ResearchArticle An MEA-Tuning Method for Design of the PID … · 2019. 7. 30. · So far, the vast majority of industrial controllers are PID controllers or their second generations

Research ArticleAn MEA-Tuning Method for Design of the PID Controller

Yongli Zhang 1 Lijun Zhang 2 and Zhiliang Dong 1

1School of Management Science and Engineering Hebei GEO University Shijiazhuang Hebei China2Earth Sciences Museum Hebei GEO University Shijiazhuang Hebei China

Correspondence should be addressed to Yongli Zhang zhangyongli086163com

Received 1 November 2018 Revised 3 December 2018 Accepted 8 January 2019 Published 20 January 2019

Guest Editor Anders E W Jarfors

Copyright copy 2019 Yongli Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The optimization and tuning of parameters is very important for the performance of the PID controller In this paper a novelparameter tuning method based on the mind evolutionary algorithm (MEA) was presented The MEA firstly transformed theproblem solutions into the population individuals embodied by code and then divided the population into superior subpopulationsand temporary subpopulations and used the similar taxis and dissimilation operations for searching the global optimal solutionIn order to verify the control performance of the MEA three classical functions and five typical industrial process control modelswere adopted for testing experiments Experimental results indicated that the proposed approach was feasible and valid the MEAwith the superior design feature and parallel structure could memorize more evolutionary information generate superior genesand enhance the efficiency and effectiveness for searching global optimal parameters In addition the MEA-tuning method can beeasily applied to real industrial practices and provides a novel and convenient solution for the optimization and tuning of the PIDcontroller

1 Introduction

The proportional integral derivative (PID) controller is themost widely used and most mature in industrial production[1 2] So far the vast majority of industrial controllersare PID controllers or their second generations owing tothe advantages of simple structure strong robustness andeasy realization [3ndash5] However once the controller char-acteristics control scheme interference form and size arebasically fixed the quality of the control system dependson the setting of the controller parameters Therefore PIDparameter tuning and optimizing is one core issue for PIDcontroller design [6 7]

The parameter tuning methods for PID controller designfall into two basic categories conventional parameter tun-ing methods and intelligent optimization algorithms Con-ventional parameter tuning methods include the empiricalmethod upwards curvemethod critical ratiomethod damp-ing oscillatory method and relay feedback method [8] TheZ-Nmethod as an empirical parameter tuning method had avery strong impact on the actual control system practically allvendors and users of the PID controller apply it or its simplemodifications in controller tuning The Z-N method was

developed by Ziegler and Nichols in seminal paper [9] whichwas based on two ideas to characterize process dynamics bytwo parameters which are easily determined experimentallyand to calculate controller parameters from the processcharacteristics by a simple formula Although widely used inpractice conventional parameter tuning methods have largeovershoot poor correction accuracy and time-consumingtuning process [10ndash13]

With the development of the intelligent control theoryintelligent optimization algorithms started to be appliedin PID parameter tuning and optimizing and achievedincomparable results that the conventional parameter tuningmethods cannot obtain For example the genetic algorithm(GA) [14ndash16] particle swarm optimization (PSO) [17ndash19]tabu search algorithm (TSA) [20ndash22] bacterial foragingalgorithm (BFA) [23ndash25] ant colony algorithm (ACA) [26]artificial bee colony (ABC) algorithm [27] and BAT searchalgorithm [28] were adopted to optimize PID controllerparameters and had achieved much better performances

Although intelligent optimization algorithms possessmerits of strong robustness good universality and few lim-ited conditions for use some intelligent algorithms still havedefects such as premature convergence and slow convergence

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 1378783 11 pageshttpsdoiorg10115520191378783

2 Mathematical Problems in Engineering

rate For example the GA PSO and TSA are all stochasticsearch algorithms Their search processes are nondetermin-istic suffer from slow convergence and easily fall into thelocal optimal solution [29 30] The parameter settings ofthe GA and ACA have not clear theoretical basis andmost parameters still need to be determined by experienceand experiment The population individual of the PSO andBAT search algorithm lacks the mutation mechanism oncetrapped in the local extreme it is difficult to get rid of [31]The complexity of the ABC algorithm programming limitsits application to a certain extent In addition there are fewcontrolled process models that adopt the ABC algorithmfor PID parameter tuning and its generality is not high[32 33] To further improve the optimization performanceand overcome the defects of traditional algorithms Chinesescholar Sun Cheng-Yi et al raised the mind evolutionaryalgorithm (MEA) based on the genetic algorithm in 1998[34] The MEA is an evolutionary algorithm simulatingthe progress of human mind and has the positive andnegative feedback mechanism wherein the positive feedbackmechanism improves toward being more beneficial to thepopulation survival so as to consolidate and develop theevolution achievement The negative feedback mechanismprevents the premature convergence of the algorithm soas to avoid the situation in which the algorithm is caughtin the local optimal solution The structural parallelismof the MEA guarantees the high search efficiency of thealgorithm overcomes the defects of the GA such as time-consuming computation and premature convergence andalso has extremely strong robustness on interference [35 36]

While theory application and engineering practices haveproved that the MEA has very high search efficiency andconvergence performance [37ndash39] few researches apply it tothe PID parameter tuning and optimizing Therefore thispaper is undertaken to establish a parameter tuning methodusing the MEA for PID controller design to fill the researchgap

The rest of this article is organized as follows Theprinciple of the MEA and MEA-tuning process for PIDcontroller design are described in Section 2 Three classicalfunctions are used to test the performance of the MEA andcompare it with the GA in Section 3 The MEA is appliedto the parameters tuning of five classical PID controllersand compared with the GA and traditional Z-N method inoptimization performance convergence time and robustnessin Section 4 Finally conclusions are drawn and futureresearches are suggested in Section 5

