- Conference Article
3
- 10.1109/cscmp45713.2019.8976505
Closed-Loop Optimal System Synthesis in the Mode Of “Special” Control of a Continuous Induction Heater
- Sep 01, 2019
- Aleksander Danilushkin
The article deals with the problem of synthesizing the system of the optimal control of transient modes of a through-type induction heater. An algorithm to control the inductor power is obtained for the case of varying the performance of the technological complex. It is shown that the optimal algorithm for the transient mode has the form of a periodic decaying piecewise continuous function of time with discontinuities of the first kind. The number of intervals of continuity is infinite. It is noted that under conditions of random noise and a wide variety of process parameters, the synthesis of a closed-loop optimal system with temperature feedback seems to be the most appropriate. A specific feature of optimal control algorithms for non-stationary modes is the most using “special” control intervals. The conditions of absolute equality between the current value of the metal temperature at the exit from the heater and the given value are satisfied on “special” intervals of the trajectory. In this case, the temperature of the metal at the exit from the heater remains constant during the all transient modes. Therefore, the synthesis of closed-loop systems with feedback on the metal temperature at the exit from the heater is, in principle, impossible. At the same time, the metal temperature inside the heater varies according to certain regularity in accordance with the optimal algorithm. This established behavior allows us to synthesize a closed-loop system on the “special” interval of optimal control as a system with feedback on temperature at some “internal” point of the heater. Analyzing the nature of the metal temperature distribution along the length of the heater in a transient mode allows to determine the coordinate of the internal point at which the temperature changes with a maximum deviation from the steady-state value. This coordinate is used to set the feedback sensor. A relationship has been established between the temperature change at the control point and the heater power on the “special” interval of the trajectory. On the plane of system parameters “inductor power – temperature at the control point”, the phase trajectory of the closed-loop optimal system on the “special” control interval is plotted. It is shown that the phase trajectory has the form of a piecewise continuous function converging to a new steady-state value. The analysis of the dependence “inductor power – temperature at the control point” shows that the feedback changes sign and gain twice within each interval of continuity. The angular coefficients and initial conditions of the optimal control switching line, the angular coefficients of the linear intervals of phase trajectory, and the sign of feedback within each control continuity interval are determined.
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