Recent trends in civil engineering & technology (vol4, issue1)
Recent Control Engineering Technology
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Transcript of Recent Control Engineering Technology
8/10/2019 Recent Control Engineering Technology
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Endra Joelianto
Engineering Physics
Bandung Institute of Technology, Indonesia
The Asahi Glass Foundation SeminarThe Asahi Glass Foundation SeminarThe Asahi Glass Foundation SeminarThe Asahi Glass Foundation Seminar
ITB, Bandung, IndonesiaITB, Bandung, IndonesiaITB, Bandung, IndonesiaITB, Bandung, IndonesiaJulyJulyJulyJuly 6, 20126, 20126, 20126, 2012
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Outline1. Introduction
2. Bake Plate
3. Multiplexed Model Predictive Control(MMPC)
4. Robust Counterpart
.
6. Conclusion
7. References
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Introduction
Integrated Circuits(ICs) mostly used in :
• Television sets• Digital Video Disc(DVD)
player
•
• etc
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Introduction
On ICs fabrication, photolithography is the most important process. Itspent about 40 to 50% total wafer process time.
Photolithography :
• temporary coat photoresist on wafer
• transfers designed pattern to photoresist
• determines the minimum feature size called Critical
mens on
N-Silicon
Source/Drain Mask
Photoresist
Field Oxide
N-Silicon
Source/Drain Mask
PR
UV Light
N-Silicon
PR
Field Oxide
N-Silicon
PR
Field Oxide
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Introduction
CD is significantly affected on modern electrical device’sperformances.
The Alignment and exposure step is the most critical process
for ICs fabrication. It is also the most challenging technology.
Post exposure bake normally uses hot plate within temperatureabout 100oC.
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Bake Plate
Post exposure bake normally uses hot plate within temperature
about 100oC. The hot plate called Bake Plate. It is the radial zones
plate, multi-zones Bake Plate.
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Bake Plate
The bake plate consists of an aluminum plate at the upside and the
heater at the bottom
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Bake Plate
The heater will transform the heat to the plate at every zone. The
system is a MIMO (Multi Input Multi Output) system with power of
electricity as the inputs (u1, u2, and u3) and temperature as theoutputs (y1, y2, and y3).
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Multiplexed Model Predictive Control(MMPC)
Model Predictive Control(MPC) can handle multivariablesystem. It means MPC can handle drawback of PIDcontroller. But, its derivation is more complex than PD
controller.
MPC operates by solving an optimization problem on-line, inreal time, to determine a plan for future operation.
, ,and adopts receding horizon.
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Multiplexed Model Predictive Control(MMPC)
Multiplexed Model Predictive Control(MMPC) :
Assume Tb is time sampling, and m is number of inputs, inMMPC, only one control input update at Tb/m time. So, afterTs time, all inputs have been update, and a fresh cycle
begins.
It reduces the computational complexity.
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∑ ∑= =
+++ ∆+−=
N
N i
N
N i
Rk ik Qik ik uw y J 1 1
2
|
2||||||ˆ||
0)2(0
00)1(
Q
Q
L
L
0)2(0
00)1(
R
R
L
L
The cost function of MMPC is given by
13
=
)(00 2 N QL
MOMM
−
=
)1(00 u N RLMOMM
0≥= T QQ
0>= T R R
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In compact form
U GU H U J T T ˆˆˆ ∆−∆∆=
ˆ −≡
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Φ
Φ−
−
−
=Ω
u
u
E
I
E
I
∆
−
−
∆−
=
max
max
max
min
min
min
ˆ
ˆ
ˆˆ
ˆ
ˆ
y
U
U
y
U
U
β
Γ −
Γ
=
0
00
0
F
Φ−
Φ=
0
0
0
0
M
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Robust Counterpart
In the case where the plant dynamics ar uncertain, robust
MPC has been developed to tackle this problem.
Recently, methodology called Robust Optimization (RO) hasbeen extensively studies in many area research.
The RO methodology is designed to solve optimization
pro ems w ere a a are uncer a n an are on y nown o
belong some uncertainty sets.
