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Distributed parameter modeling and model predictive control of weft insertion in air-jet weaving

Verteiltparametrische Modellierung und modellprädiktive Regelung des Schusseintrags beim Luftdüsenweben
Tong Wu

Tong Wu was born in 1993. He received the B. Sc. degree from Beihang University, China in 2015 and M. Sc. degree in Automation Engineering from RWTH Aachen University, Germany in 2017. Since 2017 he is a research associate and is pursuing his PhD at the Institute of Automatic Control, RWTH Aachen University. His research focuses on model-based predictive control and process automation of manufacturing systems, for example, air-jet weaving machines.

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, Marvin Huang

Marvin Huang was born in 1995. He received B. Sc. degrees in Mechanical Engineering and Computer Science from RWTH Aachen University, Germany. He was a visiting student in chemical engineering at Imperial College London. He received his M. Sc. degree in Automation Engineering from RWTH Aachen University in 2020. Since November 2020, he is pursuing his PhD as research associate at the Institute of Automatic Control, RWTH Aachen University. His research interests include distributed parameter systems and model-based control strategies for vehicles and surface vessels.

, Patrick Ochudlo

Patrick Ochudlo was born in 1993. He received both his B. Sc. degree in Mechanical Engineering and his M. Sc. degree in Automation Engineering at the RWTH Aachen University, Germany. Since March 2020, he is perusing his PhD working as a research assistant at the Institute of Automatic Control, RWTH Aachen University. His research is focused on establishing advanced estimation methods and model-based control strategies to production systems, e. g., a casting process.

, Lorenz Dörschel

Dr.-Ing. Lorenz Dörschel was born in 1989. He received the B. Sc. degree from University of Stuttgart, Germany, in Engineering Cybernetics 2011, the M. Sc. 2013 from RWTH Aachen University, Germany, in Automation Engineering and the Dr.-Ing. degree also from RWTH Aachen University in 2018. Since 2018 he works as Postdoc at the Institute of Automatic Control, RWTH Aachen University. His main areas of research cover the fields of distributed parameter systems, model reduction, model predictive control and parameter space approach techniques.

, Maximilian Kemper

Dr.-Ing. Maximilian Kemper studied mechanical engineering and economics at the RWTH Aachen University. He graduated his master’s degree in 2014, worked as a researcher at the Institut für Textiltechik (ITA) of RWTH Aachen University and received the Dr.-Ing. degree in 2020. He conducted research in the field of woven and knitted fabrics regarding both product and machine development. His personal research focuses are the field of digitalization including model-based self-optimization and control of the weaving process as well as optical quality inspection systems using artificial intelligence algorithms.

, Dirk Abel

Univ.-Prof. Dr.-Ing. Dirk Abel was born in 1958. He received both the Dipl.-Ing. degree in mechanical engineering and the Dr.-Ing. degree from RWTH Aachen University, Germany, in 1983 and 1987, respectively. In 2001, he became full professor and head of the Institute of Automatic Control, RWTH Aachen University. His main area of research covers the fields of model predictive control, nonlinear and robust control as well as rapid control prototyping in different application areas.

and Thomas Gries

Univ.-Prof. Dr.-Ing. Thomas Gries studied at the RWTH Aachen University, Germany. He holds a diploma degree in mechanical engineering and economics and a doctorate in mechanical engineering. From April 2001 onwards, he is Director of the Institut für Textiltechnik (ITA) of RWTH Aachen University. The honoris causa Professorship of Lomonossow University is the most distinguished scientific award of Russia given for his achievements. Since 2015 he is member of the National Academy of Technological Science and Engineering (acatech).

Abstract

In air-jet weaving, the braking of inserted weft threads plays a significant role in fabric quality and machine productivity. This contribution presents Model Predictive Control (MPC) which controls the weft tip’s position and velocity with an optimal braking force. The inserted weft thread is firstly modeled as a distributed parameter system. The relation between the braking force and the weft tip’s position is described by a Partial Differential Equation (PDE). By analyzing the PDE with Laplace transform and solving the PDE with a Galerkin method, a state-space model is presented. Subsequently, identification experiments of the constructed yarn brake are performed and the whole model is analyzed as well as reduced using balanced truncation. Based on the system states and input disturbance estimated by a dual Kalman filter, an MPC controls the weft tip’s position and velocity appropriately without any backward movement. Regarding model deviations and simulated measurement errors, the MPC performs robustly.

Zusammenfassung

Beim Luftdüsenweben hat das Abbremsen der eingetragenen Schussfäden einen maßgeblichen Einfluss auf die Gewebequalität und die Maschinenproduktivität. In diesem Beitrag wird eine modellprädiktive Regelung (MPC) entwickelt, die die Position und Geschwindigkeit der Fadenspitze durch das Stellen der Bremskraft regelt. Hierfür wird der Schussfaden zunächst als ein verteiltparametrisches System modelliert. Die Dynamik zwischen der Bremskraft und der Position der Fadenspitze wird durch eine partielle Differentialgleichung (PDE) beschrieben. Durch eine Analyse der PDE mittels Laplace-Transformation und Lösung der PDE mittels der Galerkin-Methode wird ein Zustandsraummodell hergeleitet. Anschließend werden Identifikationsversuche der konstruierten Fadenbremse durchgeführt, die Modelldynamik analysiert und das Modell mittels des balancierten Abschneidens reduziert. Basierend auf den mit einem Dual Kalman-Filter geschätzten Systemzuständen und Eingangsstörungen regelt eine MPC die Position und Geschwindigkeit der Fadenspitze unter Vermeidung einer Rückwärtsbewegung. Hinsichtlich Modellabweichungen und Messfehlern zeigt die vorgestellt MPC in der Simulation ein robustes Verhalten.

