Controlling the Heating of a Rod Using the Current and Preceding Time Feedback.

Using the process of heating a rod in a furnace as an example, we study the feedback control synthesis problem for plants with distributed parameters. To form the control values, it is proposed to use their linear dependence on the state values at the points of measurement, both at the current and at the preceding moments of time. The unknown coefficients involved in this dependence of the control on the measured state values are the feedback parameters. They are determined by minimizing the objective functional using first-order numerical optimization methods. To this end, formulas for the gradient of the objective functional with respect to the feedback parameters are obtained. The results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]