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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. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient proportional–integral–derivative (PID) control of a highly nonlinear double-pendulum overhead crane without the need for a payload motion feedback signal. Optimal parameters of the PID controllers are tuned by using an improved particle swarm optimization (PSO) algorithm based on vertical distance oscillations and potential energy of the crane. In contrast to a commonly used PSO algorithm based on a horizontal distance, the approach resulted in an efficient performance with a less complex controller. To test the effectiveness of the approach, extensive simulations are carried out under various crane operating conditions involving different payload masses and cable lengths. Simulation results show that the proposed controller is superior with a better trolley position response, and lower hook and payload oscillations as compared to the previously developed PSO-tuned PID controller. In addition, the controller provides a satisfactory performance without the need for a payload motion feedback signal. [ABSTRACT FROM AUTHOR]