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Robust Counterpart
Robust Counterpart(RC) is pioneered by Ben-Tal and Nemirovski.
The advantages of this approach is that the resulting optimizationproblem belongs to the class of Conic Optimization(CO), i.e.:
linear optimization (LO) problems
conic quadratic optimization (CQO) problems
semidifinite optimization (SDO) problems
w c are compu a ona y rac a e an can esolved efficiently by interior point methods. The uncertainty is modelled as an ellipsoidal uncertainty set such
that the obtained RC is modeled in one of special problems of CP,
i.e. a conic quadratic optimization(CQO) problem.
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RMMPC
Formulation
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Eliminating the uncertainty in the objectivefunction, the robust MMPC problem is then of theform
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RMMPC Results
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S S H T
=
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Experiment and Simulation
Collect experimental data using Bake Plate as a plant and
LabView 7.1
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Experiment and Simulation
System Identification
Parametric model estimation gives,Cp1=190.21 J/K, Cp2= 515.039 J/K, Cp3=557.848 J/K
rp1= 8.158 K/W, rp2= 3.1207 K/W, rp3= 1.274 K/W
= . , = .
From all the parameters we can construct the state space modelfor 3-zones bake plate as,
x = [θp1 θp2 θp3]T
u = [u1 u2 u3]T
y = [θp1 θp2 θp3]T
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Experiment and Simulation
Construct the state space model :
GuFx x +=&
Ix y =
Using System Identification Toolbox on Matlab, we get
the state space model as follow :
−
−
−
=
−
−
−
=
004471.00030697.00
003324.0004652.00007048.0
00019085.00025525.0
33
1
233
10
232
1
22
1
122
1
0121
1
11
1
RpCprpCp
rpCp RpCprpCp
rpCp RpCp
F
=
=
0017926.000
00019416.00
000052573.0
3
100
02
10
001
1
Cp
Cp
Cp
G
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Performance Specifications The control system is required to
maintain the temperature defined asfollow:
Tem erature set- oint 90oC.
Lenght of heating is not more than 4minutes.
Overshoot must be lower than 0.2oC.
Each zone has uniform temperature.
Control signal must be lower than 2.5 V.
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Parameters in Simulation
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CONCLUSIONS The paper proposed a bake plate control
system design using a robustmultiplexed model predictive controlRMMPC to roduce fast recover and
good attenuation after disturbances. The developed RMMPC using robust
counterpart methodology showed better
disturbance attenuation performancesthan the MMPC and the standard MPC.
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References
[1] K.V, Ling, B.F. Wu, and J.M. Maciejowski,”Embedded Model Predictive Control (MPC)using a FPGA”, Proc. Of the 17th World Congress , Seoul, Korea, July 6-11, 2008,pp.15250-15255.
[2] Ling KV , MPC Course at ITB/Ling KV/May08, Introduction to Model Andreas ’s paper,
NUS, MPC on Bake Plate System.[3] Maciejowski , Predictive Control with Constraints, Prentice-Hall, 2001.
[4] A. Ben-Tal and A. Nemirovski, “Robust Solutions of Uncertain Linear Programs”,Operations Research Letters , 1999, vol. 25, no. 1, pp. 1-13.
[5] D. Chaerani, Modelling Robust Design Problems via Conic Optimization , PhD Thesis,Technische Universiteit Delft, The Netherlands, 2006.
[6] J.F. Sturm, “Using SeDuMi 1.02, a Matlab Toolbox for Optimization over SymmetricCones”, Department of Econometrics, University of Tilburg, 2001.
[7] Soon L K , System Identification Method Lecture Note, School of EEE NTU, 2008.
[8] Wang QG , Linear system lecture note, Department of Computer & Electrical EngineeringNUS, 2008.
[9] Seron MM , Receding Horizon control lecture notes, University of Newcastle, 2004.[10]. E. Joelianto, R.I. Simangunsong, D. Chaerani, K.V. Ling, “The Robust Model Predictive
Control (MPC)”, Proc. IEEE International Conference on Advanced Computer Control(ICACC), Singapore, pp. 546-550, 2009.
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