i
MODELING AND DESIGN CONTROL STRATEGY
FOR UNWIND/REWIND SYSTEM
MUHAMAD FAHEZAL BIN ISMAIL
A project report submitted in partial fullfilment of the
requirements for the award of the degree of
Master of Engineering (Electrical - Mechatronics And Automatic Control)
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
MAY 2008
iii
To my beloved wife Miza , my two daughters, Aina , Imanina , and my beloved
family Ismail , Noraini , Farehan , and Hafiz. Thank for all your support .
iv
ACKNOWLEDGEMENT
Alhamdullilah, thank to Allah, because of Him we are still here and His
entire gift in this world. And most of all, for giving me opportunities to learn His
knowledge.
This work was supervised by Associate Professor Dr. Yahaya Mohd. Sam at
the Universiti Teknologi Malaysia. I greatly appreciate all his help and guidance.
I am grateful to my wife, Miza Hj. Hamid my two daughters, Nur Qurratu
‘Aina and Nur Imanina Musfirah, my parents, Hj. Ismail Hj Razali, Hjh Noraini Hj
Tumpang, Farehan and Mohd Hafiz, without whose help, encouragement and
patience I would never have gotten this thesis completed and who made it all
worthwhile.
I would also like to grateful to my brilliant and dedicated friends, Norfadzli ,
Mahmood El Emam , Mohd Izam , Lukman Hakim and Mohd Zulkhairi, who also
gave me a great deal of support and encouragement.
Finally, thank you to all the other people who have supported me during the
course of this work. Thank You! Thank You!
v
ABSTRACT
This paper presents the mathematical modeling and designing a control strategy for
unwind and rewind system. Unwind and rewind system is widely used in industry
that involved the web transportation such as textile, plastic, paper and metal.
Basically, the unwind and rewind system consists of three motors which are to
control the Unwind, Traction and Rewind. Currently, the system used Programmable
Logic Controller (PLC) to control the whole system operation. Strain gauge is used
for the system feedback. This project was replaced the PLC to computer controlled
method. A new control algorithm that based on the regulator feedback was proposed.
The tension observer is introduced as a regulator feedback and dynamic simulation
requirement.The mathematical modeling of the system is established base on the
tension control, speed control and other elements related to the system. In the control
strategy, PID (Propotional Integral and Differential) controller is used to the tension
controller and speed controller for simulation and experiment. The xPC-target box is
used as a prototype controller to the unwind and rewind tension and speed
synchronization. The validation process of the results was performed for both
simulation and experimental to see the performance of the system.
vi
ABSTRAK
Kertas ini mempersembahkan pemodelan matematik dan strategi kawalan
untuk sistem tidak mengulung dan mengulung. Sistem tidak mengulung dan
mengulung ini banyak digunakan dengan meluas dalam industri pengulungan seperti
tekstil, plastik, kertas dan besi. Secara asasnya, sistem tidak mengulung dan
mengulung mempunyai tiga buah motor digunakan untuk kawalan pada tidak
mengulung, treksi(pandu arah), dan mengulung. Pada masa sekarang sistem tersebut
menggunakan Kawalan Logik Berprogram (“PLC”) untuk kawalan seluruh operasi
sistem tersebut. Kawalan Logik Berprogram telah digantikan dengan kaedah
kawalan mengunakan komputer dalam projek ini. Algoritma kawalan baru
berasaskan sistem kawalan balas telah direka. Pemerhati tegangan diperkenalkan
sebagai kawalan balas dan juga untuk memunuhi keperluan simulasi dinamik.
Pemodelan matematik dibuat berdasarkan kawalan tegangan, kawalan laju, dan juga
elemen-elemen lain yang berkaitan dengan sistem tersebut. Dalam strategi kawalan
pula, kawalan perkadaran, kamiran dan pembezaan (“PID”) telah digunakan pada
kawalan tegangan dan kawalan laju untuk simulasi dan eksperimen.“xPC-target box”
telah digunakan sebagai kawalan prototaip untuk kesamaan laju dan mengawal
tegangan pada sistem tersebut. Proses validasi telah dilakukan pada kedua-dua
simulasi dan eksperimen untuk melihat tahap pencapain sistem tersebut.
vii
TABLE OF CONTENTS
CHAPTER
TITLE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xi
LIST OF APPENDICES
1
PAGE
xiv
INTRODUCTION
1.1
Introduction
1
1.2
Objective
2
1.3
Scope of Work
2
1.4
Project Background
4
1.5
Outline of the Thesis
6
viii
2
LITERATURE REVIEW
2.1
3
4
Overview of web transport system
METHODOLOGY
3.1
Introduction to Methodology
19
3.2
Mathematical Model of the system
20
3.3
Mathematical Model for control law
33
3.4
Dynamic Simulation of the system
34
3.5
Real Time Implementaion of the system
36
3.6
Method of Tuning PID gain
41
RESULTS AND DISCUSSIONS
4.1
Introduction on the Results and Discussion
46
4.2
Result on the Tension without Filter
47
4.3
Result on the Tension with Filter
48
4.4
Simulation Results
49
4.5
Experimental Results
54
4.6
Comparison between Simulation
and Experimnental Results
5
7
59
CONCLUSION
5.1
Introduction on the conclusion
62
5.2
Conclusion
63
5.3
Future Development
64
ix
REFERENCES
65
APPENDICES
68
x
LIST OF TABLES
TABLE NO.
TITLE
PAGE
3.1
Specification for closed loop tension control system
41
3.2
The results of tuning gain using fixed-gain method
41
3.3
Results on the PID controller gain using response
optimization.
43
Results on the PID controller gain using Ziegler Nichols
method
45
3.4
xi
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
1.1
Flow chart represents the scope of work
3
1.2
The real-time implementation setup for unwind/rewind system
5
2.1
Tension control system example with load cell.
8
2.2
Electrical equipment and drive system setup
9
2.3
Schematic of the studied web transport system
10
2.4
Experimental setup for PI-type observer
11
2.5
Outline of typical web processing line
11
2.6
A typical dancer subsystem
12
2.7
Sketch on endless experimental web platform
12
2.8
Schematic diagram of three span web transport simulator
14
2.9
Schematic diagram for define the physics of the
dancer roll assembly
15
2.10
Tension estimation (and control) using torque command signals
16
2.11
Different Configurations of Center-driven Winders
17
2.12
Speed regulated, tension controlled winder
17
2.13
Roll to roll method
18
2.14
Tension meters
18
3.1
Current system of unwind/rewind.
20
3.2
Web material in tension
21
xii
3.3
Primitive elements in the web handling process
24
3.4
A free web span control volume
25
3.5
PI-type observer with filtered inertia block
26
3.6
PI-type observer with inertia compensation
27
3.7
Proposed observer with inertia, bearing and Coulomb friction
27
3.8
Direct unwind and rewind
29
3.9
Direct unwind and rewind system with tension observer
30
3.10
The dynamic simulation block diagram
34
3.11
The real-time implementation block diagram
36
3.12
Flow chart of real time control algorithm
37
3.13
Standard procedure to setup xPC-target box with
personal computer
38
3.14
Scaling graph to calculate the value of tension for experimental and
simulation.
