Four quadrant hybrid control oriented dynamical system model of digital displacement ® units

Niels Henrik Pedersen, Per Johansen, Torben O. Andersen

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

2 Citations (Scopus)

Abstract

Proper feedback control of dynamical systems requires models that enables stability analysis, from where control laws may be established. Development of control oriented models for digital displacement (DD) fluid power units is complicated by the non-smooth behavior, which is considered the core reason for the greatly simplified state of the art control strategies for these machines. The DD unit comprises numerous pressure chambers in a modular construction, such that the power throughput is determined by the sequence of activated pressure chambers. The dynamics of each pressure chamber is governed by non-linear differential equations, while the binary input (active or inactive) is updated discretely as function of the shaft angle. Simple dynamical approximations based on continuous or discrete system theory is often inaccurate and is not applicable for such system when it is to operate in all four quadrants. Therefore, a method of applying hybrid dynamical system theory, comprising both continuous and discrete elements is proposed in this paper. The paper presents a physical oriented hybrid model accurately describing the machine dynamics. Since development of stabilizing control laws for hybrid dynamical systems is a complicated task, a simpler hybrid model only including the fundamental machine characteristics is beneficial. Therefore, a discussion and several proposals are made on how a simpler DD hybrid model may be established and used for feedback control development.
Original languageEnglish
Title of host publicationProceedings of the Bath/ASME Symposium on Fluid Power and Motion Control, FPMC2018
Number of pages9
PublisherAmerican Society of Mechanical Engineers
Publication dateSep 2018
Article numberFPMC2018-8874
ISBN (Print)978-0-7918-5196-8
ISBN (Electronic)9780791851968
DOIs
Publication statusPublished - Sep 2018
EventBATH/ASME 2018 Symposium on Fluid Power and Motion Control - Bath, United Kingdom
Duration: 12 Sep 201814 Sep 2018

Conference

ConferenceBATH/ASME 2018 Symposium on Fluid Power and Motion Control
CountryUnited Kingdom
CityBath
Period12/09/201814/09/2018

Fingerprint

Dynamical systems
System theory
Feedback control
Modular construction
Differential equations
Throughput
Fluids

Cite this

Pedersen, N. H., Johansen, P., & Andersen, T. O. (2018). Four quadrant hybrid control oriented dynamical system model of digital displacement ® units. In Proceedings of the Bath/ASME Symposium on Fluid Power and Motion Control, FPMC2018 [FPMC2018-8874] American Society of Mechanical Engineers. https://doi.org/10.1115/FPMC2018-8874
Pedersen, Niels Henrik ; Johansen, Per ; Andersen, Torben O. / Four quadrant hybrid control oriented dynamical system model of digital displacement ® units. Proceedings of the Bath/ASME Symposium on Fluid Power and Motion Control, FPMC2018. American Society of Mechanical Engineers, 2018.
@inproceedings{c4b0b051950c49faa1f243ddb435bd4f,
title = "Four quadrant hybrid control oriented dynamical system model of digital displacement {\circledR} units",
abstract = "Proper feedback control of dynamical systems requires models that enables stability analysis, from where control laws may be established. Development of control oriented models for digital displacement (DD) fluid power units is complicated by the non-smooth behavior, which is considered the core reason for the greatly simplified state of the art control strategies for these machines. The DD unit comprises numerous pressure chambers in a modular construction, such that the power throughput is determined by the sequence of activated pressure chambers. The dynamics of each pressure chamber is governed by non-linear differential equations, while the binary input (active or inactive) is updated discretely as function of the shaft angle. Simple dynamical approximations based on continuous or discrete system theory is often inaccurate and is not applicable for such system when it is to operate in all four quadrants. Therefore, a method of applying hybrid dynamical system theory, comprising both continuous and discrete elements is proposed in this paper. The paper presents a physical oriented hybrid model accurately describing the machine dynamics. Since development of stabilizing control laws for hybrid dynamical systems is a complicated task, a simpler hybrid model only including the fundamental machine characteristics is beneficial. Therefore, a discussion and several proposals are made on how a simpler DD hybrid model may be established and used for feedback control development.",
keywords = "Dynamic systems, Displacement, Hybrid control",
author = "Pedersen, {Niels Henrik} and Per Johansen and Andersen, {Torben O.}",
year = "2018",
month = "9",
doi = "10.1115/FPMC2018-8874",
language = "English",
isbn = "978-0-7918-5196-8",
booktitle = "Proceedings of the Bath/ASME Symposium on Fluid Power and Motion Control, FPMC2018",
publisher = "American Society of Mechanical Engineers",
address = "United States",

