Active Compensation in RF-driven Plasmas by Means of Selected Evolutionary Algorithms : a Comparative Study Ivan Zelinka .

Active Compensation in RF-driven Plasmas Active Compensation in RF-driven Plasmas by Means of by Means of Selected Selected Evolutionary Algorithms : a Comparative StudyEvolutionary Algorithms : a Comparative Study

Ivan Zelinkahttp://www.ft.utb.cz/people/zelinka

Email [email protected]

Tomas Bata University in ZlinFaculty of Technology

Institut of Information TechnologiesMostni 5139Zlin 760 01

Czech Republic

Structure of the Lecture IStructure of the Lecture I

S ta tus Q uo

R e ac to r s che m e

L an gm u ir p robe

C o m p en sa tion lo op

E xpe rim e n t e qu ipm e nt

F u nd am en ta ls o f e xp er im e n t

M a in idea

T erm ino logy

C on s tra in t h an d ling

T e sting

D e m o

S O M A d e sc r ip t ion

U sed a lg o r i thm s

P rev iou s e xp er im e n t

R e su lts

S A ,D E

R e su lts

S A , D E , S O M A

E xpe rim en t s e tt ing

V ide o d em on stra tion(6 m in )

C o nc lus ion

A c tiv e C o m p en sa tion in R F-d riv en P la sm as

Plasmas Status Quo IPlasmas Status Quo I

Plasmas are radically multiscale in two senses

• most plasma systems involve electrodynamics coupling across micro-, meso- and macroscale and

• plasma systems occur over most of the physically possible ranges in space, energy and density scales. The figure here illustrates where many plasma systems occur in terms of typical density and temperature conditions.

Plasmas are conductive assemblies of charged particles, neutrals and fields that exhibit collective effects. Further, plasmas carry electrical currents and generate magnetic fields. Plasmas are the most common form of matter, comprising more than 99% of the visible universe.

Major topical areas of plasma science and technology

Plasma Equilibria, dynamic and static Wave and Beam Interactions in Plasmas

Wave and Beam Interactions in Plasmas Numerical Plasmas and Simulations

Plasma Sources Plasma Theory

Plasma-based Devices Plasma Diagnostics

Plasma Sheath Industrial Plasmas

Plasmas Status Quo IIPlasmas Status Quo II

Revolution Technologies

Industrial Engines, Metallurgy

Chemical Waste handling, Catalysts

Electrical Transformers, Switches

Nuclear Reactors, Isotopes

Electronic Electronics, Semiconductors

Optical Lighting Sources, Lasers

Alan Watts of Environmental Surface Technologies in Atlanta, Georgia has suggested the following grid for organizing industrial plasmas with reference to the major "revolutions" in technology:

Plasmas Status Quo IIIPlasmas Status Quo III

Benefits at Home. High efficiency lighting; manufacturing of semiconductors for home computers, TVs and electronics; flat-panel displays; and surface treatment of synthetic cloth for dye adhesion.

Business Applications. Plasma enhanced chemistry; surface cleaning; processing of plastics; gas treatment; spraying of materials; chemical analysis; high-efficiency lighting; semiconductor production for computers, TVs and electronics; and sterilization of medical tools.

Plasmas in Transportation. Plasma spraying of surface coatings for temperature and wear resistance, treatment of engine exhaust compounds, and ion thrusters for space flight.

Plasma Thrusters for Spacecraft - test of electrostatic ion thruster in large vacuum chamber (NASA)

Plasma spraying of high-temperature resistance surface coatings for a diesel engine turbocharger housing

Microwave generated plasma around a catalyst for removal of NOx and CO from engine exhausts

Modification of Aerodynamic Drag. A flat panel with a layer of one-atmosphere plasma undergoing wind tunnel testing. This technology may lead to improvements in aircraft flight range and landing on short runways. (University of Tennessee)

Plasmas Status Quo IVPlasmas Status Quo IV

Plasma Lighting. The most prevalent man-made plasmas on our planet are the plasmas in lamps. There are primarily two types of plasma-based light sources, fluorescent lamps and high-intensity arc lamps. Fluorescent lamps find widespread use in homes, industry and commercial settings.

