Control System Design Using Finite Laplace Transform Theory

TL;DR

This paper introduces a control system design approach using the Finite Laplace Transform (FLT), addressing the limitations of traditional Laplace transform theory by considering finite time intervals relevant in engineering.

Contribution

It presents a novel design principle for linear control systems based on FLT, along with a numerical inversion method and analysis of FLT's properties compared to classical Laplace theory.

Findings

FLT does not satisfy the convolution theorem as in classical theory

FLT is conceptually similar to analog FIR digital filters

A practical numerical inversion method for FLT is demonstrated

Abstract

The Laplace transform theory violates a very fundamental requirement of all engineering systems. We show that this theory assumes that all signals must exist over infinite time interval. Since in engineering this infinite time assumption is not meaningful and feasible, this paper presents a design for linear control systems using the well known theory of Finite Laplace transform (FLT). The major contributions of this paper can be listed as: (a) A design principle for linear control systems using FLT, (b) A numerical inversion method for the FLT with examples, (c) A proof that the FLT does not satisfy the convolution theorem as normally required in engineering design and analysis, and (d) An observation that the FLT is conceptually similar to the analog equivalent of the Finite Impulse Response (FIR) digital filter.