Dymko E. Models and methods for optimal control of induction duplex process in conditions of uncertainty

The thesis is devoted to the solution of an actual scientific and practical problem - the development of optimal control methods in conditions of uncertainty. The possibility of building an adequate mathematical model of an induction duplex melting process as a control object under the conditions of impossibility of implementing an active experiment plan under production conditions is shown. Based on this, it is proposed to use the results of the parametric description by definition of the local-optimal values of the input variables based on the implementation of the ridge analysis procedure to describe the final state in the problem of finding the optimal by the final state control. It is shown how using a combined procedure of artificial orthogonalization according to a passive experiment with an arbitrary form of the experiment plan and central orthogonal planning to obtain such a parametric description. The problem of synthesizing optimal control of induction melting in IST1 / 0.8-M5 furnaces in terms of alternative strategies was solved and it was proved that when choosing a melting strategy in the “bog” phase trajectory will constantly change due to the correction of the initial state, which is caused by the change in melting rate with the selected control method. It is shown how the optimal in terms of speed control can be obtained using the Pontryagin maximum principle in terms of taking into account the uncertainty in the description of the initial state of the control object. An optimal temperature regulator was synthesized in an induction mixer based on a multi-alternative description of the final state, a characteristic feature of which is the use of optimal solutions of ridge analysis and parametric classification of the temperature regime. It is shown how such an approach can be applied to a block of logical conditions in the logical synthesis of a combined control system of an induction duplex process.