Purpose

In this paper, a novel Lyapunov–Krasovskii stable fuzzy proportional-integral-derivative (PID) (FPID) controller is introduced for load frequency control of a time-delayed micro-grid (MG) system that benefits from a fuel cell unit, wind turbine generator and plug-in electric vehicles.

Design/methodology/approach

Using the Lyapunov–Krasovskii theorem, the adaptation laws for the consequent parameters and output scaling factors of the FPID controller are developed in such a way that an upper limit (the maximum permissible value) for time delay is introduced for the stability of the closed-loop MG system. In this way, there is a stable FPID controller, the adaptive parameters of which are bounded. In the obtained adaptation laws and the way of stability analyses, there is no need to approximate the nonlinear model of the controlled system, which makes the implementation process of the proposed adaptive FPID controller much simpler.

Findings

It has been shown that for a different amount of time delay and intermittent resources/loads, the proposed adaptive FPID controller is able to enforce the frequency deviations to zero with better performance and a less amount of energy. In the proposed FPID controller, the increase in the amount of time delay leads to a small increase in the amount of overshoot/undershoot and settling time values, which indicate that the proposed controller is robust to the time delay changes.

Originality/value

Although the designed FPID controllers in the literature are very efficient in being applied to the uncertain and nonlinear systems, they suffer from stability problems. In this paper, the stability of the FPID controller has been examined in applying to the frequency control of a nonlinear input-delayed MG system. Based on the Lyapunov–Krasovskii theorem and using rigorous mathematical analyses, the stability conditions and the adaptation laws for the parameters of the FPID controller have been obtained in the presence of input delay and nonlinearities of the MG system.

中文翻译：

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基于 Lyapunov-Krasovskii 的 FPID 控制器，用于带燃料电池动力单元的时滞微电网系统中的 LFC

目的

在本文中，引入了一种新型 Lyapunov-Krasovskii 稳定模糊比例积分微分 (PID) (FPID) 控制器，用于延迟微电网 (MG) 系统的负载频率控制，该系统受益于燃料电池单元、风能涡轮发电机和插电式电动汽车。

设计/方法/方法

使用 Lyapunov-Krasovskii 定理，FPID 控制器的后续参数和输出比例因子的适应法则以这样一种方式开发，即引入时间延迟的上限（最大允许值）以确保闭环的稳定性。循环MG系统。这样，就有了一个稳定的 FPID 控制器，其自适应参数是有界的。在得到的自适应规律和稳定性分析方法中，不需要对受控系统的非线性模型进行逼近，这使得所提出的自适应 FPID 控制器的实现过程更加简单。

发现

已经表明，对于不同量的时间延迟和间歇性资源/负载，所提出的自适应 FPID 控制器能够以更好的性能和更少的能量将频率偏差强制为零。在所提出的 FPID 控制器中，时间延迟量的增加导致过冲/下冲量和稳定时间值的小幅增加，这表明所提出的控制器对时间延迟变化具有鲁棒性。

原创性/价值

尽管文献中设计的 FPID 控制器在应用于不确定和非线性系统方面非常有效，但它们存在稳定性问题。在本文中，FPID 控制器的稳定性已经在应用于非线性输入延迟 MG 系统的频率控制中进行了检验。基于 Lyapunov-Krasovskii 定理并使用严格的数学分析，获得了在 MG 系统存在输入延迟和非线性的情况下 FPID 控制器参数的稳定性条件和自适应规律。