Transverse Vibration Control of Axially Moving Web Systems by Regulation of Axial Tension Quoc Chi Nguyen*, Thanh Hai Le, and Keum-Shik Hong Abstract: In this paper, an active control s
Trang 1Transverse Vibration Control of Axially Moving Web Systems by
Regulation of Axial Tension Quoc Chi Nguyen*, Thanh Hai Le, and Keum-Shik Hong Abstract: In this paper, an active control scheme to suppress the transverse vibrations of an axially
moving web system by regulating its transport velocity to track a desired profile is investigated The
spatially varying tension and the time-varying transport velocity of the moving web are inter-related
The system dynamics includes the equations of motion of the moving web and the dynamics of the
drive rollers at boundaries of the web span The two roller motors provide control torque inputs to the
web system The strategy for vibration control is the regulation of the axial tension in reference to a
de-signed profile, so that the vibration energy of the moving web system decays The dede-signed profile for
the axial tension is designed via the total mechanical energy of the axially moving web system The
Lyapunov method is employed to derive the model-based torque control laws ensuring that the
trans-verse vibration and the velocity tracking error converge to zero exponentially The effectiveness of the
proposed control scheme is demonstrated via numerical simulations
Keywords: Axially moving string, boundary control, exponential stability, Lyapunov method, tension
regulation
1 INTRODUCTION There are various industries that use web-material
transport systems such as papers, textiles, metals,
polymers, and composites In these systems, the
application of roll-to-roll (R2R) processing yields better
performance and allows a mass production with
high-speed automation However, the mechanical vibrations
(particularly in the transverse direction) of the web
material have been the main quality- and
productivity-limiting factor, especially in high-speed precision R2R
systems Therefore, reduction of the transverse vibrations
in R2R systems has become an important research area
To solve the vibration problems in R2R systems,
boundary control (the application of control actions at
the left or right boundary) has been developed [1-16]
Since the provision of control inputs through a
supporting roller is more cost effective than the addition
of an extra actuator at a middle point in the system,
boundary control is an efficient method to control the
R2R systems
The tension and speed control problems of web handling systems have been an important research subfield [17-25] An integrated boundary control scheme that stabilizes the axial tension and the transport speed at desired set-points for axially moving materials was introduced in [17] Koc et al [18] developed an H-infinity robust control strategy including varying control gains for unwind/rewind sections to improve the robust control property under the effects of variations on the radii of unwind/rewind rollers Meanwhile, Pagilla et al [19] proposed a decentralized control scheme for a web processing line based on a dynamic model taking variations on the radii and inertia of unwind/rewind rollers into account In [21], a multivariable H-infinity control scheme is used to independently regulate the speed and tension and to reject the disturbance due to radius variations of unwind/rewind rollers for a web span Using an iterative learning control (ILC) algorithm, Zhao and Rahn [22] presented a control scheme for an axially moving system that enables a precise regulation of the tension and transport velocity It is noted that the majority of aforementioned results were obtained under the assumption that the web tension and the transport velocity were constant In practice, when the set-points
of tension and speed are changed during operation, the variations of the transport velocity and the tension can result in the transverse vibrations of the moving material [2,12] and consequently the stability of the R2R systems Transverse vibration control for axially moving systems was studied in [1-16]: Vibration control schemes for axially moving strings include [1-11] Those for axially moving beams include [12-16] Fung et al [1] developed a boundary control scheme for an axially moving string system in which adaptive boundary
© ICROS, KIEE and Springer 2015
Manuscript received February 24, 2014; revised July 22, 2014;
accepted August 26, 2014 Recommended by Associate Editor
Won-jong Kim under the direction of Editor Fuchun Sun
This research is funded by Vietnam National Foundation for
Science and Technology Development (NAFOSTED) under grant
number 107.04-2012.37 and by Vietnam National University
HoChiMinh City (VNU-HCM) under grant number C2013-20-01.
