Research Article A New Hybrid BFOA-PSO Optimization...

Research ArticleA New Hybrid BFOA-PSO Optimization Techniquefor Decoupling and Robust Control of Two-CoupledDistillation Column Process

Noha Abdelkarim1 Amr E Mohamed1 Ahmed M El-Garhy1 and Hassen T Dorrah2

1Department of Electronics Communications and Computers Faculty of Engineering Helwan University1 Sherif Street Helwan Cairo 11792 Egypt2Department of Electrical Engineering Faculty of Engineering Cairo University University Street Giza 12316 Egypt

Correspondence should be addressed to Noha Abdelkarim nohaabdelkarimacgmailcom

Received 22 April 2016 Revised 31 July 2016 Accepted 9 August 2016

Academic Editor J Alfredo Hernandez-Perez

Copyright copy 2016 Noha Abdelkarim et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The two-coupled distillation column process is a physically complicated system in many aspects Specifically the nestedinterrelationship between system inputs and outputs constitutes one of the significant challenges in system control design Mostlysuch a process is to be decoupled into several inputoutput pairings (loops) so that a single controller can be assigned for each loopIn the frame of this research the Brain Emotional Learning Based Intelligent Controller (BELBIC) forms the control structurefor each decoupled loop The paperrsquos main objective is to develop a parameterization technique for decoupling and controlschemes which ensures robust control behavior In this regard the novel optimization technique Bacterial Swarm Optimization(BSO) is utilized for the minimization of summation of the integral time-weighted squared errors (ITSEs) for all control loopsThis optimization technique constitutes a hybrid between two techniques which are the Particle Swarm and Bacterial Foragingalgorithms According to the simulation results this hybridized technique ensures lowmathematical burdens and high decouplingand control accuracyMoreover the behavior analysis of the proposedBELBIC shows a remarkable improvement in the timedomainbehavior and robustness over the conventional PID controller

1 Introduction

Controller design for multi-input multiple-output (MIMO)systems is of significant importance as they constitute themajority of physical systems However the design of suchcontrollers is confronted with the challenge to overcomethe influence of the nested interrelationship between systeminputs and outputs Based on the level of interrelationshipbetween system inputs and outputs the control structureis to be selected The systems which are characterizedwith moderate interaction between control loops can becontrolled with the decentralized control structure so that asingle controller is assigned for each control loop [1ndash5] Onthe other hand a centralized controller has to be designed forsystemswith higher level of interrelationship between controlloops [6ndash9] so that a central matrix of controllers is allocatedfor the whole MIMO system In spite of this the central-ized controllers are not widely utilized due to their high

complexity Alternatively the issue of high interrelationshipcan be alleviated by decoupling the MIMO system into sev-eral relatively independent single-input single-output (SISO)control loops [10ndash15] Accordingly the multivariable processcan be controlled based on independent loop structure Inthis paper the decoupled control structure is utilized forcontrolling the presentedMIMOsystem For the decoupler tobe designed the adequate input-output pairings are primarilydetermined through the evaluation of the system relativegains [16ndash19] Accordingly the decoupling network has tobe designed so that the interaction between control loopsis minimized [20 21] For control purposes conventionalcontrol schemes as PID can be utilized [22ndash24] It is tomention that the nonlinearity and the model imprecisionthat characterize the majority of physical systems reduce therobustness and accuracy of such controllers

Control design approaches based on intelligent algo-rithms as fuzzy logic neural network and genetic algorithms

Hindawi Publishing CorporationComputational Intelligence and NeuroscienceVolume 2016 Article ID 8985425 17 pageshttpdxdoiorg10115520168985425

2 Computational Intelligence and Neuroscience

are of increasing spread due to their proven ability to over-come system model uncertainty [25ndash27] The computationalmodel of emotional learning in mammalian brain whichis introduced in [28 29] inspired a new learning algorithmAfterwards this learning technique is deployed in the systemcontrol design presenting the novel Brain Emotional Learn-ing Based Intelligent Controller (BELBIC) [30] Thus theBrain Emotional Learning Based Intelligent Controller (BEL-BIC) has shown robustness in the control of the nonlinearand uncertain systems such as VanDer Pol oscillator Duffingforced oscillator and automatic self-balancing scale [31]washing machine [32] microheat exchanger [33] switchedreluctance motor [34] unmanned aerial vehicle [35] pathtracking of a vehicle [36] two-coupled distillation columnprocess [37] multiple-area power systems [38] and contin-uous stirred tank reactor [39 40]

The parameterization of the decoupling compensationnetwork and the BELBIC are still open research topicsCurrently the detailed analytical methods used in purpose ofthe parameterization of the decoupling compensation net-work cost excessive mathematical burdens Regarding theparameterization of BELBIC the trial and error is widely usedfor controller parameters estimation Thus the utilization ofvarious optimization techniques based on artificial intelli-gence introduces an efficient alternative in both cases [11 37]

The utilization of the biologically inspired algorithms asAnt Colony Optimization (ACO) [41] Genetic Algorithm(GA) [42] and Particle Swarm Optimization (PSO) [43 44]in optimization problems constitutes currently a promis-ing solution Recently the new evolutionary computationtechnique depending on the behavior of foraging of E colibacteria which is named as Bacterial Foraging OptimizationAlgorithm (BFOA) is proposed by [45] This technique hasbeen successfully deployed in many applications as powersystems [46ndash49] stockmarket prediction [50 51] and designof PIPID controllers [52 53]The key drawback of the BFOAis the delay in reaching the global solution because it isbased on random searching directions For this delay to beovercome the BFOA is integrated with the Particle SwarmOptimization (PSO) technique introducing the BacterialSwarmOptimization (BSO) algorithm [54] One of themajorcharacteristics of PSO technique which is inherited to theBSO algorithm is the idea of velocity updating Accordinglythe process of searching for the global solution in theBSO technique depends on the individual and global bestpositions concurrently As discussed in [55ndash58]TheBacterialSwarm Optimization (BSO) algorithm grants better perfor-mance in determining the optimum solution compared withPSO and BFOA algorithms

This research paper aims to investigate the feasibility ofapplying the Bacterial Swarm Optimization (BSO) algorithmin the field of MIMO control system As an example forMIMO system the two-coupled distillation column is to bestudied Primarily the mathematical model of the system isdecoupled into several independent loops The parametersof the decoupling compensation network are determinedbased on the summation minimization of the integral time-weighted squared outputs (ITSOs) of unpaired outputs

regarding a particular input In this regard the BSO tech-nique is utilized On the other hand an optimal BELBIC isdesigned for each decoupled control loop through the sum-mation minimization of the integral time-weighted squarederrors (ITSEs) of all loops using BSO as well For the com-parison purpose the PID controller is also implemented forthe same application so that the strength of each of consid-ered control structures can be studied

2 Two-Coupled Distillation Column Process

As formerly stated the two-coupled distillation column ishandled in this paper as an example of MIMO system In thissection the physical system is discussed Primarily thefunction of the system and its components are presentedAfterwards the system mathematical modeling and decou-pling are handled

21 System Description Distillation units are mainly utilizedfor the separation of fluid mixture components The distilla-tion column major components can be listed as follows

(i) A vertical shell in which the separation of fluidsubstances is accomplished

(ii) A cascade of trays for improving component separa-tion

(iii) A reboiler for maintaining the required heat energyfor the distillation process

(iv) A condenser for liquefying the vapor leaving thecolumn

(v) A reflux drum in which portion of the condensedliquid is recycled back to the vertical shell

The physical process considered in this research com-prises two-coupled distillation columns as shown in Figure 1Thereby ternary petrochemical mixtures can be separatedWhile the main glass column is composed of 40 bubble captrays excluding those of the boiler and condenser the sideglass column contains 10 bubble cap trays At the 22nd stagethe system intake port is located at which the fluid mixtureis to be fed The three separated fluid components are to beextracted from the process so that the heaviest and thelightest components can be provided from the bottom andthe top of themain column respectively and the intermediatecomponent is derived from the top of the side column

22 Mathematical Modeling of the Two-Coupled DistillationColumn Primarily the manipulated variables are to bedetermined Thus the selected manipulated variables are theheat input to the reboiler (QE) the vapor flow rate in thevapor transfer line (SAB) the reflux ratio in themain column(RL1) and the reflux ratio in the second column (RL2) [59]Regarding the system technical constraints the input heatenergy rateQE and the vapor flow rate SABhave to not exceedthe values 82 KW and 395m3h respectively in order toavoid flooding of the smaller side column [59] Secondly thecontrolled values are selected to be the fluid temperature at

Computational Intelligence and Neuroscience 3

Feed

Intermediatecomponent

component

component

Reflux

Reflux

RL2

RefluxRL1

drum

Refluxdrum

Condenser

Condenser

SAB

Reboiler32

30

4853

22

11

Main column 40 trays

Side column 10 trays

Numbers indicatecolumn trays

Liquid reflux

Lightest

HeaviestQE

Figure 1 The two-coupled distillation columns process

four different stages The selection of these stages is based onthe following requirements

(i) The temperatures should be sensitive to the majordisturbances as changes in feed rate and feed concen-trations

(ii) The temperatures should exhibit a fairly linear behav-ior

(iii) They should be a good indication of product quality

Accordingly the temperature at the 11th 30th 34th and48th trays are chosen to form the controlled variables [59]The mathematical model of realistic two-coupled distillationcolumn mentioned in [59] is to be used in this researchThetransfer function matrix of the considered MIMO system isstated in (1)

119866 (119904) =[[[[[[[[[[[

26169119904 + 1 minus609835119904 + 1 minus499 (02119904 + 1)(45119904 + 1) (006119904 + 1) 007135119904 + 1732 (105119904 + 1)(104119904 + 1) (014119904 + 1) minus14504119904 + 1 minus157 (023119904 + 1)(134119904 + 1) (02119904 + 1) minus014192119904 + 146 (053119904 + 1)(278119904 + 1) (009119904 + 1) minus237 (023119904 + 1)(2119904 + 1) (03119904 + 1) minus27175119904 + 1 minus036 (002119904 + 1)(247119904 + 1) (004119904 + 1)211092119904 + 1 minus211 (006119904 + 1)(238119904 + 1) (005119904 + 1) minus175216119904 + 1 minus03 (189119904 + 1)(435119904 + 1) (016119904 + 1)

]]]]]]]]]]]

(1)

As shown in the transfer function matrix the physicalsystem is characterized by the high interrelationship betweenall system inputs and outputs As discussed in the introduc-tion the control structure adopted in this paper is basedon the mathematical model decoupling so that each outputis independently controlled by a single input forming fourindependent SISO control loops

Primarily the noninteracting design is preceded by arelative gain analysis to determine the most suitable input-output pairings In this regard the relative gain array (RGA)

method is used Afterwards a decoupling compensationnetwork is designed for the reduction of residual interactions[11]

