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首页> 外文会议>International Conference Complex Systems: Control and Modeling Problems >Closed-Loop Optimal System Synthesis in the Mode Of “Special” Control of a Continuous Induction Heater
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Closed-Loop Optimal System Synthesis in the Mode Of “Special” Control of a Continuous Induction Heater

机译：连续感应加热器“特殊”控制模式下的闭环最优系统综合

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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.
机译：本文讨论了综合优化直通式感应加热器瞬态模式的系统的问题。对于改变技术组合的性能的情况，获得了一种控制电感器功率的算法。结果表明，瞬时模式的最优算法具有时间的周期性衰减分段连续函数的形式，具有第一类不连续性。连续间隔的数量是无限的。要注意的是，在随机噪声和各种过程参数的条件下，具有温度反馈的闭环最佳系统的综合似乎是最合适的。用于非平稳模式的最优控制算法的一个特定功能是最常使用“特殊”控制间隔。加热器的出口处的金属温度的当前值与给定值之间的绝对相等条件在轨迹的“特殊”间隔内得到满足。在这种情况下，在所有瞬态模式下，加热器出口处的金属温度均保持恒定。因此，原则上不可能在加热器出口处合成具有金属温度反馈的闭环系统。同时，加热器内部的金属温度根据最佳算法按照一定规律性变化。这种既定的行为使我们能够在最佳控制的“特殊”时间间隔上将闭环系统合成为在加热器的某个“内部”点具有温度反馈的系统。在瞬态模式下分析沿着加热器长度的金属温度分布的性质，可以确定温度变化的内部点的坐标，并且与稳态值的偏差最大。该坐标用于设置反馈传感器。在控制点的温度变化与轨迹“特殊”间隔上的加热器功率之间建立了关系。在系统参数“感应器功率-控制点的温度”的平面上，绘制了“特殊”控制间隔内闭环最佳系统的相位轨迹。结果表明，相轨迹具有分段连续函数的形式，收敛到新的稳态值。对“感应器功率-控制点温度”的依赖性的分析表明，在每个连续性间隔内，反馈会改变符号和增益两次。确定最佳控制切换线的角度系数和初始条件，相轨迹的线性间隔的角度系数以及每个控制连续性间隔内的反馈符号。

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