Analytical methods for designing technological trajectories of the object of labour in a phase space of states

Purpose. The development of analytical methods for designing technological motion trajectories of objects of labour in the state space with the purpose of construction of closed PDE-models, used to describe the manufacturing system. Methodology. For derivation of an equation of the labour object movement in the phase space of states, there has been applied a mathematical tool and the variational calculation methods of analytical mechanics. Findings. An equation of labour object movement in the state of space has been derived and motion integrals, related to the uniformity of time and state space have been considered. Originality. PDE-models of manufacturing systems, used for the engineering of the high performance manufacturing control systems have been improved. The offered model of technological resources transfer to the object of labour is based not on the traditional phenomenological description of the static production phenomena, but on conservation laws, which characterize the transfer process of technological resources to the object of labour and space-time structure of the manufacturing process. It allowed deriving the equation of the objects of labour movement along the manufacturing route, followed by the construction of non-steady-state equations of the PDE models on their ground for the description of the parameters status of the manufacturing process. While deriving the equations of the technological path of movement of the object of labour there were taken into consideration differential constraints, being applied by the manufacturing system to the transfer process of technological resources of the objects of labour, resulting from their interaction with production equipment and against each other in the course of transfer from one manufacturing operation to another. Practical value. Methods for driving the equation of technological path of the object of labour allow developing high-quality models of the transfer processes of the manufacturing system, which are the basis for the high-quality enterprise management system engineering with a straight flow method of industrial organization.