Non contact control of an axially moving beam by varying tension force

HO CHI MINH CITY OF SCIENCE AND TECHNOLOGY -NGUYỄN HOÀNG GIANG MASTER THESIS NON-CONTACT CONTROL OF AN AXIALLY MOVING BEAM BY VARYING TENSION FORCE ĐIỀU KHIỂN DAO ĐỘNG HỆ THỐNG VẬN CHUYỂN VẬT LIỆU MỀM BẰNG PHƯƠNG PHÁP ĐIỀU CHỈNH LỰC CĂNG VẬT LIỆU MECHATRONICS CODE: 8520114 HO CHI MINH CITY, December 2019 ACKNOWLEDGEMENT After more than a year of work, thanks to my efforts and the support of many people, my MS thesis “Non-contact control of an axially moving beam by varying tension force” was completed First of all, I would like to express my sincere gratitude to my advisor Prof Nguyen Quoc Chi of the faculty of mechanical engineering at Ho Chi Minh city of Technology for his passionate advice for his patience, motivation, and immense knowledge Besides, he gave me the access to the laboratory and provided me the best research conditions He also steered me in the right the direction whenever he thought I needed it I am also grateful to the members of Control and Automation Laboratory of the faculty of mechanical engineering at Ho Chi Minh city of Technology for helping me to design and perform the research Without their precious support I would not be able to conduct this research Last but not the least, I must express my very profound gratitude to my parents for providing me with unfailing support and continuous encouragement throughout my years of study and through the process of researching and writing this thesis I hereby declare that the thesis has been done without any plagiarism violations and does not conflict with any issue in ethics Ho Chi Minh, 17 December, 2019 Nguyen Hoang Giang ABSTRACT The main topic of the thesis is presenting a control algorithm to suppress transverse vibrations of an axially moving beam In this thesis, the equations of motion of the axially moving beam are derived by using Hamilton’s principle The Galerkin method is applied in order to reduce the PDEs describing the dynamics of the axially moving beam and into sets of ODEs For control design purposes, these ODEs are rewritten into state-space equations The proposed control algorithm is designed based on the linearization input-output approximate method The advantage of the proposed control law is to regulate the transverse displacement of the moving beam without applying external force to the material surface directly and therefore, to prevent damage of the material surface Finally, the effectiveness of the proposed control algorithm is verified by numerical simulations and experiments Keywords: Axially moving systems; Roll to roll systems; Transverse vibration control; Velocity tracking; Spatially varying tension; Galerkin method; linearization input-output approximate method CONTENTS ACKNOWLEDGEMENT ABSTRACT LIST OF FIGURES LIST OF TABLES CHAPTER INTRODUCTION 1.1 Introduction to roll-to-roll techniques and axially moving system 1.2 Literature review 1.3 Objectives and Scope 1.4 Organization of the dissertation 10 CHAPTER PRELIMINARIES 12 2.1 Hamilton Principle 12 2.2 Galerkin method 14 2.3 Spatially-varying tension model 16 2.4 Tracking control via approximate input-output linearization 18 CHAPTER DYNAMIC MODEL OF SYSTEM 20 3.1 Equations of motion 21 3.1.1 Total kinetic energy 21 3.1.2 Total potential energy 22 3.1.3 Work done 22 3.2 Hamilton’s principle 22 3.3 Galerkin method 24 CHAPTER DESIGN AN INPUT CONTROL 28 4.1 Overview of model 28 4.2 Output tracking control design 30 4.3 The change of the state variables 32 4.4 The proposed control algorithm 34 CHAPTER SIMULATION RESULTS 36 5.1 Control position and parameter 36 5.2 Simulation results 38 5.2.1 The axial transport velocity profile 39 5.2.2 The axial transport velocity profile 41 CHAPTER CONCLUSIONS 46 