39
3.15
Scaling graph to calculate the value of tension for experimental and
simulation
40
3.16
PID controller gain tuning using response optimization method
43
3.17
Transient response of unwind and rewind system
44
4.1
Tension signal capture from unwind section in experiment process 47
4.2
The signal of tension after filtered by second order low pass filter 48
4.3
The Simulink model for unwind and rewind model plant
49
4.4
The effect of tension reference at 20N
50
4.5
The effect of tension reference at 30N
51
4.6
The effect of tension reference at 40N
52
4.7
The effect of tension reference at 50N
53
4.8
The real-time Simulink model for unwind and rewind system
54
xiii
4.9
The experimental results at 20N
55
4.10
The experimental results at 30N
56
4.11
The experimental results at 40N
57
4.12
The experimental results at 50N
58
4.13
Tension result in simulation
59
4.14
Tension result in experimental
59
4.15
Unwind speed result in simulation
60
4.16
Unwind speed result in experimental
60
4.17
Rewind speed result in simulation
61
4.18
Rewind speed result in experimental
61
xiv
LIST OF APPENDICES
APPENDIX NO.
A.
TITLE
A block diagram of the real time workshop
PAGE
69
CHAPTER 1
INTRODUCTION
1.1
Introduction
In the roll to roll method, the web quality depends on the web tension maintained
throughout the process. It is essential that the web tension be controlled and maintained at
an appropriate level if a satisfactory web quality is required. Various studies have
addressed the issue of tension control in web transport systems. Two tension control
methods, namely the open loop tension controller and the closed-loop tension controller
with observer-based tension feedback (simulation) and strain gauge (experimental).
Feedback tension control using tension transducer is mostly used in the web
industry. Now, low cost and high productivity are two primary goals in design of web
transport system. One approach to achieve low cost is through the implementation of
observer technique in replace tension transducer. To achieve high productivity, it is
normally required to increase the speed process. However, as the process speed or
variation of the speed is high, system friction and inertia of rotation of rolls could cause
problems in implementation of observer techniques for tension estimation and control.
2
A new tension control algorithm with tension observer is proposed using observed
tension as a regulator feedback. The tension observer is based on the torque balance of a
roller stand, including the acceleration torque. Using this estimated tension, the new
tension controller can be constructed with faster dynamic response in case of line speed
acceleration or deceleration. The proposed scheme needs no additional hardware because
the inputs of observer, current and speed are already being monitored by the motor drive
system. The proposed controller is compared to the conventional controllers through
simulations and experiments.
1.2
Objective:
The objectives of this project are as follow:
i To establish the mathematical model of unwind/rewind system.
ii To setup experimental and simulation as a main methodology of the project.
iii To study the control performance of the system based on the results
obtained from simulation and experiment.
1.3
Scope of Work
The scope of work is clearly to establish mathematical model of unwind/rewind
system and study control performance of the system using Matlab and Simulink.
(Simulation). The next step is to plan experimental design, setup and perform the
experiment. Finally the validation process will be done based on the simulation result and
the experimental results. The scope of work can be described in the flow chart as shown
in Figure 1.1.
3
Confirmation of
project title
To establish
mathematical
model of unwind/
rewind system
To study control
performance for
tension and speed
of the system
To plan
experimental
design
To setup
experiment
To perform
experiment
To validate
simulation results
with the
experimental results
Finish Project
Figure 1.1: Flow chart represents the scope of work
4
1.4
Project Background
Winder machine is widely used in industry that involved winding operation such
as textile, paper, plastic, and metal. Basically, the winder machine system consists of
three motors which are to control the Unwind, Traction and Winder. Currently, the
system used PLC (Programmable Logic Controller) to control the whole system
operation. Load cell or strain gauge is used for the system feedback. Previously the
system doesn’t have any control algorithm applied.
This project will replace the PLC to computer controlled method. A new control
algorithm that based on the regulator feedback will be proposed. The tension observer is
introduced as a regulator feedback. Then, a real time control will be applied to control
the whole system. The synchronization of the unwind speed and rewind speed is the main
concentration to overcome the twisted problem occurred with previous controller. This
project will used the x-PC target box as an interface instrument from PC to
Unwind/Rewind system for real time control as shown in Figure 1.2.
5
Figure 1.2: The real-time implementation setup for unwind/rewind system.
6
1.5
Outline of the Thesis
The thesis presents the implementation of the mathematical modeling of
Unwind/rewind system and designs a control strategy for the system.
Chapter 2 focuses on the literature review, which introduces the overview of
Unwind/Rewind system and tension issue. The explanation begins with the previous
researches on web transport system which is similar to Unwind/Rewind. This chapter is
then described by related researches on the mathematical modelling of unwind/rewind
system, which is found to be related and facilitate to this project.
Chapter 3 provides the methodology that is used through out the work of this
project. It covers the technical explanation of this project, derivation of the dynamic
model mathematical equations using related formula and performing the experiment.
Then the model will be verified with the simulation results and experimental results.
Chapter 4 deals with the time response results and Matlab/Simulink simulation
results of the dynamic model and the real time results. The simulation results are being
compared with the experimental results for model validation.
Chapter 5 presents the conclusions of the project as well as some constructive
suggestions for further development and the contribution of this project. The project
outcome is concluded in this chapter. As for future development, some suggestions are
highlighted with the basis of the limitation of the effectiveness mathematical equation
and simulation analysis executed in this project.
7
CHAPTER 2
LITERATURE REVIEW
2.1
Overview of the web transport system
In this sub-chapter, a brief survey of previous researches about unwind/rewind
system will be highlighted.
Ho Song et al, 1998 presented a tension control algorithm with tension observer is
proposed using observed tension as a regulator feedback. The tension observer is based
on the torque balance of a roller stand, including the acceleration torque. Using this
estimated tension, a new tension controller can be constructed with faster dynamic
response in case of line speed acceleration or deceleration. The proposed scheme needs
no additional hardware because the inputs of observer, current and speed are already
being monitored by the motor drive system. As this scheme directly controls torque
current of motor, better control performance can be obtained even without the tension
8
transducer. Through the simulations and experiments with the laboratory setup, the
performance of conventional and the schemes are compared. The results had shown the
effectiveness of the proposed tension controller. Figure 2.1 shows the tension control
system example with unwind and rewind section.
ω1
ω2
τ1
τ2
Figure 2.1: Tension control system example with load cell.
