A dependable approach for inverting two classes of rational Laplace transforms, involving regular polynomials and partial sums with non-integer exponents is developed. Such types of Laplace transforms frequently emerge as the system transfer functions in the analysis of feedback control loops or process dynamics. The proposed method systematically translates the Laplace inversion problem into an integer or fractional order differential equation and yields the analytical inverse Laplace transform function utilizing the Adomian decomposition method. The method is especially useful in dealing with high-order rational transfer functions; where approaches based on the partial fraction expansion and the residue inversion theorem lose their practicality. The ready-to-use inversion formulas are presented and their usability and reliability is demonstrated through a number of case studies.

开发了一种可靠的方法来反转两类有理拉普拉斯变换，包括正则多项式和具有非整数指数的部分和。在反馈控制回路或过程动力学的分析中，这类Laplace变换经常作为系统传递函数出现。所提出的方法将拉普拉斯反演问题系统地转化为一个整数或分数阶微分方程，并利用Adomian分解方法产生解析拉普拉斯逆变换函数。该方法在处理高阶有理传递函数时特别有用。其中基于部分分数展开和残差求逆定理的方法失去了实用性。