Inside every fluorescent lamp there lurks a plasma. It is the plasma that converts electrical power to a form that causes the lamp's phosphor coating to produce the light we see. The phosphor is the white coating on the lamp wall. A fluorescent lamp is shown here with part of the phosphor coating removed to reveal the blue plasma glow inside.

New one-atmosphere plasma systems make possible new methods for surface cleaning and sterilization for food, medical, and other applications. Whereas standard heat sterilization is time consuming and irradiation can damage materials, this new plasma technology has been shown to kill bacteria on various surfaces in seconds to minutes. In addition to destroying bacteria, such plasma systems also destroy viruses, fungi and spores. These systems also provide an environmentally benign method for pre-treating surfaces. One-atmosphere plasma systems are now becoming available for various industrial applications. The photo shows laboratory testing of non-thermal amospheric pressure plasmas for the inactivation (or destruction) of microorganisms.

Plasmas Status Quo VPlasmas Status Quo V

Products manufactured using plasmas impact our daily lives on:• Computer chips and integrated circuits• Computer hard drives • Electronics • Machine tools • Medical implants and prosthetics • Audio and video tapes • Aircraft and automobile engine parts • Printing on plastic food containers • Energy-efficient window coatings • High-efficiency window coatings • Safe drinking water • Voice and data communications components • Anti-scratch and anti-glare coatings eyeglasses and other optics

Plasma technologies are important in industries with annual world markets approaching $200 billion:• Waste processing • Coatings and films • Electronics • Computer chips and integrated circuits • Advanced materials (e.g., ceramics) • High-efficiency lighting

Impact of Plasmas on TechnologyImpact of Plasmas on Technology

Motivation and Aims Motivation and Aims

• Use of evolutionary algorithms to deduce fourteen Fourier terms in a radio-frequency (RF) waveform in plasma reactor.

• Previous experiment: Dyson, A., Bryant, P., Allen, J. E. “Multiple harmonic compensation of Langmuir probes in RF discharges”, Meas. Sci. Technol. 11(2000), pp 554-559L Nolle, A Goodyear, A A Hopgood, P D Picton, N StJ Braithwaite, Automated Control of an Actively Compensated Langmuir Probe System Using Simulated Annealing

• Extension of a previous study as an comparative studySA, DE in: K.V. Price, R.Storn, Lampinen J., DE – Global Optimiser for Scientists and Engineers, Springer-VerlagSA,DE, SOMA in: journal is in searching process

Radio frequency inductively-coupled plasma source for plasma processing

Langmuir probes are important electrostatic diagnostics for RF-driven gas discharge plasmas. These RF plasmas are inherently non-linear, and many harmonics of the fundamental are generated in the plasma. RF components across the probe sheath distort the measurements made by the probes. To improve the accuracy of the measurements, these RF components must be removed. This has been achieved during this research by active compensation, i.e. by applying an RF signal to the probe tip. Not only amplitude and phase of the applied signal have to match that of the exciting RF, also its waveform has to match that of the harmonics generated in the plasma. The active compensation system uses seven harmonics to generate the required waveform. Therefore, fourteen heavily interacting parameters (seven amplitudes and seven phases) need to be tuned before measurements can be taken. Because of the magnitude of the resulting search space, it is virtually impossible to test all possible solutions within an acceptable time. An automated control system employing EAs has been developed for online tuning of the waveform. This control system has been shown to find better solutions in less time than skilled human operators do. The results are also more reproducible and hence more reliable.

Radio-frequency (RF) driven discharge plasmas are widely used in the material processing industry. Plasmas are partially ionized gases, which are not in a thermal equilibrium with their surroundings. They are used, for example, for etching, deposition and surface treatment in the semiconductor industry. In order to achieve best results, i.e. quality, it is essential for users of such plasmas to have tight control over the plasma and hence they need appropriate diagnostic tools. Better diagnostics lead to better control of the plasma and hence to better quality of the products.

Introduction Introduction

~ Plasma RF Generator

Output

Input Massflow controller

Vacuum Vessel

Schematics of a RF driven plasma systemSchematics of a RF driven plasma system

• Problem domain: low temperature plasma systems• Radio-frequency driven plasmas

• RF-powered plasmas by an external power source, usually operating on 13.56 MHz (industrial use) • The main application of RF-powered plasmas is to produce a flux of energetic ions, which can be applied continuously to a large area of work piece, e.g. for etching or deposition.

