Beyond synchronization: String instability in coupled harmonic oscillator systems. (12th August 2014)

• Record Type: Journal Article
• Authors: Yu, Bo; Freudenberg, James S.; Gillespie, R. Brent; Middleton, Richard H.
• Is Part Of: International journal of robust and nonlinear control. Volume 25:Number 15(2015)
• Page Start: 2745
• Page End: 2769
• Publication Date: 2014-08-12
• Subjects: Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.3229
• Languages: English
• ISSNs: 1049-8923

Abstract

<abstract abstract-type="main" id="rnc3229-abs-0001"> <title>Summary</title> <p id="rnc3229-para-0001">In this paper, we consider the problem of disturbance response and error amplification for a simple system of coupled harmonic oscillators. We first suppose that identical oscillators are connected in a string in which each oscillator attempts to track its predecessor by using the same control law that depends on the relative position information from its immediate predecessor. Such an oscillator string is called a homogeneous oscillator string with predecessor‐following architecture. Motivated by terminology from the problem of vehicle platooning, we say that the synchronized oscillator system is string unstable if the effect of a disturbance to the lead oscillator is amplified as it propagates along the string. With the use of a new Bode‐like integral relation that must be satisfied by the complementary sensitivity function, we provide sufficient conditions for string instability. The sufficient conditions show that any string of oscillators that satisfies certain time domain performance specifications and bandwidth limitations must necessarily be string unstable. We further introduce a concept of time headway for the oscillator system and extend our analysis of string instability to consider the heterogeneous oscillator string and a more general communication range. Copyright © 2014 John Wiley &amp; Sons, Ltd.</p> </abstract>