Control of a Multimode Double-Pendulum Overhead Crane System Using Input Shaping Controllers

This paper investigates the impact of higher derivative input shaping for minimizing both oscillations, namely hook and payload of a multimode double-pendulum overhead crane (MDPOC) system. The MDPOC has greater nonlinearities and stronger internal couplings, especially when involving two oscillation frequencies with multimode dynamic effects. With a suitable system’s natural frequency and damping ratio of the hook and payload oscillations, multimode zero-vibration (ZV-ZV), multimode zero-vibration derivative (ZVD-ZVD) and multimode zero-vibration derivative-derivative (ZVDD-ZVDD) shapers are successfully designed. More interestingly, two scenarios under a fixed cable length and a payload hoisting are considered which are closer to the real practical crane.  Thus, an average travel length (ATL)-based shaper method is also considered to further verify the effectiveness and robustness of efficient hook and payload oscillation control under payload hoisting. All the multimode input shaping is simulated using the Matlab software. The simulation results of multimode ZVDD-ZVDD shaper successfully reduced in the overall hook and payload oscillations by 97.9% and 97.2%, respectively, compared to the unshaped system, whereas the multimode ATL-ZVDD shaper reduced hook and payload oscillations by 94.8% and 94.0%, respectively. In fact, the multimode ZVDD-ZVDD and multimode ATL-ZVDD shapers demonstrate the superiority in minimizing the hook and payload oscillations compared to the multimode ZV-ZV, multimode ZVD-ZVD, ATL-ZV and ATL-ZVD shapers. This significant reduction in oscillations enhances the precision and safety of real-world crane operations in industrial settings. It has been proven that considering the additional derivative of input shaping results in a higher level of hook and payload oscillations reduction.