2 Mind Evolutionary Algorithm

21 Algorithm Principle The mind evolutionary algorithm(MEA) is a kind of evolutionary algorithm simulating theprogress of the human mind developed on the basis of theGA The MEA uses two types of operation similar taxisand dissimilation and uses population optimizing insteadof individual optimizing which avoids the defects of theGA The similar taxis operation is a process in which theindividual competes to be a winner which happens withinthe scope of a subpopulation The dissimilation operation

is the process in which a subpopulation competes to be awinner and continuously explores the new point of solutionspace which happens within the whole solution spaceIn the course of the algorithm running the similar taxisand dissimilation operation is executed repeatedly until thecondition of terminating the running of algorithm is satisfied

Compared with the GA the MEA has following advan-tages the crossover and mutation operations of the GAgenerate not only superior genes but also inferior destructivegenes and those operations have duality but the MEAuses the similar taxis and dissimilation operations whichamend the defects of the GA the similar taxis and dis-similation operations of the MEA are coordinated mutuallybut also independent mutually and any improvement onany aspect will raise the algorithmrsquos prediction accuracy thesimilar taxis and dissimilation operations have parallelismon structure which raises the algorithmrsquos search efficiencyand computation speed the MEA divides the populationsinto superior subpopulations and temporary subpopulationswhich can memorize evolutionary information more thanone generation

22 Basic Concepts The MEA follows some basic conceptsof the GA such as ldquopopulationrdquo ldquoindividualrdquo and ldquoenviron-mentrdquo but meanwhile it also adds some new concepts

221 Population and Subpopulation The MEA is a kindof learning method making optimization through iterationand all individuals in every generation of the evolutionaryprocess gather into one population A population is dividedinto several subpopulations The subpopulation contains twoclasses superior subpopulation and temporary subpopula-tion The superior subpopulation records the information ofthe winners in the global competition and the temporarysubpopulation records the process of the global competition

222 Billboard Thebillboard is equivalent to an informationplatform which provides chances of information communi-cation between the individuals or the subpopulations Thebillboard records three types of effective information theserial number of individual or subpopulation the action andthe score By utilizing the serial number of the individualor subpopulation it is convenient to distinguish differentindividuals or subpopulations the description of actionvaries from different research fields and since this articleis researching the problem of parameter optimization theaction is used to record the exact position of the individualand subpopulation the score is the evaluation of environmenton the individual action and in the optimization process byutilizing the MEA it can rapidly find out the optimized indi-viduals and populations only if the scores of every individualand subpopulation are recorded all the time The individualsin the subpopulation post up their own information on thelocal billboard and the information of each subpopulation isposted up on the global billboard

223 Similar Taxis Within the scope of a subpopulationthe process in which an individual competes to be a winneris called similar taxis In the process of a subpopulationrsquos

Mathematical Problems in Engineering 3

Meet theterminationcondition

Determine PID controllerstopological structure

Determine parameters ofthe PID controller

Obtain the optimalindividual

Verify the quality of PIDcontroller


Encode parameters aspopulation individual

Randomly initialize thepopulation individuals

No

Similar taxis operation of thetemporary subpopulations

Similar taxis operation of thesuperior subpopulations

Simulation of PID controller

Dissimilation operation

YesYes

No

PID ControllerMind evolutionary algorithm

Generate superior subpopulationsand temporarysubpopulations

Decode to obtain optimalparameter Kp Ki and Kd

Figure 1 Parameter tuning process of the PID controller by the MEA

similar taxis if a new winner cannot be generated this meansthat such subpopulation has maturedWhen a subpopulationmatures the similar taxis process of such subpopulationcomes to an endThe period of a subpopulation from its birthto maturity is called as lifetime

224 Dissimilation In the whole solution space each sub-population competes to be a winner and continuouslyexplores a new solution space point this process is knownas dissimilation Dissimilation has two definitions eachsubpopulation makes global competition and if the scoreof a temporary subpopulation is higher than the score ofa certain matured superior subpopulation such superiorsubpopulation will be replaced by the winning temporarysubpopulation and the individuals of the original superiorsubpopulation will be released if the score of a maturedtemporary subpopulation is lower than the score of anysuperior subpopulation such temporary subpopulation willbe abandoned and the individuals therein will be releasedthe released individuals will re-search and form a newtemporary subpopulation

23 Calculation Procedure The quality of the PID controllerdepends on the tuning and optimizing of parameters 119870119901119870119894 and 119870119889 To obtain the optimal PID controller theparameters 119870119901 119870119894 and 119870119889 are encoded and taken as thepopulation individual the integral of time absolute errors(ITAE) obtained from the PID controller is regarded as theindividual fitness value and then the MEA begins to evolveThrough continuous iterative evolution of the similar taxis

and dissimilation operation the optimal individual of thepopulation is finally obtained which is taken as the parameterof the PID controller after being decoded the optimal PIDcontroller is established

The tuning process of the PID controller by using theMEA is shown as Figure 1

Step 1 (initialization of the populationrsquos individual) Theparameters 119870119901 119870119894 and 119870119889 of PID controller coding in thereal number are taken as the population individual andthe integral of time absolute errors (ITAE) is regarded asthe individual fitness value and then N initial populationrsquosindividuals are generated randomly

Step 2 (generation of the superior subpopulation and tem-porary subpopulation) According to the individual fitnessvalue the 119873119904 superior individuals with the highest scoresand 119873119905 temporary individuals with the next highest scoresare picked out Taking each superior individual or tem-porary individual as center new individuals are producedand 119873119904 superior subpopulations and 119873119905 temporary sub-populations are formed named as 119866119904 and 119873119905 respec-tively The number of individuals in the subpopulation is119873119901 = N(119873119904+119873119905)Step 3 (similar taxis) To compute the fitness values of allindividuals in the superior subpopulation and temporarysubpopulation the optimal population 119892119904lowast or 119892119905lowast (namelythe center) in the subpopulation is taken as the center ofthe subpopulation and the score of the optimal individual is


taken as the score of such subpopulation The fitness valuesof 119892119904lowast and 119892119905lowast are described as below

119891119904lowast = min (119891 (119892) 119892 isin 119866119904) 1 le 119904 le 119873119904 (1)


Step 4 (judgment of subpopulationrsquos maturity) In the processof subpopulation similar taxis when the population centeris the optimal individual and no new superior individual isgenerated any more then such subpopulation matures andturns into the next step otherwise it turns into the previousstep and executes the similar taxis operation again