REFERENCES LIST OF FIGURES Figure R2R processing of a state-of-the-art nanomaterial used in flexible touchscreen displays Figure R2R applications in printing electronic devices Figure Flexible materials used in R2R processing Figure Technical textile manufacturing process using R2R techniques Figure Axially moving string/beam Figure Schematic of proposed boundary control of an axially moving string in [19] Figure Schematic of the axially moving system with MDS controller in [30] Figure Model of axially travelling string system with damping device in [8] Figure Example of large-area high-throughput roll-to-roll patterning systems used in [20], [21] Figure 10 An axially moving beam travelling system 13 Figure 11 Nominal re-model of an axially moving beam travelling system 17 Figure 12 Axially moving beam with one movable roller 21 Figure 13 The block diagram of control method 32 Figure 14 The symmetric (1) and anti-symmetric (2) modes of moving beam 36 Figure 15 The time-depended axial velocity v(t) profile 39 Figure 16 The transverse displacement according to time of velocity profile when not apply the control algorithm 40 Figure 17 The transverse displacement according to time of velocity profile when apply the control algorithm 41 Figure 18 The time-depended axial velocity v(t) profile 42 Figure 19 The transverse displacement of velocity profile according to time when not apply the control algorithm 42 Figure 20 The transverse displacement according to time of velocity profile when apply the control algorithm 43 Figure 21 The velocity profile of pushing roller 44 LIST OF TABLES Table Control parameters 37 Table System parameters 38 CHAPTER INTRODUCTION 1.1 Introduction to roll-to-roll techniques and axially moving system Roll-to-roll (R2R) is a family of manufacturing techniques involving continuous processing of a flexible substrate as it is transferred between two moving rolls of material (Fig 1) [1] R2R is an important class of substrate-based manufacturing processes in which additive and subtractive processes can be used to build structures in a continuous manner Other methods include sheet to sheet, sheets on shuttle, and roll to sheet; much of the technology potential described in this R2R Technology Assessment conveys to these associated, substrate-based manufacturing methods R2R is a “process” comprising many technologies that, when combined, can produce rolls of finished material in an efficient and costeffective manner with the benefits of high production rates and in mass quantities [2] Figure illustrates an example of R2R processing of a state-of-the-art nanomaterial used in flexible touchscreen displays Figure R2R processing of a state-of-the-art nanomaterial used in flexible touchscreen displays The manufacturing techniques developed based on R2R processing minimize human handling, and, consequently, lead to high quality Moreover, it is well known that the rolled form is convenient for storage and transport Especially, the R2R manufacturing techniques have contributed to the rapid development of flexible electronics In the field of electronic devices, R2R is the process of creating electronic devices on a roll of flexible plastic or metal foil (Fig 2) In other fields predating this use, it can refer to any process of applying coatings, printing, or performing other processes starting with a roll of a flexible material and re-reeling after the process to create an output roll Figure R2R applications in printing electronic devices From the demand for high quality and low-cost production, roll-to-roll (R2R) systems have been admitted to be the most effective system handling flexible materials such as films, textiles, papers, polymers, metal sheets… (Fig 3) [3] Therefore, the R2R systems belong to the