This research reported that a new tension control algorithm with tension observer
has been proposed using observed tension as a regulator feedback. The tension observer
is based on the torque balance of a roller stand, including the acceleration torque. Using
this estimated tension, a new tension controller can be constructed with faster dynamic
response in the case of line speed acceleration or deceleration. The performance of the
proposed controller has been compared with those of conventional open-loop and closedloop schemes in a prototype setup. Simulation and experimental results show that this
algorithm is simple and effective in controlling the tension, even in transient state.
9
M
Oscilloscope
IGBT Inverter 1
Motor 1
Encoder
DSP 1
Load cell
Host PC
DSP 2
Encoder
Oscilloscope
IGBT Inverter 2
M
Motor 2
Figure 2.2: Electrical equipment and drive system setup
Ku Chin Lin 2003 studied on the observer based tension control with friction and
Inertia Compensation. Low cost and high productivity are two primary goals in design of
a web transport system as shown Figure 2.2. One approach to achieve low cost is through
the implementation of observer techniques in replace of tension transducers. To achieve
high productivity, it is normally required to increase the process speed. However, as the
process speed or variation of the speed is high, system friction and inertia of rotation of
rolls could cause problems in implementation of observer techniques for tension
estimation and control. Few of the previous studies have considered the problems of
friction and inertia in a single article. This paper proposes an observer with friction and
inertia compensation. The proposed observer has a feedback configuration and it is able
10
to estimate web tension precisely regardless of the effects of friction and inertia.
Linearization and decentralization techniques are implemented. Design of the proposed
observer-based tension feedback controller is performed in the frequency domain.
Eccentricity of unwind roll is considered as sinusoidal disturbances to the system. A
procedure for design of the proposed controller and eccentricity of rolls are discussed.
Simulation and experimental works have been performed and they show that the
proposed observer-based tension feedback controller performs as well as a classical
tension feedback controller using a tension transducer. Figure 2.3 shows the schematic
diagram on the studied of web transport system.
Figure 2.3: Schematic of the studied web transport system.
Friction and inertia compensation are necessary in implementation of observer techniques
for tension estimation and control.
This studied presents a PI-type observer that is able to estimate web tension under
dominant influences of system friction and rotational inertia. The proposed observer has a
feedback configuration with friction and inertia being compensated. Figure 2.4 shown the
experimental setup the studied.
11
Figure 2.4: Experimental setup for PI-type observer.
Ramamurthy et al, 2005 studied on the comparative of the characteristic of active
and passive dancers. A substantial number of web process lines use dancer mechanisms
for attenuating web tension disturbances. Although passive dancer mechanisms are
commonly used in web process lines, recently there has been a growing interest in active
dancer mechanisms due to their ability to attenuate disturbances over a wide range of
frequencies. The focus of the paper is on a comparative study of active and passive
dancer mechanisms used in web processing machines for tension disturbance attenuation.
Active and passive dancers are compared using simplified analytical models. To
substantiate the analysis, results from experiments are shown and discussed. Figure 2.5
shows an outline sketch of a typical web process line. Operations such as coating,
printing, and drying are performed in the processing section.
Figure 2.5: Outline of typical web processing line.
12
Figure 2.6 shows a schematic of a typical dancer subsystem. The dancer subsystem can
be classified into two types: (i) an active dancer, and (ii) a passive dancer.
Figure 2.6: A typical dancer subsystem. Dancer subsystem is classified as an ‘‘Active
Dancer’’ if the dancer roller is driven by an actuator (represented by a rectangle with an
arrow inside it) otherwise it is a ‘‘Passive Dancer’’.
Figure 2.7: Sketch on endless experimental web platform
13
In the studied, analytical and experimental are performed to compare the performance of
passive dancer and active dancer in attenuating tension disturbances. This studied did not
investigate the effect of the sensor (mainly load cell) characteristics on the tension
control. Aspects of the sensor used as the feedback for active dancer controller, such as,
response time, the location in the process line, and the bandwidth, are other important
considerations that need to be taken into account.
Shin et al, 2005 studied on the effect of tension on the lateral dynamic and control
of a moving web. An experimental study was carried out to find the correlation between
web tension variation and the lateral motion of a moving web. The experimental results
said that if the web tension is not sufficiently high, the lateral dynamic motion is closely
related with the web tension variation. A new ‘factor’ to describe the influence of the web
tension on the lateral dynamic response was defined based on a well known traction
coefficient estimation model.
A factor to describe the influence of the slippage on the lateral dynamic response
of the web was derived based on a well known traction coefficient estimation model. The
traction coefficient can be estimated from an air-gap thickness model with which slip
condition can be determined. The slip condition is a function of a web tension, a web
speed and a velocity of a roller. The ratio of the axial displacement of a guider roller and
the lateral position of the web was measured with an open loop condition in a wide range
of operating tension and speed, and the factor which represented the effect of web tension
on a lateral behavior of the web was fitted and verified from the experimental data.
Finally the new factor was used in designing of a cross-couple controller which
included the effect of operating tension or the variation of it on the lateral motion to
regulate properly disturbances generated by a web tension.
14
The proposed factor was updated at each sampling period from measured signals
such as the web tension and the velocity of both web and roller, and used to calculate
variable control gain. Figure 2.8 shows the schematic diagram of the simulator. In each
span, the web tension was measured by a load cell and controlled by a speed control of
each roller. In the second span, two guider systems were equipped, and the lateral
position of a moving web was measured at the three positions
Figure 2.8: Schematic diagram of three span web transport simulator
An experimental study was carried out to determine the correlation between the
web tension variation and the lateral motion of a moving web. The experimental results
show that if the web tension is not sufficiently high, the lateral dynamic motion is closely
related with the web tension variation. A new factor to describe the influence of the web
tension on the lateral dynamic response was defined based on a well known traction
coefficient estimation model. The factor was used in design of a cross-couple controller
that automatically tunes proportional and integral gains of the lateral position controller
according to the web tension and velocity. Finally it was experimentally verified that this
cross couple controller could regulate successfully lateral disturbance which was
transferred from upstream span and caused by tension variation.
15
Ebler et al, 1993 carried out investigation two different ways of regulating the web
tension in an off-machine coater by using either a tension controller with load cells or a
position controller using dancer rolls. A computer model based on an existing offmachine coater that has both systems integrated will be used as the basis for this research.
The two systems will be analyzed, considering the stability of the system and its dynamic
response. Practical results based on measurements made on site will be included. The
schematic shown in Figure 2.9 has been used to develop the formulas that define the
physics of the dancer roll assembly.
Figure 2.9: Schematic diagram for define the physics of the dancer roll assembly
There is no difference between controlling tension using dancer rolls or load
cells. However, in a “clean load cell system,” where a filter of only 10 ms is necessary,
the load cell system is far superior because the gain of the controller can be increased
considerably, resulting in a far superior response and smaller drop-in tension.
