MODELING MANAGEMENT OF THE TECHNOLOGICAL PROCESS

Abstract

Approaches to multioperational technological process modeling are considered, taking into account the mutual influence of
parameters of products and technological operations. State vector of the products during the passage of
technological operations is determined by the set of relevant parameters, the quantitative and qualitative meaning of which may vary from operation to operation. Vector of the state is being
"stabilized" by introducing "fictitious" parameters. The concepts of a vector and matrices of the
relevance of the technological operation are introduced as well as the concept of projection of state
vectors on them. Vector and matrix of technological relevance of the operation assigns to it a subspace
in the state space. Ensuring injectivity of mapping of a set of technological operations to the set of
actuality vectors can be introduced by introducing additional dummy parameters. Then the set of
relevance vectors can be considered as a subset of the scope of some Boolean function that will match
the given technological process. The technological process is considered as the movement of the state
vector from the initial to the final region of the state space along a trajectory that lies in the region of
the transition. A technological operation is characterized by a set of control parameters that determine
the processing modes. The control capabilities of the operation are characterized by the intervals of
variation of the control parameters. The connection between the state vectors at the input and output of
operations is assumed to be known, for example, in the form of regression equations. The own and
external negative influences of the technological operation on the output parameters of the product are
distinguished. The operation's own influence is a critical change in the state vector, due to a change in
the control action, under the condition of nominal input parameters. The external influence of the
technological operation is that, provided that the control vector is in the nominal region, the output
parameters go beyond the nominal values due to the same violation on the part of the input parameters.
The matrix of the external influence of the operation is introduced. Intervals of values of input and
output parameters are considered. Exit of the state vector from the nominal transition area on some of
the stages is compensated by changes in the parameters of the control vector, which is modeled by
minimizing the elements of the matrix of external influence in order to get its last row close to zero.