Step 5 (dissimilation) After the subpopulation matures thescore of each subpopulation will be posted up on the globalbillboard and if the score of any temporary subpopulation119866119905 is higher than the score of any matured superior subpop-ulation 119866119904 such superior subpopulation 119866119904 will be replacedby the winning temporary subpopulation 119866119905 the individualsin the original superior subpopulation 119866119904 will be releasedthe originally winning temporary subpopulation 119866119905 will bereplaced by the new temporary subpopulation 1198661199051015840 and theindividuals in 1198661199051015840 will be evenly distributed in the solutionspace

Step 6 (iterative evolution) The superior subpopulation withthe highest fitness value in all superior subpopulations ortemporary subpopulations is selected to judge whether thetermination condition is satisfied If yes the evolution willbe terminated and if not the operation of Steps 3sim5 will berepeated

Step 7 (decoding of the optimal individual and establishingof the PID controller optimized by the MEA) When thetermination condition of the MEA is met the superiorsubpopulation center as the optimal population individualwill be decoded to obtain the parameters 119870119901 119870119894 and 119870119889of the PID controller and the optimized PID controller isestablished

3 Classical Test Functions Verification

In order to verify the validity of theMEA 3 classical functionsare selected for testing and compared with the GA The testfunctions are the Sphere function Rastrigin function andRosenbrock function

(1) The Sphere Function

119891 (119909 119910) = 1199092 + 1199102 (3)

In formula (3) x 119910 isin [minus10 10] when (xy)=(00) theSphere function reaches its minimum 0 (Figure 2)

(2) The Rastrigin Function

119891 (119909 119910) = 20 + 1199092 minus 10 cos (2120587119909) + 1199102minus 10 cos (2120587119910)

(4)

minus10minus5

05

10

minus10minus5

05

100

50

100

150

200

Figure 2 Sphere function graph

minus10minus5

05

minus10minus5

050

20

40

60

80

Figure 3 Rastrigin function graph

In formula (4) x yisin[-512512] the global optimalsolution of the Rastrigin function is 0 distributed at (00)(Figure 3)

(3) The Rosenbrock Function

119891 (119909) =119873minus1

sum119894=1

(1199092119894 minus 119909119894+1)2 + (1 minus 119909119894)2 (5)

In formula (5) x 119910 isin [minus10 10] the Rosenbrock functionis a pathological function that is hard to minimize and thetheoretical global minimum is 0 (Figure 4)

TheMEA is established due to the defect of theGA so thispaper makes a comparative test between the MEA and GAto verify the superiority of the MEA In the test parametersof the MEA and GA are set as follows evolution generationsitermax=10 population size N=200 number of superior sub-population Ns=5 number of temporary subpopulation Nt=5subpopulation size Np=20 crossover probability C=02 andmutation probability M=01 The testing results are displayedin Table 1

As shown in Table 1 the test results of three classicalfunctions prove that the optimization performance of theMEA is better than the GA In Figure 5 the fitness evolution


Table 1 Optimization results and comparison for the MEA and GA

Function Theoretical extreme MEA GAMean value Optimal value Worst value Mean value Optimal value Worst value

Sphere 0 13396 00004 47535 21702 01306 22877Rastrigin 0 59375 01557 102223 59935 20612 176934Rosenbrock 0 10562 00010 92253 25015 65593 56020

minus10minus5

05

10

minus10minus5

05

100

5000

10000

15000

Figure 4 Rosenbrock function graph

2 3 4 5 6 7 8 9 101Iterations

0

1

2

3

4

5

6

7

8

9

10

Fitn

ess

MEAGA

Figure 5 Evolutionary curves of optimal fitness for the Rosenbrockfunction

curves of the Rosenbrock function show that comparedwith the GA the MEA has faster convergence speed andhigher convergence precision The experimental results indi-cated that due to its superior design feature and parallelstructure the MEA could memorize more evolutionaryinformation and search the optimal solution more efficientlyand effectively overcoming the defects of the GA such asprecociousness easiness of falling into the local extremumand time-consuming computation

PIDr(t) e(t) u(t) c(t)

Gp(s)

Figure 6 PID control system

4 Simulation Studies

41 PID Controller and Performance Index The proportionalintegral derivative (PID) controller is widely applied in indus-trial processes The system structure of the PID controller isshown in Figure 6

The general form of one PID controller is shown as below

119906 (119905) = 119870119901119890 (119905) + 119870119894 int119905

0119890 (120591) 119889120591 + 119870119889 119889119890 (119905)119889119905 (6)

In formula (6) u(t) and e(t) represent the control signaland error signal and KpKi andKd are the proportional gainintegral gain and derivative gain respectively By enteringparameters Kp Ki and Kd the control signal is calculatedand then sent to the controlling module the controlledobject is driven If the controller is designed properly thecontrol signal will make the output error converge to asmall neighborhood of the origin to achieve the controlrequirementTherefore the optimization objective of the PIDcontroller is to obtain an optimal set of parameters (KpKi Kd) which will minimize the performance function bysearching the given controller parameters space

In general integration error indexes include the integralof squared errors (ISE) integrated absolute errors (IAE) andintegral of time absolute errors (ITAE) [40] In this paperthe ITAE is chosen as the performance indicator of the PIDcontroller The formula for calculation is as follows

119868119879119860119864 = int119879

0119905 |119890 (119905)| 119889119905 (7)

If the functional model on error is regarded as a lossfunction the integral index of formula (7) can be regardedas the control goal of a control system when it is transferredfromone state to another then it is considered that the systemhas the optimal control law with a minimal performanceindex Generally the adjustment time ts corresponding to 5or 2 error is taken as the upper bound T parameter of theintegral

Due to the existence of absolute error |119890(119905)| formula (7)is difficult to solve by the analytic method and the numericalmethods are usually chosen to solve it the specific stepsare as follows the continuous time is discretized with timestep Δ119905 meanwhile when the time 119879 = 119898Δ119905 and m are


