ResearchArticle A GODFIP Control Algorithm for an IRC

Research ArticleA GODFIP Control Algorithm for an IRC Grain Dryer

Aini Dai12 Xiaoguang Zhou1 and Xiangdong Liu3

1School of Automation Beijing University of Posts and Telecommunications Beijing 100876 China2Science and Information College Qingdao Agriculture University Qingdao 266109 China3College of Engineering China Agricultural University Beijing 100083 China

Correspondence should be addressed to Xiaoguang Zhou zxg bupt126com

Received 25 March 2017 Revised 18 July 2017 Accepted 9 August 2017 Published 20 September 2017

Academic Editor Domenico Quagliarella

Copyright copy 2017 Aini Dai et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Drying is an energy intensive and complex nonlinear process and it is difficult to control and make the traditional control meetthe challenges In order to effectively control the output grain moisture content of a combined infrared radiation and convection(IRC) grain dryer taking into account the superiority of the fuzzy control method in dealing with complex systems in this articlea genetic optimization dual fuzzy immune PID (Proportional-Integral-Derivative) (GODFIP) controller was proposed from theaspects of energy savings stability accuracy and rapidityThe structure of the GODFIP controller consists of two fuzzy controllersa PID controller an immune algorithm and a genetic optimization algorithm In addition a NARXmodel which can give relativelygood predictive output information of the IRC dryer was established and used to represent the actual drying process to verify thecontrol performance in the control simulation and anti-interference tests The effectiveness of this controller was demonstrated bycomputer simulations and the anti-interference performance comparative study with the other controllers further confirmed thesuperiority of the proposed grain drying controller which has the least value of performance objective function the shortest risingtime and the best anti-interference ability compared to the other three compared controllers

1 Introduction

Grain drying control is very important because it candecrease the grain loss by controlling the grain moisture andtemperature to the desired level and maintain the qualityfreshness and longer life storage of grainThere are parameteruncertainties or variations in the grain dying process and theestablishment of a good control system for a grain dryer is dif-ficult Drying is an energy intensive process one of the maincontrol objectives is to dry the moisture content to desiredlevel with efficient energy consumption and good qualitybesides that stability of the system and robustness of thecontroller towards any disturbances are also the fundamentalrequirements of a dryer controller [1 2]

In this research the control object is a combined infraredradiation and convection (IRC) grain dryer designed byour research group which combines the direct and indirectheating drying technology Infrared radiation drying is a newdrying technology developed in recent 30 years and now hasbecome more popular because of its advantages such as its

low drying time the reasonable quality of the final driedproduct and its greater energy savings capability in additionto its lower price compared to microwave and vacuumdrying methods [3] So far the research scope of the infraredradiation drying technology mainly focuses on the studyof experiments and simulation of drying but there are nostudies in the aspect of infrared radiation grain drying control[4ndash11] In order to meet the drying control requirements ofthe IRC dryer effective control strategies for the grain dryershould be further researched on Usually in the whole graindrying process the speed of the discharging grain motor iscontrolled (ie the adjustment of the drying time of grain inthe dryer) to realize the drying target by detecting the errorand its rate of change between the desired and the actual grainoutput moisture content according to the correspondingcontrol algorithm

Traditional control methods have encountered a lot ofobstacles because grain drying is a complicated heat andmasstransfer process which is characterized by long delay processhighly nonlinearity multidisturbance strong coupling and

HindawiMathematical Problems in EngineeringVolume 2017 Article ID 1406292 14 pageshttpsdoiorg10115520171406292

2 Mathematical Problems in Engineering

so on It is difficult to make an accurate mathematical modelof grain drying so the control of grain drying is a challengingjob [2 12] Liu and Bakker-Arkema have also reviewedsome traditional control limitations such as the controllersdesigned by Marchant Whitfied McFarlane and Courtoiset al Indeed the classical feedback control is necessary butis inadequate for controlling grain dryer [2] The controleffect of the feed-forward control is much better than thatof the feedback control only but the accuracy of the feed-forward control is affected by whether or not the systemdisturbance is measurable [13] In addition Proportional-Integral-Derivative (PID) controller is successfully applied inthe classic automatic control and still used in the control ofgrain drying now but it relies on the mathematical modeland has some limitations of which the values of the controlparameters (1198961199011015840 1198961198941015840 1198961198891015840) are not changed in the wholecontrol process and when the controlled object and theenvironment are uncertain the PID controller will be difficultto achieve satisfactory control effect and difficult to reachthe control requirements with more strict restriction onovershoot Model-predictive control (MPC) is a compoundoptimization algorithm which is based on model rollingoptimization and feedback correction it will control outputchanges by tracking the change of the set valve so it iseffective for the nonlinear and large lag process control [2]In a series of Liu and Bakker-Arkemarsquos papers a model-predictive controller (MPC) was especially designed for graindrying The simulation and field tests both showed thatthe controller performed well over a wide range of dryingconditions The distributed-parameter process model thatthe MPC employs is more comprehensive than the lumpedparameter model and provides more detailed information onthe process but it requires more computation time and stillrelies on the accuracy of the system mathematical model [2]

In all a drawback of the above-mentioned studies isthat the authors generally made several simplifications indeveloping the dryer mathematical model based on someassumptions and observations These simplifications areexpected to affect the performance of these models andconsequently their reliability in representing the real processwhen using these models for control purposes Moreoverthe mathematical models generally consist of sets of highlycomplex and nonlinear partial differential equations (PDES)with several auxiliary algebraic equations that involve trans-fer coefficients and thermophysical properties that requirehighly complicated numerical techniques to solve renderingthem undesirable options in control systems [14]

Since the 1970s the research development of computercontrol technology and artificial intelligence has providednew ways for advanced control of the grain drying thereafterdrying control comes into the intelligent control period ofwhich the fuzzy logic controller (FLC) is a typical intelli-gent controller which imitates humansrsquo decision-making andcommon sense [15 16] The FLC does not need to know themathematical model of the controlled object and only needsto accumulate the experience data of a skilled human oper-ator which is the biggest difference from the conventionalcontrol In essence the FLC provides an algorithm whichcan convert the linguistic control strategy based on expert

knowledge into an automatic control strategyThe FLC is notonly widely used in industry but also a hot research topicin the control of grain drying now [17ndash25] Combining FLCalgorithmwith traditional control algorithms the problem ofgrain drying control can be effectively solved

Fuzzy immune PID controller based on the immunefeedback mechanism combines the intelligent FLC with thetraditional PID controller and has the advantages of simplegood robustness and independence on the system modelwhich uses the characteristics of fuzzy control to learn thebiological immune feedback mechanism under the complexdisturbance and uncertain environment [26ndash29] Howeverthe algorithm also has some limitations although the PIDcontrol parameters in the control process can be changed thechange rates of parameters are the same affecting the controlperformance to a certain extent Aiming at this limitationin this paper an improved fuzzy immune PID controller isdesigned to solve the limitation of the general fuzzy immunePID control algorithm

In all based on the idea of artificial intelligence thispaper proposes an improved fuzzy immune PID controllercombined with two kinds of evolutionary algorithms theimmune feedback algorithm and the genetic optimizationalgorithm which has improved the limitation of the tradi-tional PID controller and the general fuzzy immune PIDcontroller Because the algorithm adopts two kinds of fuzzycontroller and uses the genetic algorithm to optimize theinitial controller parameters of the model the proposedcontroller in this paper is called the genetic optimizationdual fuzzy Immune PID (GODFIP) controller Based onthe GODFIP the speed of discharging grain motor can beautomatically adjusted to achieve the precise control of theoutput grain moisture of the IRC grain dryer according tothe difference and its change rate between the output grainmoisture content and the target moisture content Finally theNARX (Nonlinear Autoregressive models with ExogenousInputs) model is used to represent the actual drying processto test the effectiveness of the proposed controller and thecomparative study with the other related controllers is alsomade and the simulation results show that the control effectof GODFIP is better than that of other compared controllers

2 The Mathematical Model of Grain Dryingand Its Control Algorithm Structure

21 The Mechanical Structure of the New Grain Dryer TheIRC grain drying system has been put into use in HarbinDevelopment Zone Binxi town China Dongyu MachineryCo Ltd Fresh mature corns were purchased from a localfarm (an agricultural area in north of China)

The IRC grain dryer mechanism system is shown inFigure 1 It can be seen that the system mainly consists ofthe following parts a wet grain barn a grain dryer anddried grain barn and 3 elevators used to raise grains tothe barns and 5 belt machines used to transport of whichthe new radiation-convection grain dryer is rectangularityin shape and the overall dimensions are 475m in height206m in length and 13m in depth as shown in Figure 2

Mathematical Problems in Engineering 3

(1)

(2)

(3)(4)

(5)(6)

(7)

(10)

(9)

(8)

(11)

Figure 1 Mechanic structure diagram of the IRC grain dryer (1) Bucket elevator T1 (2) wet grain barn (3) belt conveyor P1 (4) bucketelevator T2 (5) belt conveyor P3 (6) belt conveyor P5 (7) dried grain barn (8) bucket elevator T3 (9) belt conveyor P4 (10) dryer and (11)belt conveyor P2

Cold air inlet

Electric control valve

Infrared radiationwaste gas

(13)

(12)Storage section

Convection section

Radiation section

Discharging grainsection

Graininlet

(7)

(9)

(10)

(8)

(11)

(1) (2)

(3)

(4)

(5) (6)Wastegasroom

Oilfurnace

Graindischargingwheel

Anglebox

Dryingwastegas

Combustionchamber

Figure 2 Scheme of the IRC grain dryer (1) Main hot air speed (2) Hot air temperature (3) Infrared exhaust gas temperature (4) Infraredexhaust gas velocity (5) Exhaust gas temperature and humidity (6) Drying waste gas (7) Inlet grain temperature and moisture (8) Outletgrain temperature and moisture (9) Postdrying grain temperature (10) Infrared grain temperature (11) Combustion tube temperature (12)Flue-gas temperature (13) Ambient temperature and humidity

Figure 2 is the schematic diagram of the IRC grain dryerwhich consists of four sections the storage grain section(08m in height) the convection section (11m in height) theradiation section (08m in height) and the discharging grain

section (12m in height) of which the convection section isa combination design and there are three kinds of dryingprocess to choose counter flow drying concurrent andcounter flow drying mix flow drying and the combustion