221 The Relative Gain Array The RGA matrix for 119873 times 119873system represented in (2) is used for the valuation of the inputinfluences on each system output [16ndash19] so that output ldquo119894rdquois to be paired with input ldquo119895rdquo for which 120574119894119895 is a positive valueand as close to unity as possible


++

++

+

+

+

+

++

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

T30 desired

T11 desired

T34 desired

T48 desired

minus

minus

minus

minus

GC1

GC2

GC3

GC4

W1

W2

W3

W4

QE

SAB

RL1

RL2

12058211

12058212

12058213

12058214

12058221

12058222

12058223

12058224

12058231

12058232

12058233

12058234

12058241

12058242

12058243

12058244

T11

T30

T34

T48

G11

G12

G13

G14

G21

G22

G23

G24

G31

G32

G33

G34

G41

G42

G43

G44

Figure 2 The decoupled MIMO system including controllers

RGA119873times119873 = [119866 (119904 = 0)] sdot lowast [119866 (119904 = 0)]minus119879

=[[[[[[[

12057411 12057412 sdot sdot sdot 120574111987312057421 12057422 sdot sdot sdot 1205742119873 1205741198731 1205741198732 sdot sdot sdot 120574119873119873

]]]]]]] (2)

where 119866(119904) is the transfer function matrix of the MIMOprocess and ldquosdotlowastrdquo operator implies element by element mul-tiplication

222 Decoupling Compensation Network Design ProcedureThe steady state decoupling compensation matrix illustratedin (3) is to be integrated into the given MIMO system inthe way demonstrated in (4) so that interrelationshipsbetween each input and unpaired outputs is minimized [2021] In this paper the simplest form of the decoupling com-pensationmatrix introduced in the previous study [11] whichhas unity diagonal elements is replacedwith the general form

presented in (3) This modification introduces a remark-able improvement in the system response as discussed inSection 5 Figure 2 illustrates the decoupling compensationnetwork scheme integrated with the required controllers

Λ ss =[[[[[[[

12058211 12058212 12058213 sdot sdot sdot 1205821119873minus1 120582111987312058221 12058222 12058223 sdot sdot sdot 1205822119873minus1 1205822119873 1205821198731 1205821198732 1205821198733 sdot sdot sdot 120582119873119873minus1 120582119873119873

]]]]]]] (3)

[119884 (119904)] = [119866 (119904)] [Λ ss] [119882 (119904)] (4)

where [119884(119904)] is the output vector [119882(119904)] is the input vector[119866(119904)] is the transfer function matrix of the MIMO processand [Λ ss] is the steady state decoupling compensationmatrixof MIMO process

223 Fitness FunctionDesign Asdiscussed in the former twosections the determination of the adequate system input


output pairing as well as the elementsrsquo values of the decou-pling compensationmatrix define the effectiveness of interre-lationship minimization between system inputs and outputsThe selection of the proper inputoutput pairing is alreadytackled by the relative gain array concept For the elementsrsquovalues of the decoupling compensationmatrix to be estimatedusing optimization techniques the fitness functions haveto be designed that minimize the interrelationship betweensystem inputs and their unpaired outputs

The four commonly used performance criteria for fitnessfunction design are the integral absolute error (IAE) integralsquared error (ISE) integral time-weighted squared error(ITSE) and Integral time-weighted absolute error (ITAE) Itrsquosto mention that in the context of decoupling system designthe performance criteria are concerned with the minimiza-tion of the system outputs towards the unpaired inputsrather than control system error Accordingly the corre-sponding criteria are integral absolute output (IAO) integralsquared output (ISO) integral time-weighted squared output(ITSO) and Integral time-weighted absolute output (ITAO)Although the criteria ISO and IAO grant less overshoot in thesystem dynamics none of these criteria is adopted in thisresearch due to the long settling time [56] This drawbackcould be overcome by utilizing the ITAO However this cri-terion is not used in this research for the difficulty of its ana-lytical tracking [60] Thus the ITSO performance criterionis employed in this work for ensuring the minimization ofsettling time without being confronted with unnecessaryanalytical complications

In the former research [11] the decoupling compensationmatrix elements are estimated by applying the PSO techniqueso that the integral squared outputs (ISOs) of unpairedoutputs with respect to a specific input are minimized Onthe other hand the proposed technique in this paper is basedon the minimization of the integral time-weighted squaredoutputs (ITSOs) by utilizing the BSO technique

The integral time-weighted squared outputs (ITSOs) foreach input are calculated such that

if1198821(119904) = 1119904 and11988221198823 119882119873 are zeroes thenITSO11 = intinfin

0119905 11988412 sdot 119889119905

ITSO21 = intinfin0

119905 11988422 sdot 119889119905

ITSO1198731 = intinfin0

119905 1198841198732 sdot 119889119905(5)

and if 1198822(119904) = 1119904 and 11988211198823 119882119873 are zeroesthen

ITSO12 = intinfin0

119905 11988412 sdot 119889119905ITSO22 = intinfin

0119905 11988422 sdot 119889119905

ITSO1198732 = intinfin

0119905 1198841198732 sdot 119889119905

(6)

Consecutively if 119882119873(119904) = 1119904 and 11988211198822 119882119873minus1are zeroes then



0119905 11988422 sdot 119889119905


0119905 1198841198732 sdot 119889119905

(7)

Thus the fitness function for specific input 119882119895 can bedescribed as follows

Fitness119895 = 119873sum119894=1

ITSO119894119895 119895 = 1 2 3 119873 119894 = 119902 (8)

where 119894 is the specific output subscript 119895 is the specific inputsubscript and 119902 is the subscript of the output that has beenpaired with input 1198953 Controlling of Two-Coupled

Distillation Column Process

In this section the proposed BELBIC and the conventionalPID controller are handled regarding the control structure

31 Brain Emotional Learning Based Intelligent Controller(BELBIC) Model As formerly stated the considered MIMOsystem is to be split into several decoupled SISO systems withtheminimumpossible interrelationship between themThuseach of these systems can be independently controlled In thisresearch the BELBIC adaptive control structure is utilized foreach single control loopThis control structure is based on thefunctional model of brain emotional learning introduced by[28 29] Over the past decade this control scheme hasproven its robustness in many complex control applications[31ndash40] Apart from the application in control systems thecomputational model of brain emotional learning in itsdiscrete and continuous form is discussed here respectivelyAfterwards the methodology of the proposed BSO-BELBICscheme which assigns one BELBIC for each decoupled loopis presented

The emotional learning computational model designedby [28 29] is graphically illustrated in Figure 3 In mam-malian brains the emotional learning process occurs in apart of the brain called the limbic system which consists offourmain components corresponding to the amygdala orbit-ofrontal cortex thalamus and the sensory cortex As shown


O

O

O

A

A

A MO

GO1

GO2

GO3

ΔGo

GA1

GA2

GA3

GAthAth

ΔGA

MO998400

Reward signal (Rew)

Sensory input (s)

Thal

amus

Sens

ory

cort

ex

Amygdala

Orbitofrontal cortex

InhibitoryExcitatory

PlasticLearning

Figure 3 Graphical depiction of the brain emotional learning (BEL) process [28 29]

in the figure sensory input signals are primarily passed to thethalamus model which relay the sensory information fromthe peripheral sensory systems to the sensory cortices More-over the sensory input maximum value is passed directly tothe amygdala for the fast response to be insured Then theavailable sensory data are to be processed by sensory cortexmodel Hence highly analyzed data are to be sent to theamygdala and orbitofrontal cortex models The emotionalevaluation of stimuli and the formulation of long-termmemories are carried out by the amygdala Finally theorbitofrontal cortex is supposed to inhibit inappropriateresponses from the amygdala

The outputs of the model two major components amyg-dala and orbitofrontal cortex are described in (9) and (10)respectively The feedback element MO1015840 is defined in (11) asthe subtraction of the orbitofrontal cortex inhibitory outputs(119874119894) from the summation of amygdala nodes (119860 119894) excluding119860 th node As illustrated in relation (12) the output (MO)

of the brain emotional learning model (BEL) constitutes thesubtraction of the orbitofrontal cortex inhibitory outputs (119874119894)from the summation of amygdala nodes (119860 119894) including the119860 th node

119860 119894 = 119878119894119866119860119894 (9)

119874119894 = 119878119894119866119874119894 (10)

MO1015840 = sum119894

119860 119894 minussum119894

119874119894 (excluding 119860 th node) (11)

MO = sum119894

119860 119894 minussum119894

119874119894 (including 119860 th node) (12)

where 119878119894 forms the 119894th sensory input and 119866119860 and 119866119874 are theplastic connection weights of the amygdala and orbitofrontalcortex respectively These plastic connection weights areresponsible for the emotional change towards specific object


Orbitofrontalcortex

Amygdala

Sensoryinput

Reward signalbuilder

MO Plant+

BELBIC

+

minus

minus

r eyp

u

Figure 4 Control system configuration using BELBIC

characteristicsThus they constitute the adaptive componentin the model structure as their values are to be updatedcontinuously While the formulas (13) and (14) represent thediscrete form for the change in plastic connection weights(15) and (16) constitute the continuous one It is to mentionthat the continuous form is utilized in this research

Δ119866119860119894 = 120572(119878119894max[[0Rew minussum119895

119860119895]]) (13)

Δ119866119874119894 = 120573 (119878119894 [MO1015840 minus Rew]) (14)

119889119866119860119894119889119905 = 120572 sdot 119878119894 sdot (Rew minus 119860 119894) (15)

119889119866119874119894119889119905 = 120573 sdot 119878119894 sdot (119860 119894 minus 119874119894 minus Rew) (16)

where 120572 and 120573 are learning rate constants and the symbolRew forms the reward signal The operator ldquomaxrdquo in theformula (13) is the responsible formaintaining themonotoniclearning change of amygdala This characteristic models theincapability of the amygdala to unlearn the formerly learnedemotions [28 29] In the continuous form the operatorldquomaxrdquo is eliminated for analytical simplicity [61]

The BELBIC internal structure as well as its interfacewith the controlled physical plant is illustrated in Figure 4As shown sensory input block as well as the reward signalbuilder manipulates orbitofrontal cortex and amygdala basedon the control error signal according to (17) and (18) respec-tively

119878 = 119870 sdot 119890 (17)

Rew = 119870119901 sdot 119890 + 119870119894 sdot int 119890 sdot 119889119905 + 119870119889 sdot 119889119890119889119905 (18)

where 119870 119870119901 119870119894 and 119870119889 besides the learning rate constants(120572 and 120573) constitute the controller parameters which charac-terize the controlled dynamic system behavior

The BELBIC parameterization is one of the currentchallenges confronting such a novel control structure In thisregard the utilization of optimization techniques like ParticleSwarm Optimization (PSO) has shown a robust behavior[37] In the frame of this research the feasibility of applying

the Bacterial Swarm Optimization (BSO) algorithm regard-ing the tuning process of BELBIC parameters is to be inves-tigated As mentioned in the previous section the integraltime-weighted squared errors (ITSEs) of all control loops areselected to be minimized rather than the integral-squared-errors (ISEs) for its faster settling response Accordingly thefitness function is represented in (19)

