Synthesis of the Law of Optimal Control of one Class of Objects with Parameters Variable in Time and Space

Abstract

The law of optimal control of one class of objects with parameters, variable in time and space, to which the crane electric drive system belongs, fragments in this electric drive system and change of characteristics of process of movement of cargoes in time caused by changes of the resulted moment of inertia of the electric drive system. the moment of loading during the movement of the load, and the influence of longitudinal oscillations that occur in the cable on which the load is suspended. As an optimization criterion, the functional in the form of an integral of the square of the deviations of the real angular velocity of the drive motor of the crane from its ideal trajectory is used. In synthesizing the law of optimal control, we used the mathematical model of load-moving processes of a crane created by us and published in our previous works, listed in the literature, the structure of which is constructed using as a normal differential equation with time-varying parameters. electric motor with the load moment and the reduced moment of inertia of the electric drive system and the differential equation in partial derivatives, which describes the process of longitudinal oscillations in the cable due to the mass of the load and the mass of the cable between the drum and the point of suspension. It is shown that the implementation of the synthesized law of optimal control of the electric crane drive achieves such characteristics of the cargo movement process that prevent the destruction of both cargoes and areas where these cargoes are installed, because the cargo movement process is carried out without their shock contacts due to longitudinal to which the load is suspended. An algorithm for the practical implementation of the synthesized law of optimal control of the crane electric drive system as a dynamic object with parameters variable in time and space is proposed.