A waveform command shaping control of a double pendulum with nonzero initial conditions

Abstract

In most material handling industries, input‐ and command‐shaping techniques are extensively used to transfer objects safely. In these techniques, most of the work assumes a single‐degree‐of‐freedom system with zero initial conditions, and some of these cases are not practical. In crane systems, a crane jib cannot be positioned exactly on top of the payload at the start of transfer motion, which forces the system to start with initial angles. Furthermore, when the hook is large and/or far from the payload, the system cannot be considered a single‐degree‐of‐freedom system. Not accounting for such conditions can create unwanted oscillations at the end of the motion. In this work, a closed‐form command shaping control of a double pendulum is suggested to eliminate the residual oscillations while considering nonzero initial angles. The equation of motion is derived and then solved to find the shaper constants analytically. This shaper has a selectable maneuvering time and ensures maximum cruising velocity. Several examples are implemented numerically and experimentally to evaluate the shaper's performance. Despite the nonzero initial conditions, the results showed that the shaper can effectively eliminate all induced vibrations at the end of the maneuver.