Stability analysis of mixed lumped—distributed parameter (delay) systems

✍ Scribed by E.E. Kitsios; R.F. Boucher

• Publisher: Elsevier Science
• Year: 1985
• Tongue: English
• Weight: 964 KB
• Volume: 320
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(85)90040-7

✦ Synopsis

A method is presentedfor the stability analysis of systems which include a number of delay elements. The method is based on the transmission line modelling method in which all dynamic elements are modelled by ideal, lossless transmission lines. The resulting system can be mathematically represented by a scattering matrix, a delay matrix, an internalfeedback forcing matrix and an external forcing function vector. The characteristic equation (a transcendental polynomial in es) of the system is readily derived from the above matrices. Using the z-transformation, the characteristic equation can be reduced to an algebraic polynomial and system stability is examined by employing Marden's criterion. The method is demonstrated by

examining the stability of some fluid networks. Results agree with those found elsewhere. The method can be readily applied to any systems containing wave-like elements (e.g.