This article is devoted to stability analysis of generator excitation control system that has some time delay with fractional order proportional integral derivative controller by using direct method. When the time delay exceeds certain critical values, the excitation control system becomes unstable. In order to obtain more delay margin, in control part of the system, fractional order proportional integral derivative controller is used. A formulation is obtained to find out the maximum time delay which is known as delay margin with which the system can tolerate without any loss in its stability. All the possible stability regions analytically in the parametric space of the time delay is obtained by using an exact method and it is presented in this study. The method is formulated in frequency domain. The time-domain simulations are implemented to validate theoretical delay margin results in Matlab/Simulink. When it is compared with previous researches in literature, better stability margin is obtained. The results have shown that fractional order PID controller gives wide stability area than integer order PID controller.

中文翻译：

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基于分数阶控制器的发电机励磁控制系统延迟裕度计算

本文致力于采用直接法对分数阶比例积分微分控制器具有一定时滞的发电机励磁控制系统进行稳定性分析。当时间延迟超过某些临界值时，励磁控制系统变得不稳定。为了获得更大的延迟裕度，在系统的控制部分，采用了分数阶比例积分微分控制器。获得一个公式来找出最大时间延迟，称为延迟裕度，系统可以在不损失其稳定性的情况下容忍该延迟裕度。时滞参数空间中所有可能的稳定区域是通过使用精确方法获得的，并在本研究中给出。该方法是在频域中制定的。实施时域仿真以验证 Matlab/Simulink 中的理论延迟裕度结果。与以往文献研究相比，获得了更好的稳定性裕度。结果表明，分数阶 PID 控制器比整数阶 PID 控制器提供更宽的稳定区域。