Control cabinet

Computer expert systemTouch screenComputer monitoring interface

Button and lightControl room

Figure 3 Controlling situation and equipment for the IRC grain dryer

furnace of radiation section is a side heat radiation typeequipped with some corresponding safety devices and can beautomatically ignited Capacitive moisture sensor is installedin the inlet and outlet of the grain dryer for the need ofcontrol and some other online sensors detecting the realdrying parameters are also installed as shown in Figure 2(numbers (1)ndash(13))

22 The Control System of the IRC Dryer The controllingsituation and some equipment for the grain dryer are shownin Figure 3 Programmable controller technology (PLC) +frequency converter are adopted in the control system andthe drying parameters can be real-time detected such asthe air temperature and humidity the grain moisture andtemperatureThe grain discharging speed is controlled by thefrequency converter (VFD-007M43B) installed in the controlcabinet whichworked in two operatingmodes (manualmodeor automatic mode) when working in manual mode long-term work experiences are generally needed to manuallyadjust the discharging grain speed to achieve the dryingtarget In automatic mode a reliable control algorithm is alsoneeded to automatically control the dryer

The control system of the IRC dryer is also equippedwith a computer which is connected with PLC (S7-300)through EthernetThe experimental data can be analyzed andprocessed in the computer and different drying algorithmscan be designed and tested

23 The Process of Radiation-Convection Grain Drying Asseen from Figures 1 and 2 the drying process is as follows(1) First raise the wet grain into the dryer from the wet grainbarn by the bucket elevator T2 and belt conveyors P2 andP3 when the upper limit grain level sensor is installed inthe storage section of the grain dryer alarms the wet grainfeeding is stopped and ready for drying (2) Secondly let oilfurnace heat the radiator and begin to carry out radiationdrying in the radiation section by use of the high temperatureof the radiator (3) Reuse the radiation exhaust gas of infraredradiation section and mix it with appropriate amount of coldair to achieve the regulation of the mixed air temperature bycontrolling the opening of solenoid valve and blow themixedair into the convection section through pipe to carry out theconvection drying in the convection section based on the heatandmass exchange principle (4) Finally start the discharginggrain wheel and other relevant devices then discharge thedried grain into the dried grain barn by the bucket elevatorT3 and belt conveyor P5 and end the drying

In the whole drying the speed of discharging grainmotor can be adjusted automatically by an intelligent controlalgorithm every time interval or adjusted manually by anexperience worker according to the detected drying parame-ters

24 The Identification Equation of Drying Process For thecomplex IRC grain dryer the description of the dynamicprocess of grain drying is more difficult It is an effective wayto learn the characteristics of the drying process by modelingthe input and output data [30]

241 Autoregressive Exogenous (ARX) AutoregressiveExogenous (ARX) model has been widely applied in theprediction control It does not need to know the physicalmechanism inside the complex process so it is regarded asa ldquoblack boxrdquo model It provides a fast and efficient solutionto the actual system output by means of a least squaresapproach and it has the advantages of simple structure andstrong robustness It is an autoregressive model which hasexogenous inputs and it relates the current output value ofa time series to past output values of the same series andcurrent and past values of the driving (exogenous) seriesMore details about ARX can be found in [31 32] The basicstructure of ARX model identification is shown in119860 (119911) 119910 (119896) = 119861 (119911) 119906 (119896) + 119890 (119896)

119860 (119911) = 1 + 119899119886sum119894=1

1198861119911minus119894119861 (119911) = 119911minus119905119889119899119887minus1sum

119895=0

119887119895119911minus119895(1)

where the ARX order is determined as [119899119886 119899119887 119905119889] 119899119886 is themodel order of 119860(119885) 119899119887 is the model order of 119861(119885) and119905119889 is the estimated pure time delay between the exogenousinput signal 119906(119896) and the output signal 119910(119896) 119890(119896) is a whitenoise term generally assumed to be Gaussian and White 119896represents the discrete time step

The input and output data for identification model ofgrain drying are from the drying experiment of the IRC graindryer (corn mixed flow and radiation) in December 4 2015a total of 384 sets of data and the sampling frequency is60HZ The input data of the identified drying model is thecurrent and past drying time of grain being experienced inthe dryer and the past output grain moisture content of the


grain dryer the output data of themodel is the current outputgrain moisture of the grain dryer real detected by the outputgrain moisture sensor which has been calibrated using the105∘C standard oven method (GB 5497-1985)

The corn of the drying experiment purchased from thelocal farmers is a natural harvest species number 1 XingXing(a breed name of corn) and its initial grain moisture contentis about 26 The ambient temperature is about minus 10∘Crelative humidity 60ndash70Thehot air temperature is between80 and 120∘C and the hot wind speed is 12ms

By using the identification toolbox in Matlab ident theidentified transfer function of the model is a two-order lagsystem as shown in (2) of which the identification modelorder is [2 2 1] (the input and output order are resp equalto 2 and the time delay 119905119889 is equal to 1) and 119860(119885) and 119861(119885)are as shown in (3) and (4)

119866 (119911) = 119861 (119885)119860 (119885) = 03799119911minus1 minus 03804119911minus21 minus 07471119911minus1 minus 02277119911minus2 times 119885minus1 (2)

119860 (119911) = 1 minus 07471119911minus1 minus 02277119911minus2 (3)

119861 (119911) = 03799119911minus1 minus 03804119911minus2 (4)

In this study we use mean squared error (MSE) andsquared correlation coefficient (119877) to evaluate the predictionperformance of the designed drying model shown in

MSE = 1119898119898sum119894=1

(119910119894 minus 119910119894)2 119877= radic (119898sum119898119894=1 119910119894119910119894 minus sum119898119894=1 119910119894sum119898119894=1 119910119894)2(119898sum119898119894=1 1199101198942 minus (sum119898119894=1 119910119894)2) (119898sum119898119894=1 1199101198942 minus (sum119898119894=1 119910119894)2)isin [0 1]

(5)

where119898 is the actual total number of the dataset and119910119894 and119910119894are actual and predicted values respectively the closer MSEis to zero the better the prediction performance of model isand the closer119877 (range from0 to 1) is to 1 the better themodelfits

Experimental model identification results are shown inFigure 4 The squared correlation coefficient 119877 between themodel and the measured data is equal to 955 and the MSEerror is equal to 229 lowast 10minus4 showing that the resulting linearmodel has a good approximation of the actual drying process

242 Nonlinear Autoregressive with Exogenous Input (NARX)Model The theory of linear systems identification is a rel-atively matured field [33] however as seen from Figure 4the ARX identified linear models can not adequately captureall the magnitudes of the real output response due to thehigh degree of nonlinearity of the system so in this paper anonlinearmodel known as theNonlinearAutoregressivewithExogenous input (NARX) model is developed

The NARX model has been proven to have a superiorperformance and has been successfully employed in solving

0 1 2 3 4 5 6 701

015

02

025

03

035

Time (h)

Out

put m

oistu

re co

nten

t

Measured and simulated model output

The predicted output of modelThe practical output of dryer

Figure 4 Fitting effect curve of the ARX model with the actualcurve

various types of complex nonlinearmodel problems in recentyears [34ndash38] The NARX model uses a nonlinear functionto predict the output grain moisture content of drying byregressing from the past values of system output 119910 and thepast values of exogenous input 119906 The form of the NARXmodel is shown in

119910 (119896) = 119891 [119910 (119896 minus 1) 119910 (119896 minus 2) 119910 (119896 minus 119899119886) 119909 (119896 minus 119905119889) 119909 (119896 minus 119905119889 minus 1) 119909 (119896 minus 119905119889 minus 119899119887 + 1)] (6)

where119891[∙] is a nonlinearmapping function that estimates theoutput 119910(119896) at time sample 119896 In this study the artificial neuralnetwork is used to regress the nonlinear function 119891[∙] TheNARX network model structure consists of an input layera hidden layer and an output layer of which the number ofhidden neurons is 10 and the time lags order for the inputand output series is 2 (ie 119899119886 = 119899119887 = 2) The architecture ofthe NARX model adopted in this study to predict the outputmoisture content is shown in Figure 5 where 119909(119905) is thesystem input (drying time) 119910(119905) is the system output (outputgrain moisture content) 119908 is the weights value 119887 is the biasvalue

In the case of modeling the input-output data of 384samples are randomly divided into three parts to develop aNARX model 268 training datasets 58 validation datasetsand 58 testing datasets During the training phase the pastinput and output data of training are presented to train andadjust the neural network by using the Levenberg-Marquardtalgorithm during validation the validation data are used tomeasure network generalization and to halt training whengeneralization stops improving during testing the testingdata have no effect on training data so an independentmeasure of network performance can be provided during andafter training

Table 1 andFigure 6 show the regression prediction resultsof the NARX model and it shows that the NARX model hashigh prediction accuracy of which the MSE and 119877 on testingdata are equal to 1062lowast10minus5 and 9978 respectively and thepredicted errors (the difference values between the predicted


+

b

W1

11

1

Hidden

+

Output

y(t)

y(t)

x(t)

W

W

b

10

1 2

1 2

Figure 5 The architecture of the NARX model

01015

02025

03035

Out

put a

nd ta

rget

50 100 150 200 250 300 350

0001

Erro

r

Number of sampling events (k)

50 100 150 200 250 300 350Number of sampling events (k)

minus001minus002

NARX model outputresponse

Practical dryer outputresponse

Test outputs of NARXmodel

Test outputs of dryer

Figure 6 The prediction results of the NARX model on the testingdata

Table 1 The simulation prediction results of the NARX model

Data Size Model prediction resultsMSE 119877

Training data 268 170 lowast 10minus5 9968Validation data 58 108 lowast 10minus5 9978Testing data 58 106 lowast 10minus5 9978

output values of model and the practical output values ofdryer) are basically within in plusmn1 These results indicate thatthe developed NARX model is considered as a much betterrepresentative for the nonlinear grain drying process than theARX model (MSE 229 lowast 10minus4 119877 955)

25 The Control Algorithm Structure of Grain Dryer Thereare many factors that affect the control performance of graindrying as shown in Figure 7 the main factors of whichare the grain initial temperature and inlet moisture theambient environment temperature and moisture the hotair and cooling air flow the hot air temperature and thespeed of discharging grain In addition the corn used inthe experiment is purchased from different local farmers and

each batch of grain moisture is different so it will easily leadto the variations of the grain moisture content in the dryerFurthermore the ambient temperature is below zero the iceinside the grain will affect the detection accuracy of the grainmoisture sensor Therefore grain drying is such a complexprocess that satisfactory control effect is difficult to achieve