class of axially moving system that also represent many mechanisms in civil, aerospace, and automotive engineering such as thread winders, band saws, magnetic tapes, aerial cable tramways, power transmission belts… Figure 18 The time-depended axial velocity v(t) profile Figure 19 The transverse displacement of velocity profile according to time when not apply the control algorithm 42 Figure 19 demonstrates the variation of transverse displacement according to time of transport velocity profile in the case when the control algorithm is not applied It can be concluded that the transverse vibration depends on the value of the viscous damping coefficient of the beam material From Fig 19, it is clear that without control algorithm, the transverse vibration occurs quite long, and it took approximately 5.1 seconds for vibration suppression Figure 20 The transverse displacement according to time of velocity profile when apply the control algorithm To suppressing the transverse displacement quickly, control algorithm is applied Figure 20 illustrates the transverse displacement varies with respect to time After 0.4 seconds, value of w(x,t) approaches It is obviously with control algorithm, the time to eliminate the vibration is significant improvement This control algorithm is expected to impart two improvements to performance of the system First, the transverse displacement is expected to decay and 43 suppressed completely Second, the profile for the control input, which is the velocity of the movable roller, needs to be practical Furthermore, the control input is also illustrated in Fig 20, which shows that the maximum velocity needed for vibration suppression is 1.7 meter per second Therefore, this velocity is easy to be generated by mechanism such as hydraulic motor or servo motor Figure 21 The velocity profile of pushing roller Overall, figure 15 to figure 21 shows the transverse displacement at position x= l (t ) x when and when not applying the control algorithm in two cases: a trapezoidal axial transport velocity input and a triangular axial transport velocity input The results were collected from the numerical simulations illustrating the effective of the proposed control algorithm As show in the figures, the time needed for suppressing the transverse displacement decreased noticeable from 44 second to 0.9 second that is nearly 85 percent respect to time in profile and from 5.1 second to 0.4 second that is nearly 92 percent respect to time in profile It is obviously with control algorithm, the time to eliminate the vibration is significant improvement However, the velocity profile of moving roller needed for vibration suppression is achievable, but the chattering problem caused by fast dynamics response can somewhat yields challenges in practical approach 45 CHAPTER CONCLUSIONS In this thesis, a control algorithm to suppress transverse vibrations of an axially moving beam is presented The equations of motion of the axially moving beam are derived by using Hamilton’s principle With regard to the dynamics of the axially moving beam the Galerkin method was applied to reduce the PDEs into sets of ODEs, which were rewritten into state-space equations The proposed control algorithm is designed based on the linearization input-output approximate method The advantage of the proposed control law is to regulate the transverse displacement of the moving beam without applying external force to the material surface directly and therefore, to prevent damage of the material surface Through a comparison of the simulation results (time of vibration suppression) for control and no control situation, the considerable improvement effected by applying the control algorithm to the beam system for vibration suppression were verified 46 