In this paper, we study the time optimal control problem in a DC-DC buck converter in the underdamped oscillatory regime. In particular, we derive analytic expressions for the admissible regions in the state space, satisfying the condition that every point within the region is reachable in optimal time with a single switching action. We then make use of the general result to establish the minimum and maximum variation allowed to the load in two predefined design set-ups that fulfills the time optimal single switching criteria. Finally, we make use of numerical simulations to show the performance of the proposed control under changes in the reference voltage and load resistance.

中文翻译：

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DC-DC降压转换器中的单开关可达到的工作点：时间最优控制的近似值。

在本文中，我们研究了欠阻尼振荡状态下DC-DC降压转换器中的时间最优控制问题。特别是，我们导出状态空间中可允许区域的解析表达式，满足条件是该区域内的每个点都可以在单个开关动作的最佳时间内到达。然后，我们利用一般结果在满足时间最佳单个切换标准的两个预定义设计设置中建立允许负载的最小和最大变化。最后，我们利用数值模拟来显示所提出的控制在参考电压和负载电阻变化下的性能。