Under a certain period of time and environmental con-ditions some variables can be thought to be unchanged fora certain batch of grain drying such as the grain initialtemperature and initial moisture content the ambient envi-ronment temperature and moisture the hot air temperaturehumidity and the hot air flow rate Usually in the engineeringpractice of grain drying the drying time is often taken as thecontrol variable and the output grain moisture content as theimportant controlled variable the other affection factors aretaken as the disturbance signals

The designed control scheme of this paper is shown inFigure 8 where the intelligent controller in this paper refersto the designed dual fuzzy immune PID controller and theimmune algorithm refers to the feedback control law 119890(119905)is the error between the output and the target value 119889119890119889119905is the change rate of 119890(119905) and the interference signal canbe the inlet grain moisture the ambient temperature andso on The drying time of grain in the dryer can be tunedby controlling the speed of the discharging grain motor inthe whole drying process according to the correspondingintelligent control algorithm to achieve the target value inaddition the controllerrsquos initial parameters are optimized bya genetic algorithm

3 Design of the Genetic Optimization DualFuzzy Immune PID (GODFIP) Controller

31 The General Fuzzy Immune PID Controller Design

311 Biological Immune Principle Biological immune systemcan produce antibodies against a foreign invasion of theantigen which plays the defense role The most importantcells in the immune system are the lymphocytes which aremainly two kinds B and T cells B cells are responsible forantibody production and carry out the immunity functionand T cells regulate the whole immune process T cells arecomposed of inhibit T cells (TS) and helper cells (TH) whichrespectively inhibit and help B cells respond to a stimulusWhen the antigen is increasing there are more TH cells and


The grain discharging speed

The hot air temperature

The initial grain moisture amp temperature

The hot air moisture

The hot air flowThe ambient environment temperature and moisture

Exhaust gas temperature

Exhaust gas moisture

Outlet grain moisture

Outlet grain temperature

DisturbanceInput Output

Graindryer

Figure 7 Factors affecting grain drying

Output

The discharging grain speed The target

Intelligent controller

Immune algorithm

The controlledobject

The interference signal

Genetic optimization

Frequency converter

e(t)

dedt

minus +

Figure 8 Block diagram of the control model scheme for the IRC grain dryer

less TS cells in the body which will produce more B cells thatis more antibodies when the antigen is gradually reducedTS cells will increase and inhibit the generation of TH cellsthereby reducing the B cells antibodies decreased When theantigen is eliminated the immune response is completed

Assuming that the 119896 generation amount of antigen is 120576(119896)the change rate of the number of antigens is Δ120576(119896) the outputof TH cells is TH(119896) the output of TS cell is TS(119896) accordingto the immune feedback mechanism the total stimulationreceived by B cells is 119878(119896) as shown in

119878 (119896) = TH (119896) minus TS (119896) (7)

Among them TH(119896) = 1198961120576(119896) TS(119896) = 1198962119891[120576(119896)Δ120576(119896)]120576(119896) 119891(sdot) is a nonlinear control function that repre-sents the ability to suppress external stimuli Its feedbackcontrol law is shown in (8) and thus is also called thenonlinear 119901-type controller

119878 (119896) = TH (119896) minus TS (119896)= 1198961 minus 1198962119891 [120576 (119896) Δ120576 (119896)] 120576 (119896)= 119896 1 minus 120578119891 [120576 (119896) Δ120576 (119896)] 120576 (119896) = 119870119901120576 (119896)

119870119901 = 119896 1ndash120578119891 [120576 (119896) Δ120576 (119896)] (8)

Among them 119896 = 1198961 is the speed of control response120578 = 11989611198962 is related to the stability of the response and119870119901 will change with the amount of the antigen Moreover areasonable adjustment of 119896 and 120578 is also crucial and it willenable the control system to have smaller overshoot and fasterresponse rate

312 Design of General Fuzzy Immune PID Feedback Con-troller Imitating the above immune feedback mechanism a119901-type fuzzy immune PID feedback controller is designedwhich combines the fuzzy immune controller with the gen-eral PID controller

The discrete form of the ordinary PID controller is asshown in

1199061015840 (119896) = (1198961199011015840 + 1198961198941015840119911 minus 1 + 1198961198891015840 119911 minus 1119911 ) 119890 (119896) (9)

The discrete output of the fuzzy immune PID is shown in(10) by replacing the antigen 120576(119896) and its change rate Δ120576(119896)of the fuzzy immune system with the output of general PIDcontroller 1199061015840(119896) and its change rate Δ1199061015840(119896) respectively

119906 (119896) = 1198701199011199061015840 (119896) = 119896 1 minus 120578119891 [1199061015840 (119896) Δ1199061015840 (119896)]sdot (1198961199011015840 + 1198961198941015840119911 minus 1 + 1198961198891015840 119911 minus 1119911 ) 119890 (119896)= (119896119901 + 119896119894119911 minus 1 + 119896119889119911 minus 1119911 ) 119890 (119896)

(10)

where

119896119901 = 1198961198961199011015840 1 minus 120578119891 (∙) = 1198701199011198961199011015840119896119894 = 1198961198961198941015840 1 minus 120578119891 (∙) = 1198701199011198961198941015840119896119889 = 1198961198961198891015840 1 minus 120578119891 (∙) = 1198701199011198961198891015840

(11)

Its controller structure is shown in Figure 9 and thecontrolled object is the IRC dryer the controller variable is


Immunecontroller

Integral

Proportional

Derivative

Fuzzy controller

Controlledobject(the Graindrying model)

r (k)e (k)

minus

u(k)

Δu(k)

u (k)

y (k)

f(u (k) Δu (k))

Figure 9 Structure of the fuzzy immune PID feedback controller

the output of the model 119910(119896) is the outlet grain moisture119903(119896) is the input of the control model which is a step responsefunction (the target moisture content value) 119890(119896) is the errorbetween the output and the target value 119889119890119889119905 is the changerate of 119890 1199061015840(119896) is the output of the general PID controlleru(k) is the immune controllerrsquos output which can control thedrying time of grain in the dryer (ie 119906(119896) can be used tocontrol the speed of discharging grain motor to obtain thetuning of the grain drying time)

The Mamdani fuzzy controller designed in the controlalgorithm is used to approximate the nonlinear function(119891[1199061015840(119896) Δ1199061015840(119896)]) and it has two inputs and one output Thetwo input variables of the fuzzy controller are the outputof the PID algorithm (1199061015840(119896)) and its change rate of error(Δ1199061015840(119896)) and the output variable of the fuzzy controller isa nonlinear function (119891[1199061015840(119896) Δ1199061015840(119896)]) As seen in (11) theparameters of the controllers 119896119901 119896119894 and 119896119889 can be adjustedadaptively with the change of 1199061015840(119896) and Δ1199061015840(119896) whichovercomes the limitations that the general PID controllerrsquosparameters can not be dynamically adjusted during thecontrol process

Firstly the fuzzy method of the input variables should beused to transform from the basic domain to the correspond-ing fuzzy set domain and define the quantification factor ofinput variables (1198701199061015840 119870Δ1199061015840) to get the fuzzy input (1198801015840 = 1198701199061015840 lowast1199061015840 Δ1198801015840 = 119870Δ1199061015840 lowastΔ1199061015840) so the output needs to transform fromthe fuzzy set to the basic domain In this paper the fuzzy setdomain of the input and output is [minus1 1]

Secondly the membership functions of input and outputlingual variables should be formed to determine the distri-bution of different variablesThere are commonly three typesof membership function to be used (1) normal distribution(2) triangle (3) trapezoidal The numbers of the fuzzy setsfor the input variable and output variable are used to meetthe requirements of accuracy As the numbers of the fuzzysets increase the numbers of fuzzy control rules increaseaccordingly which will improve the accuracy of control butmeantime the complexity of control is increased on thepremise of satisfying the requirement of control precisionthe least numbers of the fuzzy sets can be equal to 3 basedon the principle of determining theminimum inference rulesnumbers in addition the numbers of the fuzzy sets for theinput and the output can be unequal in order to improve the

Table 2 Knowledge rules of the fuzzy controller

119891 [1199061015840 (119896) Δ1199061015840 (119896)] Δ1199061015840 (119896)P Z N

1199061015840 (119896) P NB NS PSZ NS Z PSN NS PS PB

accuracy of control the fuzzy sets numbers for the outputvariable can be increased [39] Based on the above analysisin this paper each of the input variables has three fuzzysets positive zero negative or P Z N the output adoptsfive fuzzy sets positive big positive small zero negativesmall negative big or PB PS Z NS NB The Mamdanifuzzy controller can use the following 9 knowledge rulesshown in the Table 2 (eg if 1199061015840(119896) is P and Δ1199061015840(119896) is Pthen 119891[1199061015840(119896) Δ1199061015840(119896)] is NB) which imitating the controlprinciple of biological immune feedback The input andoutput membership functions of the fuzzy controller areshown in Figures 10(a)ndash10(c)

And then the fuzzy output can be obtained by thefuzzy inference synthesis algorithm according to the rules ofTable 2

Finally according to the fuzzy rules defuzzification willtransform the output119891(∙) of the fuzzy controller from a fuzzyset to a crisp number by using the gravity method (centroid)and the Zadeh fuzzy logic operation (AND)The relationshipsurface figure of the output and input in the universe ofdiscourse is shown in Figure 10(d)

32 Genetic Optimization Dual Fuzzy ImmunePID (GODFIP) Controller

321 The Structure of GODFIP It can also be seen from (11)that the PIDparameters (119896119901 119896119894 119896119889) have the same change rate(119870119901) which should be different in the actual control processthus affecting the control effect to some extent In this paperby adding a fuzzy PID parameter adjusting controller on thegeneral fuzzy immune PID controller to adjust the incrementvalues of the PID parameters in (11) making 1198961199011015840 1198961198941015840 1198961198891015840variable in the process of control shown in (12) the change


0 02 04 06 08 10

02040608

1D

egre

e of m

embe

rshi

pN Z P

Input variable u(k)

minus02minus04minus06minus08minus1

(a)

0 02 04 06 08 10

02040608

1

Deg

ree o

f mem

bers

hip

N Z P

Input variable Δu(k)


(b)

0 02 04 06 08 1

002040608

1

Deg

ree o

f mem

bers

hip

NB NS Z PS PB

Output variable fminus02minus04minus06minus08minus1

(c)

