【摘要】 时滞系统的特征根具有无穷多个,分布较为复杂.经典定积分法是一种分析线性多时滞系统稳定性的有效方法,但其不能直接求解系统特征根虚部对应的模态频率,而是需要先求解特征根实部,再借助其他方法如二维牛顿迭代等来对模态频率进行求解.对于大部分稳定系统而言,往往模态频率更受关注,间接对其进行求解会引入冗余步骤,增加计算量.因此本文改进了定积分法,使用新的积分路径和新的特征根平移方向,可以直接求解时滞系统的模态频率,同时保留了经典定积分法适用于多时滞系统、编程简单、效率较高的优点.论文通过两个工程实例,验证了本文方法计算系统模态频率的适用性和便捷性.更多还原

【Abstract】 The eigenvalues of a time-delay system are infinite,and exhibit complex distributions.The classical definite integral method is an effective approach for analyzing the stability of multi-time-delay systems.However,it cannot directly solve the modal frequencies,i.e.,the imaginary parts of the eigenvalues of the system,and instead requires first determining the real parts and then applying additional techniques,such as two-dimensional Newton iteration to solve the modal frequencies.For most stable systems,modal frequency is often of greater concern,and indirect determination introduces unnecessary steps and increases computational complexity.Therefore,this article extends the definite integral method by using a new integration path and a new characteristic root translation direction,which can directly solve the modal frequency of time-delay systems,while retaining the advantages of the classical definite integral method,such as being suitable for multi time-delay systems,simple programming,and high efficiency.The paper verifies the wide applicability and the effectiveness of the proposed method for calculating the modal frequencies of time-delay systems through two engineering examples.更多还原