不可逆制冷机全局稳定性分析

Global Stability Characteristics of Irreversible Refrigerators

本文分析了不可逆制冷机在给定制冷量R和最小输入功率P时的全局稳定性。利用微分方程建立不可逆制冷机模型。利用Lyapunov稳态理论构造Lyapunov函数,证明系统的全局渐进稳定性,并绘制稳态相图分析系统的全局稳态特性。分析了初始扰动和运行参数对全局稳态特性的影响。另外,用数值积分进一步证实了系统的稳态特性。最后,分析了系统的全局稳态特性和热力学特性。

The dynamic stability analysis of an irreversible refrigerator working at the minimum power input P for given cooling load R is analyzed. An irreversible refrigerator model is established based on coupled differential equations. The global asymptotic stability characteristics are proved by constructing Lyapunov function based on Lyapunov stability theory and analyzed by sketching global phase portraits. The influence of parameters such as initial and operating parameters are studied for different values. Besides, numerical integrations are carried out to corroborate the global asymptotic stability properties of the system. Finally, the dynamic stability and the thermodynamic properties of the system are analyzed.