13.56 MHzLangmuir probe

Langmuir probesLangmuir probes

• Developed in 1924 by Langmuir, are one of the oldest probes used to obtain information about low-pressure plasma properties. They are metallic electrodes, which are inserted into a plasma. By applying a positive or negative DC potential to the probe, either an ion or an electron current can be drawn from the plasma, returning via a large conducting surface such as the walls of the vacuum vessel or an electrode. This current is used to analyze the plasma properties, e.g. for the determination of the energy of electrons, electron particle density, etc.

• The region of space-charge (the sheath) that forms around a probe immersed in a plasma has a highly non-linear electrical characteristic. As a result, harmonic components of potential across this layer give rise to serious distortion of the probe’s signal. In RF-generated plasmas this is a major issue as the excitation process necessarily leads to the space potential in the plasma having RF components. As a consequence of this fact a serious distortion of the probe’s signal can be observed. It is caused by harmonic components of potential across this layer. In order to achieve accurate measures, this harmonic component has to be eliminated.

Problem Complexity and Problem Complexity and Active Active CCompensation in RF-driven ompensation in RF-driven PPlasmaslasmas and and Automated Control SystemAutomated Control System

PC with Xwos system

DC Buffer

DC Bias

Harmonic Generator RF Generator

Langmuir Probe GEC Cell

Sync

Plasma

RFRF Signal

Floating Potencial

14 Control Signals

pbn )2(

Where:n number of points in search spaceb resolution per channel in bitsp number of parameters to be optimized

• Resolution of 12 bits• Dimensionality of the search space was 14 (Dyson, A., Bryant, P., Allen, J. E. reported in “Multiple harmonic compensation of Langmuir probes in RF discharges”, Meas. Sci. Technol. 11(2000), pp 554-559 only 3 harmonics)• Search space consisted of n 3.7 x 1050 search points• Mapping out the entire search space would take approximately 1041 years i.e. 1032 x longer that our universe exist• 240s -> 10-47s

Before the xwos (xwindow waveform optimization system) control software was developed, the following requirements were identified:

• The optimization should take place within reasonable time,• The search results (fitness) over time should be plotted on-line on screen in order to allow a judgement of the quality of the result,• The operator should be able to select values for the EAs parameters,• The operator should have the opportunity to set any of the fourteen parameters manually,• The operator should have the opportunity to fine-tune the settings found by the automated system,• The DC bias (fitness parameter) had to be monitored.

The control software was developed in C++ on a 500 MHz Pentium III PC running the Linux 2.2 operating system. The graphical user interface was coded using X-Windows and OSF/Motif.

Software Software Experiment EquipmentExperiment Equipment and Requirements on XWOS System and Requirements on XWOS System

7 amplitudes 7 phases

DC Bias

History of one evolution of the best and average individual

Correlation analysiswindow

Hardware Hardware Experiment EquipmentExperiment Equipment

• All experiments were carried out at the Oxford Research Unit, The Open University, UK. Figure shows the experiment setup. Apart from the control system described above, a digital oscilloscope was used to measure the actual waveforms found by the three optimization algorithms.

• The control software was running on a PC under the Linux operating system. The algorithms used for this experiments were written in C++ and integrated in the existing Langmuir probe control software. The plasma system used was a standard GEC cell.

Optimization Algorithms UsedOptimization Algorithms Used

• Simulated Annealing (SA)• Van Ginneken, L. P. P. P., Otten, R. H. J. M.: The Annealing Algorithm (Kluwer International Series in Engineering and Computer Science,72), Kluwer Academic Publishers, 1989

• Differential Evolution (DE)• Price K.: An Introduction to Differential Evolution, in New Ideas in Optimization, D. Corne, M. Dorigo and F. Glover, Eds., s. 79–108, McGraw-Hill, London, UK, 1999.

