In this paper, we propose a method and a mathematical model for solving the problem of cargo transportation on a suspension rope by a bridge crane following a predetermined trajectory in the absence of uncontrollable pendulum sways. To this end, the principle of reduction of the second-order linearized differential equation, which describes sways in the ‘point of suspension – cargo’ system, is applied. As a result, a first-order differential equation is derived, in which the control action consists in the required acceleration of the cargo. The proposed method allows a rapid synthesis of an optimal trajectory of the suspension point for ensuring the required cargo movement trajectory in the horizontal direction without either complex mathematical calculations of the optimal control theory or the laborious algorithms of multidimensional or iterative optimization. This method can be used in the systems providing the automated control of bridge cranes with the function of restricting uncontrolled cargo sways, as well as in those having a new prospective function of cargo transportation maintenance along a predetermined trajectory.
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