00510

1

005

f

minus05

minus05 minus1

minus1

Δu (k)

u(k)

(d)

Figure 10 Degree of membership function plots (a) 1199061015840(119896) (b) Δ1199061015840(119896) (c) 119891 and (d) relationship surface figure of the output and input

Dryingmodel

Fuzzy immunecontroller

PID controller

Fuzzy PIDparameterscontroller

Geneticoptimizationalgorithm

r (k) e (k)

minus

dedt ΔkpΔki Δkd

u(k)

u (k)

f(u Δu)

minus1ku

y (k)dudt

Immune controller(k )

Optimizing parameters kp ki kd k and so on

1 minus f(u Δu)Kp =

Figure 11 Structure of the genetic optimization dual fuzzy immune PID (GODFIP) controller

rates of the PID parameters (119896119901 119896119894 119896119889) in (11) are not thesame 1198961199011015840 (119896) = 1198961199011015840 + Δ1198961199011015840 (119896)

1198961198941015840 (119896) = 1198961198941015840 + Δ1198961198941015840 (119896) 1198961198891015840 (119896) = 1198961198891015840 + Δ1198961198891015840 (119896)

(12)

In addition in the process of control there is somedifficulty in selecting the parameters (1198961199011015840 1198961198941015840 1198961198891015840 k 120578)which is often time consuming and affects the control effectto some extent Moreover a reasonable adjustment of 119896and 120578 is also crucial and it will enable the control systemto have smaller overshoot and faster response So geneticalgorithm is adopted to optimize the parameters of theGODFIP controller and the optimal control is realized

Therefore in this paper a genetic optimization dual fuzzyimmune PID (GODFIP) controller is designed which notonly can improve the limitation of the general fuzzy immunePID control but also can find the optimal parameters (1198961199011015840 1198961198941015840

1198961198891015840 k and 120578) according to the control situationThe structureof GODFIP controller is as shown in Figure 11

In Figure 11 119903(119896) is the reference target input 119890(119896) is theerror between the output and the target value 119889119890119889119905 is thechange rate of 119890 1199061015840(119896) is the output of the PID controllerafter parameter adjustment (ie the input of fuzzy immunecontroller)119891(∙) is the nonlinear function119906(119896) is the immunecontrollerrsquos output which can control the drying time thedrying model is the controlled object 119910(119896) is the output ofmodel (ie the output grain moisture)

Taking the output grain moisture 119910(119896) as the controlledvariable and the output of the fuzzy immune controller 119906(119896)as the control variable the drying time of grain 119879dry(119896) in thedryer can be adjusted to realize the control target

In the drying experiment by the experiment of calcu-lating the grain weight of being discharged from the dryerwithin an hour (20HZ 3126 th 10HZ 1753 th) the linearinverse relationship between the speed of discharging motorand the drying time is obtained ((119906 = minus119896119906 lowast 119879dry(119896) + 119888))


Table 3 PID parameters tuning rules of fuzzy PID parameters controller

119889119890119889119905Δ1198961199011015840 Δ1198961198941015840 Δ1198961198891015840NB NM NS ZE PS PM PB NB NM NS ZE PS PM PB NB NM NS ZE PS PM PB

119890NB PB PB PM PM PS ZE ZE NB NB NM NM NS ZE ZE PS NS NB NB NB NM PSNM PB PB PM PS PS ZE ZE NB NB NM NS NS ZE ZE PS NS NB NB NB NM PSNS PM PM PM PM ZE NS NS NB NM NS NS ZE PS PS ZE NS NM NM NS NS ZEZE PM PM PS ZE NS NM NM NM NM NS ZE PS PM PM ZE NS NS NS NS NS ZEPS PS PS ZE NS NS NM NM NM NS ZE PS PS PM PB ZE ZE ZE ZE ZE ZE ZEPM PS ZE NS NM NM NM NB ZE ZE PS PS PM PB PB PB NS PS PS PS PS PBPB ZE ZE NM NM NM NB NB ZE ZE PS PM PM PB PB PB PM PM PM PS PS PB

A brief introduction to the design principle of fuzzy PIDparameter controller and genetic algorithm of the controlstructure of GODFIP are as follows (Sections 322 and 323)

322 Fuzzy PID Parameter Controller In Figure 11 there aretwo inputs for the fuzzy PID parameter controller 119890 and119889119890119889119905 three outputs Δ1198961199011015840 Δ1198961198941015840 and Δ1198961198891015840 (ie three PIDparameters increment values) the universe of discourse ofthe input and output is [minus3 3] Δ1198961199011015840 Δ1198961198941015840 and Δ1198961198891015840 can bededuced from the fuzzy rules shown in Table 3The fuzzy PIDparameter controller can change the increment values of thePID parameters dynamically according to the fuzzy rules bytracking the error signal and its change rate

323 Genetic Optimization Algorithm Genetic algorithm isa stochastic global optimization method that mimics themetaphor of the natural biological evolution Accordingto the fitness function value the global optimal solutioncan be obtained by the genetic evolution The fitness valueof each individual in the population is calculated by thefitness function and provided to the operator for selectioncrossover andmutation and screening individuals to find thebest by retaining the best fitness value and eliminating thepoor fitness values If the termination condition is satisfiedthen the optimal individual is used to be assigned to theparameters of the controller otherwise continue to calculatethe new species until the global optimal value is found

So we can use genetic algorithm to optimize the controlparameters (1198961199011015840 1198961198941015840 1198961198891015840 119896 120578) The basic genetic processesare selection crossover and mutationThe process of geneticalgorithm is as follows

(1) Parameter coding real code is adopted and for agiven parameter range [min max] the real numbercoding is equal to min + (max minusmin) lowast rand

(2) Population initialization the individual coding lengthis 8 (119896119901 119896119894 119896119889 119896 120578 and 3 proportional coefficientsused in the control structure) the population sizeis 20 the generations of evolution are 100 and thetermination error is 1119890 minus 6 In order to avoid theblindness of searching for the best the initial valuesof parameters are firstly obtained by the first run ofthe genetic algorithm and then take this as the centerto both sides to find the best

(3) Determining fitness function theminimumobjectivefunction of parameter selection is obtained from theaspects of reducing energy loss stability accuracyand rapidity and to be provided for the operatorselection and judgment To prevent the control inputof the controlled object too large and save the energyconsumption the output of the fuzzy immune con-troller is also added to the objective function and theoptimal function of the controller is shown in

119869 = intinfin0

[1199081 |119890 (119905)| + 1199082119906 (119905)2] 119889119905 + 1199083119905119903 (13)

where 119890(119905) is the system error 119906(119905) is the output of the fuzzyimmune controller 119905119903 is the rising time 1199081 1199082 and 1199083 arethe weights

In order to avoid overshoot the penalty function isadopted as shown in (14) (1199084 ≫ 1199081) err119910(119905) = 119910(119905)minus119910(119905minus1)where 119910(119905) is the output of the controlled object 120575 is thesize of the overshoot to be controlled once the overshoot isgenerated it will be used as the optimal indicator

if |119890 (119905)| gt 120575then 119869

= intinfin0

[1199081 |119890 (119905)| + 11990821199062 (119905) + 1199084 1003816100381610038161003816err119910 (119905)1003816100381610038161003816] 119889119905+ 1199083119905119903

(14)

4 Simulation and Discussion

41 Control Simulation Based on NARX Model In order toverify the effectiveness of the proposed GODFIP controllerin the grain drying control the following controllers thegeneral PID controller the fuzzy PID controller the fuzzyimmune PID controller and the GODFIP controller arerespectively designed and simulated to be compared withthe GODFIP controller by programming in the Matlab Ascan be seen from Section 25 the NARX drying model has abetter modeling accuracy and performsmuch better than theARX drying model so it can be considered to be a reliablerepresentative of the IRC dryer In this control simulationthe NARX model is selected to represent the actual dryingprocess to verify the control performance


0 10 20 30 40 50 60 70 80 90 100Generation

Fitn

ess v

alue

Best 16448 Mean 27333

Best fitnessMean fitness

100

101

102

103

Figure 12 The fitness curve of optimization simulation for theGODFIP controller

During the simulation the controlled variable is theoutput grain moisture content 119910(119896) of which the initialvalue is set to 26 the control variable is the speed of thedischarging grain motor the input of each model is thestep response function (final value = 15) mimicking thetarget grain moisture the step response curves of differentcontrollers are compared within 100 sampling events

The optimal solutions of control parameters of theGODFIP controller are evaluated by a real-coded geneticalgorithm The fitness curve of the optimization simulationis shown in Figure 12 and the best objective function value 119869is equal to 16448 after 63 generations and the optimal PIDparameters are respectively as follows

(1) 1198961199011015840 = 2601 (2) 1198961198941015840 = 1551 (3) 1198961198891015840 = 1137 (4)119896 = 253 (5) 120578 = 8328 (6)ndash(8) other three proportionalcoefficients minus8426 5062 1939

In order to achieve a fair comparison the genetic opti-mization algorithm is also used to optimize the other threecontrollers Moreover three runs of the genetic optimizationalgorithm program are made to avoid the stochastic errorfor each controller finally the average value of the objectivefunction value 119869 is considered as the performance measure ofeach controller

Figure 13 compares the performances of different con-trollers in controlling the NARX drying model and thecontrol simulation results are as shown in Table 4 where thedefinition of 119905119903 120575 119910(119905119901) 119910(infin) 1199051199041 and 1199051199042 is as follows

The rising time to the target value 119905119903 is the time to reach95 of the steady state for the first time in the transientprocess

Maximum overshoot 120575 is as shown in

120575 = (119910 (119905119901) minus 119910 (infin))119910 (infin) (15)

where 119910(119905119901) is the first peak value of the system response and119910(infin) is the steady value of the system responseAdjusting time 1199051199041is the time required from the first peak

value 119910(119905119901) to the steady value 119910(infin) that falls betweenthe deviations allowed (plusmn5) and is maintained within theallowable range

The adjusting time 1199051199042 is the time to the steady value afterthe interference disappears

10 20 30 40 50 60013

015

017

019

021

023

025

027028

Number of sample events (k)

Out

put m

oistu

re co

nten

t

The target value

(1)(2)

(4)(3)

(1) The general PIDcontroller

(2) The Fuzzy PIDcontroller

(3) The Fuzzy immune PIDcontroller

(4) The GODFIPcontroller

Figure 13 Simulation results comparison of different controllers forthe grain drying process of IRC dryer

