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Realizations of a special class of admittances with strictly lower complexity than canonical forms

Realizations of a special class of admittances with strictly lower complexity than canonical forms
Realizations of a special class of admittances with strictly lower complexity than canonical forms
This paper investigates the simplified realization problem of a special class of positive-real admittances similar to biquadratic functions but with an extra pole at the origin, which is widely used in the analysis of suspension systems. The results in this paper are motivated by passive mechanical control with the inerter. The concept of strictly lower complexity is first defined, whose indices in this paper are the total number of elements, the number of resistors (dampers), and the number of capacitors (inerters). We then derive a necessary and sufficient condition for this class of admittance to be realized by the networks that are of strictly lower complexity than the canonical realization by the Foster Preamble method. To solve this problem, it is shown that it suffices to consider the following: 1) networks with at most four elements, 2) irreducible five-element resistor-inductor (RL) networks, and 3) irreducible five-element resisitor-inductor-capacitor (RLC) networks. Other cases are shown to be impossible. By finding their corresponding network configurations through a series of constraints and deriving the corresponding realizability conditions, the final condition can be obtained. Finally, the U-V plane and numerical examples are provided to illustrate the theoretical results.
network synthesis, inerter, passivity, transformerless synthesis, cononical realization
1549-8328
2465-2473
Chen, M.Z.Q.
374e0856-90ca-4ab4-8561-f7f687e47575
Wang, Kai
3acbc899-cb32-4885-876f-d7b353577dfb
Shu, Zhan
ea5dc18c-d375-4db0-bbcc-dd0229f3a1cb
Li, Chanying
c96acbc3-6c4f-4e9e-84f9-f448a4389b1a
Chen, M.Z.Q.
374e0856-90ca-4ab4-8561-f7f687e47575
Wang, Kai
3acbc899-cb32-4885-876f-d7b353577dfb
Shu, Zhan
ea5dc18c-d375-4db0-bbcc-dd0229f3a1cb
Li, Chanying
c96acbc3-6c4f-4e9e-84f9-f448a4389b1a

Chen, M.Z.Q., Wang, Kai, Shu, Zhan and Li, Chanying (2013) Realizations of a special class of admittances with strictly lower complexity than canonical forms. IEEE Transactions on Circuits and Systems I: Regular Papers, 60 (9), 2465-2473. (doi:10.1109/TCSI.2013.2245471).

Record type: Article

Abstract

This paper investigates the simplified realization problem of a special class of positive-real admittances similar to biquadratic functions but with an extra pole at the origin, which is widely used in the analysis of suspension systems. The results in this paper are motivated by passive mechanical control with the inerter. The concept of strictly lower complexity is first defined, whose indices in this paper are the total number of elements, the number of resistors (dampers), and the number of capacitors (inerters). We then derive a necessary and sufficient condition for this class of admittance to be realized by the networks that are of strictly lower complexity than the canonical realization by the Foster Preamble method. To solve this problem, it is shown that it suffices to consider the following: 1) networks with at most four elements, 2) irreducible five-element resistor-inductor (RL) networks, and 3) irreducible five-element resisitor-inductor-capacitor (RLC) networks. Other cases are shown to be impossible. By finding their corresponding network configurations through a series of constraints and deriving the corresponding realizability conditions, the final condition can be obtained. Finally, the U-V plane and numerical examples are provided to illustrate the theoretical results.

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More information

Published date: September 2013
Keywords: network synthesis, inerter, passivity, transformerless synthesis, cononical realization
Organisations: Mechatronics

Identifiers

Local EPrints ID: 360106
URI: https://eprints.soton.ac.uk/id/eprint/360106
ISSN: 1549-8328
PURE UUID: 7cd665dc-c73d-4dd8-bdaf-03c697dc4168
ORCID for Zhan Shu: ORCID iD orcid.org/0000-0002-5933-254X

Catalogue record

Date deposited: 26 Nov 2013 11:33
Last modified: 06 Jun 2018 12:30

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