• Self-Organizing Migrating Algorithm (SOMA)• Zelinka Ivan , „SOMA – Self Organizing Migrating Algorithm“,chapter 7, 33 p. in: B.V. Babu, G. Onwubolu (eds), New Optimization Techniques in Engineering, Springer-Verlag

SOMA –SOMA – Main Idea Main Idea

The main idea on which SOMA is based is competetive-cooperative behavior of the intelligent beings who are together solving given task. Examples can be observed arround the world:

• Ants• Bees• Termites• Wolves• People

• Gold miners of 19th century• Battle strategies• …

Bacause of used philosophy, terminology used with this algorithm a little bitt differ from standard terminology used with classics EAs.

At http://www.ft.utb.cz/people/zelinka/soma/ are available source codes, test functions, and more...

SOMA –SOMA – Terminology and Recommended ParametersTerminology and Recommended Parameters

Parameter name Recommended range Remark

PathLength <1.1, 3> Controlling parameter

Step <.11, PathLength> Controlling parameter

PRT <0, 1> Controlling parameter

Dim Given by problem Number of arguments in cost function

PopSize <10, up to user> Controlling parameter

Migrations <10, up to user> Stopping parameter

MinDiv <arbitrary negative, up to user > Stopping parameter

-400 -200 200 400

-400

-200

200

400

If < MinDiv then End

SOMA –SOMA – Principles Principles

• Parameter definition - Migrations, MinDiv, PopSize, PathLength, Step, PRT, Specimen and Dimension of the problem.

• Start of SOMA - population generating

• Run of SOMA

precisely

}}} Hi Lo, { {Real, ,}}, Hi Lo, { {Integer, Hi}, {Lo, {{Real,Specimen

parampopLo

jLo

jHi

jjiji njnixxxrndxP ,,1,,,1)( )()()(,

)0(,

)0(

(1)

(2)

PathLengthtoStepbytkdePRTtmrr ,,00 (3)

PathLengthtoStepbytkdePRTtxxxx MKstartji

MKjL

MKstartji

MKji ,,0)( ,,,,,

1,

(4)

MK

startji

MKstartjit

MKjitMK

ji x

xfxfMinx

,,

,,cos,cos1,

)())(( (5)

SOMA parameters PRT vector, for each individual is generated new one

Step 0,3 If Rand < PRT then 1 else 0 1PathLength 3 If Rand < PRT then 1 else 0 0PRT 0,1 If Rand < PRT then 1 else 0 0MinDiv 0,1 If Rand < PRT then 1 else 0 1Migrations 1000 If Rand < PRT then 1 else 0 0PopSize 7 If Rand < PRT then 1 else 0 1

Cost function f(x)= Abs(Parameter 1)+ Abs(Parameter 2) +...+ Abs(Parameter 5)

Active individual Leader

Individual 1 Individual 2 Individual 3 Individual 4 Individual 5 Individual 6 Individual 7

CV 204,91528 261,3632 163,79679 121,73019 107,52784 121,06024 120,20974Parameter 1 3,0615753 -46,63569 5,0246553 38,723912 35,822343 0,0715185 23,761224Parameter 2 2,5117282 54,036685 85,104704 0,2928606 24,111443 4,2879691 20,384665Parameter 3 46,75014 51,282894 11,347164 3,0796963 24,657689 60,241731 33,437248Parameter 4 72,486617 15,080129 2,916686 3,6713463 5,8142407 4,5385164 4,0482021Parameter 5 6,316564 57,155744 58,829537 26,610056 12,43856 23,891907 4,2271271Parameter 6 73,788657 -37,17206 0,5740442 49,352316 4,6835676 28,028598 34,351273

New positions

t = 0 t = 1 t = 2 t = 8 t = 9 t = 10

CV 261,3632 221,28934 186,89373 … 384,17836 424,25222 464,32608-46,63569 -21,89828 2,8391294 … 151,26359 176,001 200,7384154,036685 54,036685 54,036685 … 54,036685 54,036685 54,03668551,282894 51,282894 51,282894 … 51,282894 51,282894 51,28289415,080129 12,300362 9,5205959 … -7,158003 -9,937769 -12,7175457,155744 57,155744 57,155744 … 57,155744 57,155744 57,155744-37,17206 -24,61537 -12,05868 … 63,281441 75,838128 88,394815

CV 261,3632 Individual 186,89373 Individual with lower CV of all-46,63569 with 2,839129454,036685 lower 54,03668551,282894 CV 51,282894