16
Valenzeula et al, 2003 are proposes and evaluates sheet tension estimation using only
conventional motor and control signals, present in all newer drive controllers, integrated
into a process model observer. This observer-based approach eliminates the need for the
invasive tension transducers, and may also be used to replace the inaccurate indirect
speed control schemes. The proposed tension estimator is shown in Figure 2.10 for the
two-section system.
Figure 2.10: Tension estimation (and control) using torque command signals.
A new sensorless sheet tension control for the dry end of a Paper Machine has been
presented and evaluated. This system eliminates the sheet tension sensors, and only uses
the same current signals actually required in the speed/torque control of the drives.
17
Zhijun Liu, 1999 has studied the comprehensive dynamic analysis of center driven web
winder controls. The modeling and dynamic behaviors of the winder systems are
described. Then, different control strategies are analyzed and discussed. There exist
various mechanical configurations of center driven web winders. Two different
configurations are shown in Figure 2.11.
Figure 2.11: Different Configurations of Center-driven Winders.
Figure 2.12: Speed regulated, tension controlled winder.
18
Cheng et al, 2005 has studied the PI type closed loop torque observer. The purpose of
having this method is to estimate external load torque acting on unwind roll. Figure 2.13
shown the roll to roll method and Figure 2.14 shown the tension meters method between
load cell and dancer roll.
Figure 2.13: Roll to roll method
Figure 2.14: Tension meters: (a) Load cell (b) Dancer roll
This study has developed an observer-based tension feedback controller for a
direct drive web transport system using the observer web tension as regular feedback
signal. Based on measurement of unwind motor speed, motor current, and unwind roll
radius, the proposed method successfully estimates the web tension using an indirect
method. In a series of DSP-based experiments, the performance of the proposed
controller has been compared with the results obtained using the conventional open-loop
tension controller and the closed-loop tension controller with a tension meter.
19
CHAPTER 3
METHODOLOGY
3.1 Introduction
This chapter is focuses on the establishment of the dynamic model and the
mathematical model of the unwind/rewind system. Firstly, the system behavior will be
studied to obtain the dynamic model and mathematical model. The modeling will covered
the Hooke law, stress of material used, and primitive element. The design of control gain
will be based on the Ziegler Nichols method, the fixed-gain PID controller, Observerbased tension feedback controllers and using SIMULINK response optimization with
signal constraint block. The used model will be verified with the published papers. The
next part is to obtain the mathematical model where the plant parameter for the system is
obtained from existing papers. The model is expressed in state – space form in order to
get the system responses by using computer simulation. The experimental part will be
done by using real time experimental instrument which is xPC-target box. The validation
process will be based on the simulation results and experimental results.
20
3.2 Mathematical model of the system.
3.2.1
System overview
Figure3.1 has shown the overview picture of the current system. In this
arrangement, the web is wound out from the unwind roll, passes through the two
idle rollers and first strain gauge. Then it will pass through the traction rollers and
another two idle rollers. The purpose of this section is to guide the moving web to
the second strain gauge and last two idle rollers until the web rewind back at
constant angle.
Figure 3.1: Current system of unwind/rewind.
21
3.2.2
Web behavior fundamentals:
Consider a web material intension as shown in Figure 3.2:
Figure 3.2: Web material in tension.
Within the range of behavior of the web material, the elongation δ is proportional
to both the tensile force P and the length L of the material. The elongation also is
observed to be inversely proportional to the cross-sectional area A of the material.
Robert Hooke first established the relationship among the elongation, tensile force,
length, and the cross-sectional area represented in equation. 3.1:
δ=
PL
AE
[3.1]
where E is a constant for any given material and is called the modulus of
elasticity of the material tension. The relationship represented in equation 3.2 is
known as Hooke’s law can also described as
σ = Eε
[3.2]
where
Stress σ =
P
δ
and strain ε =
A
L
From equation. 3.2, Hooke’s law is concluded that stress is proportional to strain.
22
3.2.3
System Modeling specification
The mathematical model of the system will be based on the tension control and
speed control. The literature review on the tension control will be based on the
various study have address the issue of tension control in web transport system. The
parameter involve on this system consists of angular velocities of unwind, traction,
and rewind motor. The torque of the motors, the moment of inertia, the web tension,
the radius of unwind and rewind rolls, the damping coefficient and spring constant
of the web, respectively. The Laplace transform will be used in the transfer function.
ωu =
1
(τ u +Ru tw )
Ju s
Angular velocity for unwind roll (rad/s)
[3.3]
ωr =
1
(τ r + Rrtw )
Jr s
Angular velocity for rewind (rad/s)
[3.4]
Tension (kg)
[3.5]
K
(Ruωu − Rrωr )
Cs +1
K
ωref =
Cs +1
tw =
JU
Tension
to
speed
converter/Unwind
reference(rad/s)
speed
[3.6]
Total moment of inertia of the unwind roll and
motor (kg/m/s2)
Jr
Total moment of inertia of the rewind roll and
motor (kg/m/s2)
tw
Web tension(N)
Ru
Radius of the unwind roll(mm)
Rr
Radius of the rewind roll(mm)
23
τ uf
Torque due to friction at unwind shaft (kg/m)
τ rf
Torque due to friction rewind shaft (kg/m)
τu
Torque generated by the unwind motor (kg/m)
τr
Torque generated by the rewind motor (kg/m)
νu
Tangential velocity at the periphery of the unwind roll
(m/s)
νr
Tangential velocity at the periphery of the rewind rolls
(m/s)
L
Total length of web (m)
K
Spring constant of web (kg/m)
uu
Input voltage to the unwind motor (V)
ur
Input voltage to the rewind motor (V)
Ku
Torque constant of the unwind motor (kg/m/V)
Kr
Torque constant of the rewind motor (kg/m/V)
Bu
Coefficient of bearing friction (kg-m-s/rad)
Cu
Magnitude of torque (kg-m).
24
3.2.4
Definition of primitive element
To facilitate the modeling and analysis of web transport systems, the
concept of “primitive element” was established. Examples of primitive
elements are a free web span, various types of rollers and rolls, and a web
interacting with roller. (Refer to Figure 3.3). A web transport system can
be thought of as a combination of primitive elements.
Figure 3.3: Primitive elements in the web handling process.
25
The free web span shown in Figure 3.4 is the most fundamental primitive
element found in web processing. This element is terminated by a roller(s) or
roll at each end of span.
