### Abstract

Original language | English |
---|---|

Title of host publication | Proceedings of the Bath/ASME Symposium on Fluid Power and Motion Control, FPMC2018 |

Number of pages | 9 |

Publisher | American Society of Mechanical Engineers |

Publication date | Sep 2018 |

Article number | FPMC2018-8874 |

ISBN (Print) | 978-0-7918-5196-8 |

ISBN (Electronic) | 9780791851968 |

DOIs | |

Publication status | Published - Sep 2018 |

Event | BATH/ASME 2018 Symposium on Fluid Power and Motion Control - Bath, United Kingdom Duration: 12 Sep 2018 → 14 Sep 2018 |

### Conference

Conference | BATH/ASME 2018 Symposium on Fluid Power and Motion Control |
---|---|

Country | United Kingdom |

City | Bath |

Period | 12/09/2018 → 14/09/2018 |

### Fingerprint

### Cite this

^{®}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

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^{®}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.

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-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 -

^{®}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