拉普拉斯变换的两个新运算法则

Two New Laws of Laplace Transforms

推导出了拉普拉斯变换乘法运算法则和除法运算法则,进一步给出了线性系统增加闭环零点或闭环极点时时间响应的计算式,应用这些计算公式,分析了闭环零点和闭环极点对时间响应的影响。分析结果表明:增加闭环零点或实数闭环极点不会改变时间响应的振荡性,在线性系统中,离虚轴越远的闭环零点和闭环极点对时间响应影响越小。

This paper derived multiplication law and division law of Laplace transforms. In accordance with the laws, the time response formulas of linear systems were further deduced when a close-loop zero or a close-loop pole was added to the systems. By using the formulas, the influence of the added close-loop zero and close- loop pole on the time response were analysed. The analytical results show that the added close-loop zero or close-loop pole does not change vibratility of the time response. The farther a close-loop zero or a close-loop pole is to the imaginary axis, the less it has influence on the time response in a linear system.