Figure 3.4: A free web span control volume
3.2.5
Tension observer
3.2.5.1 Tension observer with inertia compensation
In the study of web tension transport system, the formula to estimate web
tension as follows:
t obs (t ) =
1
[ J u α (t ) + K u u u (t )]
Ru
[3.7]
where α u (t ) denotes filtered angular acceleration of the unwind roll. The
filtered angular acceleration is computed by taking derivative of the measured
angular velocity of unwind roll, and then passing through a second-order lowpass filter as follows:
⎛
ω n2
⎜
α u ( s) = ⎜ 2
2
⎝ s + 2ξω n s + ω n
⎞
⎟
⎟
⎠
[3.8]
26
The propose tension observer that has a feedback configuration and a
filtered inertia block J u s (1 + J u s N ) as shown in Figure 3.5. By the Mason’s
rule, the output of the observer is
τ obs ( s) =
t obs ( s ) =
K po s + K io
⎡
⎤ ⎡U u ( s )⎤
Jus
⋅
−
K
J
s
u
u
⎢
⎥ ⋅ ⎢ω ( s ) ⎥
J u s 2 + K po s + K io ⎣ 1 + J u s N
⎦ ⎣ u ⎦
τ obs ( s )
Ru
[3.9]
[3.10]
Figure 3.5: PI-type observer with filtered inertia block
Proper values of N are 3~10. The larger the value of is, the faster the observer
responses can be. The stability of observer can be guaranteed by proper design
of the PI gains, K po and K io . When uu (t ) is a constant, the estimated torque
tobs (t ) will converge to K u uu , even though the unwind roll has acceleration or
deceleration inertia. The observer is good as a torque observer. However, it is
not good as a tension observer if acceleration or deceleration inertia of the roll
arises continued to propose another observer. The outputs of the filtered
inertia block were used as feed forward signals and added into the estimated
torque. The sum of the filtered inertia and estimated torque provides good
27
estimates of web tension in spite of acceleration or deceleration inertia of the
roll. The output of the observer is
t obs =
1
Ru
⎤
⎡
Jus
⋅ ωu s ⎥
⎢τ obs ( s ) +
1+ Jus N
⎦
⎣
[3.11]
By the final-value theorem, the steady state of web tension will converge to
lim t obs (t ) =
t →∞
1
(J uα u + K u u u )
Ru
[3.12]
Figure 3.6: PI-type observer with inertia compensation.
Figure 3.7: Proposed observer with inertia, bearing and Coulomb friction.
28
3.2.5.2 Tension observer with friction and inertia compensation
Figure 3.8 shows an extension of the observer in Figure 3.7 to including bearing
and Coulomb friction into the observer model. The output of the observer in
Figure 3.8 is
t obs ( s ) =
+
1
Ru
K f Jus
1+ Ju s N
⎛
⎡
⎤ ⎡ u (s) ⎤
Jus
⋅ ⎜⎜ M ( s ) ⋅ ⎢ K u ⋅
− J u s − Bu ⎥ ⋅ ⎢ u ⎥
1+ Ju s N
⎣
⎦ ⎣ω u ( s )⎦
⎝
⋅ ωu (s) +
where M ( s ) =
⎞
Cu
⋅ sgn[ω u (t )]⎟⎟
s
⎠
K po s + K io
J u s + ( K po + Bu ) s + K io
2
[3.13]
[3.14]
[3.15]
3.2.5.3 Design of observer gain
In Figure 3.8, the proposed tension observer with friction and inertia
compensation has two input signals (i.e., the input voltage to the unwind motor
and the angular velocity of the unwind roll). The output of the proposed observer
can be written as follows:
t obs =
Cu
1 ⎧
⎫
sign[ω u (t )]⎬
⎨M 1 ( s )u u ( s ) + M 2 ( s )ω u ( s ) +
Ru ⎩
s
⎭
[3.16]
where
M 1 ( s) = K u M ( s)
[3.17]
⎧⎪
⎡ J u2 s 2
J s ⎞⎤ ⎫⎪
1
⎛
M 2 (s) =
⋅ ⎨K f J u s − M ( s) ⎢
+ Bu ⎜1 + u ⎟⎥ ⎬
N ⎠⎦ ⎪⎭
1 + J u s N ⎪⎩
⎝
⎣ N
[3.18]
In general, the proposed observer has one real pole and two complex conjugated
poles. The real pole will become less dominant by selecting a larger value of N.
The observer time constant is 2 J u ( K po + Bu ) . The larger the proportional gain
K po is selected, the more damped the observer responses are. As a rule of thumb,
29
observer responses are designed to be five–ten times faster than those of openloop systems. A procedure for calculating the PI gains of the proposed observer is
summarized as follows:
Step 1
Assign a larger value of N (e.g.,N=10).
Step 2
Let the observer time constant be five–ten times less than that of
the open-loop system.
3.2.6
Step 3
Select a proper observer damping ratio (e.g., ξ = 1 ).
Step 4
Compute the observer PI gains, K po and K io .
Observer based tension feedback controller
Simultaneous control of the process speed and web tension is required in the
studied system. A common strategy involves in control of the speed of the rewind
motor and control of web tension through regulating the torque generated by the
unwind motor. Figure 3.9 shows a classical approach of PI control of the speed
and the tension. The speed loop is closed with measured angular velocity of the
rewind roll and the tension loop is closed with measured tension as the feedback
signals. Direct unwind and rewind system with measured tension feedback
control.
Figure 3.8: Direct unwind and rewind
30
Figure 3.9: Direct unwind and rewind system with tension observer
This study is primarily concerned with observer-based tension feedback
control without using a tension transducer. The tensions observers represent in the
previous section are to be employed to estimate web tension. The estimated
tension will be used as feedback signals to form the tension loop. Figure 3.10
shows a block diagram of the studied system under the proposed observer-based
tension feedback control and speed control.
31
For the studied system, the dynamics of web tension are nonlinear. System
stability analysis and analytic design of the control gains is difficult. Therefore,
we perform linearization of the system equations around an operating condition,
and write the linearized equations in the following matrix from:
& ⎤ ⎡ −B
⎡J u Ω
u
u
⎢ & ⎥ ⎢
⎢ Tw ⎥ = ⎢− KRu
& ⎥ ⎢ 0
⎢JrΩ
r⎦
⎣
⎣
0 ⎤ ⎡− K u
− v ro L KRr ⎥⎥ ⋅ ⎢⎢ 0
− Rr
− Br ⎥⎦ ⎢⎣ 0
Ru
0⎤
⎡U ⎤
0 ⎥⎥ ⋅ ⎢ u ⎥
U
K r ⎥⎦ ⎣ r ⎦
[3.19]
where the following notation are used.
Tw :
Changes in web tension from an operating value (kg).
Ωu :
Changes in angular velocity of the unwind roll from an operating
value (rad/s).
Ωr :
Changes in angular velocity of the rewind roll from an operating
value (rad/s)
Uu :
Changes in input voltage to the unwind motor from an operating
value (V).