Quoc Chi Nguyen and Thanh Hai Le are with the Department
of Mechatronics, Ho Chi Minh City University of Technology,
268 Ly Thuong Kiet, District 10, Ho Chi Minh City, Vietnam
(e-mails: {nqchi, lthai}@hcmut.edu.vn)
Keum-Shik Hong is with the School of Mechanical
Engineer-ing, Pusan National University, 2 Busandaehak-ro,
Geumjeong-gu, Busan 609-735, Korea (e-mail: kshong@pusan.ac.kr)
* Corresponding author
Trang 2control laws were employed on a mass-damper-spring
mechanism to suppress the vibrations Nguyen and Hong
[7] proposed a robust adaptive boundary control scheme
for an axially moving string of unknown system
parameters under spatially varying tension and unknown
boundary disturbance Li and Rahn [11] introduced an
adaptive isolation scheme for an axially moving system,
which were divided into two spans by a transverse force
actuator, to reduce the transverse vibration of the
controlled span to zero under bounded disturbances in
the uncontrolled span These achievements show that the
vibration control problem has been intensively
investigated by researchers However, there are few
researches that investigate vibration control problem
together with other control problems, e.g., tension
control and speed control, etc The first work that studied
a combination of transverse vibration control and speed
control for an axially moving web was presented in [2],
where the transport speed was regulated by two control
torques applied to the drive rollers at boundaries, and the
transverse vibration was suppressed via an actuator in the
middle of the web span Recently, Nguyen and Hong [8]
developed an active control scheme that can suppress
both longitudinal and transverse vibrations and to drive
the transport velocity of the string simultaneously
In this paper, we develop an active control scheme that
suppresses the transverse vibrations while regulating the
transport speed of an axially moving web system It is
noted that the investigated control problem differs from
the work [2] In [2], the transverse vibration was
suppressed by control forces exerted from a mechanical
guide located at the middle of the web span In this paper,
the vibration control strategy is to regulate the axial
tension to track a designed profile according to which the
vibration energy is dissipated This control strategy is
implemented using two control torques applied to the
rollers at boundaries These control torques also play the
role of control inputs in making the transport velocity In
this formulation, the web dynamics and the roller
dynamics are coupled The Lyapunov energy-based
method is employed to derive the torque control laws
ensuring that the transverse vibration and the speed
tracking error converge to zero exponentially Finally,
the numerical simulations are provided to confirm the
effectiveness of the proposed control method
Contributions of this paper are: First, a novel active
control scheme for suppressing the transverse vibration
of an axially moving web is presented: Contrary to the
conventional methods (boundary or distributed controls)
that use external forces, the proposed control method
regulates the axial tension of the web Henceforth, an
unexpected damage on the web surface due to external
forces can be prevented Second, the proposed control
method is able to provide vibration suppression and
transport velocity tracking simultaneously Third, the
exponential stability of the proposed control system is
achieved
The remainder of this paper is organized as follows
Section 2 introduces a dynamic model of the considered
system (an axially moving viscoelastic string), in which a
nonlinear partial differential equation (PDE) governs the transverse displacement, and the boundary conditions determine the dynamics of the rollers Section 3 presents the proposed control scheme design A Lyapunov function-based stability analysis of the closed-loop control system and the proof of exponential stability also are discussed Section 4 includes numerical simulation results that illustrate the effectiveness of the proposed control scheme Finally, Section 5 draws conclusions