Fitness function = intinfin0

119905 (11987930 desired minus 11987930)2 sdot 119889119905+ intinfin0



119905 (11987948 desired minus 11987948)2 sdot 119889119905

(19)

Twenty-four parameters (six for each loop) should betuned simultaneously with the aim of minimizing the fitnessfunction

32 PID Control Themain terms that constitute the conven-tional PID controller are the proportional the integral andthe derivative termsThe three terms are added to each otheras shown in Figure 5 The transfer function of the conven-tional PID controller is stated in (20)

119866119888 (119904) = 119870119901 + 119870119894119904 + 119904119870119889 (20)

where119870119901119870119894 and119870119889 are proportional gain integral gain anda derivative gain respectively

The Bacterial Swarm Optimization (BSO) algorithm isutilized regarding the parameterization of PID controllerswith the same policies as BELBICs

4 Bacterial Swarm Optimization Algorithm

Bacterial Swarm Optimization Algorithm (BSO) forms ahybrid between two efficient optimization techniques Thesealgorithms are the Particle Swarm Optimization (PSO) andthe Bacterial Foraging Optimization Algorithm (BFOA)


+

+

+

Kp

Kis

sKd

Error signal Control signal

Figure 5 Block diagram of the conventional PID controller

PSO is a stochastic optimization approach inspired fromthe behavior of the flock of birds insects and fish Everysingle particle in the search space adjusts its own directionbased on its own experience as well as the experience of themost successful particle in the swarm [43 44] Neverthelessthe optimization technique based on the PSO algorithmmaylead to entrapment in local optimum solution rather thancatch the global one due to the rapidity and simplicity of thealgorithm [62]

On the other hand BFOA is a new bio-inspired algorithmdepending on foraging behavior of Escherichia coli (E coli)bacteria [45] Bacteria have the tendency to group around thenutrient-rich regions by the activity named chemotaxis Thebacteria which fail to reach nutrient-rich areasmay die due tothe nutrient lack However the ones that survived reproducethe next generation in nutrient-rich areas Once the currentliving environment becomes inconvenient to the bacteriait tends to disperse randomly to search for an alternativeenvironment Consequently the optimization technique thatsimulates the foraging behavior of these bacteria requires along time for achieving the global optimum solution due tothe dependence on random search directions [57]

The time consumed by BFOAfinding the global optimumsolution can be reduced by granting the E coli bacteria theability of exchanging social informationThis ability is inher-ited from the PSO technique forming the BSO algorithmTherefore BSO algorithm requires less time for the optimumsolution determination while maintaining the BFOA abilityin finding a new solution with elimination and dispersalThus the BSO algorithm solves the insufficient scatteringproblem that confronted the PSO algorithm Furthermorethe chemotaxis step of BSO technique safeguards against thePSO shortcoming regarding the weak search ability

As mentioned the BSO technique is utilized for theparameterization of the decoupling compensation network aswell as the BELBICAs an overview the procedure of applyingthe proposed technique on the case study is demonstrated inthe process chart in Figure 6 Afterwards the basic flowchartof the BSO algorithm is presented in Figure 7 Moreover thepseudocode of the BSO algorithm is stated delivering moredetails

The pseudocode of the BSO algorithm is as follows

Step 1 The initialization of all stated parameters 119901 119878 119878119903119873119888119873119904 119873re 119873ed 119875ed 119862(119894) (119894 = 1 2 119878) Delta 119908 1198621 1198622 1198771and 1198772 where

(i) 119901 is dimension of search space

The mathematical model of realistictwo-coupled distillation column process

The relative gain array (RGA) methodis used to determine the most suitable

input-output pairings

A decoupling compensation network isdesigned

A scheme of Brain Emotional LearningBased Intelligent Controller (BELBIC)

is designed

The BSO technique is utilized to obtainthe optimal value of the controller

parameter

The fitness functions of BSO techniqueare deduced

The BSO technique is used to estimatethe values of steady state decoupling

compensation matrix

Figure 6 Process chart for the main steps of applying the proposedtechnique on the case study

(ii) 119878 is the number of bacteria(iii) 119878119903 is the number of bacteria splits per generation(iv) 119873119888 is the number of chemotactic steps(v) 119873119904 is the limits of the length of a swim(vi) 119873re is the reproduction steps number(vii) 119873ed is the amount of elimination-dispersal events(viii) 119875ed is the elimination-dispersal probability(ix) 119862(119894) is the bacteria step size length(x) Delta is the direction of each bacteria(xi) 119908 is the weight of inertia(xii) 1198621 is the weight of local information(xiii) 1198622 is the weight of global information(xiv) 1198771 1198772 are two Random numbers

Step 2 Loop of elimination and dispersal 119897 = 119897 + 1


Start

Stop

Initialize all variables Set allloop counters to zero

Increase elimination-dispersion loop counter

l = l + 1

No

No

NoNo

No

No

Yes

YesYes

Yes

Yes

l lt Ned

Find out thebest solution in

the wholeswarm

Increase reproductionloop counterk = k + 1

k lt Nre

Increase chemotacticloop counterj = j + 1

j lt Nc

Perform reproduction(by killing the worse

half of population andsplitting the better

half into two)

Increase bacteriumindex i = i + 1

Z

Y

Z

i lt s

Compute fitness function J(i j k l)

Jlast = J(i j k l)

Update positionP(i j + 1 k l) = P(i j k l) + C(i) lowast Delta(i)

Compute fitness function J(i j + 1 k l)

Set swim counterm = 0

Ym lt Ns

m = m + 1

Setm = Ns

J(i j + 1 k l) lt Jlast


P(i j + 1 k l) = P(i j + 1 k l) + C(i) lowast Delta(i)Set Jlast = J(i j + 1 k l) and let

Perform elimination

bacterium is chosen

eliminate and disperseone to a random

location

according to Ped

Tumble direction is update by

Delta = V

V = w lowast V + C1 lowast R1 (PLbest minus Pcurrent) +

C2 lowast R2 (PGbest minus Pcurrent)

bacteriaUpdate PLbest and PGbest for each

dispersal (for i = 1 2 S)

Figure 7 Flowchart of BSO algorithm

Step 3 Loop of reproduction 119896 = 119896 + 1Step 4 Loop of chemotaxis 119895 = 119895 + 1Substep 41 For 119894 = 1 2 119878 each bacterium 119894 moves achemotactic step as follows

(a) Calculate cost function 119869(119894 119895 119896 119897)(b) Let 119869last = 119869(119894 119895 119896 119897) to save the current value of the

cost function in order to be able to compare it withthe one determined in the next swim

(c) Let 119869local(119894 119895) = 119869last the better cost per each bacteriais going to be chosen to be the local best 119869local

(d) Update position 119875(119894 119895 + 1 119896 119897) = 119875(119894 119895 119896 119897) + 119862(119894) lowastDelta(119894)

(e) Calculate cost function 119869(119894 119895 + 1 119896 119897)(f) Swim

(i) Let119898 = 0 (counter for swim length)(ii) While 119898 lt 119873119904 (if have not climbed down too

long)

(1) Let119898 = 119898 + 1(2) If 119869(119894 119895 + 1 119896 119897) lt 119869last (if doing better) let119869last = 119869(119894 119895 + 1 119896 119897) and let

119875 (119894 119895 + 1 119896 119897) = 119875 (119894 119895 + 1 119896 119897) + 119862 (119894) lowast Delta (119894) (21)

and use this 119875(119894 119895 + 1 119896 119897) to calculate thenew 119869(119894 119895 + 1 119896 119897)

(3) For each bacteria estimate the current posi-tion and local cost

119875current (119894 119895 + 1) = 119875 (119894 119895 + 1 119896 119897) 119869local (119894 119895 + 1) = 119869 (119894 119895 + 1 119896 119897) (22)


(4) Else let119875current (119894 119895 + 1) = 119875 (119894 119895 + 1 119896 119897) 119869local (119894 119895 + 1) = 119869 (119894 119895 + 1 119896 119897)

119898 = 119873119904(23)

(5) While statement end

(g) Go to next bacterium (119894 + 1) if 119894 = 119878 (ie go to (b) toexecute the next bacterium)

Substep 42 For each bacteria estimate the local best position(119875119871best) and global best position (119875119866best)

Substep 43 For each bacteria estimate the new direction as

119881 = 119908 lowast 119881 + 1198621 lowast 1198771 (119875119871best minus 119875current) + 1198622lowast 1198772 (119875119866best minus 119875current)

Delta = 119881(24)

Step 5 (if 119895 lt 119873119888 go to Step 4) In this situation keep onchemotaxis since the life of the bacteria is not terminated

Step 6 (reproduction)

Substep 61 For 119896 and 119897 and for each 119894 = 1 2 119878 the healthof the bacterium 119894 is given by

119869119894health = 119873119888+1sum119895=1

119869 (119894 119895 119896 119897) (25)

Sort bacteria cost 119869health in ascending order (greater costindicates lower health)

Substep 62 The 119878119903 bacteria with the lowest 119869health values splitand the rest of the 119878119903 bacteria dieStep 7 (if 119896 lt 119873re return to Step 3) In this instance thespecified maximum number of reproduction steps is notover therefore the bacteria begin a new generation of achemotactic loop

Step 8 (elimination dispersal) For 119894 = 1 2 119878 withprobability 119875ed eliminate and then disperse one to a randomplace If 119897 lt 119873ed then go to Step 2 otherwise end

5 Simulation and Results

The decoupled physical system and its controllers aredesigned and simulated with MATLAB Simulnik

The RGA method is applied on the mathematical modelof the two-coupled distillation column process and theresulted matrix is given by

RGA4times4 =[[[[[[

minus00429 05629 04083 0071714559 05558 minus09138 minus00980minus04647 minus31110 44832 0092600517 29923 minus29777 09337

]]]]]] (26)

According to the RGA matrix the suitable input-outputpairing is

(11987911 minus SAB) (11987930 minusQE) (11987934 minus RL1) (11987948 minus RL2)

(27)

Depending on the suitable pairing the fitness functionsof the 1st 2nd 3rd and 4th input are described in (28) (29)(30) and (31) respectively

Fitness1 = ITSO11 + ITSO31 + ITSO41= (161857646415 lowast 120582211)

+ (minus312082022860 lowast 12058211 lowast 12058221)+ (minus290857046263 lowast 12058211 lowast 12058231)+ (minus21043533818 lowast 12058211 lowast 12058241)+ (236264201763 lowast 120582221)+ (405186618661 lowast 12058221 lowast 12058231)+ (10532256938 lowast 12058221 lowast 12058241)+ (176253775018 lowast 120582231)+ (11426987804 lowast 12058231 lowast 12058241)+ (1123171448 lowast 120582241)

