AI 中文总结
研究由入口压力和出口质量流率控制的管道气体流动的数学模型，通过提升算子转化为抽象微分方程，推导傅里叶系数表示，建立周期解条件，应用于氢传输模型评估周期运行状态。
AI 中文摘要
考虑了由入口压力和出口质量流率控制的管道内气体流动的数学模型，其形式为具有适当状态方程的等温欧拉方程。在边界控制系统框架内，利用适当的提升算子将该模型转化为非线性抽象微分方程。通过解析推导了该抽象方程的傅里叶系数表示。在抽象空间中建立了一类具有连续可微控制的非线性控制系统存在周期解的条件。并将此框架应用于实际氢传输模型，以评估供需周期性波动下的周期运行状态。
英文摘要
A mathematical model of gas flow in a pipeline controlled by the inlet pressure and the outlet mass flow flux is considered in the form of the isothermal Euler equations with an appropriate equation of state. Within the framework of boundary control systems, this model is transformed into a nonlinear abstract differential equation using an appropriate lifting operator. For this abstract equation, a representation in terms of Fourier coefficients is derived analytically. Conditions for the existence of periodic solutions to a broad class of nonlinear control systems with continuously differentiable controls are established in abstract spaces. This framework is applied to a realistic hydrogen transport model to evaluate periodic operating regimes under periodic fluctuations in supply and demand.
Comments12 pages
