recent control engineering technology

8/10/2019 Recent Control Engineering Technology

http://slidepdf.com/reader/full/recent-control-engineering-technology 1/29

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



Outline1. Introduction

2. Bake Plate

3. Multiplexed Model Predictive Control(MMPC)

4. Robust Counterpart

.

6. Conclusion

7. References

2



3



Introduction

Integrated Circuits(ICs) mostly used in :

• Television sets• Digital Video Disc(DVD)

player

•

• etc

4



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

5



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.

6



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.

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 theoutputs (y1, y2, and y3).

9



10



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.

11



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.

12



∑ ∑= =

+++ ∆+−=

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



In compact form

U GU H U J T T ˆˆˆ ∆−∆∆=

ˆ −≡

14

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



15



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.

16



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.

17



RMMPC

Formulation

18

Eliminating the uncertainty in the objectivefunction, the robust MMPC problem is then of theform



RMMPC Results

19

S S H T

=



20



Experiment and Simulation

Collect experimental data using Bake Plate as a plant and

LabView 7.1

21




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

22




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

23



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.

24



Parameters in Simulation

25



26



27



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.

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 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.

29

recent control engineering technology

Documents