(28)



(29)


+ (minus309183154051 lowast 12058213 lowast 12058223)+ (minus281560403138 lowast 12058213 lowast 12058233)+ (minus14729857141 lowast 12058213 lowast 12058243)+ (218692602750 lowast 120582223)+ (363962344688 lowast 12058223 lowast 12058233)


+ (4030395905 lowast 12058223 lowast 12058243)+ (152128590003 lowast 120582233)+ (3905125127 lowast 12058233 lowast 12058243)+ (573184117 lowast 120582243)(30)



(31)

The BSO algorithm parametersrsquo values which are utilizedto implement an optimized decoupling network as well as anoptimized BELBIC are summarized in Table 1 The resultingvalues of the steady state decoupling compensation elementsthat minimize the above fitness functions are summarized inTable 2

The resulting best gainsrsquo values for different BELBICsthat minimize the summation of the integral time-weightedsquared errors (ITSEs) for different decoupled loops arepresented in Table 3 The best gainsrsquo values of the designedconventional PID controllers are shown in Table 4 The PIDcontrollersrsquo parameters are determined utilizing the samealgorithm utilized for the design of BELBICs In this regardproposed BSO algorithmwith the same gains given in Table 1is used to minimize the same fitness function

The dynamic behavior of the system is analyzed based onits step response based on the sequential step input shown inFigure 8 In Figure 9 the decoupled system response on thegiven step sequence is illustrated As shown the experimentalresults demonstrate the efficiency of the designed decouplingtechnique Thus the interrelationship between system inputsand their unpaired outputs is noticeably minimized com-pared to the formerly deployed techniques [11] Accordinglythe spikes in the response of the decoupled system outputson the unpaired inputs are significantly reduced The stepresponse of the designed closed loop control system is shownin Figure 10

For verification purposes the response of the designedcontrol scheme which is based on the minimization ofITSEs of all control loops utilizing the BSO algorithm iscompared to that of the latest research that considers thesame application It is to mention that the control scheme ofthe previous research is mainly based on the minimizationof the ISE using the PSO algorithm [37] In Figure 11 the

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

Reference temperature of each tray

T30

desir

edT11

desir

edT34

desir

edT48

desir

ed

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

Figure 8 Step changes in system inputs [37]

proposed technique is compared to the former study in termsof step response Moreover the steady state errors for bothcontrollers are stated in Table 5

As shown the control scheme presented in this researchoffers a valuable improvement in the last three control loops(11987911 11987934 and 11987948) in terms of minimizing steady state errors

The step response of the proposed BELBICs and con-ventional PID controllers is compared in the presence of adisturbance stepwith the final value of ldquo1rdquo at the 500th secondin the first and the third decoupled loop The simulationresults are presented in Figure 12 In the figure it is clearlyrecognizable that the robustness of the proposed BELBICsis higher than that of the conventional PID controllersregarding the handling of the unexpected disturbance Thecontrolled system using BELBICs is better damped as wellOn the other side the PID controllers in all control loopsachieve remarkably less steady state error

For comparison purpose the PID controllers aredesigned by utilizing the PSO technique for minimizing thesummation of the integral time-weighted squared errors(ITSEs) of system control loops This controller is to becompared with the one designed using the BSO algorithmregarding the integral time-weighted squared errors (ITSEs)for each control loop which are listed in Table 6 Theremarkable difference between both algorithms regardingITSEs indicates that the BSO technique is more efficient indetermining the global best solution in the field of MIMOcontrol system

6 Conclusions

The challenge of decoupling and controlling higher ordermulti-input multioutput (MIMO) process is tackled in this


Table 1 Gains of BSO

Parameter Symbol BSO for decoupling network implementation BSO for BELBIC implementationNumber of bacteria in the population 119878 50 50Dimension of search space 119901 4 24Maximum number of swim length 119873119904 4 4Maximum number of chemotactic steps 119873119888 100 20Number of reproductive steps 119873re 4 2Number of elimination dispersal events 119873ed 2 2Elimination dispersal probability 119875ed 025 025Step size 119862(119894) 005 005Cognitive factor 1198621 12 12Social acceleration factors 1198622 05 05Momentuminertia 119908 09 09

Table 2 Resulting values of steady state decoupling compensation elements based on BSO

Fitness function Final value of fitness function Values of steady state decoupling elements (120582s)Fitness1 98506 12058211 = 02453 12058221 = minus04755 12058231 = 07210 12058241 = 08564Fitness2 05941 12058212 = minus00195 12058222 = minus01090 12058232 = minus00967 12058242 = 11934Fitness3 76138 12058213 = minus00481 12058223 = 06249 12058233 = minus07904 12058243 = minus01218Fitness4 03040 12058214 = minus00026 12058224 = 01492 12058234 = minus01790 12058244 = 03273

Table 3 The proper gains of the BELBICs optimized by the BSO for different loops

Loop Gains120572 120573 119870 119870119901 119870119894 119870119889(QE 11987930) 02321 08914 minus04830 34765 00028 minus06471(SAB 11987911) 03418 minus13651 03936 minus215658 minus10949 minus07771(RL1 11987934) 873587 minus89268 minus01020 294672 173183 146593(RL2 11987948) 174282 226201 02650 minus622460 minus06042 108162

Table 4 The proper gains of the PID controllers optimized by theBSO for different loops

Loop Gains119870119901 119870119894 119870119889(QE 11987930) 19662 03524 07445(SAB 11987911) 10643 19718 02621(RL1 11987934) 16276 14202 minus00366(RL2 11987948) 00784 minus30889 08859

Table 5 The steady state errors for all loops after control

Loop Steady state errorsFormer technique Proposed technique(QE 11987930) 0087510 01189(SAB 11987911) 0019915 00117(RL1 11987934) 0036152 00041(RL2 11987948) 0189710 00207

research The Bacterial Swarm Optimization (BSO) tech-nique is used to develop an optimized scheme for decoupling

Table 6 Comparison between PID controllers designed by PSOand BSO algorithms regarding integral time-weighted squared errorITSE

Loop ITSEPSO technique BSO technique(QE 11987930) 115703 32552(SAB 11987911) 04473 18333(RL1 11987934) 27937 18592(RL2 11987948) 118501 59165

Summation 266614 128642

highly interactive 4 input4 output two-coupled distillationcolumn processes The scheme consists of two stages In thefirst stage the optimum group of fitness functions is deter-mined through the analysis of precalculated proper pairingwhich is based on the derived relative gain array (RGA)The derivation of the RGA is based on the transfer functionmatrix of the physical process In the second stage thevalues of decoupling compensation elements (120582s) that min-imize the interactions are estimated based on the formerly


0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus1

01

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus02

002

Time (hr)

Decoupled system step response in respect to thetemperature in each tray

Figure 9 The outputs of different decoupled loops in case of no controllers

0 100 200 300 400 500 600 700 800 900 1000minus05

105

0

15

minus05

105

0

minus05

105

0

minus05

105

0

15

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

Closed loop system step response in respect to thetemperature in each tray

Figure 10 The outputs of different decoupled loops in the presence of the controller

driven fitness functions Designing the decoupled systembased on the general form of the decoupling compensationmatrix showed a remarkable improvement in the systemdynamics compared to the utilization of the simple formof the compensation matrix The simulation results showedthe efficiency of the proposed BSO technique in estimating

steady state decoupling compensation elements values Forcontrol purpose a scheme of Brain Emotional LearningBased Intelligent Controller (BELBIC) is designed and opti-mized using BSO algorithm to obtain the optimal valuesof controllersrsquo parameters Furthermore PID controllers aredeveloped using the same optimization technique in order


100 110 120minus02

0020406

Closed loop system step response in respect to the temperature in each tray

200 210 2200

05

1

Time (hr) Time (hr) Time (hr) Time (hr)




290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1

100 105minus08minus06minus04minus02

0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48

The proposed techniqueThe formerly studiedtechnique




Figure 11 Comparison between the step response of the proposed technique and that of the formerly studied technique

to validate the robustness of the BELBIC The robust controlbehavior of the designed BELBIC-based control scheme isvalidated in the simulation results The BELBIC designedusing the BSO algorithm showed a remarkable improvementin the transient and steady state errors of the last three controlloops compared with the controller designed utilizing thePSO technique

List of Symbols

QE Heat input to the reboilerSAB Vapor flow rate in the vapor transfer lineRL1 Reflux ratio in the main columnRL2 Reflux ratio in the second column11987911 Temperature at the 11th tray11987930 Temperature at the 30th tray11987934 Temperature at the 34th tray11987948 Temperature at the 48th tray119866(119904) Transfer function matrix of the process in 119904

domain

120574119894119895 Relative gain between the output ldquo119894rdquo and inputldquo119895rdquoΛ ss Steady state decoupling compensation matrix120582119894119895 Decoupling compensation element between theoutput ldquo119894rdquo and input ldquo119895rdquo119884(119904) Output vector of the process119882(119904) Input vector of the decoupling network

MO The model output of Brain Emotional LearningBased Intelligent Controller (BELBIC)119874119894 Orbitofrontal cortex node119860 119894 Amygdala node119878119894 The 119894th sensory input119866119860 Plastic connection weights of the amygdala119866119874 Plastic connection weights of the orbitofrontalcortex120572 The amygdala learning rate120573 The orbitofrontal cortex learning rate

Rew The reward signal119890 Error signal


100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

The designed BELBICThe PID controller




Figure 12 Comparison between the step response of the designed BELBIC and that of the PID controller in the presence of disturbance at119905 = 500 seconds

119870 119870119901119870119894119870119889 Controller parameters11987930 desired Reference signal for output 1198793011987911 desired Reference signal for output 1198791111987934 desired Reference signal for output 1198793411987948 desired Reference signal for output 11987948119901 Dimension of search space119878 The number of bacteria119878119903 The number of bacteria splits per generation119873119888 The number of chemotactic steps119873119904 Limits of the length of a swim119873re The reproduction steps number119873ed The amount of elimination-dispersal events119875ed Elimination-dispersal probability119862(119894) The bacteria step size lengthDelta The direction of each bacteria1198621 Weight of local information1198622 Weight of global information1198771 1198772 Two random numbers

Competing Interests

The authors declare that they have no competing interests

References

[1] I-L Chien H-P Huang and J-C Yang ldquoA simple multilooptuning method for PID controllers with no proportional kickrdquoIndustrial and Engineering Chemistry Research vol 38 no 4 pp1456ndash1468 1999

[2] F Vazquez FMorilla and S Dormido ldquoAn iterativemethod fortuning decentralized PID controllersrdquo in Proceedings of the 14thIFACWorld Congress Beijing China 1999

[3] M Lee K Lee C Kim and J Lee ldquoAnalytical design ofmultiloop PID controllers for desired closed-loop responsesrdquoAIChE Journal vol 50 no 7 pp 1631ndash1635 2004


