摘要
在一个瞬态传热系统中,依赖于时间变化的温度集总参数模型利用分数阶微分方程进行拟合近似,分数阶微分方程的阶数取决于传热学中的毕渥数.利用Laplace变换得到该分数阶微分方程的Mittag-Leffler函数形式的解析解.从研究数据结果可知,与利用传统的指数函数逼近拟合效果对比,分数阶控制系统对真实数据的拟合效果具有更高的精确程度.
This paper is presented to show that time-dependent temperatures in a transient and conductive system can be approximately modeled by a fractional-order differential equation, and the order of which depends on the Blot number. Analytical solutions of these equations can be written in terms of the Mittag- Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.
出处
《北京建筑工程学院学报》
2013年第4期62-64,共3页
Journal of Beijing Institute of Civil Engineering and Architecture
基金
国家自然科学基金(21206009)
北京市人才强教项目(PHR201107123)
