Rod temperature regulation using current and time-delayed feedback

Abstract

The synthesis problem of control of objects with distributed parameters with feedback is investigated on the example of the process of heating a rod in a furnace. To generate the values of control actions, we propose to use their linear de- pendence on the values of the state at the measurement points, both at the current and previous moments of time. The unknown coefficients involved in this dependence of control on the measured state values are feedback parameters. They are deter- mined by minimizing the objective functional using numerical methods of first-order optimization. Formulas for the gradient of the objective functional with respect to the feedback parameters are obtained. The results of numerical experiments are presented.