Laplace变换下分数阶时滞系统稳定性建模研究  

Stability modeling of fractional delay systems based on laplace transform

作　　者：韩瑜[1] HAN Yu(Shanxi Radio and Television University,Xi＇an Shanxi,710119)

机构地区：[1]陕西广播电视大学

出　　处：《自动化与仪器仪表》2018年第9期49-52,共4页Automation & Instrumentation

摘　　要：分析Laplace变换下分数阶时滞系统稳定性,提高控制系统的稳定性和收敛性,在连续有界的仿射域中构建分数阶时滞系统的控制对象模型,采用连续有界的Lognormal分布建立分数阶时滞系统的稳态平衡模型,采用Laplace变换进行特征分解,用似然比估计方法进行分数阶时滞系统的稳定平衡解估计,在有限域边界条件下实现分数阶时滞系统稳定性建模。研究表明,构建的Laplace变换下分数阶时滞系统具有恒稳定性和渐进收敛性,在时滞二自由度控制中具有很好的鲁棒控制效能。The stability of fractional delay system under Laplace transform is analyzed to improve the stability and convergence of the control system. The control object model of fractional delay system is constructed in the continuous bounded affine domain. The steady-state equilibrium model of fractional time-delay systems is established by using the continuous bounded Lognormal distribution, and the Laplace transform is used to decompose the eigenvalues. The method of likelihood ratio estimation is used to estimate the stable equilibrium solutions of fractional time-delay systems, and the stability modeling of fractional time-delay systems is realized under the boundary conditions in finite fields. The results show that the fractional time-delay system constructed by Laplace transform has constant stability and asymptotic convergence, and it has good robust control performance in two-degree-of-freedom control with time-delay.

关 键 词：LAPLACE变换 分数阶时滞系统 时滞二自由度控制 Lognormal分布 

分 类 号：O175.8[理学—数学]