}

Pedersen, NH, Johansen, P & Andersen, TO 2018, Four quadrant hybrid control oriented dynamical system model of digital displacement ® units. in Proceedings of the Bath/ASME Symposium on Fluid Power and Motion Control, FPMC2018., FPMC2018-8874, American Society of Mechanical Engineers, Bath, United Kingdom, 12/09/2018. https://doi.org/10.1115/FPMC2018-8874

Four quadrant hybrid control oriented dynamical system model of digital displacement ® units. / Pedersen, Niels Henrik; Johansen, Per; Andersen, Torben O.

Proceedings of the Bath/ASME Symposium on Fluid Power and Motion Control, FPMC2018. American Society of Mechanical Engineers, 2018. FPMC2018-8874.

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

TY - GEN

T1 - Four quadrant hybrid control oriented dynamical system model of digital displacement ® units

AU - Pedersen, Niels Henrik

AU - Johansen, Per

AU - Andersen, Torben O.

PY - 2018/9

Y1 - 2018/9

N2 - Proper feedback control of dynamical systems requires models that enables stability analysis, from where control laws may be established. Development of control oriented models for digital displacement (DD) fluid power units is complicated by the non-smooth behavior, which is considered the core reason for the greatly simplified state of the art control strategies for these machines. The DD unit comprises numerous pressure chambers in a modular construction, such that the power throughput is determined by the sequence of activated pressure chambers. The dynamics of each pressure chamber is governed by non-linear differential equations, while the binary input (active or inactive) is updated discretely as function of the shaft angle. Simple dynamical approximations based on continuous or discrete system theory is often inaccurate and is not applicable for such system when it is to operate in all four quadrants. Therefore, a method of applying hybrid dynamical system theory, comprising both continuous and discrete elements is proposed in this paper. The paper presents a physical oriented hybrid model accurately describing the machine dynamics. Since development of stabilizing control laws for hybrid dynamical systems is a complicated task, a simpler hybrid model only including the fundamental machine characteristics is beneficial. Therefore, a discussion and several proposals are made on how a simpler DD hybrid model may be established and used for feedback control development.

AB - Proper feedback control of dynamical systems requires models that enables stability analysis, from where control laws may be established. Development of control oriented models for digital displacement (DD) fluid power units is complicated by the non-smooth behavior, which is considered the core reason for the greatly simplified state of the art control strategies for these machines. The DD unit comprises numerous pressure chambers in a modular construction, such that the power throughput is determined by the sequence of activated pressure chambers. The dynamics of each pressure chamber is governed by non-linear differential equations, while the binary input (active or inactive) is updated discretely as function of the shaft angle. Simple dynamical approximations based on continuous or discrete system theory is often inaccurate and is not applicable for such system when it is to operate in all four quadrants. Therefore, a method of applying hybrid dynamical system theory, comprising both continuous and discrete elements is proposed in this paper. The paper presents a physical oriented hybrid model accurately describing the machine dynamics. Since development of stabilizing control laws for hybrid dynamical systems is a complicated task, a simpler hybrid model only including the fundamental machine characteristics is beneficial. Therefore, a discussion and several proposals are made on how a simpler DD hybrid model may be established and used for feedback control development.

KW - Dynamic systems

KW - Displacement

KW - Hybrid control

UR - http://www.scopus.com/inward/record.url?scp=85047010472&partnerID=8YFLogxK

U2 - 10.1115/FPMC2018-8874

DO - 10.1115/FPMC2018-8874

M3 - Article in proceeding

SN - 978-0-7918-5196-8

BT - Proceedings of the Bath/ASME Symposium on Fluid Power and Motion Control, FPMC2018

PB - American Society of Mechanical Engineers

ER -

Pedersen NH, Johansen P, Andersen TO. Four quadrant hybrid control oriented dynamical system model of digital displacement ® units. In Proceedings of the Bath/ASME Symposium on Fluid Power and Motion Control, FPMC2018. American Society of Mechanical Engineers. 2018. FPMC2018-8874 https://doi.org/10.1115/FPMC2018-8874