2 PROBLEM FORMULATION Fig 1 shows the schematic of the axially moving web driven by two rollers at boundaries The left boundary is fixed in the sense that the movement of the web in the vertical direction is restricted Conversely, at the right boundary, a damper mechanism allows its transverse (vertical) movement In this paper, the moving web is modeled as an axially moving string
Let t be the time, x the spatial coordinate along the longitude of motion, w(x,t) the transverse displacement at the spatial coordinate x and time t, l the distance between two fixed rollers, ρ the mass per unit length of the web,
cv the viscous damping coefficient of the web, ca the damping coefficient of the damper, and v(t) the time-varying transport velocity T(x,t) denotes the spatially varying tension of the web Two parameters of the rollers include the moment of inertia J and the radius r
In this paper, the partial derivatives are denoted as follows: ()t = ∂ ∂/ t and ()x = ∂ ∂/ x For notational convenience, instead of wx (x,t) and wt (x,t), wx and wt
will be used; other similar abbreviations will be employed subsequently
The equations of motion of the axially moving string are given as follows, see [2]
2
( ) ( ) 0
(1) with boundary conditions
(0, ) 0, t
2 (ca−ρv w l t) ( , ) ( ( , )t + T l t −ρv w l t) ( , ) 0.x = (3) The initial transverse displacement and velocity, respectively, are given as
l
w(x,t)
T 2
r
T 1
x
a
Fig 1 The schematic of the axially moving web
Trang 3( ,0) ( ),
The velocity dynamics is obtained as
2J ( ) ( ) ( ) ( ( ) ( )) ,
r
where T1(t) and T2(t) are the time varying tensions from
the respective adjacent spans The distributed web
tension is defined as
1
2
( ) ( , )
( ) ( ) 2 ( ) ( ) ( ) ,
τ
+
where T0 is the axial tension of the undisturbed web
Subsequently, the following equations are obtained
3
T x t
la
1 3
3
( ( ) ( )),
xa T t T t
la
− +
where a1, a2, and a3 are defined as
2
2 2 ,
2
3 CONTROL DESIGN
The control objective is to suppress the transverse
vibration of the moving web while regulating the
transport velocity so that the desired profile is tracked
Based on the Lyapunov energy-based method, a control
scheme employing the control torques τ1(t) and τ2(t) is
derived to achieve the exponential convergence of the
transverse vibration and the speed tracking error to zero
The speed tracking error is defined as follows:
( ) ( ) d( ),
where vd (t) is the desired speed of the moving web
Differentiating (12) with respect to time and substituting
(5) into (12), we arrive at
2 ( ) ( ) ( ) ( ( ) ( ))
2
d
J
r
J
v t lr
r
ρ
(13)
Based on the structure of (13), the input control torques
are designed to satisfy the following equation
J
r
(14)
where kv is a positive control gain Utilizing (14), we obtain
v
J
r ρ
Assumption 1: It is assumed that the desired speed, the time derivatives of the desired speed, and the initial speed tracking error are bounded as follows:
1 ( ) , d
v t ≤ξ v td( ) ≤ξ2, e(0) ≤ξ3, (16) where ξ =i( 1,2,3)i are positive constants
Assumption 2: The time varying tensions T1(t) and
T2(t) are assumed to be bounded as follows:
1
1( ) T,
Assumption 3: The axial tension of the undisturbed web T0, the material tension in the adjacent span T2, and the damping coefficient of the damper ca are assumed to
be sufficiently large such that the following inequalities hold
2
3 2
3 1
3 2
(0)
v
v
T
ra
Ja
ρξ ρ
+
> +
(18)
1 3
a
The vibration energy of the moving web [1,12] is given
as
E t = ∫ ρ w +v t w dx+ ∫ Tw dx (20) Applying the material derivative operator d dt = / / t v / ,x
∂ ∂ + ∂ ∂ the time derivative of E(t) is obtained as follows
2 0
2
0
2
1
2
1
2
l
l
∫
∫
(21) where (1) has been utilized Integrating by parts, the
terms in (21) are further simplified as follows:
0
w Tw +Tw w dx= w Tw
2 0
Trang 4Utilizing (14)-(15), we obtain
0
2 0
2
1 ( , ) ( , ) ( , ) ( )
2 ( , ) ( , )
l
l
x
w l t T l t w l t T vT w dx
vT l t w l t
+
∫
∫
(24)
Remark 1: From (24), the following notes are made
(i) The viscous damping force reduces the mechanical
vibration energy This can be seen from the presence of
2
− ∫ + (ii) The varying tension can add
energy to the web span This is justified by the last two
terms of (24) On this technical basis, a control scheme
that uses the two control torques at boundaries to
regulate the spatially varying tension to make the time
derivative of T(x,t) (i.e., T vTt+ x) negative is now
developed