Table 2 Models for general controlled processes

Type Mathematical model Model features

I119890minus1205911199041 + 119904 First-order time-delay process

120591=0512 120591=05 in this study

II119890minus120591119904(1 + 119904)2 Second-order time-delay process

120591=0512 120591=1 in this study

III119890minus119904

119904(1 + 119904) Nonoscillating process

IV1 minus 119886119904(1 + 119904)2 Nonminimum phase process

a=051 a=05 in this study

V1

(1 + 119904)119899 High-order process

n=468 n=6 in this study

the integers of the appropriate size the discrete time vectort[n](n=12 m) is obtained When t is small enough theITAE can be calculated according to

119868119879119860119864 =119898

sum119894=0

119905 [119894] |119890 [119894]| Δ119905 (8)

The process of PID parameter tuning using the MEA isactually an optimization problemThe parameter set (Kp KiKd) is regarded as the particle position vector P(KpKiKd)in the optimization space Kp Ki and Kd are restrictedto [0 Kpm] [0 Kim] and [0 Kdm] respectively and theITAE performance index is chosen as the fitness functionof the algorithm Through the iteration of the MEA a setof parameters that minimize the ITAE value of the systemresponse is found

42 Simulation Experiment In order to verify the controlperformance of the MEA 5 typical industrial process controlmodels Gp(s) are selected as the research models as shownin Table 2 Five typical industrial process control models areself-balanced and nonoscillating process with time lag of thefirst order self-balanced and nonoscillating process with timelag of the second order nonoscillating process without self-balance nonminimum phase process with reverse character-istics and high-order process

According to the structural characteristics of the PIDcontroller the parameters to be optimized are Kp Ki andKd Then the parameters Kp Ki and Kd are encoded as thepopulation individual the individual length is 3 equal toparameter number In order to compare algorithm perfor-mance different algorithms need to set the same experimen-tal conditions so the population size is set to 200 the numberof superior population or temporary population size is 5 thesubpopulation size is 20 the evolution generations are set to10 the crossover probability is set to 02 and the mutationprobability is set to 01

(1) Industrial Process Control Model ITheMEA GA and Z-Nmethods were adopted to search the optimal PID parameters

MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

Am

plitu

de

Figure 7 Closed-loop step response with process I

of industrial process control model I respectively the PIDparameters (Kp Ki Kd) and performance indexes (ITAE ts)obtained were listed in Table 3

Table 3 shows that the MEA-tuning method has the bestfitting performance (ITAE=03463) and the fastest conver-gence speed (ts=26910) followed by the GA-tuning method(ITAE=05758 ts=56440) and the Z-N-tuning method(ITAE=07332 ts=62987)

The obtained PID parameters (Kp Ki Kd) were broughtinto process model I and the unit step responses of the MEAGA and Z-N methods are obtained respectively throughSimulink (Figure 7) Figure 7 also proves that the MEA-tuning method controls process control model I more stablyand faster

(2) Industrial Process Control Model II The optimal PIDparameters (Kp Ki Kd) and performance indexes (ITAE


Table 3 PID parameters and performances of industrial process control model I

Parameter MEA GA Z-N119870p 17898 17449 22800Ki 13770 15492 26576Kd 02788 04228 04890ts 26910 56440 62987ITAE 03463 05758 07332

Table 4 PID parameters and performances of industrial process control model II


MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)

Figure 8 Closed-loop step response with process II

ts) tuned by the MEA GA and Z-N methods are obtainedas shown in Table 4 The performance indexes (ITAEts) obtained by the MEA GA and Z-N methods are(ITAE=28671 ts=90798) (ITAE=32592 ts=95050) and(ITAE=39535 ts=135319) respectively Obviously the MEA-tuningmethod has the least ITAE and the fastest search speed

In order to further verify the effectiveness of the MEASimulink was used to investigate the unit step responseof typical model control system II The results show thatcompared with the GA and Z-Nmethods theMEA canmakeprocess control model II reach a stable state more quickly(Figure 8)

(3) Industrial Process Control Model III The optimal PIDparameters (Kp Ki Kd) and performance indexes (ITAEts) of industrial process control model III were obtained

by the MEA GA and Z-N methods and listed in Table 5Compared with the GA method (ITAE=237167) and Z-N method (ITAE=237657) the MEA method can greatlyimprove the control performance (ITAE=112763) and thesearch speed of the MEA method is also improved slightly(ts=152005) The unit step responses also show that theMEA method tunes process control model III with a smallerfluctuation range and faster convergence speed (Figure 9)

(4) Industrial Process Control Model V The optimal PIDparameters (Kp Ki Kd) and performance indexes (ITAE ts)of industrial process control model V were obtained by theMEA GA and Z-Nmethods and listed in Table 6 Comparedwith the GA method (ITAE=24037 ts=72594) and Z-Nmethod (ITAE=24623 ts=87442) the MEA method hasless ITAE and shorter calculation time greatly improvingthe control performance (ITAE=07536) and search speed(ts=33309) The GA has a slight advantage over the Z-Nmethod but it is not significant The unit step responses alsoshow that the MEA method tunes process control model Vwith a smaller fluctuation range and faster convergence speed(Figure 10)

(5) Industrial Process Control Model IVTheMEA GA and Z-N methods were used to search the optimal PID parametersof industrial process control model IV respectively then thePID parameters (Kp Ki Kd) were obtained and put intoprocess control model IV through Simulink the performanceindexes (ITAE ts) were obtained and listed in Table 7

Compared with the GA (ITAE=194274 ts=181772) andZ-Nmethod (ITAE=213847 ts=200000) theMEA improvesthe control performance and computing speed but not bymuch (ITAE=157474 ts=161596) The unit step responsesalso show that none of the three methods achieve completecontrol of process control model IV within 20 seconds butthe MEA method has the smallest fluctuation range and thebest performance (Figure 11)

The above simulation results show that during the opti-mization process the MEA constantly searches for betterparameters and the ITAE index decreases continuously


