New Method of Solving the Proper Rational Function and Application to Electrical Control System

The paper is dedicated to develop a new method of addressing the linear nonhomogeneous time-invariant differential equation with same differential numbers for inputs and outputs. The Laplace transformed output of the electrical state-space equation is a rational function with the same degrees of the numerator and the denominator, and then the bored processes involving the long division of both complicated polynomials, the expanded multiplication of all polynomial factors, the differentiation of complicated polynomials and the complex derivations of all partial fraction parameters are inevitable for existing traditional methods. However, by applying the proposed method in this paper, we can explicitly express the general form of the desired output solution and directly solve the desired problem with shorter time than those traditional approaches. To give the significant applications of the new proposed method, we apply it to address the famous electrical circuit based on our recent researches of Chen's electrical unifying approach.

Automated summary

This paper introduces a new method for addressing linear nonhomogeneous time-invariant differential equations, which is more efficient than traditional methods and can directly solve the problem. The significant applications of this method are demonstrated through its application to electrical circuit problems, based on recent research in Chen's electrical unifying approach.