Synthesis of Control of the Movement of Measurement Points of the State and Power of Heat Sources at the Ends of the Rod

Abstract

Using the example of controlling the dynamics of the movement of sensors for measuring the temperature state on a rod, the problem of synthesizing control actions in systems with distributed parameters is investigated. Feedback is achieved by measuring the state of the process using moving remote measuring devices (sensors). Linear dependencies of the current values of control actions on the boundary conditions and on the movement of measuring devices from the measured temperature values both at the current and at past moments of the process state are proposed. In the problems, the constant feedback parameters, that is, the coefficients involved in these dependencies, are synthesized. As a result, the feedback control problem is formulated as a problem of parametric optimal control of an object with distributed parameters. To determine the optimal values of the feedback parameters, formulas for the gradient of the objective functional were obtained, which make it possible to use effective numerical methods of first-order optimization. The results of numerical experiments are presented.