Table 5 PID parameters and performances of industrial process control model III


Table 6 PID parameters and performances of industrial process control model V


MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

16

18

Am

plitu

de

Figure 9 Closed-loop step response with process III

finally the unstable controlled object gradually reaches asteady state this proves that the MEA-tuning PID controllerwell realizes the tuning and optimization of the controlledobject Compared with the GA and Z-N methods the MEAcan obtain satisfactory PID parameters for control systemswithin a few generations the ITAE obtained is lower and theconvergence speed is faster Therefore the MEA is superiorto the GA and Z-N methods

5 Conclusion

The performance of the traditional PID control dependson the set of the parameters therefore an MEA-tuningmethod is proposed to search globally the optimal controllerparameters The MEA approach has superior design featuresand parallelism on structure which raises the efficiency andeffectiveness for searching global optimal parameters In

MEAGAZ-N

minus04

minus02

0

02

04

06

08

1

12

14

16

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)

Figure 10 Closed-loop step response with process V

order to verify the performance of the MEA three classicalfunctions and five typical industrial process control modelsare employed for simulation and testing the simulationresults were compared with those of the GA and Z-Nmethods The main results and conclusions are summarizedas follows

The experimental results of three classical functions(Sphere function Rastrigin function and Rosenbrock func-tion) indicate that the MEA has faster convergence speedand higher convergence precision than the GA due to thesuperior design feature and parallel structure the MEA canmemorize more evolutionary information and search theoptimal solution more efficiently and effectively overcomingthe defects of the GA such as precociousness easinessof falling into the local extremum and time-consumingcomputation


Table 7 PID parameters and performances of industrial process control model IV


MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)

Figure 11 Closed-loop step response with process IV

The simulation experiments of five typical industrialprocess control models also show that the MEA can capturebetter PID parameters (Kp Ki Kd) and lower ITAE theMEA-tuning PID controller well realizes the tuning andoptimization of the controlled object the unstable controlledobject gradually reaches a steady state meanwhile the MEAis superior to the GA and Z-N methods in speed andoptimization performance

Experiments indicated that the MEA-tuning methodproposed in this study is feasible and valid which offers apractical and novel approach for the design of the tradi-tional PID controller However future work should focuson the comparison researches between the MEA and otherintelligent algorithms other PID controllers such as thePSO-PID controller TSA-PID controller BFA-PID con-troller ACA-PID controller and ABC-PID controller shouldbe introduced into the tuning and optimization of thetraditional PID controller and compared with the MEA-PID controller to verify its effectiveness and advantageMoreover the MEA approach should be further tested anddeveloped through other practical application fields such asregression fitting pattern recognition and job planning andscheduling

Abbreviations

PID Proportional integral derivativeMEA Mind evolutionary algorithmZ-N Ziegler and NicholsGA Genetic algorithmPSO Particle swarm optimizationTSA Tabu search algorithmBFA Bacterial foraging algorithmACA Ant colony algorithmITAE Integral of time absolute errorsISE Integral of squared errors

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This research was funded by theNational Social Science Fundof China (Grant No 17BGL202)

References

[1] S Bennett ldquoThe past of PID controllersrdquo Annual Reviews inControl vol 25 pp 43ndash53 2001

[2] V Chopra S K Singla and L Dewan ldquoComparative analysisof tuning a PID controller using intelligent methodsrdquo ActaPolytechnica Hungarica vol 11 no 8 pp 235ndash249 2014

[3] M J Er and Y L Sun ldquoHybrid fuzzy proportional-integralplus conventional derivative control of linear and nonlinearsystemsrdquo IEEETransactions on Industrial Electronics vol 48 no6 pp 1109ndash1117 2001

[4] M Kushwah and A Patra ldquoTuning PID controller for speedcontrol of DC motor using soft computing techniques-Areviewrdquo Advance in Electronic and Electric Engineering vol 4no 2 pp 141ndash148 2014

[5] C Zou C Manzie and D Nesic ldquoA Framework for Sim-plification of PDE-Based Lithium-Ion Battery Modelsrdquo IEEETransactions on Control Systems Technology vol 24 no 5 pp1594ndash1609 2016

[6] J B Odili M N M Kahar and A Noraziah ldquoParameters-Tuning of PID controller for automatic voltage regulators usingthe African buffalo optimizationrdquo PLoS ONE vol 12 no 4 pe0175901 2017


[7] Y Luo and Z Chen ldquoOptimization for PID control param-eters on hydraulic servo control system based on the novelcompound evolutionary algorithmrdquo in Proceedings of the 2ndInternational Conference on Computer Modeling and Simulation(ICCMS rsquo10) pp 40ndash43 IEEE January 2010

[8] T Hagglund and K J Astrom ldquoRevisiting the Ziegler-Nicholstuning rules for PI controlrdquo Asian Journal of Control vol 4 no4 pp 364ndash380 2002

[9] J G Ziegler andN BNichols ldquoOptimum settings for automaticcontrollersrdquo Journal of Dynamic Systems Measurement andControl vol 46 no 2B pp 220ndash222 1993

[10] A Giwa and S Karacan ldquoDecoupling PID control of a reactivepacked distillation columnrdquo International Journal of Engineer-ing amp Technical Research vol 1 no 6 2012

[11] M Korkmaz O Aydogdu and H Dogan ldquoDesign and per-formance comparison of variable parameter nonlinear PIDcontroller and genetic algorithm based PID controllerrdquo inProceedings of the 2012 International Symposium on Innovationsin Intelligent Systems and Applications (INISTA) pp 1ndash5 IEEETrabzon Turkey July 2012

[12] S Y S Hussien H I Jaafar N A Selamat F S Daudand A F Z Abidin ldquoPID control tuning via Particle SwarmOptimization for coupled tank systemrdquo International Journal ofSoft Computing amp Engineering vol 4 no 2 pp 202ndash206 2014

[13] M W Foley R H Julien and B R Copeland ldquoA comparisonof PID controller tuning methodsrdquo The Canadian Journal ofChemical Engineering vol 83 no 4 pp 712ndash722 2010

