The object of current research is a multi-section transport conveyor. The actual control problem of the flow parameters of a multi-section conveyor-type transport system with a given control quality criterion is solved. Algorithms for optimal control of the flow of material coming from the input accumulating bunkers into the collection section of the conveyor, ensuring the filling of the accumulating tank in the minimum time were synthesized. An admissible control of the material flow from the accumulating bunkers is found, which allow filling the accumulating tank, taking into account the given distribution of the material along the section of the collection conveyor at the initial and final moments of the filling time with minimal energy consumption. The synthesis of algorithms for optimal control of the material flow from accumulating bunkers became possible due to the determination of differential constraints in the optimal control problem based on an analytical distributed model of a transport conveyor section. The distinctive features of the results obtained are that the allowable controls contain restrictions on the maximum allowable load of material on the conveyor belt and take into account the initial and final distribution of material along the collection conveyor section. Also, a feature of the obtained results is the consideration of variable transport delay in the transport conveyor control model. The application area of the results is the mining industry. The developed models make it possible to synthesize algorithms for optimal control of the flow parameters of the transport system for a mining enterprise, taking into account the transport delay in the incoming of material at the output of the conveyor section. The condition for the practical use of the results obtained is the presence of measuring sensors in the sections of the transport conveyor that determine the belt speed and the amount of material in the accumulating bunkers.

longitudinal dynamic stresses and investigate the peculiarities of the propagation of dynamic stresses along the route of material transportation. Methodology. To calculate the value of static and dynamic stresses arising in the conveyor belt, the apparatus of mathematical physics was used. Findings. A wave equation is written that determines the propagation of longitudinal vibrations in a conveyor belt, the material of which corresponds to the Maxwell-element model. An expression is obtained for calculating the speed of propagation of elastic vibrations along the conveyor belt, the frequency of vibrations and their wavelength. The characteristic relaxation time of disturbances is determined. The method of successive approximation was used to solve the wave equation. The estimation of the characteristic time of acceleration of the conveyor belt, at which there is no destruction of the material of the conveyor belt, is given. Originality. PDE-models of conveyor-type transport systems are improved, which are used to design belt speed control systems under restrictions on speed control modes. It is shown that under the modes of acceleration or deceleration of the conveyor belt, the effects associated with the occurrence and propagation of dynamic stresses along the conveyor belt, due to the characteristics of the material corresponding to the Maxwell-element model, are insignificant. Practical value. The results obtained make it possible to determine the limitations on the modes of acceleration or deceleration of the conveyor belt, preventing its damage and increased wear. This opens up prospects for designing effective control systems for the parameters of a conveyor belt, unevenly loaded with material along the transport route.

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The features of the propagation of dynamic stresses in a conveyor belt, the material properties of which correspond to the Maxwell element model, are considered. Analytical expressions are presented for calculating the dynamic elastic modulus, the loss modulus, and the angle of mechanical loss depending on the frequency of longitudinal oscillations in the belt of an extended transport conveyor. To analyze the dynamic stress propagation process, dimensionless parameters are introduced that characterize the specific features of the viscoelastic process in a conveyor belt, the material properties of which correspond to the Maxwell element model. The transition to the dimensionless Maxwell element model is made and the analysis of the relationship between stress and deformation of a conveyor belt element for extremely large and small values of dimensionless parameters is made. The substantiation of the scope of the Maxwell element model is given. It is shown that at sufficiently high frequencies of longitudinal stress oscillations in a conveyor belt, at which the oscillation period is much less than the characteristic oscillation decay time, the relationship between stress and deformation of the conveyor belt element corresponds to Hooke's law. A qualitative analysis of the relaxation time was carried out for a conveyor belt material, the properties of which correspond to the Maxwell element model. The analysis of the propagation of dynamic stresses in the conveyor belt for the characteristic operating modes of the transport conveyor is carried out. The conveyor operating mode with a constant deformation rate of the belt element; the mode in which a constant load is suddenly applied to the belt element; the conveyor operating mode with an instantly applied load to the belt element were investigated. It was determined that in cases where the characteristic process time significantly exceeds the stress relaxation time in the conveyor belt or the longitudinal oscillation period is much less than the stress relaxation time in the conveyor belt, the Maxwell element model can be replaced with a sufficient degree of accuracy by the Hooke element model.