Bounded Disturbance Amplification for Mass Chains with Passive Interconnection

TL;DR

This paper analyzes how passive interconnections in mass chains affect disturbance amplification, providing a method to ensure boundedness of transfer functions in large systems, relevant for earthquake-resistant buildings and vehicle platoons.

Contribution

It introduces a novel representation of transfer functions as complex iterative maps, enabling the analysis of disturbance amplification in passive mass chains.

Findings

Transfer functions can be represented as complex iterative maps.

Boundedness of the H-infinity norm is achievable for certain interconnection impedances.

Method applies to large N systems, such as multi-storey buildings and vehicle platoons.

Abstract

This paper introduces the problem of passive control of a chain of N identical masses in which there is an identical passive connection between neighbouring masses and a similar connection to a movable point. The problem arises in the design of multi-storey buildings which are subjected to earthquake disturbances, but applies in other situations, for example vehicle platoons. The paper studies the scalar transfer functions from the disturbance to a given intermass displacement. It is shown that these transfer functions can be conveniently represented in the form of complex iterative maps and that these maps provide a method to establish boundedness in N of the H-infinity norm of these transfer functions for certain choices of interconnection impedance.