Ur :
Changes in input voltage to the rewind motor from an operating
value (V).
v ro :
Operating value of tangential velocity of the rewind roll (m/s)
For simplicity, measured tension is used in design of the tension control law. The
control law is
(
)
U u (t ) = K pu + K iu ∫ dt ⋅ [Td (t ) − Tw (t )]
[3.20]
and speed control law is
(
)
U r (t ) = K pr + K ir ∫ dt ⋅ [Ω d (t ) − Ω r (t )]
[3.21]
32
By taking the Laplace transform of equations (3.19)–(3.21) and after
manipulation, we can have
⎡ Tw ( s ) ⎤ ⎡ M 11 ( s ) M 12 ( s ) ⎤ ⎡ Td ( s ) ⎤
⎢Ω ( s ) ⎥ = ⎢ M ( s ) M ( s ) ⎥ ⋅ ⎢Ω ( s ) ⎥
22
⎣ r ⎦ ⎣ 21
⎦ ⎣ d ⎦
where
M 11 ( s ) = a 21 ( s )b11 ( s ) Δ ( s )
M 12 ( s ) = a 23 ( s )b32 ( s ) Δ( s )
M 21 ( s ) = a 21 ( s )a32 b11 ( s ) Δ ( s )
M 22 ( s ) = [1 − a12 ( s )a 21 ( s )]b32 ( s ) Δ( s )
Δ( s ) = 1 − a12 ( s )a 21 ( s ) − a 23 ( s )a32 ( s )
a12 ( s ) =
(R
u
+ K u K pu )s + K u K iu
s ( J u s + Bu )
a 21 ( s ) =
− KRu
s + v ro L
a 23 ( s ) =
− KRr
s + v ro L
a32 ( s ) =
− Rr s
J r s + ( Br + K r K pr ) s + K r K ir
b11 ( s ) =
b32 ( s ) =
2
− K u ( K pu s + K iu )
s ( J u s + Bu )
K r ( K pr s + K ir )
J r s + ( Br + K r K pr ) s + K r K ir
2
[3.22]
33
3.2.7
Assumption of mathematical model
To simplify the derivation of the mathematical model for the system, we must
have an assumption such as, the mathematical models of the rewind, traction, and
unwind motors and their drives can be expressed in terms of first order differential
equations. The dynamic of the web can be described by a first order system with a
damping effect. There are no slip occurs between the web and the rolls. The gear
ratio between motor and roll is one to one. There is no mass transfer between the
web material and the environment ( i.e no humidification or evaporation). The web
cross section in the outstretched state does not vary along the web. The web is
perfectly elastic.
3.3 Mathematical model for control law
The controller design of the unwind/rewind system is designed based on the
following equation:
1
Ki =
β0
ζω
[3.23]
Kp =
⎞
1 ⎛ 2ζω n β 0 K i
⎜
+ ω n2 − α 0 ⎟⎟
2
⎜
β0 ⎝
ωn
⎠
[3.24]
Kd =
⎞
1 ⎛ β0 Ki
⎜ 2 + 2ζω n − α 1 ⎟
⎟
β 0 ⎜⎝ ω n
⎠
[3.25]
where
KRu ω u KRr ω r
+
α0 =
C
C
α1 =
β0 =
τr
Jr
τu
Ju
+
Rr + t w
Jr
+
Ru + t w
Ju
The gain of Kp, Ki and Kd is model based on the mathematical model of the
unwind and rewind system.
34
3.4 Dynamic simulation of the system.
3.4.1
Dynamic simulation for tension and speed
After completing the mathematical model of the whole system, we need to do a
simulation by using Matlab/Simulink as Computer Aided Engineering software.
The dynamic simulation which is consists of all the parameters must be done with
the block diagram. Figure 3.11 shown the dynamic simulation block diagram
Figure 3.10: The dynamic simulation block diagram.
35
3.4.2
Tension control system
The system currently controlled by PLC without any control algorithms
applied to the system. A new tension control algorithms with tension observer
is proposed as a simulation by computer. The closed-loop tension controller
with propose tension observer will be used as a second control algorithm. PID
controller will be implementing to the tension controller. Three methods is
applied for implementing the controller gain tuning are a fixed-gain PID
controller, response optimization PID controller and Ziegler Nichols method.
The tension controller is assigned in unwind section based on the previous
studied. The tension observer is replaced the strain gauge (real time
transducer). The second order low pass filter is added to minimize the noise
inevitably. The tension to speed converter block function is to convert tension
to speed so that the unwind speed can be synchronized with rewind speed.
3.4.3
Speed control system
The speed controller was implemented into rewind section. The purposed
of this controller is to ensure the synchronization for both unwind and rewind
speed of motor can be maintained at certain value. The effect of the
synchronization of the speed can avoid the plastic web become twisted. The
gain tuning of the speed PID controller is based on the same method of
tension PID controller. The speed of unwind is less than rewind speed on the
first start up until they have synchronization speed for both motors. The
different value of tension references is affected the variation of rewind speed
based Figure 3.11.
36
3.5 Real time implementation of the system
3.5.1
Layout of the experiment
Figure 3.12; show the design of experimental block diagram for real-time
implementation. This Simulink block diagram will be based on the Figure 3.12 block
diagram.
Figure 3.11: The real-time implementation block diagram
The software of the xPC-target box will be downloading from personal computer
to the box. The xPC-target box can be consider as second personal computer or
prototype We need to setup the operating system of the xPC target box before
downloading. For this experiment, we use C code or C++ code to convert the
Simulink block diagram into structure text language which is need to use in xPC
target box operating system. The system is running based on the time period that
we set in Simulink block diagram environment The result of the experimental will
be captured and send back to personal computer.
37
3.5.2
Real time control algorithm
Figure 3.12: Flow chart of real time control algorithm.
38
Figure 3.13 shown the standard procedure to operate the xPC-target box as
prototype controller to the unwind/rewind system. Beginning with the build
model command, the Simulink block diagram model is converting into C code
or C++ code. Then the compilation process will ensure the coding of the
program is correct. If not success, the Simulink model need convert and compile
again. After compilation success the software will download to programming
code into xPC-target box. The xPC-target box will send and received signal to
unwind and rewind system. After the real-time control process is done, we need
to upload data from xPC target box into personal computer. We can plot the
graph based on the data taken from the xPC-target box. Figure 3.14 show the
standard setup for xPC-target box and personal computer.
Figure 3.13: Standard procedure to setup xPC-target box with personal computer
39
3.5.3
Scaling graph for tension versus voltage
Figure 3.14: Scaling graph to calculate the value of tension for experimental and
simulation.
The purpose of having the scaling graph is because we want to get the ratio
value between unwind/rewind system and xPC target box voltage value (Figure
3.15). The graph in figure is used for tension reference. This value is converting
based on the linear equation law. The value is converted into voltage so that we
can use for simulation and experimental purposed. The tension analysis is
focusing on the Unwind section.
40
3.5.4
Scaling graph for speed versus voltage.
Figure 3.15: Scaling graph to calculate the value of tension for experimental and
simulation
Figure 3.16 show the graph of speed versus voltage. The speed is measured at
Rewind section. The reason to have this scaling graph is used for ratio value
between unwind/rewind system and xPC target box. The speed reference value is
used in simulation and experiment purposed for the unwind/rewind system.
