In this paper, the effects of the mass moment of inertia of the payload on the anti-swing control of an overhead crane will be investigated with realistic computer simulations. In this simulation study, an overhead crane will be controlled by using one of the conventional anti-swing control schemes that do not take into account the rotational swing dynamics of the payload with respect to its mass center.First, the dynamic equations of motion of an overhead crane are derived with rope length kept constant, based on Lagrange’s equations, in which both the mass and the mass moment inertia of the payload are considered in the Lagranian. As a result, the crane dynamics has three degrees of freedom: the trolley position, the swing angle of the rope, and the rotational swing angle of the payload relative to the rope swing angle, but the crane dynamics has only one control input: the force input to the trolley. Thus, the resulting crane dynamics is highly underactuated. The new dynamic model is quite compared to the conventional dynamic models based on a point mass assumption of the payload. The gravity terms behave like nonlinear softening springs for both the payload swing relative to the trolley and the rotational payload swing with respect to its mass center, but the damping is almost zero for these swing motions.The motion of the overhead crane will be controlled by using an existing anti-swing trajectory generator and an anti-swing control algorithm that consider only the rope swing motion relative to the trolley, thus excluding the effects of the rotational swing dynamics of the payload with respect to its mass center. In this case, the unmodelled rotational swing dynamics of the payload can be considered as dynamic disturbances to the conventional anti-swing control algorithm. The effects of the unmodelled rotational swing dynamics on the performances of the conventional anti-swing control algorithm will be analyzed with different values of the mass moment of inertia of the payload, via realistic simulation studies.In this simulation study, a delay of one-sampling period will be included in the feedback loop as in practical control applications in industry. The trapezoidal rule (via the bilinear Z transform) will be used for the integrations included in the anti-swing trajectory generation and control scheme. For high simulation accuracy, the dynamic equations of motion of the crane will be solved by using the fourth-order Runge-Kutta formula with an adaptive step size.

A Study on the Effects of Unmodelled Rotational Load Swing Dynamics on the Anti-Swing Control of an Overhead Crane

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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