To stabilize the system given by the governing
equation (1) and the boundary conditions (2) and (3), the
following control torque laws are proposed
3
3
( )t a vd J rl T t T t( ) ( )
a r
ρ
2
2 2
1
(0) exp k rv
ρξ
2
1(sgn( ) 1 v) ,
ρ ξ
3
( ) ( ( )t T t T t r k e t( )) v ( ) J rlT t T t( ) ( )
a
ρ
2
2 2
1
(0) exp k rv
ρξ
2
1(sgn( ) 1 v)
ρ ξ
The axially moving web system under the proposed
control laws is a closed-loop system in that the control
signals use the transport speed information Prior to the
analysis of the stability of the closed-loop system, the
following lemma is introduced
Lemma 1 [7]: Given u x t( , ) :[0, ]l ×ℜ → ℜ+ , if u(0,
) 0,
t = then
0
( , ) l x( , ) ,
0lu x t dx l( , ) ≤ 0lu x t dxx( , )
Theorem 1: Consider system (1) with boundary
conditions (2) and (3), and speed tracking error dynamics
(13) The control gain kv in control laws (25) and (26) is
chosen to satisfy inequality (18) Then, (i) control laws
(25) and (26) ensure that the transverse displacement of
the web converges to zero exponentially in the following
sense
min
2
( , ) l (0)exp( ),
where λ is given as
2 1 max
T
ρ ξ λ
ρ
(ii) The transport speed tracking error converges to zero exponentially in the following sense
2
2 v
k r
e t e
ρ
+
Proof: (i) Substituting (3), (7), and (8) into (24), we obtain
0 ( ) v l( t x) (0, ) (0, )x
E t = −c ∫ w +vw dx vT− t w t
2 1
2 0
2
1 2
2 2
1 2
2 1
( ) 2 ( )
l
d
v
v
v
J
r
v
k Jl lrx
Jl lrx
rk
τ
ρ
ρ ρ
ρ
ρ ρ
⎢
⎢⎣
+ +
+
⎤
−
2
2
a
v T l t
ρ ρ
−
It should be noted that the following equation is employed to obtain (32)
2
v d
k r J
ρ
+
Substitution of (25) into (32) yields:
0 2
2 1
0 min
2
( , ) ( ( , ) ) ( , ) ( , ).
l
l v
x a
x a
r k v
T x t w dx T
T l t c v T l t
w l t
ρ ξ
ρ
−
−
−
−
∫
∫
(34)
Since Assumptions 1~3 hold, the following inequalities are obtained
which yields ( ) (0)exp( )
Using (27) in Lemma 1, we obtain
min
0
l x
T
From (37), (29) is proved (ii) The solution of (15) gives (31)
Trang 5Remark 2: The implementation of torque control laws
(25) and (26) requires the measurements of v(t), T1(t),
and T2(t) and exact knowledge of r, l, J, vd(t) The axial
speed can be achieved with a tachometer or an encoder at
the right roller The tensions T1(t) and T2(t) in the
respective adjacent spans can be measured by adding
tension sensors near the left and right rollers
Remark 3: From (29), the boundedness of w(x,t) is
obtained, and it is concluded that w(x,t) converges to
zero exponentially From (31), the exponential
convergence of the axial velocity v(t) to the desired
speed vd (t) is achieved It is shown that the larger value
of kv results in the faster convergence of v(t) to vd (t)
However, the limit of kv is given by (18)
Remark 4: From (34), it can be concluded that, with
the proposed control laws (25) and (26), the stability of
the axially moving system (1)-(3) is independent to the
viscous damping and the mass per unit length
4 SIMULATION RESUTLS
The finite difference method is employed to find an
approximate solution for the PDE with the initial and
boundary conditions given by (1)-(4) The convergence
scheme is based on the central (for the string span) and
forward/backward (for the left/right boundary) difference
methods The system parameters used in simulation are
the following: ρ = 0.7, l = 4, cv = 0.001, ca = 0.25, r = 0.2,
J = 2.2, T0 = 200, T1 = 100 + 10sin(20t), and T2 = 150 +
10sin(20t) Let the initial conditions of the string be
w(x,0) = 0.5sin(πx/l) and wt (x,0) = 0
The dynamical responses of the axially moving web
were simulated in two cases In the first case, no
vibration control was considered, and only the damping
force exerted from the damper and the viscous damping
force of the web reduced the vibration energy The
transport velocity was driven to track a typical velocity
profile (dotted line) widely used in practice as shown in
Fig 2 In this case, the following simple control laws are
used
J
r
τ =⎛⎜ρ + ⎞⎟ + − −
2( ) 0.t
In the second case, the torque control laws (25) and (26)
are applied to suppress the transverse vibration and to
drive the axial speed The control gain kv selected for the
case of no vibration control is 40 Meanwhile, the control
gain kv in (25) and (26) is set to satisfy the inequality
(17), that is, 1.6
As shown in Fig 2, the performance of the transport
