The Optimal Control Problem for Output Material Flow on Conveyor Belt with Input Accumulating Bunker

The article is devoted to the synthesis of optimal control of conveyor belt with the accumulating input bunker. Much attention is given to the model of the conveyor belt with a constant speed of the belt. Simulation of the conveyor belt is carried out in the one-moment approximation using partial differential equations. The conveyor belt is represented as a distributed system. The used PDE-model of the conveyor belt allows to determine the state of the flow parameters for a given technological position as a function of time. We consider the optimal control problem for flow parameters of the conveyor belt. The problem consists in ensuring the minimum deviation of the output material flow from a given target amount. The control is carried out by the material flow amount, which comes from the accumulating bunker into the conveyor belt input. In the synthesis of optimal control, we take into account the limitations on the size of the accumulating bunker, as well as on both max and min amounts of control. We construct optimal control of the material flow amount coming from the accumulating bunker. Also, we determine the conditions to switch control modes, and estimate time period between the moments of the switching.

Keywords

conveyor; production line; subject of labour; PDE-model of production; parameters of the state of the production line; technological position; transition period; production control systems; optimal control; Pontryagin function; Lagrange function; differential constraints; accumulating bunker; distributed system.

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