41
3.6
Method of tuning PID gain.
3.6.1
Fixed gain
Using equation (3.23) through (3.25) PID (Proportional, Integral and
Derivative) controller can be designed for given system parameter values and
specifications for the closed-loop tension control system. The desired
specifications for the closed loop tension control system are given in Table 3.1.
Table 3.1: Specification for closed loop tension control system
Steady-state error
Ess = 0
Damping coefficient of closed loop system
ζ = 0.7
Natural frequency of closed loop system
ωn = 10
The result of the PID tuning gain can be obtained as the following Table 3.2:
Table 3.2: The results of tuning gain using fixed-gain method
Controller
Kp
Ki
Kd
P
0.8975
0
0
PI
0.835
2.4
PID
1.098
5.265
0.0512
42
3.6.2
Simulink Response optimization
Simulink Response Optimization provides a graphical user interface (GUI) to
assist in the tuning and optimization of control systems and physical systems. We
can either directly tune response signals within Simulink models or tune
responses of LTI systems within a SISO Design Task (requires the Control
System Toolbox).
We can tune parameters within a nonlinear Simulink model to meet timedomain performance requirements by graphically constraining signals within a
time-domain window or tracking and closely matching a reference signal. We can
tune any number of Simulink variables including scalars, vectors, and matrices. In
addition, you can place uncertainty bounds on other variables in the model for
robust design. Simulink Response Optimization makes attaining performance
objectives and optimizing tuned parameters an intuitive and easy process.
Figure 3.17 shows the GUI of tuning PID controller using Simulink response
optimization method. The tuning process was tuned in 2 time of frequent taken to
get best result of PID controller gain for unwind and rewind system. This tuning
process is applied both tension PID controller and speed PID controller
43
Figure 3.16: PID controller gain tuning using response optimization method.
The result of response optimization method can be obtained as the following
Table 3.3:
Table 3.3: Results on the PID controller gain using response optimization.
Controller
1st tuning
2nd tuning
Kp
0.9468
0.8975
Ki
4.2334
4.1567
Kd
0.0677
0.0459
Tuning Frequent
Gain
44
3.6.3
Ziegler Nichols
Ziegler and Nichols conducted numerous experiments and proposed rules for
determining values of Kp, Ki, Kd based on the transient response of system plant.
Figure 3.18 show the transient response of the unwind rewind system based on the
Ziegler Nichols method.
Figure 3.17: Transient response of unwind and rewind system
L = Time delay of the reaction curve = 0.105 seconds
T= Time constant = 0.098 seconds
45
The result of the PID controller gain using Ziegler Nichols as the following Table
3.4:
Table3.4: Results on the PID controller gain using Ziegler Nichols method
Controller
P
PI
PID
3.6.4
Kp
T/L (0.933)
0.9 * T/L (0.84)
1.2 * T/L (1.12)
Ki
0
0.27 * T/L2 (2.4)
0.6 * T/L2 (5.3)
Kd
0
0
0.6 * T (0.059)
Comparison between three method
The three method shown that the values of each Kp, Ki, and Kd give a similar
values. In this thesis, the gain values from 3 methods are used since effect to the
tension PID controller and speed PID controller are same. The detail results were
explained in chapter four of this thesis.
46
CHAPTER 4
RESULT AND DISCUSSION
4.1
Introduction on the result and discussion
This chapter is divided into five sub chapters; that consist of result on the tension
without filter, result on the tension with filter, simulation result, experiment results, and
comparison between simulation and experimental results. The result in each subchapter
was taken from the real time experiment with unwind and rewind system in Unikl MFI
system room. The simulation results are based on the Simulink model which is
approximately design similar to the real-time unwind and rewind system.
47
4.2
Result on the tension without filter
The result on the tension without filter is captured from the experiment process. In
sub chapter 3.5.2 was explained in the procedure to get the result. The result is not
filtered as shown in figure 4.1. The signal was captured from strain gauge as transducers
to measure tension value from unwind section. The range of the tension measurement is
from 10N to 100N. The analog signal range is from 0 VDC to 10VDC. As we can see
from figure 4.1, the noise occurred during measurement process. As the measured tension
contains measurement noise inevitably, a second order low pass is added in the Simulink
model for experiment. We can see the results in sub chapter 4.3 which eliminate the
measurement noise.
Figure 4.1: Tension signal capture from unwind section in experiment process
48
4.3
Result on the tension with filter
Figure 4.2: The signal of tension after filtered by second order low pass filter
The second order low pass filter in equation (4.1) was added to the Simulink model
for both experiment and simulation.
Jus
ωu
s + Ju Jr s + Ju
2
[4.1]
As a result in Figure 4.2, the tension signal become smooth compared to the result in
Figure 4.1. This signal was used as a feedback signal to tension PID controller. In the
next sub chapter we can see the five different tension reference are applied for both
simulation and experiment.
49
4.4
Simulation results
In the simulation results, the signal and data are captured four times. The reason to
have four times sends and received data is to see the variation effect of the tension
reference. The simulation result can bee obtains in computer simulation mode in Matlab
and Simulink. Some of the block model developed based on the control system toolbox
and response optimization tool box. Figure 4.3 shows the Simulink model for unwind and
rewind system applied on this thesis methodology.
Figure 4.3: The Simulink model for unwind and rewind model plant
50
4.4.1
Simulation result on tension reference at 20N
After tension reference at 20N is applied, the following Figure 4.4 is
shown the effect to the tension, unwind speed and rewind speed. The variation
of the three signals given can be considered as an initial effect for system. The
value of gain tension PID controller and speed PID controller is based on the
three method of tuning gain in as mention sub chapter 3.6. The speed response
can be considered in transient response for unwind and rewind section. The
tension have oscillation occurred within 2 seconds in simulation period.
Figure 4.4: The effect of tension reference at 20N
51
4.4.2
Simulation result on tension reference at 30N
Tension reference at 30N is applied, the following Figure 4.5 is shown the
effect to the tension, unwind speed and rewind speed. The tension is decrease
due the effect of tension reference. The signal response still similar with effect
of 20N, the tension PID controller gain is maintained. The unwind speed is
increased but rewind speed is decreased. The rewind speed still lead the unwind
speed to avoid any twist occurred when transporting plastic web.
Figure 4.5: The effect of tension reference at 30N
52
4.4.3
Simulation result on tension reference at 40N
In Figure 4.6, is shown the effect of tension reference at 40N applied to
unwind and rewind system. The tension, unwind speed, and rewind speed are
increased. This situation happens because the plant model effect to the tension
PID controller and speed PID controller. The rewind speed and unwind speed is
nearly synchronize
Figure 4.6: The effect of tension reference at 40N
53
4.4.4
Simulation result on tension reference at 50N
In Figure 4.7 the effect of tension references at 50N is slightly maintain
for tension, unwind speed and rewind speed. The different between unwind
speed and rewind speed is not large. Otherwise the rewind speed still lead the
web transport system than the unwind speed. The simulation is done at this
tension reference.