42 The Anti-Interference Test Simulation Based on NARXModel The dynamic influence factors of the grain dryingprocess are a lot and the influence of various disturbancefactors in the control process easily leads to the variationsof the output grain moisture In order to verify the anti-interference performances of the controllers the interferencesignal with the amplitude of 002 at sampling number 105is added to represent a possible increase in the initialmoisture of grain that enters the IRC dryer which is shownin Figure 14(a) and this anti-interference simulation test iswithin 200 sampling events The anti-interference perfor-mance comparison results are shown in Figure 14(b)

43 Simulation Result Discussion

(1) The Optimization Results The genetic optimization algo-rithm is used to achieve the optimal control of the GODFIPcontroller the fuzzy immune PID controller the fuzzy PIDcontroller and the general PID controller based on theperformance objective function from the aspects of energysavings stability accuracy and rapidity As can be seen fromthe comparison results shown in Table 4 the 119869 value ofthe GODFIP is equal to 16450 and is obviously less thanthe compared controllers which is about 353 decreasecompared to the fuzzy immune PID controller about 919decrease compared to the fuzzy PID controller and about9368 decrease compared to the general PID controllerHence the GODFIP controller has achieved the best controlperformances in terms of accomplishing the least value of119869 compared to the other three controllers showing theeffectiveness of the GODFIP controller

(2)The Overshoot the Adjusting Time 1199051199041 and the Rising Time119905119903 Overshoot adjusting time and rising time are importantindexes to judge a controllerrsquos performance reflecting the

12 Mathematical Problems in EngineeringO

utpu

t moi

sture

cont

ent

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018



(a)

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018


Out

put m

oistu

re co

nten

t

(3)

(4)

(2)(1)

(2) The fuzzy PIDcontroller


(3) The fuzzy immune PIDcontroller


(b)

Figure 14The anti-interference effect comparisons between the GODFIP controller and the other controllers (a) the interference signal and(b) the anti-interference effect comparison results

Table 4 Control performance comparisons of different controllers

Controllers 119869 120575 119910(119905119901) 119905119903 (number of samples) 1199051199041 (number of samples) 1199051199042 (number of samples)General PID 26046 013 01502 57 0 39Fuzzy PID 20348 007 01501 20 0 30General fuzzy immune PID 17052 000 01500 8 0 13GODFIP 16450 000 01500 5 0 10

control stability of the system not oscillating wildly (inthe drying control reflecting the output moisture contentfluctuations) and the rapidity of the system response-rapidlytracking control of the target signal By the simulation com-parisons of Figure 13 and the control performance values ofTable 4 owing to the adopted genetic optimization algorithmon the controllers the overshoot and the adjusting time 1199051199041of all compared controllers are almost zero showing theexcellent optimal ability of genetic algorithm It can also beseen that the rising time to the target value of the GODFIPcontroller is 5 samplings which is about 375 decreasecompared to the general fuzzy immune PID controller (8samples) about 75 decrease compared to the fuzzy PIDcontroller (20 samples) and about 912 decrease comparedto the general PID controller (57 samples) showing theeffectiveness of the GODFIP control algorithm

Under the same optimization conditions the PID con-troller and the fuzzy PID controller need more samples tothe target value than the other two immune controllers (theGODFIP and the fuzzy immune PID) in order to accomplishthe optimal control target in fact it is impractical for thegrain drying process because it will cause an inefficient energyconsumption and bad dried grain quality The GODFIPcontroller and the fuzzy immune PID controller are bothsuperior to the PID controller and the fuzzy PID controllerwhich not only can the stability of the control system beachieved but also the systemoutput can be rapidly adjusted to

the target value showing the advantage of the immune algo-rithm In addition the GODFIP controller has performedbetter compared to the fuzzy immune PID controller so theGODFIP controller is more suitable for the IRC dryer thanthe other compared controllers

(3) The Anti-Interference Test As can be seen from Fig-ure 14 the GODFIP controller has the best anti-interferenceperformances compared to the other three controllers thatit can quickly respond to and track the interference signaland can adjust the output value to the target value rapidlyand steadily after the interference disappears moreover thefluctuations affected by the interference are less Howeverfor the same test the general PID controller and the fuzzyPID controller have showed oscillatory behavior when aninterference exits during the drying process of which thegeneral PID controller has taken nearly 39 samples and thefuzzy PID controller has taken nearly 30 samples to reachthe desired moisture content level showing the inefficiencyof handling the effect of interference by the two controllersand inferior to the anti-interference ability of the GODFIPcontroller Moreover the GODFIP controller has improvedthe anti-interference performance of the fuzzy immune PIDcontroller of which 3 samples to the target value are reducedcompared to the fuzzy immune PID controller The anti-interference performance test further verifies the robustnessof the proposed GODFIP controller over an uncertainty


range of condition and demonstrates that it is a suitablecontroller for the IRC grain dryer

5 Conclusion

In this paper a genetic optimization dual fuzzy immunePID (GODFIP) controller based on the immune feedbackmechanism is designed and simulated to control an IRCgrain dryer represented by an identified Autoregressive withExogenous input (NARX) model The NARX model has ahigher model approximation accuracy (MSE 1062 lowast 10minus5R 9978) than the identified linear ARX model (MSE229 lowast 10minus4 R 955) so the NARX model is a bettercandidate in representing the nonlinear dynamics of theIRC grain dryer to verify the control performances of theGODFIP controller In order to achieve a fair comparisonthe genetic optimization algorithm is utilized to optimize theproposed GODFIP controller and the other three comparedcontrollers based on the performance objective function 119869from the aspects of energy savings stability accuracy andrapidity Finally the control simulation comparison and theanti-interference simulation test are made As can be seenfrom the simulation results of Figures 13 and 14 and Table 4the GODFIP controller has the least value of 119869 comparedto the other three controllers which is equal to 1645 about353 decrease compared to the fuzzy immune PID about919 decrease compared to the fuzzy PID controller andabout 9368 decrease compared to the PID and the shortestrising time about 375 decrease compared to the fuzzyimmune PID about 75 decrease compared to the fuzzyPID and about 912 decrease compared to the PID andhas the best anti-interference ability which can adjust theoutput to the target value rapidly and steadily It is testedfrom the simulation results that the GODFIP controller hasimproved the control performance of the fuzzy immune PIDcontroller and is obviously superior to the PID controllerand the fuzzy PID controller so the GODFIP controller cantrack the target value rapidly and steadily and can handle theuncertainty conditions of complex systems to some extentwhich is more suitable for such a complex system as graindrying The big difference between this control method andthe traditional control method is that it is not dependent onthe transfer function of the controlled object The proposedGODFIP controller can provide an effective reference for theactual control strategy of the grain drying process andmay beapplied to control the real IRC dryer in future works

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Aini Dai mainly engaged in the research of grain drying con-trol and intelligent control Xiaoguang Zhou mainly engagedin the research of control theory and its application inengineering Xiangdong Liu mainly engaged in the researchof drying technology and theory of agricultural products

Acknowledgments

The authors of this paper would like to acknowledge theChina National Common Weal Industrial Special ScientificResearch Funds for Grain Industry (no 201413006) and the111 Project (B08004) for funding of this study the cooperationof the research group and the experimental help of theengineers in Dongyu Machinery Co Ltd China

References

[1] Q Liu and F W Bakker-Arkema ldquoAutomatic control of cross-flow grain dryers part 2 design of a model-predictive con-trollerrdquo Journal of Agricultural Engineering Research vol 80 no2 pp 173ndash181 2001

[2] Q Liu andFWBakker-Arkema ldquoAmodel-predictive controllerfor grain dryingrdquo Journal of Food Engineering vol 49 no 4 pp321ndash326 2001

[3] Y K Pan X ZWang andXD LiuModernDrying TechnologyChemical Industry Publisher Beijing China 2007

[4] M H Riadh S A B Ahmad M H Marhaban and A C SohldquoInfrared heating in food drying an overviewrdquo Drying Technol-ogy vol 33 no 3 pp 322ndash335 2015

[5] X Wang Q Hu B Xiao D Yang and X Liu ldquoModeling sim-ulation of combined convective and infrared radiation in ricedrying processrdquo Transactions of the Chinese Society for Agricul-tural Machinery vol 44 no 9 pp 145ndash151 2013

[6] P Dufour D Blanc Y Toure and P Laurent ldquoInfrared dryingprocess of an experimental water painting Model predictivecontrolrdquo Drying Technology vol 22 no 1-2 pp 269ndash284 2004

[7] L Luo ldquoA mathematical model for vacuum far-infrared dryingof potato slicesrdquo Drying Technology vol 32 no 2 pp 180ndash1892014

[8] T M Afzal and T Abe ldquoSome fundamental attributes of farinfrared radiation drying of potatordquo Drying Technology vol 17no 1-2 pp 137ndash155 1999

[9] R Dhib ldquoInfrared drying from process modeling to advancedprocess controlrdquo Drying Technology vol 25 no 1 pp 97ndash1052007

[10] J Wang ldquoA single-layer model for far-infrared radiation dyingof onion slicesrdquoDrying Technology vol 20 no 10 pp 1941ndash19532002

[11] C Likitrattanaporn and A Noomhorm ldquoEffects of simulta-neous parboiling and drying by infrared radiation heating onparboiled rice qualityrdquo Drying Technology vol 29 no 9 pp1066ndash1075 2011

[12] A S Mujumdar ldquoEditorial the Making of the Handbook ofIndustrial Dryingrdquo Drying Technology vol 32 no 6 pp 627-628 2014

[13] D M Bruce and N J B McFarlane ldquoControl of mixed-flowgrain driers testing of a feedback-plus-feedforward algorithmrdquoJournal of Agricultural Engineering Research vol 52 no C pp11ndash23 1992

[14] O F Lutfy S B MohdNoor M HMarhaban and K A AbbasldquoNon-linear modelling and control of a conveyor-belt graindryer utilizing neuro-fuzzy systemsrdquo Proceedings of the Insti-tution of Mechanical Engineers Part I Journal of Systems andControl Engineering vol 225 no 5 pp 611ndash622 2011

[15] M Negnevitsky Artificial intelligence a guide to intelligentsystems Addison-Wesley publisher New Jersey NJ USA 2005


[16] F Han W F Wu and H Zhu ldquoControl status and developingtrend of grain drying processrdquo Journal of The Chinese Cerealsand Oils Association vol 24 no 5 pp 150ndash153 2009

