Optimal control of thermal exposure source in the processes of vapor phase deposition

We consider a mathematical model that describes the process of heating a silica tube by a movable heat source. The model is represented in the form of a one-dimensional heat conduction equation. Based on this model, we solve the problem of optimal stabilizing control with distributed control and distributed observation for the linearized problem. The value of the gas mixture flow rate, which determines the power of the heat source, was selected as a control influence. The aim of the control was to minimize possible temperature deviations from the programmed regimes of the silica pipes alloying. We obtained necessary optimality conditions in the form of an optimization system consisting of two partial differential equations. A law for finding the optimal control function, which explicitly depends on the solution of the mentioned system of equations, was obtained as well. Ultimately, we carried out the numerical solution of the optimization system and obtained quantitative results for the control function. We also calculated and analyzed the temperature distributions in various control modes.