AbdelAty A M, Fouda Mohammed E, Elbarawy Menna T M M, Radwan A G
Engineering Mathematics and Physics Dept., Faculty of Engineering, Fayoum University, Egypt.
Engineering Mathematics and Physics Dept., Faculty of Engineering, Cairo University, Egypt.
J Adv Res. 2020 Dec 3;32:119-131. doi: 10.1016/j.jare.2020.11.014. eCollection 2021 Sep.
Optimal charging of circuits is a well-studied problem in the integer-order domain due to its importance from economic and system temperature hazards perspectives. However, the fractional-order counterpart of this problem requires investigation.
This study aims to find approximate solutions of the most energy-efficient input charging function in fractional-order circuits.
This paper uses a meta-heuristic optimization technique called Cuckoo search optimizer to attain the maximum charging efficiency of three common fractional-order circuits. An analytical expression of the fractional capacitor voltage is suggested such that it satisfies the boundary conditions of the optimal charging problem. The problem is formulated as a fractional-order calculus of variations problem with compositional functional. The numerical solutions are obtained with the meta-heuristic optimization algorithm's help to avoid the complexities of the analytical approach.
he efficiency surfaces and input voltage charging curves are discussed for fractional-order in the range .
The optimized charging function can approximate the optimal charging curve using at most 4 terms. The charging time and the resistive parameters have the most dominant effect on charging efficiency at constant fractional-order .
由于从经济和系统温度危害的角度来看，电路的最优充电是整数阶域中一个经过充分研究的问题。然而，这个问题的分数阶对应问题需要进行研究。
本研究旨在找到分数阶电路中最节能的输入充电函数的近似解。
本文使用一种称为布谷鸟搜索优化器的元启发式优化技术，以实现三种常见分数阶电路的最大充电效率。提出了分数电容电压的解析表达式，使其满足最优充电问题的边界条件。该问题被表述为一个具有组合泛函的分数阶变分问题。借助元启发式优化算法获得数值解，以避免解析方法的复杂性。
讨论了分数阶在 范围内的效率曲面和输入电压充电曲线。
优化后的充电函数最多使用4项就能近似最优充电曲线。在恒定分数阶 时，充电时间和电阻参数对充电效率的影响最为显著。
