Caputo-Fabrizio定义下分数阶RLC网络系统建模及系统分析

For the singular point of traditional fractional order Caputo definition and its inapplicability for describing the modelling and dynamic characteristics of nonlinear electronics, this project carries on the modeling and system performance research of fractional inductance, fractional capacitance, and fractional RLC tank system based on a new fractional definition (Caputo-Fabrizio definition). The C-F definition can describe the different dielectric properties of the material, improve the description of structure, material and dynamic characteristics, and enrich the models of fractional inductance and capacitance. For the lack of research of the controllability, observability, and stability of fractional RLC tank system, especially that with C-F definition, this project proposes the controllability and observability theorem of fractional RLC tank system with C-F definition, and also provides the Lyapunov stability theorem of fractional RLC tank system with C-F definition. In this way, the control strategy research of fractional RLC tank system with C-F definition would be improved, and the theoretical research of fractional RLC tank system would be enhanced. Finally, based on C-F definition, the fractional mutual inductance of T-type network is analyzed, and would be applied in practical coupler and transformer systems.

针对传统分数阶Caputo微积分定义对电子元件建模模型的结构、材料和动态表征力不够，且具有奇异点等问题。而Caputo-Fabrizio（简称C-F）定义能消除奇异点，且具有更好的材料结构特性描述能力。开展C-F定义下电感电容及其RLC网络和T型互感网络分数阶模型研究，提高模型的结构、材料和动态表征力，提高模型准确度，同时丰富分数阶电感电容的模型。针对分数阶RLC网络系统的可控可观性、稳定性等系统控制性能研究尚不完善，尤其是C-F定义下RLC网络系统分析方法欠缺。开展分数阶网络系统分析的理论研究，提出C-F定义下RLC网络系统可达性、可控可观性等系统控制性能分析方法，提出分数阶RLC网络系统李雅普诺夫稳定性定理，为C-F定义下分数阶RLC网络系统控制研究提供有效的理论方法。并推进分数阶RLC网络系统分析理论。本项目将上述分数阶模型系统用于无线充电耦合线圈和变压器等实际系统中。