracy of crane operations. However, large-size payloads may transform the crane model from a simple-pendulum system to a double-pendulum system. Control systems that consider only one mode of oscillations of a double pendulum may excite large oscillations in the other mode. In multi-degree-of-freedom systems, command-shaping controllers designed for the first mode may eliminate oscillations of higher modes provided that their frequencies are odd integer multiples of the first mode frequency. In this work, a hybrid command-shaper is designed to generate acceleration commands to suppress travel and residual oscillations of a double-pendulum overhead crane. The shaper consists of a primary double-step command-shaper complemented by a virtual feedback system. The primary command-shaper is designed to eliminate oscillations in a slightly modified version of the crane model with frequencies satisfying the odd integer multiple criterion. The virtual feedback loop is then used to modify the commands of the primary shaper to accommodate the difference between the modified and the original models of the crane. It is shown that the suggested hybrid command-shaper is capable of minimizing oscillations of both modes of a scaled experimental double-pendulum model of an overhead crane. Results show that the hybrid command-shaper produces a reduction of 95% in residual oscillations in both modes of the double pendulum over the time-optimal rigid-body commands.