… …

Individual 1 Individual 2 Individual 3 Individual 4 Individual 5 Individual 6 Individual 7

CV 204,91528 186,89373Parameter 1 3,0615753 2,8391294Parameter 2 2,5117282 54,036685Parameter 3 46,75014 51,282894Parameter 4 72,486617 9,5205959Parameter 5 6,316564 57,155744Parameter 6 73,788657 -12,05868

MasstoStepbyt

PRTtxxxx jML

startjiML

jLML

startjiML

ji

,,0

)( ,,,,,1

,

SOMA –SOMA – Principles Principles

0 100 200 300 400 500

-500

-400

-300

-200

-100

0

Leader

Individual

Step

Position givenby parameter PathLength

PRT=[0,1]

PRT=[1,1]

Versions:

AllToOne AllToOneRandomly AllToAll AllToAllAdaptive

1

2

3

4

L

1

2

3 4

SOMA –SOMA – Basic VersionsBasic Versions

SOMA’s ability to avoid local minimas - during migration loops is created false „function“ - polyhedron and individuals move along to edges of this polyhedron

SOMA –SOMA – AAbility to bility to AAvoid void LLocal ocal MMinimas inimas

• Handling of boundary constraints• Boundary position setting• Reset of wrong parameter• Spiral movement on N+1 dimensional sphere• Random replacement

• Handling of integer variables• Rounding in the population• Rounding in the “cost function argument input”

• Handling of discrete variables• Integer index use

• Handling of constraints given to the fitness• Penalty

SOMA –SOMA – Constraints HandlingConstraints Handling

x2 {-1.2, 2.69, 110, 256.3569, …..}

{1, 2, 3, 4, …..}

Discrete (original) parameter of individual…

…and its integer index – alternate parameter usedin evolution process

Fcost(x1,x2,….xn)

no

yes

SOMA –SOMA – Problem Complexity Problem Complexity

-100-50

0

50

100

-100

-50

0

50100

0

0.5

1

1.5

2

-100-50

0

50

100

-100

-50

0

50100

-10

-5

0

5

10

-10

-5

0

5

10

0

0.5

1

1.5

2

-10

-5

0

5

10

-10

-5

0

5

10

• Objective function - • unimodal : multimodal• Linear – nonlinear• None-fractal type (but because everything in the real world has constrains, fractal type functions can also be optimized)• Defined at real, integer or discrete argument spaces• Constrained, multiobjective• Needle-in-haystack problems• NP problems

• Degree of parameter interactions : low – high, separable – non-separable

• Type of variables : continuous – discrete / integer / mixed

• Number of variables : low – high

• Search space : small – large, finite – infinite, continuous – non-continuous

SOMA –SOMA – Selected Tests ISelected Tests I

SOMA –SOMA – Selected Tests IISelected Tests II

0 200000 400000 600000 800000 1 106 1.2 106

Number of Cost Function Evaluations

60000

40000

20000

0

tsoCeulaV

0 100000 200000 300000 400000 500000 600000Number of Cost Function Evaluations

0

100

200

300

400

tsoCeulaV

0 20 40 60 80 100Parameter

0.1

0.05

0

0.05

0.1

retemaraPeulav

EggHolder StretchedSine

StretchedSine

3rd De Jong's function 4th De Jong's functionSphere model, 1st De Jong's function

Rosenbrock's saddle

Rastrigin's function Schwefel's function Griewangk's functionStretched V sine wave

function (Ackley)

Test function (Ackley) Ackley's function Test function - egg holder Rana's function

Pathological function Michalewicz's function

-4-2

02

4-4

-2

0

2

4

-1

-0.5

0

0.5

-4-2

02

4Cosine wave function (Masters)

SOMA –SOMA – Tests FunctionsTests Functions

m0Chemical reactor

optimization and controlChemical reactor structural stability Analytic programming

Mechanical engineeringexamples

1

3

5

7

9

11

V

46

810

1214

1618

20

W

00.250.5

0.751

m

1

3

5

7

9

11

V

Fuzzy controller settingPredictive model

estimation

0 500 1000150020002500Time020406080100120

erutarepmeT

AntenaInverse Fractal Problem

SOMA –SOMA – Selected ProblemsSelected Problems

Previous ExperimentsPrevious Experiments

• SA had shown better floating potential than human operator• SA had shown smaller diversity in floating potential and time

