This paper focuses on the problem of fractional controller stabilization for a first-order time-delay systems. For this reason, we utilize the Hermite–Biehler and Pontryagin theorems to compute the complete set of the stabilizing parameters. The widespread industrial utilization of PID controllers and the potentiality of their noninteger order representation justify a timely interest in tuning techniques. Step responses are calculated through parameters inside and outside stability region to prove the method efficiency.

中文翻译：

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时滞系统的通用非整数阶控制器

本文重点研究一阶时滞系统的分数阶控制器镇定问题。出于这个原因，我们利用 Hermite-Biehler 和 Pontryagin 定理来计算完整的稳定参数集。PID控制器的广泛工业应用及其非整数阶表示的潜力证明了对调整技术的及时兴趣。阶跃响应通过计算 稳定域内外的参数来证明方法的有效性。