[17] S M Lewis G Fitts M Kelly and L Dale ldquoA fuzzy logic-basedspatial suitability model for drought-tolerant switchgrass in theUnited Statesrdquo Computers and Electronics in Agriculture vol103 pp 39ndash47 2014

[18] S El Ferik M Tariq Nasir and U Baroudi ldquoA behavioral adap-tive fuzzy controller of multi robots in a cluster spacerdquo AppliedSoft Computing vol 44 pp 117ndash127 2016

[19] A V Taprantzis C I Siettos andG V Bafas ldquoFuzzy control of afluidized bed dryerrdquo Drying Technology vol 15 no 2 pp 511ndash537 1997

[20] H Mansor S B Mohd Noor R K Raja Ahmad F S Taip andO F Lutfy ldquoIntelligent control of grain drying process usingfuzzy logic controllerrdquo Journal of Food Agriculture and Environ-ment vol 8 no 2 pp 145ndash149 2010

[21] N Perrot C Bonazzi and G Trystram ldquoApplication of fuzzyrules-based models to prediction of quality degradation of riceandmaize during hot air dryingrdquoDrying Technology vol 16 no8 pp 1533ndash1565 1998

[22] Q Zhang and J B Litchfield ldquoKnowledge representation in agrain drier fuzzy logic controllerrdquo Journal of Agricultural Engi-neering Research vol 57 no 4 pp 269ndash278 1994

[23] O F LutfyH Selamat and S BMohdNoor ldquoIntelligentmodel-ing and control of a conveyor belt grain dryer using a simplifiedtype 2 neuro-fuzzy controllerrdquoDrying Technology vol 33 no 10pp 1210ndash1222 2015

[24] M S Liu C W Wu and H Wang ldquoSimulation of grain dryingprocess by a fuzzy expert systemrdquo Transactions of the ChineseSociety of Agricultural Machinery vol 32 no 4 pp 54ndash56 2001

[25] L Sun and Z Zhu ldquoFuzzy Aeration Control for In-Bin StoredGrainrdquo in Proceedings of the International Conference on DigitalManufacturing and Automation ICDMA rsquo13 pp 626ndash629 June2013

[26] S K Tiwari and G Kaur ldquoAnalysis of fuzzy pid and immunepid controller for three tank liquid level controlrdquo InternationalJournal of Soft Computing and Engineering vol 1 no 4 2011

[27] T Zheng X Xiao and Y Ren ldquoFuzzy immune PID speedcontrol system and its simulation in industrial sewingmachinerdquoMechanical and Electrical Engineering Magazine vol 25 no 12pp 19ndash22 2008

[28] F Hu and W N Zhou ldquoApplication of fuzzy immune PIDcontroller based on particle swarm optimization in powerplant steam temperature control systemrdquo Advanced MaterialsResearch vol 950 pp 257ndash262 2014

[29] G D Li and M X Wang ldquoFuzzy immune-PID controller andits application in caustic processrdquoComputer Engineering vol 35no 1 pp 218ndash220 2009

[30] T Zhou Introduction to the System Identification of ControlTsinghua University Publisher Beijing China 2004

[31] F Soderstrom ldquoLeast squares parameter estimation ofcontinuous-time ARX models from discrete-time datardquo IEEETransactions on Automatic Control vol 42 no 5 pp 659ndash6731997

[32] D Liberati S Cerutti E Di Ponzio V Ventimiglia and LZaninelli ldquoThe implementation of an autoregressivemodel withexogenous input in a single sweep visual evoked potential anal-ysisrdquo Journal of Biomedical Engineering vol 11 no 4 pp 285ndash292 1989

[33] W-X Zhao and W X Zheng ldquoNonparametric algorithmsfor identification of nonlinear autoregressive systems withexogenous inputsrdquo IFAC Proceedings Volumes vol 42 no 10pp 1609ndash1614 2009

[34] N Mohd and N Aziz ldquoPerformance and robustness evaluationof nonlinear autoregressive with exogenous input model pre-dictive control in controlling industrial fermentation processrdquoJournal of Cleaner Production vol 136 pp 42ndash50 2016

[35] B C Ng I Z M Darus H Jamaluddin and H M KamarldquoDynamic modelling of an automotive variable speed airconditioning system using nonlinear autoregressive exogenousneural networksrdquoAppliedThermal Engineering vol 73 no 1 pp1253ndash1267 2014

[36] R W K Chan J K K Yuen E W M Lee and M ArashpourldquoApplication of Nonlinear-Autoregressive-Exogenous model topredict the hysteretic behaviour of passive control systemsrdquoEngineering Structures vol 85 pp 1ndash10 2015

[37] C V Mai M D Spiridonakos E N Chatzi and B SudretldquoSurrogate modeling for stochastic dynamical systems by com-bining nonlinear autoregressive with exogenous input modelsand polynomial chaos expansionsrdquo International Journal forUncertainty Quantification vol 6 no 4 pp 313ndash339 2016

[38] A Andalib and F Atry ldquoMulti-step ahead forecasts for electric-ity prices using NARX a new approach a critical analysis ofone-step ahead forecastsrdquo Energy Conversion and Managementvol 50 no 3 pp 739ndash747 2009

[39] L T Koczy ldquoFuzzy if then rulemodels and their transformationinto one anotherrdquo IEEE Transactions on Systems Man andCybernetics Part A Systems and Humans vol 26 no 5 pp 621ndash637 1996

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


so on It is difficult to make an accurate mathematical modelof grain drying so the control of grain drying is a challengingjob [2 12] Liu and Bakker-Arkema have also reviewedsome traditional control limitations such as the controllersdesigned by Marchant Whitfied McFarlane and Courtoiset al Indeed the classical feedback control is necessary butis inadequate for controlling grain dryer [2] The controleffect of the feed-forward control is much better than thatof the feedback control only but the accuracy of the feed-forward control is affected by whether or not the systemdisturbance is measurable [13] In addition Proportional-Integral-Derivative (PID) controller is successfully applied inthe classic automatic control and still used in the control ofgrain drying now but it relies on the mathematical modeland has some limitations of which the values of the controlparameters (1198961199011015840 1198961198941015840 1198961198891015840) are not changed in the wholecontrol process and when the controlled object and theenvironment are uncertain the PID controller will be difficultto achieve satisfactory control effect and difficult to reachthe control requirements with more strict restriction onovershoot Model-predictive control (MPC) is a compoundoptimization algorithm which is based on model rollingoptimization and feedback correction it will control outputchanges by tracking the change of the set valve so it iseffective for the nonlinear and large lag process control [2]In a series of Liu and Bakker-Arkemarsquos papers a model-predictive controller (MPC) was especially designed for graindrying The simulation and field tests both showed thatthe controller performed well over a wide range of dryingconditions The distributed-parameter process model thatthe MPC employs is more comprehensive than the lumpedparameter model and provides more detailed information onthe process but it requires more computation time and stillrelies on the accuracy of the system mathematical model [2]

In all a drawback of the above-mentioned studies isthat the authors generally made several simplifications indeveloping the dryer mathematical model based on someassumptions and observations These simplifications areexpected to affect the performance of these models andconsequently their reliability in representing the real processwhen using these models for control purposes Moreoverthe mathematical models generally consist of sets of highlycomplex and nonlinear partial differential equations (PDES)with several auxiliary algebraic equations that involve trans-fer coefficients and thermophysical properties that requirehighly complicated numerical techniques to solve renderingthem undesirable options in control systems [14]

Since the 1970s the research development of computercontrol technology and artificial intelligence has providednew ways for advanced control of the grain drying thereafterdrying control comes into the intelligent control period ofwhich the fuzzy logic controller (FLC) is a typical intelli-gent controller which imitates humansrsquo decision-making andcommon sense [15 16] The FLC does not need to know themathematical model of the controlled object and only needsto accumulate the experience data of a skilled human oper-ator which is the biggest difference from the conventionalcontrol In essence the FLC provides an algorithm whichcan convert the linguistic control strategy based on expert

knowledge into an automatic control strategyThe FLC is notonly widely used in industry but also a hot research topicin the control of grain drying now [17ndash25] Combining FLCalgorithmwith traditional control algorithms the problem ofgrain drying control can be effectively solved

Fuzzy immune PID controller based on the immunefeedback mechanism combines the intelligent FLC with thetraditional PID controller and has the advantages of simplegood robustness and independence on the system modelwhich uses the characteristics of fuzzy control to learn thebiological immune feedback mechanism under the complexdisturbance and uncertain environment [26ndash29] Howeverthe algorithm also has some limitations although the PIDcontrol parameters in the control process can be changed thechange rates of parameters are the same affecting the controlperformance to a certain extent Aiming at this limitationin this paper an improved fuzzy immune PID controller isdesigned to solve the limitation of the general fuzzy immunePID control algorithm

In all based on the idea of artificial intelligence thispaper proposes an improved fuzzy immune PID controllercombined with two kinds of evolutionary algorithms theimmune feedback algorithm and the genetic optimizationalgorithm which has improved the limitation of the tradi-tional PID controller and the general fuzzy immune PIDcontroller Because the algorithm adopts two kinds of fuzzycontroller and uses the genetic algorithm to optimize theinitial controller parameters of the model the proposedcontroller in this paper is called the genetic optimizationdual fuzzy Immune PID (GODFIP) controller Based onthe GODFIP the speed of discharging grain motor can beautomatically adjusted to achieve the precise control of theoutput grain moisture of the IRC grain dryer according tothe difference and its change rate between the output grainmoisture content and the target moisture content Finally theNARX (Nonlinear Autoregressive models with ExogenousInputs) model is used to represent the actual drying processto test the effectiveness of the proposed controller and thecomparative study with the other related controllers is alsomade and the simulation results show that the control effectof GODFIP is better than that of other compared controllers

2 The Mathematical Model of Grain Dryingand Its Control Algorithm Structure

21 The Mechanical Structure of the New Grain Dryer TheIRC grain drying system has been put into use in HarbinDevelopment Zone Binxi town China Dongyu MachineryCo Ltd Fresh mature corns were purchased from a localfarm (an agricultural area in north of China)

The IRC grain dryer mechanism system is shown inFigure 1 It can be seen that the system mainly consists ofthe following parts a wet grain barn a grain dryer anddried grain barn and 3 elevators used to raise grains tothe barns and 5 belt machines used to transport of whichthe new radiation-convection grain dryer is rectangularityin shape and the overall dimensions are 475m in height206m in length and 13m in depth as shown in Figure 2