For following experiments were parameters set so that used EA showed the best performance as much as possible

Experiment Setting – SA, DEExperiment Setting – SA, DE

Plasma parameters

Gas Argon

Power 50 W

Pressure 100 mTorr

Flow rate 95 sccm

Plasma parameters used for the experiments

Parameter settings for the optimization algorithms used in experiments

Results I – SA, DEResults I – SA, DE

0 2000 4000 6000 8000 10000 12000Cost Function Evaluation

2700

2800

2900

3000

3100

3200

3300

ssentiF

Deviation

Average

Best

0 2000 4000 6000 8000 10000 12000Cost Function Evaluation

2000

2200

2400

2600

2800

3000

3200

ssentiF

Deviation

Average

Best

DE

SA

All data were carefully collected and used to draw a “flow of all histories” so that average, minimal and maximal values can be easily observed.

1 2 3 4 5 6 7 8 9 10 11 12 13 14Parameter

0

1000

2000

3000

ssentiF

1 2 3 4 5 6 7 8 9 10 11 12 13 14

DE

SA

1 2 3 4 5 6 7 8 9 10 11 12 13 14Parameter

0

1000

2000

3000

4000

ssentiF

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Results II – SA, DEResults II – SA, DE

Efficiency of used algorithms can be also judge according to correctness and reproducibility of reached results based on “statistical” point of view

0 5 108 1107 1.5 107 2 107

Times50000

100000

150000

200000

250000

300000

egatloVV

DE

SA

0 5 108 1107 1.5 107 2 107

Times100000

150000

200000

250000

300000

350000

egatloVV

Results III – SA, DEResults III – SA, DE

Results were used to restore waveforms observed on osciloscope. Here are depicted average values, minimal and maximal values reached during all experiments.

DE SAAlgorithm

3310

3320

3330

3340

3350ssentiF

DE SA

Results VI – SA, DEResults VI – SA, DE

Results were used to create an algorithm efficiency chart to show efficiency of both algorithms. They shows minimal, maximal and average values reached during the active compensation of RF-driven plasmas.

Experiment Setting – SA, DE and SOMAExperiment Setting – SA, DE and SOMA

Plasma parameters

Gas Argon

Power 50 W

Pressure 100 mTorr

Flow rate 95 sccm

Plasma parameters used for the experiments

Parameter settings for the optimization algorithms used in experiments

Results I – SA, DE and SOMAResults I – SA, DE and SOMA

0 2000 4000 6000 8000 10000 12000Cost Function Evaluation

2600

2700

2800

2900

3000

3100

3200

3300

ssentiF

Deviation

Average

Best

DE

SA

0 2000 4000 6000 8000 10000 12000Cost Function Evaluation

2000

2200

2400

2600

2800

3000

3200

ssentiF

Deviation

Average

Best

2000 4000 6000 8000 10000 12000Cost Function Evaluation

2900

3000

3100

3200

3300

ssentiF

Deviation

Average

Best

SOMA

All data were carefully collected and used to draw a “flow of all histories” so that average, minimal and maximal values can be easily observed.

Results II – SA, DE and SOMAResults II – SA, DE and SOMA

DE

SA

SOMA

1 2 3 4 5 6 7 8 9 10 11 12 13 14Parameter

0

1000

2000

3000

4000

ssentiF

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 2 3 4 5 6 7 8 9 10 11 12 13 14Parameter

0

1000

2000

3000

4000

ssentiF

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 2 3 4 5 6 7 8 9 10 11 12 13 14Parameter

0

1000

2000

3000

4000

ssentiF

1 2 3 4 5 6 7 8 9 10 11 12 13 14

All data were carefully collected and used to draw a “flow of all histories” so that average, minimal and maximal values can be easily observed.

