Stability analysis of linear continuous time-delay feedback systems†

Abstract

This paper deals primarily with the stability criteria for closed-loop systems whose controlled plants comprise a proportional, single integration, or double integration characteristic, together with a true time-delay. These plants are considered in turn to be controlled by simple proportional, lead or lag controllers. Systems of these relatively simple forms are often used as first approximations in the initial analysis of practical industrial situations, and analysis on both root-locus and frequency-response bases is taken to the extent that the solutions of relatively simple transcendental/trigonometric equations are involved. However, the results are immediately useful in many practical problems and can be readily extended. It is believed that the mathematical techniques, simple as they are, and the associated analyses, have not been presented before in this compact and collated form.