[14] A Harrag and S Messalti ldquoVariable step size modified PampOMPPT algorithm using GA-based hybrid offlineonline PIDcontrollerrdquoRenewableamp Sustainable Energy Reviews vol 49 pp1247ndash1260 2015

[15] X H Liu X H Chen X H Zheng S P Li and Z BWang ldquoDevelopment of a GA-Fuzzy-Immune PID Controllerwith Incomplete Derivation for Robot Dexterous Handrdquo TheScientific World Journal vol 2014 Article ID 564137 10 pages2014

[16] C-H Cheng P-J Cheng and M-J Xie ldquoCurrent sharing ofparalleled DC-DC converters using GA-based PID controllersrdquoExpert Systems with Applications vol 37 no 1 pp 733ndash7402010

[17] S Ahmadi S Abdi andM Kakavand ldquoMaximum power pointtracking of a proton exchange membrane fuel cell system usingPSO-PID controllerrdquo International Journal of Hydrogen Energyvol 42 no 32 pp 20430ndash20443 2017

[18] I Atacak and B Kucuk ldquoPSO-based PID controller design foran energy conversion system using compressed airrdquo Tehnickivjesnik vol 24 no 3 pp 671ndash679 2017

[19] Y Ye C-B Yin Y Gong and J-J Zhou ldquoPosition control ofnonlinear hydraulic system using an improved PSO based PIDcontrollerrdquo Mechanical Systems and Signal Processing vol 83pp 241ndash259 2017

[20] A Ates and C Yeroglu ldquoOptimal fractional order PID designvia Tabu Search based algorithmrdquo ISA Transactions no 60 pp109ndash118 2016

[21] O Roeva and T Slavov ldquoPID controller tuning based onmetaheuristic algorithms for bioprocess controlrdquo Biotechnologyamp Biotechnological Equipment vol 26 no 5 pp 3267ndash32772012

[22] A Bagis ldquoTabu search algorithm based PID controller tuningfor desired system specificationsrdquo Journal of The FranklinInstitute vol 348 no 10 pp 2795ndash2812 2011

[23] D H Kim ldquoHybrid GA-BF based intelligent PID controllertuning for AVR systemrdquo Applied Soft Computing vol 11 no 1pp 11ndash22 2011

[24] A Shamel andN Ghadimi ldquoHybrid PSOTVACBFA techniquefor tuning of robust PID controller of fuel cell voltagerdquo IndianJournal of Chemical Technology no 23 pp 171ndash178 2016

[25] E S Ali and S M Abd-Elazim ldquoBFOA based design of PIDcontroller for two area Load FrequencyControl with nonlinear-itiesrdquo International Journal of Electrical Poweramp Energy Systemsno 51 pp 224ndash231 2013

[26] M Unal H Erdal and V Topuz ldquoTrajectory tracking perfor-mance comparison between genetic algorithm and ant colonyoptimization for PID controller tuning on pressure processrdquoComputer Applications in Engineering Education vol 20 no 3pp 518ndash528 2012

[27] A S Oshaba E S Ali and S M Abd Elazim ldquoPI controllerdesign using ABC algorithm for MPPT of PV system supplyingDCmotor pump loadrdquoNeural Computing and Applications vol28 no 2 pp 353ndash364 2017

[28] A S Oshaba E S Ali and S M Abd Elazim ldquoPI controllerdesign for MPPT of photovoltaic system supplying SRM viaBAT search algorithmrdquoNeural Computing andApplications vol28 no 4 pp 651ndash667 2017

[29] N Yusup AM Zain and S Z M Hashim ldquoEvolutionary tech-niques in optimizing machining parameters review and recentapplications (2007ndash2011)rdquoExpert Systems with Applications vol39 no 10 pp 9909ndash9927 2012

[30] A K Dwivedi S Ghosh and N D Londhe ldquoReview andAnalysis of Evolutionary Optimization-Based Techniques forFIR Filter Designrdquo Circuits Systems and Signal Processing pp1ndash22 2018

[31] B J Saharia H Brahma and N Sarmah ldquoA review of algo-rithms for control and optimization for energy managementof hybrid renewable energy systemsrdquo Journal of Renewable andSustainable Energy vol 10 no 5 p 053502 2018

[32] D Karaboga B Gorkemli C Ozturk and N Karaboga ldquoAcomprehensive survey artificial bee colony (ABC) algorithmand applicationsrdquo Artificial Intelligence Review vol 42 pp 21ndash57 2014

[33] Z Li W Wang Y Yan and Z Li ldquoPS-ABC A hybrid algo-rithm based on particle swarm and artificial bee colony forhigh-dimensional optimization problemsrdquo Expert Systems withApplications vol 42 no 22 pp 8881ndash8895 2015

[34] C Sun Y Sun and L Wei ldquoMind-evolution-based machinelearning framework and the implementation of optimizationrdquoinProceedings of the IEEE International Conference on IntelligentEngineering Systems (INESrsquo98) pp 355ndash359 1998

[35] C Sun X Zhou and W Wang ldquoMind evolutionary com-putation and applicationsrdquo Journal of Communication andComputer vol 1 no 1 pp 13ndash21 2004

[36] XZhou andC Sun ldquoPareto-MECand its convergence analysisrdquoJisuanji GongchengComputer Engineering vol 33 no 10 pp233ndash236 2007

[37] H Liu H Tian X Liang and Y Li ldquoNew wind speedforecasting approaches using fast ensemble empirical modeldecomposition genetic algorithm Mind Evolutionary Algo-rithm and Artificial Neural Networksrdquo Journal of RenewableEnergy vol 83 pp 1066ndash1075 2015

[38] G Yan G Xie Y Qiu and Z Chen ldquoMEA based nonlinearitycorrection algorithm for the VCO of LFMCW radar levelgaugerdquo in Rough Sets Fuzzy Sets Data Mining and GranularComputing Springer Berlin Germany 2005


[39] G Li and W H Li ldquoFace occlusion recognition based onMEBMLrdquo Journal of Jilin University vol 44 no 5 pp 1410ndash14162014

