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 dependence 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 determined 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.