Results III – SA, DE and SOMAResults III – SA, DE and SOMA

DE

SA

SOMA

0 5108 1107 1.5 107 2107

Times50000

100000

150000

200000

250000

300000

egatloVV

0 5108 1107 1.5 107 2107

Times100000

150000

200000

250000

300000

egatloVV

0 5108 1107 1.5 107 2107

Times100000

150000

200000

250000

300000

egatloVV

Results were used to restore waveforms observed on osciloscope. Here are depicted average, minimal and maximal values reached during all experiments.

Results III a) – SA, DE and SOMAResults III a) – SA, DE and SOMA

DE

SA

SOMA

0 5108 1 107 1.5 107 2107

Times50000

100000

150000

200000

250000

300000

egatloVV

Used algorithm: SA Date: 080802All Wave Forms of Plasma Reactor

0 5108 1 107 1.5 107 2107

Times100000

150000

200000

250000

300000

egatloVV

Used algorithm: SOMA Date: 080802All Wave Forms of Plasma Reactor

0 5108 1 107 1.5 107 2107

Times100000

150000

200000

250000

300000

350000

egatloVV

Used algorithm: DE Date: 080802All Wave Forms of Plasma Reactor

Here are all waveforms “in one” just for demonstration. Average, minimal and maximal values reached during all experiments cannot be observed here.

DE SA SOMAAlgorithm

3280

3300

3320

3340

ssentiF

DE SA SOMA

0 5 10 15 20Experimet No.

18.6

18.8

19

19.2

19.4

19.6

CDsaiBV

SA Box, SOMA Triangle, DE XMean for SA18.964 SOMA19.3245 DE19.263

SA_SOMA _DE Experiments on Plasma Reactor

SADESOMASA FitDE FitSOMA Fit

Results VI – SA, DE and SOMAResults VI – SA, DE and SOMA

SA SOMA DEAlgorithm

0

5

10

15

20

25

ycneuqerF

SA SOMA DE

1st2nd

3rd

Draw

1st

2nd 3rdDraw

1st

2nd

3rd

Draw

SA, SOMA, DE

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Experiment

18.4

18.6

18.8

19

19.2

19.4

19.6

ssentiF

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Results were used to create four charts: four different view on algorithm efficiency

ConclusionConclusion

Ability to be used: all three algorithms can be used for active compensation in RF-driven plasmas. However, based on results it is clear that SOMA and DE has greater potential for this task. Preciseness and reproducibility: one of the crucial points in science is reproducibility, i.e. the ability to achieve the same results for two identical experiments. In practical applications like this one, a high degree of reproducibility is needed. From figures it is visible, that SOMA and DE has a greater reproducibility than SA. They are is also more precise than SA. Speed: the speed of the optimization process was not determined by the computer power available, but by the time constants of the analogue equipment, e.g. harmonic box. Therefore, all three algorithms have shown similar speed performance in this specific application. Diversity: is tightly connected with preciseness and reproducibility. From this point of view SOMA and DE performed almost three times better than SA. If one remembers that plasmas are highly nonlinear dynamical systems with complicated behavior, then the results produced by SOMA and DE are very sufficient.

Algorithms efficiency: from figures it is clearly visible that the best results were obtained by SOMA algorithm, second place took DE and third SA. While results given by SA are significantly the worst one, in the case of SOMA and DE should be mentioned that difference between them was wery small – almost negligible. This small difference shows, that both algorithms are highly usable for dealing with systems kind of “blackbox” which plasma reactor in fact is.

Dynamical position of global extreme: global extreme (thus whole cost function landscape) was not static in time. During above described experiments which took almost 12 hours of noninterrupted works (for 5 days ), plasma in reactor changed its behaviour. This change was linear dependent. Based on experiences with SOMA and DE, it can be stated that both algorithms has follows global extreme (or founded suboptimal solution) position quite well.

AcknowledgementsAcknowledgements

This work was partly funded by the

• Ministry of Education of the Czech Republic, under grant reference MSM 26500014, • Grant Agency of the Czech Republic under grand references GACR 102/03/0070 and GACR 102/02/0204.

The authors whish to express their thanks to

• Lars Nolle School of Computing and Technology, The Nottingham Trent University, Burton Street, Nottingham, NG1 4BU, UK

• A.A. Hopgood• N.St.J. Braithwaite Oxford Research Unit, The Open University• Alec Goodyear • Jafar Al-Kuzee

for assistance with the plasma equipment.