(1)

(2)

(3)(4)

(5)(6)

(7)

(10)

(9)

(8)

(11)


Cold air inlet



(13)

(12)Storage section

Convection section

Radiation section


Graininlet

(7)

(9)

(10)

(8)

(11)

(1) (2)

(3)

(4)

(5) (6)Wastegasroom

Oilfurnace


Anglebox

Dryingwastegas

Combustionchamber





Control cabinet











119860 (119911) = 1 + 119899119886sum119894=1


119895=0

119887119895119911minus119895(1)











MSE = 1119898119898sum119894=1


(5)





0 1 2 3 4 5 6 701

015

02

025

03

035

Time (h)

Out

put m

oistu

re co

nten

t










+

b

W1

11

1

Hidden

+

Output

y(t)

y(t)

x(t)

W

W

b

10

1 2

1 2


01015

02025

03035

Out

put a

nd ta

rget

50 100 150 200 250 300 350

0001

Erro

r



minus001minus002




























Graindryer


Output



Immune algorithm




Frequency converter

e(t)

dedt

minus +




119878 (119896) = TH (119896) minus TS (119896) (7)



119870119901 = 119896 1ndash120578119891 [120576 (119896) Δ120576 (119896)] (8)




1199061015840 (119896) = (1198961199011015840 + 1198961198941015840119911 minus 1 + 1198961198891015840 119911 minus 1119911 ) 119890 (119896) (9)



(10)

where


(11)



Immunecontroller

Integral

Proportional

Derivative

Fuzzy controller


r (k)e (k)

minus

u(k)

Δu(k)

u (k)

y (k)

f(u (k) Δu (k))







119891 [1199061015840 (119896) Δ1199061015840 (119896)] Δ1199061015840 (119896)P Z N








0 02 04 06 08 10

02040608

1D

egre

e of m

embe

rshi

pN Z P

Input variable u(k)


(a)

0 02 04 06 08 10

02040608

1

Deg

ree o

f mem

bers

hip

N Z P



(b)

0 02 04 06 08 1

002040608

1

Deg

ree o

f mem

bers

hip

NB NS Z PS PB


(c)

00510

1

005

f

minus05

minus05 minus1

minus1

Δu (k)

u(k)

(d)


Dryingmodel


PID controller



r (k) e (k)

minus

dedt ΔkpΔki Δkd

u(k)

u (k)

f(u Δu)

minus1ku

y (k)dudt






1198961198941015840 (119896) = 1198961198941015840 + Δ1198961198941015840 (119896) 1198961198891015840 (119896) = 1198961198891015840 + Δ1198961198891015840 (119896)

(12)


















119869 = intinfin0

[1199081 |119890 (119905)| + 1199082119906 (119905)2] 119889119905 + 1199083119905119903 (13)



if |119890 (119905)| gt 120575then 119869

= intinfin0

[1199081 |119890 (119905)| + 11990821199062 (119905) + 1199084 1003816100381610038161003816err119910 (119905)1003816100381610038161003816] 119889119905+ 1199083119905119903

(14)




0 10 20 30 40 50 60 70 80 90 100Generation

Fitn

ess v

alue

Best 16448 Mean 27333


100

101

102

103













10 20 30 40 50 60013

015

017

019

021

023

025

027028


Out

put m

oistu

re co

nten

t

The target value

(1)(2)

(4)(3)











utpu

t moi

sture

cont

ent

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018



(a)

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018


Out

put m

oistu

re co

nten

t

(3)

(4)

(2)(1)





(b)










5 Conclusion






Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





(1)

(2)

(3)(4)

(5)(6)

(7)

(10)

(9)

(8)

(11)


Cold air inlet



(13)

(12)Storage section

Convection section

Radiation section


Graininlet

(7)

(9)

(10)

(8)

(11)

(1) (2)

(3)

(4)

(5) (6)Wastegasroom

Oilfurnace


Anglebox

Dryingwastegas

Combustionchamber





Control cabinet











119860 (119911) = 1 + 119899119886sum119894=1


119895=0

119887119895119911minus119895(1)











MSE = 1119898119898sum119894=1


(5)





0 1 2 3 4 5 6 701

015

02

025

03

035

Time (h)

Out

put m

oistu

re co

nten

t










+

b

W1

11

1

Hidden

+

Output

y(t)

y(t)

x(t)

W

W

b

10

1 2

1 2


01015

02025

03035

Out

put a

nd ta

rget

50 100 150 200 250 300 350

0001

Erro

r



minus001minus002




























Graindryer


Output



Immune algorithm




Frequency converter

e(t)

dedt

minus +




119878 (119896) = TH (119896) minus TS (119896) (7)



119870119901 = 119896 1ndash120578119891 [120576 (119896) Δ120576 (119896)] (8)




1199061015840 (119896) = (1198961199011015840 + 1198961198941015840119911 minus 1 + 1198961198891015840 119911 minus 1119911 ) 119890 (119896) (9)



(10)

where


(11)



Immunecontroller

Integral

Proportional

Derivative

Fuzzy controller


r (k)e (k)

minus

u(k)

Δu(k)

u (k)

y (k)

f(u (k) Δu (k))







119891 [1199061015840 (119896) Δ1199061015840 (119896)] Δ1199061015840 (119896)P Z N








0 02 04 06 08 10

02040608

1D

egre

e of m

embe

rshi

pN Z P

Input variable u(k)


(a)

0 02 04 06 08 10

02040608

1

Deg

ree o

f mem

bers

hip

N Z P



(b)

0 02 04 06 08 1

002040608

1

Deg

ree o

f mem

bers

hip

NB NS Z PS PB


(c)

00510

1

005

f

minus05

minus05 minus1

minus1

Δu (k)

u(k)

(d)


Dryingmodel


PID controller



r (k) e (k)

minus

dedt ΔkpΔki Δkd

u(k)

u (k)

f(u Δu)

minus1ku

y (k)dudt






1198961198941015840 (119896) = 1198961198941015840 + Δ1198961198941015840 (119896) 1198961198891015840 (119896) = 1198961198891015840 + Δ1198961198891015840 (119896)

(12)


















119869 = intinfin0

[1199081 |119890 (119905)| + 1199082119906 (119905)2] 119889119905 + 1199083119905119903 (13)



if |119890 (119905)| gt 120575then 119869

= intinfin0

[1199081 |119890 (119905)| + 11990821199062 (119905) + 1199084 1003816100381610038161003816err119910 (119905)1003816100381610038161003816] 119889119905+ 1199083119905119903

(14)




0 10 20 30 40 50 60 70 80 90 100Generation

Fitn

ess v

alue

Best 16448 Mean 27333


100

101

102

103













10 20 30 40 50 60013

015

017

019

021

023

025

027028


Out

put m

oistu

re co

nten

t

The target value

(1)(2)

(4)(3)











utpu

t moi

sture

cont

ent

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018



(a)

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018


Out

put m

oistu

re co

nten

t

(3)

(4)

(2)(1)





(b)










5 Conclusion






Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





Control cabinet











119860 (119911) = 1 + 119899119886sum119894=1


119895=0

119887119895119911minus119895(1)











MSE = 1119898119898sum119894=1


(5)





0 1 2 3 4 5 6 701

015

02

025

03

035

Time (h)

Out

put m

oistu

re co

nten

t










+

b

W1

11

1

Hidden

+

Output

y(t)

y(t)

x(t)

W

W

b

10

1 2

1 2


01015

02025

03035

Out

put a

nd ta

rget

50 100 150 200 250 300 350

0001

Erro

r



minus001minus002




























Graindryer


Output



Immune algorithm




Frequency converter

e(t)

dedt

minus +




119878 (119896) = TH (119896) minus TS (119896) (7)



119870119901 = 119896 1ndash120578119891 [120576 (119896) Δ120576 (119896)] (8)




1199061015840 (119896) = (1198961199011015840 + 1198961198941015840119911 minus 1 + 1198961198891015840 119911 minus 1119911 ) 119890 (119896) (9)



(10)

where


(11)



Immunecontroller

Integral

Proportional

Derivative

Fuzzy controller


r (k)e (k)

minus

u(k)

Δu(k)

u (k)

y (k)

f(u (k) Δu (k))







119891 [1199061015840 (119896) Δ1199061015840 (119896)] Δ1199061015840 (119896)P Z N








0 02 04 06 08 10

02040608

1D

egre

e of m

embe

rshi

pN Z P

Input variable u(k)


(a)

0 02 04 06 08 10

02040608

1

Deg

ree o

f mem

bers

hip

N Z P



(b)

0 02 04 06 08 1

002040608

1

Deg

ree o

f mem

bers

hip

NB NS Z PS PB


(c)

00510

1

005

f

minus05

minus05 minus1

minus1

Δu (k)

u(k)

(d)


Dryingmodel


PID controller



r (k) e (k)

minus

dedt ΔkpΔki Δkd

u(k)

u (k)

f(u Δu)

minus1ku

y (k)dudt






1198961198941015840 (119896) = 1198961198941015840 + Δ1198961198941015840 (119896) 1198961198891015840 (119896) = 1198961198891015840 + Δ1198961198891015840 (119896)

(12)


















119869 = intinfin0

[1199081 |119890 (119905)| + 1199082119906 (119905)2] 119889119905 + 1199083119905119903 (13)



if |119890 (119905)| gt 120575then 119869

= intinfin0

[1199081 |119890 (119905)| + 11990821199062 (119905) + 1199084 1003816100381610038161003816err119910 (119905)1003816100381610038161003816] 119889119905+ 1199083119905119903

(14)




0 10 20 30 40 50 60 70 80 90 100Generation

Fitn

ess v

alue

Best 16448 Mean 27333


100

101

102

103













10 20 30 40 50 60013

015

017

019

021

023

025

027028


Out

put m

oistu

re co

nten

t

The target value

(1)(2)

(4)(3)











utpu

t moi

sture

cont

ent

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018



(a)

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018


Out

put m

oistu

re co

nten

t

(3)

(4)

(2)(1)





(b)










5 Conclusion






Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of












MSE = 1119898119898sum119894=1


(5)





0 1 2 3 4 5 6 701

015

02

025

03

035

Time (h)

Out

put m

oistu

re co

nten

t










+

b

W1

11

1

Hidden

+

Output

y(t)

y(t)

x(t)

