Endra Joelianto - ITB

Endra Joelianto
Engineering Physics
Bandung Institute of Technology, Indonesia
The The Asahi Asahi Glass Glass Foundation Foundation Seminar
Seminar
ITB, ITB, Bandung, Bandung, Indonesia Indonesia
Indonesia
July July 6, 2012 2012

Outline
1. Introduction
2. Bake Plate
3. Multiplexed Model Predictive Control(MMPC)
4. Robust Counterpart
5. Experiment and Simulation
6. Conclusion
7. References
2

Introduction
Integrated Circuits(ICs) mostly used in :
• Television sets
• Digital Video Disc(DVD)
player
• Cellular phone
• etc
4

Introduction
On ICs fabrication, photolithography is the most important process. It
spent 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
Dimension(CD)
Source/Drain Mask
PR
Photoresist
N-Silicon
N-Silicon
Field Oxide
Field Oxide
Source/Drain Mask
PR
PR
N-Silicon
N-Silicon
UV Light
Field Oxide
5

Introduction
CD is significantly affected on modern electrical device’s
performances.
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 temperature
about 100 o C.
6

Bake Plate
Post exposure bake normally uses hot plate within temperature
about 100 o C. The hot plate called Bake Plate. It is the radial zones
plate, multi-zones Bake Plate.
7

Bake Plate
The bake plate consists of an aluminum plate at the upside and the
heater at the bottom
8

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 the
outputs (y1, y2, and y3).
9

Multiplexed Model Predictive Control(MMPC)
Model Predictive Control(MPC) can handle multivariable
system. It means MPC can handle drawback of PID
controller. But, its derivation is more complex than PD
controller.
MPC operates by solving an optimization problem on-line, in
real time, to determine a plan for future operation.
MPC determine optimal input signal, minimizes cost function,
and adopts receding horizon.
11

Multiplexed Model Predictive Control(MMPC)
Multiplexed Model Predictive Control(MMPC) :
Assume Tb is time sampling, and m is number of inputs, in
MMPC, only one control input update at Tb/m time. So, after
Ts time, all inputs have been update, and a fresh cycle
begins.
It reduces the computational complexity.
12

J
=
The cost function of MMPC is given by
N
ˆ
∑
2
|| y ∑
k + i − wk
+ i || Q +
i=
N
i=
N
1 1
N
|| Δu
⎡Q(
1)
0 L 0 ⎤
⎢
⎥
= ⎢
0 Q(
2)
L 0
Q
⎥
⎢ ⎥
⎢
⎥
⎦
⎢ Q =
M M O M
⎣ 0 0 L Q(
N2)
Q
R
= T
Q
= T
R
≥
>
0
0
k + i|
k
||
2
R
⎡R(
1)
0 L 0 ⎤
⎢
⎥
= ⎢
0 R(
2)
L 0
R
⎥
⎢ ⎥
⎢
⎥
⎦
⎢ R =
M M O M
⎣ 0 0 L R(
Nu
−1)
13

In compact form
U
G
U
H
U
J
T
T ˆ
ˆ
ˆ Δ
−
Δ
Δ
=
ω
≤
ΩΔU ˆ )
(
)
1
( k
Mx
k
Fu +
−
+
≡ β
ω
14
ω
≤
ΩΔU ˆ )
(
)
1
( k
Mx
k
Fu +
−
+
≡ β
ω
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
Φ
Φ
−
−
−
=
Ω
u
u
E
I
E
I
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
Δ
−
−
Δ
−
=
max
max
max
min
min
min
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
y
U
U
y
U
U
β
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
Γ
−
Γ
=
0
0
0
0
F
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
Φ
−
Φ
=
0
0
0
0
M

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) has
been extensively studies in many area research.
The RO methodology is designed to solve optimization
problems where data are uncertain and are only known to
belong some uncertainty sets.
16

Robust Counterpart
Robust Counterpart(RC) is pioneered by Ben-Tal and Nemirovski.
The advantages of this approach is that the resulting optimization
problem belongs to the class of Conic Optimization(CO), i.e.:
linear optimization (LO) problems
conic quadratic optimization (CQO) problems
semidifinite optimization (SDO) problems
which are computationally tractable and can be
solved 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.
17

RMMPC
Formulation
Eliminating the uncertainty in the objective
function, the robust MMPC problem is then of the
form
18

RMMPC Results
H
=
S
T
S
19

Experiment and Simulation
Collect experimental data using Bake Plate as a plant and
LabView 7.1
21

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
rp12= rp12= 2.754 K/W, rp23=0.583 K/W
From all the parameters we can construct the state space model
for 3-zones bake plate as,
x = [θp1 θp2 θp3] T
u = [u1 u2 u3] T
y = [θp1 θp2 θp3] T
22

Experiment and Simulation
Construct the state space model :
x & = Fx + Gu
y =
Ix
Using System Identification Toolbox on Matlab, we get
the state space model as follow :
⎡ − 1 1
⎢
⎢
Cp1Rp1
Cp1rp12
⎢ 1 −1
F =
⎢Cp2rp12
Cp2Rp2
⎢
1
⎢ 0
⎢⎣
Cp3rp23
⎡ 1
⎢
⎢
Cp1
G = ⎢ 0
⎢
⎢
⎢ 0
⎢⎣
0
1
Cp2
0
0
0
1
3
Cp
⎤
⎥
⎥ ⎡0
⎥ =
⎢
⎥ ⎢
⎥ ⎢⎣
⎥
⎥⎦
⎤
0 ⎥
⎥ ⎡−
0.
0025525
1 ⎥ =
⎢
⎥ ⎢
0.
0007048
Cp2rp23
−1
⎥ ⎢⎣
0
⎥
Cp3Rp3
⎥⎦
. 0052573
0
0
0
0.
0019416
0
0.
0019085
−
0.
004652
0.
0030697
0 ⎤
0
⎥
⎥
0.
0017926⎥⎦
0 ⎤
0.
003324
⎥
⎥
− 0.
004471⎥⎦
23

Performance Specifications
The control system is required to
maintain the temperature defined as
follow:
Temperature set-point 90o Temperature set-point 90 C.
Lenght of heating is not more than 4
minutes.
Overshoot must be lower than 0.2 o C.
Each zone has uniform temperature.
Control signal must be lower than 2.5 V.
24

Parameters in Simulation
25

CONCLUSIONS
The paper proposed a bake plate control
system design using a robust
multiplexed model predictive control
(RMMPC) to produce fast recovery and
good attenuation after disturbances.
The developed RMMPC using robust
counterpart methodology showed better
disturbance attenuation performances
than the MMPC and the standard MPC.
28

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 Symmetric
Cones”, 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 Engineering
NUS, 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.
29