[4] Q Xiong and W-J Cai ldquoEffective transfer function methodfor decentralized control system design of multi-input multi-output processesrdquo Journal of Process Control vol 16 no 8 pp773ndash784 2006

[5] T N L Vu and M Lee ldquoIndependent design of multi-loopPIPID controllers for interacting multivariable processesrdquoJournal of Process Control vol 20 no 8 pp 922ndash933 2010

[6] J Lieslehto ldquoMIMO controller design using SISO controllerdesign methodsrdquo in Proceedings of the 13th IFAC WorldCongress San Francisco Calif USA 1996

[7] Q-G Wang Y Zhang and M-S Chiu ldquoNon-interactingcontrol design for multivariable industrial processesrdquo Journal ofProcess Control vol 13 no 3 pp 253ndash265 2003

[8] W Zhang L Chen and L Ou ldquoAlgebraic solution to H2 controlproblems II The multivariable decoupling caserdquo Industrial ampEngineering Chemistry Research vol 45 no 21 pp 7163ndash71762006

[9] T Liu W Zhang and F Gao ldquoAnalytical decoupling controlstrategy using a unity feedback control structure for MIMOprocesses with time delaysrdquo Journal of Process Control vol 17no 2 pp 173ndash186 2007

[10] MWaller J B Waller and K V Waller ldquoDecoupling revisitedrdquoIndustrial amp Engineering Chemistry Research vol 42 no 20 pp4575ndash4577 2003

[11] A M El-Garhy and M E El-Shimy ldquoDevelopment of decou-pling scheme for high order MIMO process based on PSOtechniquerdquo Applied Intelligence vol 26 no 3 pp 217ndash229 2007

[12] W-J Cai W Ni M-J He and C-Y Ni ldquoNormalized decou-plingmdasha new approach for MIMO process control systemdesignrdquo Industrial and Engineering Chemistry Research vol 47no 19 pp 7347ndash7356 2008

[13] B T Jevtovic and M R Matauek ldquoPID controller design ofTITO system based on ideal decouplerrdquo Journal of ProcessControl vol 20 no 7 pp 869ndash876 2010

[14] J Garrido F Vazquez and F Morilla ldquoAn extended approachof inverted decouplingrdquo Journal of Process Control vol 21 no 1pp 55ndash68 2011

[15] C Rajapandiyan and M Chidambaram ldquoController design forMIMO processes based on simple decoupled equivalent trans-fer functions and simplified decouplerrdquo Industrial and Engineer-ing Chemistry Research vol 51 no 38 pp 12398ndash12410 2012

[16] E Bristol ldquoOn a new measure of interaction for multivariableprocess controlrdquo IEEE Transactions on Automatic Control vol11 no 1 pp 133ndash134 1966

[17] F G Shinskey Process-Control Systems McGraw-Hill NewYork NY USA 2nd edition 1979

[18] T J McAvoy Interaction Analysis Instrument Society ofAmer-ica Research Triangle Park Durham NC USA 1983

[19] M T Tham Multivariable Control An Introduction to Decou-pling Control Department of Chemical and Process Engineer-ing University of Newcastle Tyne Newcastle upon Tyne UK1999

[20] C S Zalkind ldquoPractical approach to Non-interacting controlParts I and IIrdquo Ins Cont Systems vol 40 1967

[21] W L Luyben ldquoDistillation decouplingrdquo AIChE Journal vol 16no 2 pp 198ndash203 1970

[22] M J Lengare R H Chile L M Waghmare and B Par-mar ldquoAuto tuning of PID controller for MIMO processesrdquoInternational Journal of Electrical Computer Electronics andCommunication Engineering vol 2 pp 113ndash116 2008

[23] Y Zhang S Li and Q Zhu ldquoBackstepping-enhanced decen-tralised PID control for MIMO processes with an experimentalstudyrdquo IET Control Theory amp Applications vol 1 no 3 pp 704ndash712 2007

[24] T S Chang and A N Gundes ldquoPID controller design withguaranteed stability margin for MIMO systemsrdquo in Proceedingsof the World Congress on Engineering and Computer Science(WCECS rsquo07) pp 747ndash752 2007

[25] T Takagi and M Sugeno ldquoFuzzy identification of systems andits applications to modeling and controlrdquo IEEE Transactions onSystems Man and Cybernetics vol 15 no 1 pp 116ndash132 1985

[26] K S Narendra andK Parthasarathy ldquoIdentification and controlof dynamical systems using neural networksrdquo IEEE Transac-tions on Neural Networks vol 1 no 1 pp 4ndash27 1990

[27] R-J Wai J-D Lee and K-H Su ldquoSupervisory enhancedgenetic algorithm control for indirect field-oriented inductionmotor driverdquo in Proceedings of the IEEE International JointConference on Neural Networks vol 2 pp 1239ndash1244 IEEE July2004

[28] J Moren and C A Balkenius ldquoComputational model of emo-tional learning in the Amygdalardquo in From Animals to Animats6 pp 115ndash124 2000

[29] J Moren Emotion and learning a computational model of theAmygdala [PhD thesis] Lund University Lund Sweden 2002

[30] C Lucas D Shahmirzadi and N Sheikholeslami ldquoIntroducingBELBIC brain emotional learning based intelligent controllerrdquoIntelligent Automation and Soft Computing vol 10 no 1 pp 11ndash22 2004

[31] A RMehrabian and C Lucas ldquoEmotional learning based intel-ligent robust adaptive controller for stable uncertain nonlinearsystemsrdquo International Journal of Computational Intelligencevol 2 no 4 pp 246ndash252 2005

[32] C Lucas R M Milasi and B N Araabi ldquoIntelligent modelingand control of washing machine using locally linear neuro-fuzzy (LLNF) modeling and modified brain emotional learningbased intelligent controller (BELBIC)rdquoAsian Journal of Controlvol 8 no 4 pp 393ndash400 2006

[33] H Rouhani M Jalili B N Araabi W Eppler and C LucasldquoBrain emotional learning based intelligent controller appliedto neurofuzzy model of micro-heat exchangerrdquo Expert Systemswith Applications vol 32 no 3 pp 911ndash918 2007

[34] H Rouhani A Sadeghzadeh C Lucas and B N Araabi ldquoEmo-tional learning based intelligent speed and position controlapplied to neurofuzzy model of switched reluctance motorrdquoControl and Cybernetics vol 36 no 1 pp 75ndash95 2007

[35] H Guoyong Z Ziyang and W Daobo ldquoBrain emotionallearning based intelligent controller for nonlinear systemrdquoin Proceedings of the 2008 2nd International Symposium onIntelligent Information Technology Application (IITA rsquo08) vol 2pp 660ndash663 IEEE Shanghai China December 2008

[36] S Jafarzadeh R Mirheidari M R J Motlagh and M Barkhor-dari ldquoDesigning PID and BELBIC controllers in path trackingproblemrdquo International Journal of Computers Communicationsand Control vol 3 pp 343ndash348 2008

[37] H T Dorrah A M El-Garhy and M E El-Shimy ldquoPSO-BELBIC scheme for two-coupled distillation column processrdquoJournal of Advanced Research vol 2 no 1 pp 73ndash83 2011

[38] S Ale Aghaee C Lucas and K Amiri Zadeh ldquoApplyingbrain emotional learning based intelligent controller (belbic) tomultiple-area power systemsrdquo Asian Journal of Control vol 14no 6 pp 1580ndash1588 2012


[39] A Jain G Jain and A Kuchhal ldquoBrain emotional learningbased intelligent controller and its application to continuousstirred tank reactorrdquo Computer Engineering and IntelligentSystems vol 4 no 5 pp 1ndash9 2013

[40] M K Sharma and A Kumar ldquoPerformance comparison ofBrain Emotional Learning-Based Intelligent Controller (BEL-BIC) and PI controller for Continually Stirred Tank Heater(CSTH)rdquo in Computational Advancement in CommunicationCircuits and Systems pp 293ndash301 Springer India 2015

[41] A Colorni M Dorigo and V Maniezzo ldquoDistributed opti-mization by ant coloniesrdquo in Proceedings of the 1st EuropeanConference on Artificial Life vol 142 pp 134ndash142 Paris FranceDecember 1991

[42] D Whitley ldquoA genetic algorithm tutorialrdquo Statistics and Com-puting vol 4 no 2 pp 65ndash85 1994

[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks Part 1 (of 6) pp 1942ndash1948 Piscataway NJ USADecember 1995

[44] Eberhart and Y Shi ldquoParticle swarm optimization devel-opments applications and resourcesrdquo in Proceedings of theCongress on Evolutionary Computation IEEE Service CenterSeoul Republic of Korea May 2001

[45] KM Passino ldquoBiomimicry of bacterial foraging for distributedoptimization and controlrdquo IEEE Control Systems Magazine vol22 no 3 pp 52ndash67 2002

[46] E S Ali and S M Abd-Elazim ldquoBacteria foraging optimizationalgorithm based load frequency controller for interconnectedpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 33 no 3 pp 633ndash638 2011

[47] K S Kumar and T Jayabarathi ldquoPower system reconfigurationand loss minimization for an distribution systems using bacte-rial foraging optimization algorithmrdquo International Journal ofElectrical Power and Energy Systems vol 36 no 1 pp 13ndash172012

[48] S M Abd-Elazim and E S Ali ldquoPower system stabilityenhancement via bacteria foraging optimization algorithmrdquoArabian Journal for Science and Engineering vol 38 no 3 pp599ndash611 2013

[49] MM deMenezes P B deAraujo and F E deVargas ldquoBacterialforaging optimization algorithm used to adjust the parametersof Power System Stabilizers and Thyristor Controlled SeriesCapacitor-Power Oscillation Damping controllerrdquo in Proceed-ings of the 11th IEEEIAS International Conference on IndustryApplications (INDUSCON rsquo14) pp 1ndash6 IEEE Juiz de ForaBrazil December 2014

[50] R Majhi G Panda G Sahoo P K Dash and D P Das ldquoStockmarket prediction of SampP 500 andDJIA using bacterial foragingoptimization techniquerdquo in Proceedings of the IEEE Congresson Evolutionary Computation (CEC rsquo07) pp 2569ndash2575 IEEESingapore September 2007

[51] RMajhi G Panda BMajhi andG Sahoo ldquoEfficient predictionof stock market indices using adaptive bacterial foraging opti-mization (ABFO) and BFO based techniquesrdquo Expert Systemswith Applications vol 36 no 6 pp 10097ndash10104 2009

[52] C Li Application of Bacterial Foraging Optimization PID Con-trol in VAV System Shandong Normal University School ofInformation Science amp Engineering Jinan China 2013

[53] A S Oshaba and E S Ali ldquoBacteria foraging a new techniquefor speed control of DC series motor supplied by photovoltaicsystemrdquo International Journal of WSEAS Transactions on PowerSystems vol 9 pp 185ndash195 2014

