Mass chains with passive interconnection: Complex iterative maps and scalability

Kaoru Yamamoto; Malcolm C. Smith

doi:10.1109/CDC.2013.6759855

Mass chains with passive interconnection: Complex iterative maps and scalability

Kaoru Yamamoto, Malcolm C. Smith

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

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 will study the scalar transfer functions from the disturbance to a given intermass displacement. It will be 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 _∞-norm of these transfer functions for certain choices of interconnection impedance.

Original language	English
Title of host publication	2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	37-42
Number of pages	6
ISBN (Print)	9781467357173
DOIs	https://doi.org/10.1109/CDC.2013.6759855
Publication status	Published - 2013
Externally published	Yes
Event	52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy Duration: Dec 10 2013 → Dec 13 2013

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	52nd IEEE Conference on Decision and Control, CDC 2013
Country/Territory	Italy
City	Florence
Period	12/10/13 → 12/13/13

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2013.6759855

Cite this

Yamamoto, K., & Smith, M. C. (2013). Mass chains with passive interconnection: Complex iterative maps and scalability. In 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013 (pp. 37-42). Article 6759855 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6759855

Mass chains with passive interconnection: Complex iterative maps and scalability. / Yamamoto, Kaoru; Smith, Malcolm C.
2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013. Institute of Electrical and Electronics Engineers Inc., 2013. p. 37-42 6759855 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Yamamoto, K & Smith, MC 2013, Mass chains with passive interconnection: Complex iterative maps and scalability. in 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013., 6759855, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 37-42, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, 12/10/13. https://doi.org/10.1109/CDC.2013.6759855

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AB - 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 will study the scalar transfer functions from the disturbance to a given intermass displacement. It will be 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 ∞-norm of these transfer functions for certain choices of interconnection impedance.

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Mass chains with passive interconnection: Complex iterative maps and scalability

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