speed tracking control in the case of no vibration control
(red curve) has better quality than the one in the case of
vibration control (blue curve): the settling time in the
case of no vibration control is 1.5 s, whereas it takes 2 s
in the case of vibration control This can be explained by
referring to (15) again, where the convergence speed of
the speed tracking error e(t) depends on the value of kv
0 0.5 1 1.5 2 2.5
Time [s]
desired velocity velocity in vibration control case velocity in no vibration control case
Fig 2 Comparison of transport velocity tracking in the cases of no vibration control (red) and vibration control (blue)
-0.4 -0.2 0 0.2 0.4 0.6
Time [s]
Fig 3 Transverse displacement of the web at x = l/2 in the case of no vibration control
Fig 3 shows that the transverse vibration can be suppressed if the viscous damping coefficient and the damping coefficient of the damper are sufficiently large But this type of suppression requires a great amount time: in our case, it took almost 14 s Meanwhile, the active vibration control scheme using control laws (24) and (25) obtains a good performance as shown in Fig 4
In the acceleration period, the transverse displacement converges to zero within 2 s When the acceleration has ended, and the constant axial speed is maintained, there
is residual vibration that is also suppressed within 2 s This also happens with the deceleration period
To illustrate the robustness of the proposed control laws to the unknown system parameters, the dynamic response of the web-handling system was simulated with the assumption: The proposed control laws with the control gain kv = 1.6 is obtained by using the nominal value of the viscous damping cv = 0.001 while the actual viscous damping in the web-handling system is cv = 0.0005 As shown in Fig 5, the control laws stabilized the web-handling system The vibration suppression was achieved within 3 s The similar simulation was carried
Trang 6out, where the unknown mass per unit length was
assumed The nominal value of mass per unit length is
0.7 while the actual value is 1 With the control law
using the nominal value of the mass per unit length, it took 2 s for the vibration suppression, see Fig 6 The two simulation results shown in Figs 5-6 illustrate the robustness of the proposed control laws to the variations
of the viscous damping and the mass per unit length This is consistent with the theoretical point inferred in Remark 4 Since the convergence of the speed tracking error depends on the control gain kv and the mass per unit length ρ (see (31)), the difference between the nominal value and the actual value of the viscous damping does not affect to the performance of the speed tracking control (red curve in Fig 7)
The larger mass per unit length made slower convergence of the speed tracking error (blue curve in Fig 7) The velocity profile (dotted line) including three levels (as shown in Fig 8) was used to verify the effectiveness of the proposed control laws As shown in Fig 8, the transport velocity (solid line) tracks the desired velocity profile Fig 9 shows the convergence of the transverse vibration Through these simulation results, the effectiveness of the proposed control scheme was verified
0 0.5 1 1.5 2 2.5
Time [s]
Fig 7 Comparison of transport velocity tracking with the system parameter uncertainties of the viscous damping (red) and the mas per unit length (blue)
0 0.5 1 1.5 2 2.5 3
Time [s]
Fig 8 The transport velocity tracks the desired velocity profile (three levels of velocity)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Time [s]
Fig 4 Transverse displacement of the web at x = l/2 in
the case of vibration control
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Time [s]
Fig 5 Transverse displacement at x = l/2: The
differ-ence between the nominal value (used in the
control laws) and the actual value of the viscous
damping is 0.0005
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Time [s]
Fig 6 Transverse displacement of the web at x = l/2:
The difference between the nominal value (used
in the control laws) and the actual value of the
mass per unit length is 0.3
Trang 70 2 4 6 8 10 12 14 16 18 20
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Time [s]
