The solution to reduce of oscillations for the hook and payload in two degrees of freedom- pendulum crane trolley model in the jib plane to increase crane’s production capacity and safety using passive control method

Abstract

When controlling a trolley in the jib plane at high speeds, it causes significant swingings of the payload and the hook with large amplitudes. This is detrimental to safety, the accuracy of load positioning, the effectiveness of crane movements, and overall crane’s productivity, especially in the case of intelligent cranes used for automated assembly tasks. This paper presents a study on a passive control method applied to the problem of reducing the oscillations of the hook and payload in a two-degree-of-freedom crane trolley model operating in the jib plane. In practice, the angular velocities of the payload and the hook always oscillate during most crane trolley movements. Such a practical issue necessitates a passive controller with significant advantages such as simplicity, ease of implementation, high reliability, rapid response to vibrations, stability, safety, and no requirement for external energy sources to quickly minimize the oscillations of the hook and payload. The paper begins with an overview and a discussion on the necessity of applying passive control methods to minimize oscillations of the hook and payload. It then presents some fundamental issues related to the passive control method. Subsequently, a passive controller is designed and applied to the two-degree-of-freedom pendulum model of the crane trolley in the plane of the jib. Fourthly, the stability of the passive control system is analyzed and demonstrated using Lyapunov’s stability theory. Fifthly, several numerical simulation results using Matlab are provided to support for designing of the passive controller. Sixthly, comments on the simulation results are made to support the controller design. Finally, a comparative evaluation is presented to assess the effectiveness of the passive control method in reducing oscillations compared to other control methods previously studied, followed by conclusions.