Award Identifier / Grant number: 19299N

Funding statement: This work was supported by the German Federal Ministry for Economic Affairs and Energy [IGF Project 19299N], in compliance with a resolution of the German Bundestag.

About the authors

Tong Wu

Tong Wu was born in 1993. He received the B. Sc. degree from Beihang University, China in 2015 and M. Sc. degree in Automation Engineering from RWTH Aachen University, Germany in 2017. Since 2017 he is a research associate and is pursuing his PhD at the Institute of Automatic Control, RWTH Aachen University. His research focuses on model-based predictive control and process automation of manufacturing systems, for example, air-jet weaving machines.

Marvin Huang

Marvin Huang was born in 1995. He received B. Sc. degrees in Mechanical Engineering and Computer Science from RWTH Aachen University, Germany. He was a visiting student in chemical engineering at Imperial College London. He received his M. Sc. degree in Automation Engineering from RWTH Aachen University in 2020. Since November 2020, he is pursuing his PhD as research associate at the Institute of Automatic Control, RWTH Aachen University. His research interests include distributed parameter systems and model-based control strategies for vehicles and surface vessels.

Patrick Ochudlo

Patrick Ochudlo was born in 1993. He received both his B. Sc. degree in Mechanical Engineering and his M. Sc. degree in Automation Engineering at the RWTH Aachen University, Germany. Since March 2020, he is perusing his PhD working as a research assistant at the Institute of Automatic Control, RWTH Aachen University. His research is focused on establishing advanced estimation methods and model-based control strategies to production systems, e. g., a casting process.

Lorenz Dörschel

Dr.-Ing. Lorenz Dörschel was born in 1989. He received the B. Sc. degree from University of Stuttgart, Germany, in Engineering Cybernetics 2011, the M. Sc. 2013 from RWTH Aachen University, Germany, in Automation Engineering and the Dr.-Ing. degree also from RWTH Aachen University in 2018. Since 2018 he works as Postdoc at the Institute of Automatic Control, RWTH Aachen University. His main areas of research cover the fields of distributed parameter systems, model reduction, model predictive control and parameter space approach techniques.

Maximilian Kemper

Dr.-Ing. Maximilian Kemper studied mechanical engineering and economics at the RWTH Aachen University. He graduated his master’s degree in 2014, worked as a researcher at the Institut für Textiltechik (ITA) of RWTH Aachen University and received the Dr.-Ing. degree in 2020. He conducted research in the field of woven and knitted fabrics regarding both product and machine development. His personal research focuses are the field of digitalization including model-based self-optimization and control of the weaving process as well as optical quality inspection systems using artificial intelligence algorithms.

Dirk Abel

Univ.-Prof. Dr.-Ing. Dirk Abel was born in 1958. He received both the Dipl.-Ing. degree in mechanical engineering and the Dr.-Ing. degree from RWTH Aachen University, Germany, in 1983 and 1987, respectively. In 2001, he became full professor and head of the Institute of Automatic Control, RWTH Aachen University. His main area of research covers the fields of model predictive control, nonlinear and robust control as well as rapid control prototyping in different application areas.

Thomas Gries

Univ.-Prof. Dr.-Ing. Thomas Gries studied at the RWTH Aachen University, Germany. He holds a diploma degree in mechanical engineering and economics and a doctorate in mechanical engineering. From April 2001 onwards, he is Director of the Institut für Textiltechnik (ITA) of RWTH Aachen University. The honoris causa Professorship of Lomonossow University is the most distinguished scientific award of Russia given for his achievements. Since 2015 he is member of the National Academy of Technological Science and Engineering (acatech).

Appendix A
Table 2

Description of symbols during modeling in Section 2.

A system matrix
A w cross-section area
B input matrix
c w resistance coefficient
C output matrix
C β output matrix for weights
d input disturbance
D G diameter of weft thread
E Young’s modulus
F Aero aerodynamic force
F Aero, appr approximated aerodynamic force
F B braking force
F D viscous damping force
F E spring force
L length of weft thread
p position
R l boundary condition function
s k , + / poles of PDE transfer function
s 1 weft tip’s position
t time coordinate
u system input
v air velocity of compressed air in reed channel
v 0 initial weft velocity
v 1 weft tip’s velocity
w displacement
w h inhomogeneous part of PDE solution
w ˜ homogeneous part of PDE solution
x state vector
X material coordinate
Δ X volume element’s width
y β weight vector
Z input disturbance matrix
α aerodynamic coefficient
β h , β k weight of basis function
ϵ strain tensor
ϵ 0 initial strain tensor
η damping coefficient
Π PDE of weft during braking
ρ air air density
ϕ h basis functions of solution space
Φ L transformation matrix
ψ test basis functions
Ω domain of material coordinate

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Received: 2021-02-01
Accepted: 2021-06-07
Published Online: 2021-08-10
Published in Print: 2021-08-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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