[54] W M Korani H T Dorrah and H M Emara ldquoBacterial for-aging oriented by particle swarm optimization strategy for PIDtuningrdquo in Proceedings of the IEEE International Symposium onComputational Intelligence in Robotics and Automation (CIRArsquo09) pp 445ndash450 December 2009

[55] A Biswas S Dasgupta S Das and A Abraham ldquoSynergy ofPSO and bacterial foraging optimizationmdasha comparative studyon numerical benchmarksrdquo in Innovations in Hybrid IntelligentSystems pp 255ndash263 Springer Berlin Germany 2007

[56] R Anguluri A Abraham and V Snasel ldquoA hybrid bacterialforagingmdashPSO algorithm based tuning of optimal FOPI speedcontrollerrdquo Acta Montanistica Slovaca vol 16 no 1 pp 55ndash652011

[57] SM Abd-Elazim and E S Ali ldquoSynergy of particle swarm opti-mization and bacterial foraging for TCSC damping controllerdesignrdquo International Journal of WSEAS Transactions on PowerSystems vol 8 pp 74ndash84 2013

[58] S M Abd-Elazim and E S Ali ldquoA hybrid particle swarmoptimization and bacterial foraging for power system stabilityenhancementrdquo Complexity vol 21 no 2 pp 245ndash255 2015

[59] L Lang and E D Gilles ldquoA case-study of multivariable controlfor a multicomponent distillation unit on a pilot plant scalerdquo inProceedings of the IEEE American Control Conference pp 101ndash106 Pittsburgh Pa USA June 1989

[60] H Unbehauen ldquoControl systems robotics and automationmdashvolII-controller design in time-domainrdquo in Encyclopedia of LifeSupport Systems (EOLSS) Developed under the Auspices of theUNESCO The Encyclopedia of Life Support Systems (EOLSS)Paris France 2009 httpwwweolssnet

[61] A Jain Computational modeling of the brain limbic systemand its application in control engineering [PhD thesis] ThaparUniversity 2009

[62] D P Rini SM Shamsuddin and S S Yuhaniz ldquoParticle swarmoptimization technique system and challengesrdquo InternationalJournal of Computer Applications vol 14 no 1 pp 19ndash26 2011

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



are of increasing spread due to their proven ability to over-come system model uncertainty [25ndash27] The computationalmodel of emotional learning in mammalian brain whichis introduced in [28 29] inspired a new learning algorithmAfterwards this learning technique is deployed in the systemcontrol design presenting the novel Brain Emotional Learn-ing Based Intelligent Controller (BELBIC) [30] Thus theBrain Emotional Learning Based Intelligent Controller (BEL-BIC) has shown robustness in the control of the nonlinearand uncertain systems such as VanDer Pol oscillator Duffingforced oscillator and automatic self-balancing scale [31]washing machine [32] microheat exchanger [33] switchedreluctance motor [34] unmanned aerial vehicle [35] pathtracking of a vehicle [36] two-coupled distillation columnprocess [37] multiple-area power systems [38] and contin-uous stirred tank reactor [39 40]

The parameterization of the decoupling compensationnetwork and the BELBIC are still open research topicsCurrently the detailed analytical methods used in purpose ofthe parameterization of the decoupling compensation net-work cost excessive mathematical burdens Regarding theparameterization of BELBIC the trial and error is widely usedfor controller parameters estimation Thus the utilization ofvarious optimization techniques based on artificial intelli-gence introduces an efficient alternative in both cases [11 37]

The utilization of the biologically inspired algorithms asAnt Colony Optimization (ACO) [41] Genetic Algorithm(GA) [42] and Particle Swarm Optimization (PSO) [43 44]in optimization problems constitutes currently a promis-ing solution Recently the new evolutionary computationtechnique depending on the behavior of foraging of E colibacteria which is named as Bacterial Foraging OptimizationAlgorithm (BFOA) is proposed by [45] This technique hasbeen successfully deployed in many applications as powersystems [46ndash49] stockmarket prediction [50 51] and designof PIPID controllers [52 53]The key drawback of the BFOAis the delay in reaching the global solution because it isbased on random searching directions For this delay to beovercome the BFOA is integrated with the Particle SwarmOptimization (PSO) technique introducing the BacterialSwarmOptimization (BSO) algorithm [54] One of themajorcharacteristics of PSO technique which is inherited to theBSO algorithm is the idea of velocity updating Accordinglythe process of searching for the global solution in theBSO technique depends on the individual and global bestpositions concurrently As discussed in [55ndash58]TheBacterialSwarm Optimization (BSO) algorithm grants better perfor-mance in determining the optimum solution compared withPSO and BFOA algorithms

This research paper aims to investigate the feasibility ofapplying the Bacterial Swarm Optimization (BSO) algorithmin the field of MIMO control system As an example forMIMO system the two-coupled distillation column is to bestudied Primarily the mathematical model of the system isdecoupled into several independent loops The parametersof the decoupling compensation network are determinedbased on the summation minimization of the integral time-weighted squared outputs (ITSOs) of unpaired outputs

regarding a particular input In this regard the BSO tech-nique is utilized On the other hand an optimal BELBIC isdesigned for each decoupled control loop through the sum-mation minimization of the integral time-weighted squarederrors (ITSEs) of all loops using BSO as well For the com-parison purpose the PID controller is also implemented forthe same application so that the strength of each of consid-ered control structures can be studied

2 Two-Coupled Distillation Column Process

As formerly stated the two-coupled distillation column ishandled in this paper as an example of MIMO system In thissection the physical system is discussed Primarily thefunction of the system and its components are presentedAfterwards the system mathematical modeling and decou-pling are handled

21 System Description Distillation units are mainly utilizedfor the separation of fluid mixture components The distilla-tion column major components can be listed as follows

(i) A vertical shell in which the separation of fluidsubstances is accomplished

(ii) A cascade of trays for improving component separa-tion

(iii) A reboiler for maintaining the required heat energyfor the distillation process

(iv) A condenser for liquefying the vapor leaving thecolumn

(v) A reflux drum in which portion of the condensedliquid is recycled back to the vertical shell

The physical process considered in this research com-prises two-coupled distillation columns as shown in Figure 1Thereby ternary petrochemical mixtures can be separatedWhile the main glass column is composed of 40 bubble captrays excluding those of the boiler and condenser the sideglass column contains 10 bubble cap trays At the 22nd stagethe system intake port is located at which the fluid mixtureis to be fed The three separated fluid components are to beextracted from the process so that the heaviest and thelightest components can be provided from the bottom andthe top of themain column respectively and the intermediatecomponent is derived from the top of the side column

22 Mathematical Modeling of the Two-Coupled DistillationColumn Primarily the manipulated variables are to bedetermined Thus the selected manipulated variables are theheat input to the reboiler (QE) the vapor flow rate in thevapor transfer line (SAB) the reflux ratio in themain column(RL1) and the reflux ratio in the second column (RL2) [59]Regarding the system technical constraints the input heatenergy rateQE and the vapor flow rate SABhave to not exceedthe values 82 KW and 395m3h respectively in order toavoid flooding of the smaller side column [59] Secondly thecontrolled values are selected to be the fluid temperature at


Feed


component

component

Reflux

Reflux

RL2

RefluxRL1

drum

Refluxdrum

Condenser

Condenser

SAB

Reboiler32

30

4853

22

11




Liquid reflux

Lightest

HeaviestQE







119866 (119904) =[[[[[[[[[[[


]]]]]]]]]]]

(1)






++

++

+

+

+

+

++

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

T30 desired

T11 desired

T34 desired

T48 desired

minus

minus

minus

minus

GC1

GC2

GC3

GC4

W1

W2

W3

W4

QE

SAB

RL1

RL2

12058211

12058212

12058213

12058214

12058221

12058222

12058223

12058224

12058231

12058232

12058233

12058234

12058241

12058242

12058243

12058244

T11

T30

T34

T48

G11

G12

G13

G14

G21

G22

G23

G24

G31

G32

G33

G34

G41

G42

G43

G44



=[[[[[[[


]]]]]]] (2)




Λ ss =[[[[[[[


]]]]]]] (3)

[119884 (119904)] = [119866 (119904)] [Λ ss] [119882 (119904)] (4)









0119905 11988412 sdot 119889119905

ITSO21 = intinfin0

119905 11988422 sdot 119889119905


119905 1198841198732 sdot 119889119905(5)


ITSO12 = intinfin0


0119905 11988422 sdot 119889119905


0119905 1198841198732 sdot 119889119905

(6)




0119905 11988422 sdot 119889119905


0119905 1198841198732 sdot 119889119905

(7)


Fitness119895 = 119873sum119894=1

ITSO119894119895 119895 = 1 2 3 119873 119894 = 119902 (8)







O

O

O

A

A

A MO

GO1

GO2

GO3

ΔGo

GA1

GA2

GA3

GAthAth

ΔGA

MO998400

Reward signal (Rew)

Sensory input (s)

Thal

amus

Sens

ory

cort

ex

Amygdala



PlasticLearning





119860 119894 = 119878119894119866119860119894 (9)

119874119894 = 119878119894119866119874119894 (10)

MO1015840 = sum119894

119860 119894 minussum119894


MO = sum119894

119860 119894 minussum119894




Orbitofrontalcortex

Amygdala

Sensoryinput


MO Plant+

BELBIC

+

minus

minus

r eyp

u




119860119895]]) (13)

Δ119866119874119894 = 120573 (119878119894 [MO1015840 minus Rew]) (14)





119878 = 119870 sdot 119890 (17)










(19)



119866119888 (119904) = 119870119901 + 119870119894119904 + 119904119870119889 (20)






+

+

+

Kp

Kis

sKd















is designed


parameter



compensation matrix





Start

Stop



l = l + 1

No

No

NoNo

No

No

Yes

YesYes

Yes

Yes

l lt Ned


the wholeswarm


k lt Nre


j lt Nc



half into two)


Z

Y

Z

i lt s


Jlast = J(i j k l)




Ym lt Ns

m = m + 1

Setm = Ns




Perform elimination

bacterium is chosen


location

according to Ped


Delta = V













long)


119875 (119894 119895 + 1 119896 119897) = 119875 (119894 119895 + 1 119896 119897) + 119862 (119894) lowast Delta (119894) (21)



119875current (119894 119895 + 1) = 119875 (119894 119895 + 1 119896 119897) 119869local (119894 119895 + 1) = 119869 (119894 119895 + 1 119896 119897) (22)



119898 = 119873119904(23)






Delta = 119881(24)




119869119894health = 119873119888+1sum119895=1

119869 (119894 119895 119896 119897) (25)







RGA4times4 =[[[[[[


]]]]]] (26)



(27)




(28)



(29)







(31)





0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)


T30

desir

edT11

desir

edT34

desir

edT48

desir

ed

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)






6 Conclusions
















Summation 266614 128642



0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus1

01

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus02

002

Time (hr)



