Composite Trapezoidal Rule for Numerical Inverse Laplace Transform of Rational Functions in LTI Control Systems with C++ Programming

Abstract

This paper presents a development of numerical methods for the inverse Laplace transform to analysis LTI (Linear Time Invariant) control systems by computer. The open source Standard C++ Library is used to create the programmatic objects by OOP (Object- Oriented Programming) for the numerical inverse Laplace transform object that uses numerical integration to the Bromwich integral. The composite trapezoidal rule is implemented on the simplified Bromwich integral which is real value integration that has only one cosine factor. The accuracy of numerical integration will be met by varying step size of the trapezoidal rule according to specified tolerance. The other numerical methods such that Laguerre’s method, Horner’s algorithm, synthetic division and nested multiplication will be included in the created programmatic objects for finding zeros of polynomial in order to avoid all singular points of integrand of Bromwich integral to make analytic integrand on contour of integration. The numerical inverse Laplace transform object of this article gives satisfactory results in both of the numerical inverse Laplace transform to the proper rational functions and unit step response of LTI control systems.