Parametric Time-Optimization of Two-Channel Control of Related Objects with Distributed Parameters - Rapoport, E. Ya; Ilina, N. A. (2022 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), 2022)
A formulation and constructive technology for solving parametrizable problems of two-channel time-optimal boundary control of two physically inhomogeneous objects with distributed parameters described by linear heat conduction equations under conditions of a given accuracy of uniform approximating the resultant spatial distribution of the controlled variable to the desired state are proposed. The two objects are considered under conditions of perfect thermal contact of interacting surfaces. The developed technology uses a special method for describing the studied temperature fields in a form containing uniformly converging series. The finite integral transformations method is used to search for the input-output characteristic of an object with distributed parameters with two control actions. The developed technique uses the parametrization procedure of the sought control actions and the subsequent reduction to the special form of the task of semi-infinite optimization, which is solved by the scheme of the alternance method. The alternance properties of the final temperature state at the end of the optimal process lead to a basic system of relations, which, in the presence of additional information about the shape of the temperature distribution curve, is reduced to a system of equations that can be solved with all unknowns and complicated by an additional restriction on the same duration of the control process for two control actions.