Figure 4.7: The effect of tension reference at 50N
54
4.5
Experimental results
The experimental results was captured based on the experimental methodology that
applied in unwind and rewind system plant. The result is not capture directly to the xPCtarget box. After real time implementation, we need to upload the data then plot the graph
as the following results. Figure 4.8 show the Simulink model for real-time experiment.
The model is different compared with simulation model because we need include real
time block model from real-time workshop toolbox.
Figure 4.8: The real-time Simulink model for unwind and rewind system
55
4.5.1
Experimental result on tension reference at 20N
In Figure 4.9, the results on the tension, unwind speed, and rewind speed
obtained from the real-time implementation. The tension PID controller gain and
speed PID controller gain is same as what we implement in the simulation
controllers. Tension signal from strain gauge are filtered via second order low
pass filter to eliminate noise. The speed of unwind is less than rewind speed. The
gap is large between two sections.
Figure 4.9: The experimental results at 20N
56
4.5.2
Experimental result on tension reference at 30N
Tension reference at 30N was effected the signal response for unwind and
rewind system (Figure 9.10). Even though the signal responses are slightly same
from the previous results, the system can operate as normal condition.
Figure 4.10: The experimental results at 30N
57
4.5.3
Experimental result on tension reference at 40N
In figure 4.11, the tension reference is change to 40N to see the performance
of signal response. This time the unwind speed and rewind speed slightly similar
and start to tend synchronization in both section. The tension is decrease due to
the synchronization speed of both motors.
Figure 4.11: The experimental results at 40N
58
4.5.4
Experimental result on tension reference at 50N
For Figure 4.12, the rewind speed is leading unwind speed. This is what we
want to achieve to avoid twisted on the plastic web transport. Tension is increased
but not too high. Both tension and speed PID controller was take part in their roles
to ensure that the problem is not occurs.
Figure 4.12: The experimental result at 50N
59
4.6
Comparison between simulation and experimental results
4.6.1
Tension result between simulation and experimental
4.6.2.1
Tension result at 50N
Figure 4.13: Tension result in simulation
Figure 4.14: Tension result in experimental
Based on the Figure 4.13 and Figure 4.14, the tension response between
simulation and experimental is different. The settling time for simulation is
faster than the experimental. In the simulation we can see the possible
disturbance occurred is not high compared to the experimental. The tension
value in experiment is high because the radiuses of web for each unwind and
rewind section is going to be same.
In the 50N tension reference is the best observations for control strategy in
unwind and rewind section. Some of improvement can be suggested to the
future development of this thesis and will be discuss on this sub chapter.
60
4.6.2
Unwind speed response between simulation and experimental
4.6.2.1
Unwind speed result at 50N tension reference
Figure 4.15: Unwind speed result in simulation
Figure 4.16: Unwind speed result in experimental
Based on Figure 4.15 and Figure 4.16, the unwind speed in simulation is
very smooth in term of control strategy. Since the measurement noise occurs
when the strain gauge send feedback signalto xPC-target box, the speed of
unwind is decreased compared to simulation. Otherwise, the tension PID
controller and speed PID controller for experimental did their job very well to
maintain both section speed.
61
4.6.3
4.6.3.1
Rewind speed response between simulation and experimental
Rewind speed result at 50N tension reference
Figure 4.17: Rewind speed result in simulation
Figure 4.18: Rewind speed result in experimental
Based on the Figure 4.17 and Figure 4.18, rewind speed transient response
is better in simulation compared to experimental. Since the rewind speed
is decreased in experimental, the important point that we want to see is the
rewind speed is still lead the situation when plastic web is transporting.
Tension PID controller and speed PID controller were take their role to
ensure the tension is not too high and the speed of unwind and rewind are
synchronize. The main problem before is considered solved and need
improvement in term of control strategy to the unwind and rewind system.
62
CHAPTER 5
CONCLUSION
5.1
Introduction on the conclusion
In this chapter, the conclusion of the project as well as some constructive
suggestions for further development and the contribution of this project will discussed.
The project outcomes are concluded in this chapter. As for future development, some
suggestions are highlighted with the basis of the limitation of the effectiveness
mathematical equation, new or advance control technique implementation and simulation
analysis executed in this project. The aim of the suggestions is no other than to improve
the study.
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5.2
Conclusion
The dynamic mathematical modeling of unwind and rewind system and the
control law of the system is recognized. The dynamic model is validated with the
dynamic model from the published papers based on the dynamic model itself and the time
responses result. The real-time experimental results also have shown the approximately
validated with the dynamic simulation model.
The tension PID controller and speed PID controller for unwind and rewind
system shown that the plastic web material can be handling without facing any twisted
problem. The three methods of tuning PID gain showed that the value of Kp, Ki, and Kd
as similar for each of them. The different of the gain value is very small. Any value of
gain selected from either Ziegler Nichols or Response Optimization or fixed gain can be
used in simulation and experimental.
PC-based control was successfully replace the PLC role to control tension and
speed of unwind and rewind system with better performance. The second order of filter
applied to the system to eliminate the noise and undesired frequencies that exist in the
input system. The higher the speed of rewind, the better performance of the web transport
system.
The xPC-target box can be considered as a prototype PID controller since some
consideration must be taken. This prototype controller is suitable for modeling, simulate,
and generate real-time programming to any Mechatronics system on the study of system
performance. This recommendation for generate an idea to persuade my PhD research.
64
5.3
Future development
Since the PID controller is considering classical control, the control strategy can
be improved with new technique of PID controller such as Fuzzy-PID controller, and
adaptive PID controller.
For advanced technique of control strategy, we can apply any state variable or
feedback control system such Linear Quadratic Regulator (LQR), Linear Quadratic
Gaussian (LQG) and multivariable H infinity. All type of controller a recommend to
apply to current prototype controller unit (xPC-target box)
65
References
Journals
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User Manual:
xPC-Target box user manual (Matlab/Simulink) 2005
Real-time workshop user manual (Matlab/Simulink) 2005
Response optimization user manual (Matlab/Simulink 2005
68
APPENDICES
69
A. BLOCK DIAGRAM FOR AN ANALOG INPUT AND OUTPUT DRIVER
REAL TIME WORKSHOP OPTIONS IN THE CONFIGURATION
PARAMETER DIALOG
70
BLOCK PARAMETER FOR ANALOG INPUT BLOCK
BLOCK PARAMETER FOR ANALOG OUTPUT BLOCK
71
xPC SCOPE PARAMETER BLOCK
CONTROLLER BLOCK DIAGRAM WITH xPC SCOPE AND OUT BLOCK
72
73