NUMERICAL METHODS OF SOLUTION OF PROBLEMS ABOUT TIME OPTIMAL TRANSFERENCE OF LOAD ON THE ROPE WITH VARYING LENGTH

Abstract

Introduction. Small hoisting machines, such as self-propelled hoists or lightweight overhead cranes, transporting loads on a flexible suspension, are often included in automatic systems that perform various technological processes. Significantly complicate the control of the crane and lead to the lengthening of its working cycle arising from the movement of the truck oscillations of the load on a flexible suspension. The calculated controls should provide damping of such vibrations when the cart approaches the end point of the path. Goal. The paper investigates methods for determining the optimal time or close to it in terms of the effectiveness of controls for light bridge cranes when they carry cargo on a suspension of varying lengths. Results. In the course of the study, a search method for optimal control of light cranes and a calculation program based on it were proposed, which allow one to determine control parameters that provide the fastest possible travel of a crane truck with a load on a suspension whose length varies according to a given law. It was found that the trolley control optimal in speed is a piecewise constant function of time. The number and duration of intervals of constancy of the control parameter depend on the relationship between the length of the suspension and the rate of change. With a constant suspension length, the number of optimal control intervals increases with increasing duration of the trolley. For modern cranes, a relationship between the suspension length and its rate of change is characteristic, in which the optimal control may consist of a sufficiently large number of intervals, which may complicate its implementation. The paper substantiates that it is advisable to search for a quasi-optimal control consisting of only three intervals. In this case, you can use significantly less complex and timeconsuming methods and programs for calculating controls. The performed calculations show that the quasi-optimal control consisting of three intervals is practically not inferior to strictly optimal in efficiency. It is proved that the same methods and programs can be used to calculate quasi-optimal controls, consisting of five intervals, when the oscillations of the load are damped at the stages of acceleration and deceleration. Conclusions. In this work, we propose a method for calculating the optimal time control and some types of control of automatic lightweight bridge cranes that are close to it in efficiency and provide damping of the load vibrations during its transportation on a flexible suspension of variable length. The considered types of control have a simple structure and can be implemented with modern automation equipment.