REFERENCES [1] Jeffrey D Morse, “Nanofabrication Technologies for Roll-to-Roll Processing”, Report from the NIST-NNN Workshop, September 2011 [2] Jurgen Willmann, Daniel Stocker, and Edgar Dorsam, “Characteristics and evaluation criteria of substrate-based manufacturing Is roll-to-roll the best soltion for printed electronics?”, Organic Electronics, 15 (2014), 1631-1640 [3] K Jain, M Klosner, and M Zemel, “Flexible electronics and displays: highresolution, roll-to-roll, projection lithography and photoablation processing technologies for high-throughput production”, Proceedings of the IEEE, vol 93, pp 1500-1510, 2005 [4] M H Ghayesh and H Farokhi, “Nonlinear dynamical behavior of axially 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%control output and system values e=200; r=0.0002; for i = 2:n Numerator(i)=e*(q1(i-1)+q2(i-1)); Denominator(i)=4/3/l(i-1)*((sign(abs(q1(i-1)*o2-q2(i-1)*o1)-r)+1)*(q1(i1)*o2-q2(i-1)*o1)+((sign(r-abs(q1(i-1)*o2-q2(i-1)*o1))+1)*r)); Proposedcontrol(i)=Numerator(i)/Denominator(i); ddl(i)=Proposedcontrol(i) ; if y(i-1)>= yc dl(i)=dl(i-1)+dt*ddl(i); else if l(i-1)>=l(1) dl(i)=-l(i-1)*c; 52 else dl(i)=0; end end l(i)=l(i-1)+dt*dl(i); %System matrix K11(i)=b*pi^4/(2*l(i)^3)-pi^2*(v(i)^2+dv(i)*l(i))/(2*l(i))+(dv(i)+a*(l(i)lf)/(l(i)*lf))*pi^2/4+pi^2*v(i)*dl(i)/(2*l(i))-pi^2*dl(i)^2/(6*l(i)); K21(i)=-20/9*(a*(l(i)-lf)/(l(i)*lf)+2*v(i)*dl(i)/l(i)-2*dl(i)^2/l(i))+4/3*((c*dl(i)c*v(i))-32/9*dv(i))+8/3*ddl(i)/l(i); K12(i)=-20/9*(a*(l(i)-lf)/(l(i)*lf)+2*v(i)*dl(i)/l(i)-2*dl(i)^2/l(i))-4/3*((c*dl(i)c*v(i))-8/9*dv(i))-8/3*ddl(i)/l(i); K22(i)=16*b*pi^4/(2*l(i)^3)-4*pi^2*(v(i)^2+dv(i)*l(i))/(l(i)*2)+(dv(i)+a*(l(i)lf)/(l(i)*lf))*pi^2+4*pi^2*v(i)*dl(i)/(l(i)*2)-4*pi^2*dl(i)^2/(6*l(i)); C21(i)=-4*v(i)/3+4*dl(i)/3; C12(i)=4*v(i)/3-4*dl(i)/3; C11(i)=c*l(i)/2+dl(i)/2; M(i)=l(i)/2; Ax(i)=M(i)/dt^2+C11(i)/dt+K11(i); Bx(i)=K21(i)+C21(i)/dt; Cx(i)=q1(i-1)*(M(i)/dt^2+C11(i)/dt)+dq1(i-1)*M(i)/dt+q2(i-1)*C21(i)/dt; Ex(i)=M(i)/dt^2+C11(i)/dt+K22(i); Dx(i)=K12(i)+C12(i)/dt; Fx(i)=q2(i-1)*(M(i)/dt^2+C11(i)/dt)+dq2(i-1)*M(i)/dt+q1(i-1)*C12(i)/dt; q1(i)=(Fx(i)*Bx(i)-Ex(i)*Cx(i))/(Dx(i)*Bx(i)-Ex(i)*Ax(i)); q2(i)=(Fx(i)*Ax(i)-Dx(i)*Cx(i))/(Ex(i)*Ax(i)-Bx(i)*Dx(i)); dq1(i)=(q1(i)-q1(i-1))/dt; 53 dq2(i)=(q2(i)-q2(i-1))/dt; %system output y(i)=o1*q1(i)+o2*q2(i); end figure; plot(t,y); xlabel('time [s]'); ylabel(' w[l/4]’); title('Profile2’); 54 CURRICULUM VITAE Full name: GIANG HOANG NGUYEN Gender: Male Date of birth: September 5, 1993 Marital status: Single Emails: 1770539@hcmut.edu.vn giangnguyenhoang.tl@gmail.com Cell phone: 098 819 6759 Hometown: Hanoi - Vietnam Education: Degree Field Institution Date Conferred Bachelor Mechanical Hanoi University Aug 2011 – Aug Degree Engineering of Science and 2016 Technology Master Degree Mechanical Ho Chi Minh City Engineering of Technology Employment: 55 Aug 2017 Name of Employment Position Date Conferred Kyudenko Vietnam Mechanical engineer Sept 2016 – Mar 2017 Autonics Vina Operation engineer Sept 2019 Publications [1] Nguyen Hoang Giang, Nguyen Quoc Chi “Non-contact control of axially moving beam by varying tension force”, National Conference on Mechanical Engineering and Manufacturing, Vietnam, p.208-213 56 ... more than a year of work, thanks to my efforts and the support of many people, my MS thesis ? ?Non- contact control of an axially moving beam by varying tension force? ?? was completed First of all,... topic of the thesis is presenting a control algorithm to suppress transverse vibrations of an axially moving beam In this thesis, the equations of motion of the axially moving beam are derived by. .. Figure 10 An axially moving beam travelling system 13 Figure 11 Nominal re-model of an axially moving beam travelling system 17 Figure 12 Axially moving beam with one movable