Fig 9 Transverse displacement at x = l/2 in the case of
the desired velocity profile (dotted line) in Fig 8
5 CONCLUSION
In this paper, an active control scheme was developed
for the transverse vibration suppression and the transport
speed tracking of an axially moving web system The
control scheme employed two control torques applied to
the rollers at boundaries The basis of the proposed
control strategy for vibration suppression was the
regulation of the axial tension to dissipate the vibration
energy The torque control laws were designed based on
the original PDE model and Lyapunov energy-based
method The exponential convergence of the transverse
vibration and the speed tracking error to zero were
achieved It is concluded that the proposed control
scheme can provide a viable solution for web-handling
systems, in which the vibration control is required to be
considered together with speed tracking control
REFERENCES [1] R.-F Fung, J W Wu, and S L Wu, “Exponential
stabilization of an axially moving string by linear
boundary feedback,” Automatica, vol 35, no 1, pp
177-181, 1999
[2] S P Nagarkatti, F Zhang, B T Costic, and D M
Dawson, “Speed tracking and transverse vibration
control of axially accelerating web,” Mechanical
System and Signal Processing, vol 16, no 2-3, pp
337-356, 2002
[3] K.-J Yang, K.-S Hong, and F Matsuno, “Robust
boundary control of an axially moving string by
us-ing a PR transfer function,” IEEE Trans on
Auto-matic Control, vol 50, no 12, pp 2053-2058, 2005
[4] K.-S Hong, C W Kim, and K T Hong,
“Boun-dary control of an axially moving belt system in a
thin-metal production line,” International Journal
of Control, Automation, and Systems, vol 2, no 1,
pp 55-67, 2004
[5] C.-W Kim, H Park, and K.-S Hong, “Boundary
control of axially moving continua: application to a
zinc galvanizing line,” International Journal of
Control, Automation, and Systems, vol 3, no 4, pp
601-611, 2005
[6] C.-S Kim and K.-S Hong, “Boundary control of
container cranes the perspective of controlling an
axially moving string system,” International Jour-nal of Control, Automation, and Systems, vol 7, no
3, pp 437-445, 2009
[7] Q C Nguyen and K.-S Hong, “Asymptotic stabi-lization of a nonlinear axially moving string by adaptive boundary control,” Journal of Sound and Vibration, vol 329, no 22, pp 4588-4603, 2010 [8] Q C Nguyen and K.-S Hong, “Simultaneous con-trol of longitudinal and transverse vibrations of an axially moving string with velocity tracking,” Journal of Sound and Vibration, vol 331, no 13,
pp 3006-3019, 2012
[9] M P Omran, A Amani, and H G Lemu, “Analyt-ical approximation of nonlinear vibration of string with large amplitudes,” Journal of Mechanical Science and Technology, vol 27, no 4, pp
981-986, 2013
[10] W D Zhu and J Ni, “Energetics and stability of translating media with an arbitrary varying length,” ASME Journal of Vibration and Acoustics, vol 122,
no 3, pp 295-304, 2000
[11] Y Li and C D Rahn, “Adaptive vibration isolation for axially moving beams,” IEEE/ASME Trans on Mechatronics, vol 5, no.4, pp 419-428, 2000 [12] K.-J Yang, K.-S Hong, and F Matsuno, “Robust adaptive control of an axially moving string under spatiotemporally varying tension,” Journal of Sound and Vibration, vol 273, no 4-5, pp
1007-1029, 2004
[13] M Y Park, S Kim, and I Paek, “Frequency analy-sis of a tower-cable coupled system,” Journal of Mechanical Science and Technology, vol 27, no 6,
pp 1731-1737, 2013
[14] H.-R Kim, K.-W Kim, and W.-S Yoo, “Transient and steady-state analysis of a thin cable unwinding from a pay-out dispenser,” Journal of Mechanical Science and Technology, vol 27, no 2, pp
353-358, 2013
[15] Q C Nguyen and K.-S Hong, “Stabilization of an axially moving web via regulation of axial veloci-ty,” Journal of Sound and Vibration, vol 330, no
20, pp 4676-4688, 2011
[16] Q C Nguyen and K.-S Hong, “Transverse vibra-tion control of axially moving membranes by regu-lation of axial velocity,” IEEE Trans on Control Systems Technology, vol 20, no 4, pp 1124-1131,
2012
[17] S P Nagarkatti, F Zhang, C D Rahn, and D M Dawson, “Tension and speed regulation for axially moving materials,” ASME Journal of Dynamic Sys-tem, Measurement, and Control, vol 122, no 3, pp 445-453, 2000
[18] H Koc, D Knittel, M de Mathelin, and G Abba,