0 100 200 300 400 500 600 700 800 900 1000minus05

105

0

15

minus05

105

0

minus05

105

0

minus05

105

0

15

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)






100 110 120minus02

0020406


200 210 2200

05

1





290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1


0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48







List of Symbols


domain





100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Feed


component

component

Reflux

Reflux

RL2

RefluxRL1

drum

Refluxdrum

Condenser

Condenser

SAB

Reboiler32

30

4853

22

11




Liquid reflux

Lightest

HeaviestQE







119866 (119904) =[[[[[[[[[[[


]]]]]]]]]]]

(1)






++

++

+

+

+

+

++

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

T30 desired

T11 desired

T34 desired

T48 desired

minus

minus

minus

minus

GC1

GC2

GC3

GC4

W1

W2

W3

W4

QE

SAB

RL1

RL2

12058211

12058212

12058213

12058214

12058221

12058222

12058223

12058224

12058231

12058232

12058233

12058234

12058241

12058242

12058243

12058244

T11

T30

T34

T48

G11

G12

G13

G14

G21

G22

G23

G24

G31

G32

G33

G34

G41

G42

G43

G44



=[[[[[[[


]]]]]]] (2)




Λ ss =[[[[[[[


]]]]]]] (3)

[119884 (119904)] = [119866 (119904)] [Λ ss] [119882 (119904)] (4)









0119905 11988412 sdot 119889119905

ITSO21 = intinfin0

119905 11988422 sdot 119889119905


119905 1198841198732 sdot 119889119905(5)


ITSO12 = intinfin0


0119905 11988422 sdot 119889119905


0119905 1198841198732 sdot 119889119905

(6)




0119905 11988422 sdot 119889119905


0119905 1198841198732 sdot 119889119905

(7)


Fitness119895 = 119873sum119894=1

ITSO119894119895 119895 = 1 2 3 119873 119894 = 119902 (8)







O

O

O

A

A

A MO

GO1

GO2

GO3

ΔGo

GA1

GA2

GA3

GAthAth

ΔGA

MO998400

Reward signal (Rew)

Sensory input (s)

Thal

amus

Sens

ory

cort

ex

Amygdala



PlasticLearning





119860 119894 = 119878119894119866119860119894 (9)

119874119894 = 119878119894119866119874119894 (10)

MO1015840 = sum119894

119860 119894 minussum119894


MO = sum119894

119860 119894 minussum119894




Orbitofrontalcortex

Amygdala

Sensoryinput


MO Plant+

BELBIC

+

minus

minus

r eyp

u




119860119895]]) (13)

Δ119866119874119894 = 120573 (119878119894 [MO1015840 minus Rew]) (14)





119878 = 119870 sdot 119890 (17)










(19)



119866119888 (119904) = 119870119901 + 119870119894119904 + 119904119870119889 (20)






+

+

+

Kp

Kis

sKd















is designed


parameter



compensation matrix





Start

Stop



l = l + 1

No

No

NoNo

No

No

Yes

YesYes

Yes

Yes

l lt Ned


the wholeswarm


k lt Nre


j lt Nc



half into two)


Z

Y

Z

i lt s


Jlast = J(i j k l)




Ym lt Ns

m = m + 1

Setm = Ns




Perform elimination

bacterium is chosen


location

according to Ped


Delta = V













long)


119875 (119894 119895 + 1 119896 119897) = 119875 (119894 119895 + 1 119896 119897) + 119862 (119894) lowast Delta (119894) (21)



119875current (119894 119895 + 1) = 119875 (119894 119895 + 1 119896 119897) 119869local (119894 119895 + 1) = 119869 (119894 119895 + 1 119896 119897) (22)



119898 = 119873119904(23)






Delta = 119881(24)




119869119894health = 119873119888+1sum119895=1

119869 (119894 119895 119896 119897) (25)







RGA4times4 =[[[[[[


]]]]]] (26)



(27)




(28)



(29)







(31)





0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)


T30

desir

edT11

desir

edT34

desir

edT48

desir

ed

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)






6 Conclusions
















Summation 266614 128642



0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus1

01

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus02

002

Time (hr)



0 100 200 300 400 500 600 700 800 900 1000minus05

105

0

15

minus05

105

0

minus05

105

0

minus05

105

0

15

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)






100 110 120minus02

0020406


200 210 2200

05

1





290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1


0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48







List of Symbols


domain





100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




++

++

+

+

+

+

++

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

T30 desired

T11 desired

T34 desired

T48 desired

minus

minus

minus

minus

GC1

GC2

GC3

GC4

W1

W2

W3

W4

QE

SAB

RL1

RL2

12058211

12058212

12058213

12058214

12058221

12058222

12058223

12058224

12058231

12058232

12058233

12058234

12058241

12058242

12058243

12058244

T11

T30

T34

T48

G11

G12

G13

G14

G21

G22

G23

G24

G31

G32

G33

G34

G41

G42

G43

G44



=[[[[[[[


]]]]]]] (2)




Λ ss =[[[[[[[


]]]]]]] (3)

[119884 (119904)] = [119866 (119904)] [Λ ss] [119882 (119904)] (4)









0119905 11988412 sdot 119889119905

ITSO21 = intinfin0

119905 11988422 sdot 119889119905


119905 1198841198732 sdot 119889119905(5)


ITSO12 = intinfin0


0119905 11988422 sdot 119889119905


0119905 1198841198732 sdot 119889119905

(6)




0119905 11988422 sdot 119889119905


0119905 1198841198732 sdot 119889119905

(7)


Fitness119895 = 119873sum119894=1

ITSO119894119895 119895 = 1 2 3 119873 119894 = 119902 (8)







O

O

O

A

A

A MO

GO1

GO2

GO3

ΔGo

GA1

GA2

GA3

GAthAth

ΔGA

MO998400

Reward signal (Rew)

Sensory input (s)

Thal

amus

Sens

ory

cort

ex

Amygdala



PlasticLearning





119860 119894 = 119878119894119866119860119894 (9)

119874119894 = 119878119894119866119874119894 (10)

MO1015840 = sum119894

119860 119894 minussum119894


MO = sum119894

119860 119894 minussum119894




Orbitofrontalcortex

Amygdala

Sensoryinput


MO Plant+

BELBIC

+

minus

minus

r eyp

u




119860119895]]) (13)

Δ119866119874119894 = 120573 (119878119894 [MO1015840 minus Rew]) (14)





119878 = 119870 sdot 119890 (17)










(19)



119866119888 (119904) = 119870119901 + 119870119894119904 + 119904119870119889 (20)






+

+

+

Kp

Kis

sKd















is designed


parameter



compensation matrix





Start

Stop



l = l + 1

No

No

NoNo

No

No

Yes

YesYes

Yes

Yes

l lt Ned


the wholeswarm


k lt Nre


j lt Nc



half into two)


Z

Y

Z

i lt s


Jlast = J(i j k l)




Ym lt Ns

m = m + 1

Setm = Ns




Perform elimination

bacterium is chosen


location

according to Ped


Delta = V













long)


119875 (119894 119895 + 1 119896 119897) = 119875 (119894 119895 + 1 119896 119897) + 119862 (119894) lowast Delta (119894) (21)



119875current (119894 119895 + 1) = 119875 (119894 119895 + 1 119896 119897) 119869local (119894 119895 + 1) = 119869 (119894 119895 + 1 119896 119897) (22)



119898 = 119873119904(23)






Delta = 119881(24)




119869119894health = 119873119888+1sum119895=1

119869 (119894 119895 119896 119897) (25)







RGA4times4 =[[[[[[


]]]]]] (26)



(27)




(28)



(29)







(31)





0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)


T30

desir

edT11

desir

edT34

desir

edT48

desir

ed

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)






6 Conclusions
















Summation 266614 128642



0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus1

01

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus02

002

Time (hr)



0 100 200 300 400 500 600 700 800 900 1000minus05

105

0

15

minus05

105

0

minus05

105

0

minus05

105

0

15

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)






100 110 120minus02

0020406


200 210 2200

05

1





290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1


0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48







List of Symbols


domain





100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in









0119905 11988412 sdot 119889119905

ITSO21 = intinfin0

119905 11988422 sdot 119889119905


119905 1198841198732 sdot 119889119905(5)


ITSO12 = intinfin0


0119905 11988422 sdot 119889119905


0119905 1198841198732 sdot 119889119905

(6)




0119905 11988422 sdot 119889119905


0119905 1198841198732 sdot 119889119905

(7)


Fitness119895 = 119873sum119894=1

ITSO119894119895 119895 = 1 2 3 119873 119894 = 119902 (8)







O

O

O

A

A

A MO

GO1

GO2

GO3

ΔGo

GA1

GA2

GA3

GAthAth

ΔGA

MO998400

Reward signal (Rew)

Sensory input (s)

Thal

amus

Sens

ory

cort

ex

Amygdala



PlasticLearning





119860 119894 = 119878119894119866119860119894 (9)

119874119894 = 119878119894119866119874119894 (10)

MO1015840 = sum119894

119860 119894 minussum119894


MO = sum119894

119860 119894 minussum119894




Orbitofrontalcortex

Amygdala

Sensoryinput


MO Plant+

BELBIC

+

minus

minus

r eyp

u




119860119895]]) (13)

Δ119866119874119894 = 120573 (119878119894 [MO1015840 minus Rew]) (14)





119878 = 119870 sdot 119890 (17)










(19)



119866119888 (119904) = 119870119901 + 119870119894119904 + 119904119870119889 (20)






+

+

+

Kp

Kis

sKd















is designed


parameter



compensation matrix





Start

Stop



l = l + 1

No

No

NoNo

No

No

Yes

YesYes

Yes

Yes

l lt Ned


the wholeswarm


k lt Nre


j lt Nc



half into two)


Z

Y

Z

i lt s


Jlast = J(i j k l)




Ym lt Ns

m = m + 1

Setm = Ns




Perform elimination

bacterium is chosen


location

according to Ped


Delta = V













long)


119875 (119894 119895 + 1 119896 119897) = 119875 (119894 119895 + 1 119896 119897) + 119862 (119894) lowast Delta (119894) (21)



119875current (119894 119895 + 1) = 119875 (119894 119895 + 1 119896 119897) 119869local (119894 119895 + 1) = 119869 (119894 119895 + 1 119896 119897) (22)



119898 = 119873119904(23)






Delta = 119881(24)




119869119894health = 119873119888+1sum119895=1

119869 (119894 119895 119896 119897) (25)







RGA4times4 =[[[[[[


]]]]]] (26)



(27)




(28)



(29)







(31)





0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)


T30

desir

edT11

desir

edT34

desir

edT48

desir

ed

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)






6 Conclusions
















Summation 266614 128642



0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus1

01

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus02

002

Time (hr)



0 100 200 300 400 500 600 700 800 900 1000minus05

105

0

15

minus05

105

0

minus05

105

0

minus05

105

0

15

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)