[40] K J Astrom and T Hagglund PID Controllers Theory DesignAnd Tuning Instrument society of America Research TrianglePark NC USA 1995

Hindawiwwwhindawicom Volume 2018

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Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Submit your manuscripts atwwwhindawicom


rate For example the GA PSO and TSA are all stochasticsearch algorithms Their search processes are nondetermin-istic suffer from slow convergence and easily fall into thelocal optimal solution [29 30] The parameter settings ofthe GA and ACA have not clear theoretical basis andmost parameters still need to be determined by experienceand experiment The population individual of the PSO andBAT search algorithm lacks the mutation mechanism oncetrapped in the local extreme it is difficult to get rid of [31]The complexity of the ABC algorithm programming limitsits application to a certain extent In addition there are fewcontrolled process models that adopt the ABC algorithmfor PID parameter tuning and its generality is not high[32 33] To further improve the optimization performanceand overcome the defects of traditional algorithms Chinesescholar Sun Cheng-Yi et al raised the mind evolutionaryalgorithm (MEA) based on the genetic algorithm in 1998[34] The MEA is an evolutionary algorithm simulatingthe progress of human mind and has the positive andnegative feedback mechanism wherein the positive feedbackmechanism improves toward being more beneficial to thepopulation survival so as to consolidate and develop theevolution achievement The negative feedback mechanismprevents the premature convergence of the algorithm soas to avoid the situation in which the algorithm is caughtin the local optimal solution The structural parallelismof the MEA guarantees the high search efficiency of thealgorithm overcomes the defects of the GA such as time-consuming computation and premature convergence andalso has extremely strong robustness on interference [35 36]

While theory application and engineering practices haveproved that the MEA has very high search efficiency andconvergence performance [37ndash39] few researches apply it tothe PID parameter tuning and optimizing Therefore thispaper is undertaken to establish a parameter tuning methodusing the MEA for PID controller design to fill the researchgap

The rest of this article is organized as follows Theprinciple of the MEA and MEA-tuning process for PIDcontroller design are described in Section 2 Three classicalfunctions are used to test the performance of the MEA andcompare it with the GA in Section 3 The MEA is appliedto the parameters tuning of five classical PID controllersand compared with the GA and traditional Z-N method inoptimization performance convergence time and robustnessin Section 4 Finally conclusions are drawn and futureresearches are suggested in Section 5

2 Mind Evolutionary Algorithm

21 Algorithm Principle The mind evolutionary algorithm(MEA) is a kind of evolutionary algorithm simulating theprogress of the human mind developed on the basis of theGA The MEA uses two types of operation similar taxisand dissimilation and uses population optimizing insteadof individual optimizing which avoids the defects of theGA The similar taxis operation is a process in which theindividual competes to be a winner which happens withinthe scope of a subpopulation The dissimilation operation

is the process in which a subpopulation competes to be awinner and continuously explores the new point of solutionspace which happens within the whole solution spaceIn the course of the algorithm running the similar taxisand dissimilation operation is executed repeatedly until thecondition of terminating the running of algorithm is satisfied

Compared with the GA the MEA has following advan-tages the crossover and mutation operations of the GAgenerate not only superior genes but also inferior destructivegenes and those operations have duality but the MEAuses the similar taxis and dissimilation operations whichamend the defects of the GA the similar taxis and dis-similation operations of the MEA are coordinated mutuallybut also independent mutually and any improvement onany aspect will raise the algorithmrsquos prediction accuracy thesimilar taxis and dissimilation operations have parallelismon structure which raises the algorithmrsquos search efficiencyand computation speed the MEA divides the populationsinto superior subpopulations and temporary subpopulationswhich can memorize evolutionary information more thanone generation

22 Basic Concepts The MEA follows some basic conceptsof the GA such as ldquopopulationrdquo ldquoindividualrdquo and ldquoenviron-mentrdquo but meanwhile it also adds some new concepts

221 Population and Subpopulation The MEA is a kindof learning method making optimization through iterationand all individuals in every generation of the evolutionaryprocess gather into one population A population is dividedinto several subpopulations The subpopulation contains twoclasses superior subpopulation and temporary subpopula-tion The superior subpopulation records the information ofthe winners in the global competition and the temporarysubpopulation records the process of the global competition

222 Billboard Thebillboard is equivalent to an informationplatform which provides chances of information communi-cation between the individuals or the subpopulations Thebillboard records three types of effective information theserial number of individual or subpopulation the action andthe score By utilizing the serial number of the individualor subpopulation it is convenient to distinguish differentindividuals or subpopulations the description of actionvaries from different research fields and since this articleis researching the problem of parameter optimization theaction is used to record the exact position of the individualand subpopulation the score is the evaluation of environmenton the individual action and in the optimization process byutilizing the MEA it can rapidly find out the optimized indi-viduals and populations only if the scores of every individualand subpopulation are recorded all the time The individualsin the subpopulation post up their own information on thelocal billboard and the information of each subpopulation isposted up on the global billboard

223 Similar Taxis Within the scope of a subpopulationthe process in which an individual competes to be a winneris called similar taxis In the process of a subpopulationrsquos










No





YesYes

No























119891 (119909 119910) = 1199092 + 1199102 (3)




(4)

minus10minus5

05

10

minus10minus5

05

100

50

100

150

200


minus10minus5

05

minus10minus5

050

20

40

60

80




119891 (119909) =119873minus1

sum119894=1

(1199092119894 minus 119909119894+1)2 + (1 minus 119909119894)2 (5)








minus10minus5

05

10

minus10minus5

05

100

5000

10000

15000


2 3 4 5 6 7 8 9 101Iterations

0

1

2

3

4

5

6

7

8

9

10

Fitn

ess

MEAGA




Gp(s)





119906 (119905) = 119870119901119890 (119905) + 119870119894 int119905

0119890 (120591) 119889120591 + 119870119889 119889119890 (119905)119889119905 (6)



119868119879119860119864 = int119879

0119905 |119890 (119905)| 119889119905 (7)