“Modeling and robust control of winding systems for elastic webs,” IEEE Trans on Control Systems Technology, vol 10, no 2, pp 197-208, 2002 [19] P R Pagilla, N B Siraskar, and R V Dwivedula,
“Decentralized control of web processing lines,” IEEE Trans on Control Systems Technology, vol
15, no 1, pp 106-117, 2007
Trang 8[20] P R Pagilla, R V Dwivedula, Y Zhu, and L P
Perera, “Periodic tension disturbance attenuation in
web process lines using active dancers,” ASME
Journal of Dynamics System, Measurement and
Control, vol 125, no 3, pp 361-371, 2003
[21] A Benlatreche, D Knittel, and E Ostertag,
“Ro-bust decentralized control strategies for large-scale
web handling system,” Control Engineering
Prac-tice, vol 16, no 6 pp 736-750, 2008
[22] H Zhao and C D Rahn, “Iterative learning
veloc-ity and tension control for single span axially
mov-ing materials,” ASME Journal of Dynamic System,
Measurement, and Control, vol 130, no.5, pp
051003.1-051003.6, 2008
[23] H D Xing, D.-H Li, and W.-S Cui, “Robust
con-trol guaranteeing uniform ultimate boundedness for
a class of mismatched uncertain parabolic
distrib-uted parameter systems,” International Journal of
Control, Automation, and Systems, vol 11, no 4,
pp 728-733, 2013
[24] S Rachidi, R Channa, and A Karama, “2D inverse
problem in a distributed parameter system,”
Inter-national Journal of Control, Automation, and
Sys-tems, vol 11, no 6, pp 1106-1111, 2013
[25] W Wang, S Ma, and C Zhang, “Stability and
static output feedback stabilization for a class of
nonlinear discrete-time singular switched systems.”
International Journal of Control, Automation, and
Systems, vol 11, no 6, pp 1138-1148, 2013
Quoc Chi Nguyen received his B.S
degree in Mechanical Engineering from
Ho Chi Minh City University of Tech-nology, Vietnam, in 2002, an M.S de-gree in Cybernetics from Ho Chi Minh City University of Technology, Vietnam,
in 2006, and a Ph.D degree in Mechani-cal Engineering from the Pusan National University, Korea, in 2012 Dr Nguyen was a Marie Curie FP7 postdoctoral fellow at the School of
Mechanical Engineering, Tel Aviv University, from 2013 to
2014 He has been a faculty member in the Department of
Mechatronics Engineering, Ho Chi Minh University of
Tech-nology since 2002 Dr Nguyen’s current research interests
include MEMS control, nonlinear systems theory, adaptive
control, and distributed parameter systems
Thanh Hai Le received his B.S degree
in Mechatronics Engineering from Ho Chi Minh City University of Technology, Vietnam, in 2003, an M.S degree in Bio-mechatronic Engineering from Sung-KyunKwan University, Korea, in 2007, and a Ph.D degree in Bio-mechatronic Engineering from the SungKyunKwan University, Korea, in 2011 He has been
a faculty member in the Department of Mechatronics
Engineer-ing, Ho Chi Minh University of Technology since 2011 Dr
Le’s current research interests include nonlinear systems theory,
robotics, and image processing
Keum-Shik Hong received his B.S
de-gree in Mechanical Design and Produc-tion Engineering from Seoul NaProduc-tional University in 1979, an M.S degree in Mechanical Engineering from Columbia University, New York, in 1987, and both
an M.S degree in Applied Mathematics and a Ph.D degree in Mechanical Engi-neering from the University of Illinois at Urbana-Champaign (UIUC) in 1991 Dr Hong served as Edi-tor-in-Chief of the Journal of Mechanical Science and Tech-nology (2008-2011), and served as an Associate Editor for Automatica (2000-2006), and as Deputy Editor-in-Chief for the International Journal of Control, Automation, and Systems (2003-2005) He also served as General Secretary of the Asian Control Association (2006-2008) Dr Hong was Organizing Chair of the ICROS-SICE International Joint Conference 2009, Fukuoka, Japan His laboratory, Integrated Dynamics and Con-trol Engineering Laboratory, was designated as a National Re-search Laboratory by the MEST of Korea in 2003 Dr Hong received various awards including the Presidential Award of Korea (2007) for his contributions in academia Dr Hong’s current research interests include brain-computer interface, nonlinear systems theory, adaptive control, distributed parame-ter systems, autonomous systems, and innovative control appli-cations in brain engineering