100 110 120minus02

0020406


200 210 2200

05

1





290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1


0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48







List of Symbols


domain





100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




O

O

O

A

A

A MO

GO1

GO2

GO3

ΔGo

GA1

GA2

GA3

GAthAth

ΔGA

MO998400

Reward signal (Rew)

Sensory input (s)

Thal

amus

Sens

ory

cort

ex

Amygdala



PlasticLearning





119860 119894 = 119878119894119866119860119894 (9)

119874119894 = 119878119894119866119874119894 (10)

MO1015840 = sum119894

119860 119894 minussum119894


MO = sum119894

119860 119894 minussum119894




Orbitofrontalcortex

Amygdala

Sensoryinput


MO Plant+

BELBIC

+

minus

minus

r eyp

u




119860119895]]) (13)

Δ119866119874119894 = 120573 (119878119894 [MO1015840 minus Rew]) (14)





119878 = 119870 sdot 119890 (17)










(19)



119866119888 (119904) = 119870119901 + 119870119894119904 + 119904119870119889 (20)






+

+

+

Kp

Kis

sKd















is designed


parameter



compensation matrix





Start

Stop



l = l + 1

No

No

NoNo

No

No

Yes

YesYes

Yes

Yes

l lt Ned


the wholeswarm


k lt Nre


j lt Nc



half into two)


Z

Y

Z

i lt s


Jlast = J(i j k l)




Ym lt Ns

m = m + 1

Setm = Ns




Perform elimination

bacterium is chosen


location

according to Ped


Delta = V













long)


119875 (119894 119895 + 1 119896 119897) = 119875 (119894 119895 + 1 119896 119897) + 119862 (119894) lowast Delta (119894) (21)



119875current (119894 119895 + 1) = 119875 (119894 119895 + 1 119896 119897) 119869local (119894 119895 + 1) = 119869 (119894 119895 + 1 119896 119897) (22)



119898 = 119873119904(23)






Delta = 119881(24)




119869119894health = 119873119888+1sum119895=1

119869 (119894 119895 119896 119897) (25)







RGA4times4 =[[[[[[


]]]]]] (26)



(27)




(28)



(29)







(31)





0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)


T30

desir

edT11

desir

edT34

desir

edT48

desir

ed

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)






6 Conclusions
















Summation 266614 128642



0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus1

01

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus02

002

Time (hr)



0 100 200 300 400 500 600 700 800 900 1000minus05

105

0

15

minus05

105

0

minus05

105

0

minus05

105

0

15

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)






100 110 120minus02

0020406


200 210 2200

05

1





290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1


0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48







List of Symbols


domain





100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Orbitofrontalcortex

Amygdala

Sensoryinput


MO Plant+

BELBIC

+

minus

minus

r eyp

u




119860119895]]) (13)

Δ119866119874119894 = 120573 (119878119894 [MO1015840 minus Rew]) (14)





119878 = 119870 sdot 119890 (17)










(19)



119866119888 (119904) = 119870119901 + 119870119894119904 + 119904119870119889 (20)






+

+

+

Kp

Kis

sKd















is designed


parameter



compensation matrix





Start

Stop



l = l + 1

No

No

NoNo

No

No

Yes

YesYes

Yes

Yes

l lt Ned


the wholeswarm


k lt Nre


j lt Nc



half into two)


Z

Y

Z

i lt s


Jlast = J(i j k l)




Ym lt Ns

m = m + 1

Setm = Ns




Perform elimination

bacterium is chosen


location

according to Ped


Delta = V













long)


119875 (119894 119895 + 1 119896 119897) = 119875 (119894 119895 + 1 119896 119897) + 119862 (119894) lowast Delta (119894) (21)



119875current (119894 119895 + 1) = 119875 (119894 119895 + 1 119896 119897) 119869local (119894 119895 + 1) = 119869 (119894 119895 + 1 119896 119897) (22)



119898 = 119873119904(23)






Delta = 119881(24)




119869119894health = 119873119888+1sum119895=1

119869 (119894 119895 119896 119897) (25)







RGA4times4 =[[[[[[


]]]]]] (26)



(27)




(28)



(29)







(31)





0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)


T30

desir

edT11

desir

edT34

desir

edT48

desir

ed

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)






6 Conclusions
















Summation 266614 128642



0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus1

01

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus02

002

Time (hr)



0 100 200 300 400 500 600 700 800 900 1000minus05

105

0

15

minus05

105

0

minus05

105

0

minus05

105

0

15

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)






100 110 120minus02

0020406


200 210 2200

05

1





290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1


0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48







List of Symbols


domain





100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




+

+

+

Kp

Kis

sKd















is designed


parameter



compensation matrix





Start

Stop



l = l + 1

No

No

NoNo

No

No

Yes

YesYes

Yes

Yes

l lt Ned


the wholeswarm


k lt Nre


j lt Nc



half into two)


Z

Y

Z

i lt s


Jlast = J(i j k l)




Ym lt Ns

m = m + 1

Setm = Ns




Perform elimination

bacterium is chosen


location

according to Ped


Delta = V













long)


119875 (119894 119895 + 1 119896 119897) = 119875 (119894 119895 + 1 119896 119897) + 119862 (119894) lowast Delta (119894) (21)



119875current (119894 119895 + 1) = 119875 (119894 119895 + 1 119896 119897) 119869local (119894 119895 + 1) = 119869 (119894 119895 + 1 119896 119897) (22)



119898 = 119873119904(23)






Delta = 119881(24)




119869119894health = 119873119888+1sum119895=1

119869 (119894 119895 119896 119897) (25)







RGA4times4 =[[[[[[


]]]]]] (26)



(27)




(28)



(29)







(31)





0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)


T30

desir

edT11

desir

edT34

desir

edT48

desir

ed

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)






6 Conclusions
















Summation 266614 128642



0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus1

01

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus02

002

Time (hr)



0 100 200 300 400 500 600 700 800 900 1000minus05

105

0

15

minus05

105

0

minus05

105

0

minus05

105

0

15

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)






100 110 120minus02

0020406


200 210 2200

05

1





290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1


0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48







List of Symbols


domain





100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Start

Stop



l = l + 1

No

No

NoNo

No

No

Yes

YesYes

Yes

Yes

l lt Ned


the wholeswarm


k lt Nre


j lt Nc



half into two)


Z

Y

Z

i lt s


Jlast = J(i j k l)




Ym lt Ns

m = m + 1

Setm = Ns




Perform elimination

bacterium is chosen


location

according to Ped


Delta = V













long)


119875 (119894 119895 + 1 119896 119897) = 119875 (119894 119895 + 1 119896 119897) + 119862 (119894) lowast Delta (119894) (21)



119875current (119894 119895 + 1) = 119875 (119894 119895 + 1 119896 119897) 119869local (119894 119895 + 1) = 119869 (119894 119895 + 1 119896 119897) (22)



119898 = 119873119904(23)






Delta = 119881(24)




119869119894health = 119873119888+1sum119895=1

119869 (119894 119895 119896 119897) (25)







RGA4times4 =[[[[[[


]]]]]] (26)



(27)




(28)



(29)







(31)





0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)


T30

desir

edT11

desir

edT34

desir

edT48

desir

ed

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)






6 Conclusions
















Summation 266614 128642



0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus1

01

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus02

002

Time (hr)



0 100 200 300 400 500 600 700 800 900 1000minus05

105

0

15

minus05

105

0

minus05

105

0

minus05

105

0

15

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)






100 110 120minus02

0020406


200 210 2200

05

1





290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1


0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48







List of Symbols


domain





100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119898 = 119873119904(23)






Delta = 119881(24)




119869119894health = 119873119888+1sum119895=1

119869 (119894 119895 119896 119897) (25)







RGA4times4 =[[[[[[


]]]]]] (26)



(27)




(28)



(29)







(31)





0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)


T30

desir

edT11

desir

edT34

desir

edT48

desir

ed

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)






6 Conclusions
















Summation 266614 128642



0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus1

01

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus02

002

Time (hr)



0 100 200 300 400 500 600 700 800 900 1000minus05

105

0

15

minus05

105

0

minus05

105

0

minus05

105

0

15

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)






100 110 120minus02

0020406


200 210 2200

05

1





290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1


0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48







List of Symbols


domain





100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







(31)





0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)


T30

desir

edT11

desir

edT34

desir

edT48

desir

ed

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus2

02

Time (hr)






6 Conclusions
















Summation 266614 128642



0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus1

01

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus02

002

Time (hr)



0 100 200 300 400 500 600 700 800 900 1000minus05

105

0

15

minus05

105

0

minus05

105

0

minus05

105

0

15

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)






100 110 120minus02

0020406


200 210 2200

05

1





290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1


0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48







List of Symbols


domain





100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in

















Summation 266614 128642



0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus1

01

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus02

002

Time (hr)



0 100 200 300 400 500 600 700 800 900 1000minus05

105

0

15

minus05

105

0

minus05

105

0

minus05

105

0

15

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)






100 110 120minus02

0020406


200 210 2200

05

1





290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1


0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48







List of Symbols


domain





100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000minus1

10

2

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus1

01

Time (hr)

0 100 200 300 400 500 600 700 800 900 1000minus02

002

Time (hr)



0 100 200 300 400 500 600 700 800 900 1000minus05

105

0

15

minus05

105

0

minus05

105

0

minus05

105

0

15

Time (hr)

T30

T11

T34

T48

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)

0 100 200 300 400 500 600 700 800 900 1000Time (hr)






100 110 120minus02

0020406


200 210 2200

05

1





290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1


0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48







List of Symbols


domain





100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




100 110 120minus02

0020406


200 210 2200

05

1





290 300 31002040608

112

040608

112

400 410 420

100 1050

05

1

200 205

08

09

1

298 300 30208

1

12

400 402 40408

09

1

100 105

minus01 minus01

minus01

0

01

200 210 220

minus0050

005

300 3500

05

05

1

390 400 41008

09

1


0

200 205 210

0

01

2995 300 3005 301minus02

0

02

400 450 5000

1

T30

T30

T30

T30

T11

T11

T11

T11

T34

T34

T34

T34

T48

T48

T48

T48







List of Symbols


domain





100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




100 110 120minus04

minus02

0

02

200 220 240

0

05

1

15

05

05

05

15

05

15

290 300 310

1

400 500 600

040608

08

112

06

08

12

08

12

14

08

12

100 110 120 1300

1

200 210 220

1

300 310 320

1

400 500 600

1

100 110 120

minus01

0

01

minus01

01

02

200 210 220 230

0

300 3500

1

400 500 600

1

100 110 120

0


200 220 240minus04

minus02

0

02

minus04

minus02

02

290 300 310 320minus02

0

02

400 500 6000

1





T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48

T30

T11

T34

T48







Competing Interests


References








































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Research Article A New Hybrid BFOA-PSO Optimization...

Documents

Transcript of Research Article A New Hybrid BFOA-PSO Optimization...