120591=0512 120591=05 in this study


120591=0512 120591=1 in this study





V1




119868119879119860119864 =119898

sum119894=0

119905 [119894] |119890 [119894]| Δ119905 (8)





MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

Am

plitu

de











MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)















MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

16

18

Am

plitu

de



5 Conclusion


MEAGAZ-N

minus04

minus02

0

02

04

06

08

1

12

14

16

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)







MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)




Abbreviations


Data Availability




Acknowledgments


References


















































Journal of












Journal of







Volume 2018






Volume 2018

















No





YesYes

No























119891 (119909 119910) = 1199092 + 1199102 (3)




(4)

minus10minus5

05

10

minus10minus5

05

100

50

100

150

200


minus10minus5

05

minus10minus5

050

20

40

60

80




119891 (119909) =119873minus1

sum119894=1

(1199092119894 minus 119909119894+1)2 + (1 minus 119909119894)2 (5)








minus10minus5

05

10

minus10minus5

05

100

5000

10000

15000


2 3 4 5 6 7 8 9 101Iterations

0

1

2

3

4

5

6

7

8

9

10

Fitn

ess

MEAGA




Gp(s)





119906 (119905) = 119870119901119890 (119905) + 119870119894 int119905

0119890 (120591) 119889120591 + 119870119889 119889119890 (119905)119889119905 (6)



119868119879119860119864 = int119879

0119905 |119890 (119905)| 119889119905 (7)







120591=0512 120591=05 in this study


120591=0512 120591=1 in this study





V1




119868119879119860119864 =119898

sum119894=0

119905 [119894] |119890 [119894]| Δ119905 (8)





MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

Am

plitu

de











MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)















MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

16

18

Am

plitu

de



5 Conclusion


MEAGAZ-N

minus04

minus02

0

02

04

06

08

1

12

14

16

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)







MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)




Abbreviations


Data Availability




Acknowledgments


References


















































Journal of












Journal of







Volume 2018






Volume 2018



















119891 (119909 119910) = 1199092 + 1199102 (3)




(4)

minus10minus5

05

10

minus10minus5

05

100

50

100

150

200


minus10minus5

05

minus10minus5

050

20

40

60

80




119891 (119909) =119873minus1

sum119894=1

(1199092119894 minus 119909119894+1)2 + (1 minus 119909119894)2 (5)








minus10minus5

05

10

minus10minus5

05

100

5000

10000

15000


2 3 4 5 6 7 8 9 101Iterations

0

1

2

3

4

5

6

7

8

9

10

Fitn

ess

MEAGA




Gp(s)





119906 (119905) = 119870119901119890 (119905) + 119870119894 int119905

0119890 (120591) 119889120591 + 119870119889 119889119890 (119905)119889119905 (6)



119868119879119860119864 = int119879

0119905 |119890 (119905)| 119889119905 (7)







120591=0512 120591=05 in this study


120591=0512 120591=1 in this study





V1




119868119879119860119864 =119898

sum119894=0

119905 [119894] |119890 [119894]| Δ119905 (8)





MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

Am

plitu

de











MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)















MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

16

18

Am

plitu

de



5 Conclusion


MEAGAZ-N

minus04

minus02

0

02

04

06

08

1

12

14

16

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)







MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)




Abbreviations


Data Availability




Acknowledgments


References


















































Journal of












Journal of







Volume 2018






Volume 2018












minus10minus5

05

10

minus10minus5

05

100

5000

10000

15000


2 3 4 5 6 7 8 9 101Iterations

0

1

2

3

4

5

6

7

8

9

10

Fitn

ess

MEAGA




Gp(s)





119906 (119905) = 119870119901119890 (119905) + 119870119894 int119905

0119890 (120591) 119889120591 + 119870119889 119889119890 (119905)119889119905 (6)



119868119879119860119864 = int119879

0119905 |119890 (119905)| 119889119905 (7)







120591=0512 120591=05 in this study


120591=0512 120591=1 in this study





V1




119868119879119860119864 =119898

sum119894=0

119905 [119894] |119890 [119894]| Δ119905 (8)





MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

Am

plitu

de











MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)















MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

16

18

Am

plitu

de



5 Conclusion


MEAGAZ-N

minus04

minus02

0

02

04

06

08

1

12

14

16

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)







MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)




Abbreviations


Data Availability




Acknowledgments


References


















































Journal of












Journal of







Volume 2018






Volume 2018












120591=0512 120591=05 in this study


120591=0512 120591=1 in this study





V1




119868119879119860119864 =119898

sum119894=0

119905 [119894] |119890 [119894]| Δ119905 (8)





MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

Am

plitu

de











MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)















MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

16

18

Am

plitu

de



5 Conclusion


MEAGAZ-N

minus04

minus02

0

02

04

06

08

1

12

14

16

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)







MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)




Abbreviations


Data Availability




Acknowledgments


References


















































Journal of












Journal of







Volume 2018






Volume 2018













MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)















MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

16

18

Am

plitu

de



5 Conclusion


MEAGAZ-N

minus04

minus02

0

02

04

06

08

1

12

14

16

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)







MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)




Abbreviations


Data Availability




Acknowledgments


References


















































Journal of












Journal of







Volume 2018






Volume 2018













MEAGAZ-N

2 4 6 8 10 12 14 16 18 200Time (sec)

0

02

04

06

08

1

12

14

16

18

Am

plitu

de



5 Conclusion


MEAGAZ-N

minus04

minus02

0

02

04

06

08

1

12

14

16

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)







MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)




Abbreviations


Data Availability




Acknowledgments


References


















































Journal of












Journal of







Volume 2018






Volume 2018











MEAGAZ-N

0

02

04

06

08

1

12

14

Am

plitu

de

2 4 6 8 10 12 14 16 18 200Time (sec)




Abbreviations


Data Availability




Acknowledgments


References


















































Journal of












Journal of







Volume 2018






Volume 2018



















































Journal of












Journal of







Volume 2018






Volume 2018


















Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








Documents

ResearchArticle An MEA-Tuning Method for Design of the PID … · 2019. 7. 30. · So far, the vast majority of industrial controllers are PID controllers or their second generations