Synthesis of Algorithms and Optimal Control System of Start-Up Modes of Continuous Induction Installation

Abstract

The problem of optimization of starting conditions of a continuous induction heating installation is examined. In the work, an optimal algorithm for controlling the process of starting the heater to a given operating mode is obtained by the accuracy criterion. The optimal phase portrait consists of two intervals: the interval of bounded moving and the “special” region. It is shown that the “special” region represents a periodic piecewise continuous function asymptotically approaching a required final value. The synthesis of a looped optimal system is complicated by the fact that at the “special” control interval the temperature of the metal at the exit of the heater does not change. It was found that the temperature of the metal inside the heater varies according to a certain law in accordance with the optimal algorithm. This circumstance allows synthesizing a looped optimal system at the “special” interval as a system with feedback on the metal temperature at some “internal” point of the heater. A connection is established between the temperature change at the control point and the control algorithm. It is shown that the phase trajectory has the form of a piecewise constant function that converges to a steady-state value. The coordinate of the installation location of the feedback sensor is determined. The dependence of the number of control intervals on the tolerable error of approximating the output quantity to a required value is given.