W

W

b

10

1 2

1 2


01015

02025

03035

Out

put a

nd ta

rget

50 100 150 200 250 300 350

0001

Erro

r



minus001minus002




























Graindryer


Output



Immune algorithm




Frequency converter

e(t)

dedt

minus +




119878 (119896) = TH (119896) minus TS (119896) (7)



119870119901 = 119896 1ndash120578119891 [120576 (119896) Δ120576 (119896)] (8)




1199061015840 (119896) = (1198961199011015840 + 1198961198941015840119911 minus 1 + 1198961198891015840 119911 minus 1119911 ) 119890 (119896) (9)



(10)

where


(11)



Immunecontroller

Integral

Proportional

Derivative

Fuzzy controller


r (k)e (k)

minus

u(k)

Δu(k)

u (k)

y (k)

f(u (k) Δu (k))







119891 [1199061015840 (119896) Δ1199061015840 (119896)] Δ1199061015840 (119896)P Z N








0 02 04 06 08 10

02040608

1D

egre

e of m

embe

rshi

pN Z P

Input variable u(k)


(a)

0 02 04 06 08 10

02040608

1

Deg

ree o

f mem

bers

hip

N Z P



(b)

0 02 04 06 08 1

002040608

1

Deg

ree o

f mem

bers

hip

NB NS Z PS PB


(c)

00510

1

005

f

minus05

minus05 minus1

minus1

Δu (k)

u(k)

(d)


Dryingmodel


PID controller



r (k) e (k)

minus

dedt ΔkpΔki Δkd

u(k)

u (k)

f(u Δu)

minus1ku

y (k)dudt






1198961198941015840 (119896) = 1198961198941015840 + Δ1198961198941015840 (119896) 1198961198891015840 (119896) = 1198961198891015840 + Δ1198961198891015840 (119896)

(12)


















119869 = intinfin0

[1199081 |119890 (119905)| + 1199082119906 (119905)2] 119889119905 + 1199083119905119903 (13)



if |119890 (119905)| gt 120575then 119869

= intinfin0

[1199081 |119890 (119905)| + 11990821199062 (119905) + 1199084 1003816100381610038161003816err119910 (119905)1003816100381610038161003816] 119889119905+ 1199083119905119903

(14)




0 10 20 30 40 50 60 70 80 90 100Generation

Fitn

ess v

alue

Best 16448 Mean 27333


100

101

102

103













10 20 30 40 50 60013

015

017

019

021

023

025

027028


Out

put m

oistu

re co

nten

t

The target value

(1)(2)

(4)(3)











utpu

t moi

sture

cont

ent

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018



(a)

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018


Out

put m

oistu

re co

nten

t

(3)

(4)

(2)(1)





(b)










5 Conclusion






Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





+

b

W1

11

1

Hidden

+

Output

y(t)

y(t)

x(t)

W

W

b

10

1 2

1 2


01015

02025

03035

Out

put a

nd ta

rget

50 100 150 200 250 300 350

0001

Erro

r



minus001minus002




























Graindryer


Output



Immune algorithm




Frequency converter

e(t)

dedt

minus +




119878 (119896) = TH (119896) minus TS (119896) (7)



119870119901 = 119896 1ndash120578119891 [120576 (119896) Δ120576 (119896)] (8)




1199061015840 (119896) = (1198961199011015840 + 1198961198941015840119911 minus 1 + 1198961198891015840 119911 minus 1119911 ) 119890 (119896) (9)



(10)

where


(11)



Immunecontroller

Integral

Proportional

Derivative

Fuzzy controller


r (k)e (k)

minus

u(k)

Δu(k)

u (k)

y (k)

f(u (k) Δu (k))







119891 [1199061015840 (119896) Δ1199061015840 (119896)] Δ1199061015840 (119896)P Z N








0 02 04 06 08 10

02040608

1D

egre

e of m

embe

rshi

pN Z P

Input variable u(k)


(a)

0 02 04 06 08 10

02040608

1

Deg

ree o

f mem

bers

hip

N Z P



(b)

0 02 04 06 08 1

002040608

1

Deg

ree o

f mem

bers

hip

NB NS Z PS PB


(c)

00510

1

005

f

minus05

minus05 minus1

minus1

Δu (k)

u(k)

(d)


Dryingmodel


PID controller



r (k) e (k)

minus

dedt ΔkpΔki Δkd

u(k)

u (k)

f(u Δu)

minus1ku

y (k)dudt






1198961198941015840 (119896) = 1198961198941015840 + Δ1198961198941015840 (119896) 1198961198891015840 (119896) = 1198961198891015840 + Δ1198961198891015840 (119896)

(12)


















119869 = intinfin0

[1199081 |119890 (119905)| + 1199082119906 (119905)2] 119889119905 + 1199083119905119903 (13)



if |119890 (119905)| gt 120575then 119869

= intinfin0

[1199081 |119890 (119905)| + 11990821199062 (119905) + 1199084 1003816100381610038161003816err119910 (119905)1003816100381610038161003816] 119889119905+ 1199083119905119903

(14)




0 10 20 30 40 50 60 70 80 90 100Generation

Fitn

ess v

alue

Best 16448 Mean 27333


100

101

102

103













10 20 30 40 50 60013

015

017

019

021

023

025

027028


Out

put m

oistu

re co

nten

t

The target value

(1)(2)

(4)(3)











utpu

t moi

sture

cont

ent

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018



(a)

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018


Out

put m

oistu

re co

nten

t

(3)

(4)

(2)(1)





(b)










5 Conclusion






Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of















Graindryer


Output



Immune algorithm




Frequency converter

e(t)

dedt

minus +




119878 (119896) = TH (119896) minus TS (119896) (7)



119870119901 = 119896 1ndash120578119891 [120576 (119896) Δ120576 (119896)] (8)




1199061015840 (119896) = (1198961199011015840 + 1198961198941015840119911 minus 1 + 1198961198891015840 119911 minus 1119911 ) 119890 (119896) (9)



(10)

where


(11)



Immunecontroller

Integral

Proportional

Derivative

Fuzzy controller


r (k)e (k)

minus

u(k)

Δu(k)

u (k)

y (k)

f(u (k) Δu (k))







119891 [1199061015840 (119896) Δ1199061015840 (119896)] Δ1199061015840 (119896)P Z N








0 02 04 06 08 10

02040608

1D

egre

e of m

embe

rshi

pN Z P

Input variable u(k)


(a)

0 02 04 06 08 10

02040608

1

Deg

ree o

f mem

bers

hip

N Z P



(b)

0 02 04 06 08 1

002040608

1

Deg

ree o

f mem

bers

hip

NB NS Z PS PB


(c)

00510

1

005

f

minus05

minus05 minus1

minus1

Δu (k)

u(k)

(d)


Dryingmodel


PID controller



r (k) e (k)

minus

dedt ΔkpΔki Δkd

u(k)

u (k)

f(u Δu)

minus1ku

y (k)dudt






1198961198941015840 (119896) = 1198961198941015840 + Δ1198961198941015840 (119896) 1198961198891015840 (119896) = 1198961198891015840 + Δ1198961198891015840 (119896)

(12)


















119869 = intinfin0

[1199081 |119890 (119905)| + 1199082119906 (119905)2] 119889119905 + 1199083119905119903 (13)



if |119890 (119905)| gt 120575then 119869

= intinfin0

[1199081 |119890 (119905)| + 11990821199062 (119905) + 1199084 1003816100381610038161003816err119910 (119905)1003816100381610038161003816] 119889119905+ 1199083119905119903

(14)




0 10 20 30 40 50 60 70 80 90 100Generation

Fitn

ess v

alue

Best 16448 Mean 27333


100

101

102

103













10 20 30 40 50 60013

015

017

019

021

023

025

027028


Out

put m

oistu

re co

nten

t

The target value

(1)(2)

(4)(3)











utpu

t moi

sture

cont

ent

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018



(a)

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018


Out

put m

oistu

re co

nten

t

(3)

(4)

(2)(1)





(b)










5 Conclusion






Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





Immunecontroller

Integral

Proportional

Derivative

Fuzzy controller


r (k)e (k)

minus

u(k)

Δu(k)

u (k)

y (k)

f(u (k) Δu (k))







119891 [1199061015840 (119896) Δ1199061015840 (119896)] Δ1199061015840 (119896)P Z N








0 02 04 06 08 10

02040608

1D

egre

e of m

embe

rshi

pN Z P

Input variable u(k)


(a)

0 02 04 06 08 10

02040608

1

Deg

ree o

f mem

bers

hip

N Z P



(b)

0 02 04 06 08 1

002040608

1

Deg

ree o

f mem

bers

hip

NB NS Z PS PB


(c)

00510

1

005

f

minus05

minus05 minus1

minus1

Δu (k)

u(k)

(d)


Dryingmodel


PID controller



r (k) e (k)

minus

dedt ΔkpΔki Δkd

u(k)

u (k)

f(u Δu)

minus1ku

y (k)dudt






1198961198941015840 (119896) = 1198961198941015840 + Δ1198961198941015840 (119896) 1198961198891015840 (119896) = 1198961198891015840 + Δ1198961198891015840 (119896)

(12)


















119869 = intinfin0

[1199081 |119890 (119905)| + 1199082119906 (119905)2] 119889119905 + 1199083119905119903 (13)



if |119890 (119905)| gt 120575then 119869

= intinfin0

[1199081 |119890 (119905)| + 11990821199062 (119905) + 1199084 1003816100381610038161003816err119910 (119905)1003816100381610038161003816] 119889119905+ 1199083119905119903

(14)




0 10 20 30 40 50 60 70 80 90 100Generation

Fitn

ess v

alue

Best 16448 Mean 27333


100

101

102

103













10 20 30 40 50 60013

015

017

019

021

023

025

027028


Out

put m

oistu

re co

nten

t

The target value

(1)(2)

(4)(3)











utpu

t moi

sture

cont

ent

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018



(a)

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018


Out

put m

oistu

re co

nten

t

(3)

(4)

(2)(1)





(b)










5 Conclusion






Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





0 02 04 06 08 10

02040608

1D

egre

e of m

embe

rshi

pN Z P

Input variable u(k)


(a)

0 02 04 06 08 10

02040608

1

Deg

ree o

f mem

bers

hip

N Z P



(b)

0 02 04 06 08 1

002040608

1

Deg

ree o

f mem

bers

hip

NB NS Z PS PB


(c)

00510

1

005

f

minus05

minus05 minus1

minus1

Δu (k)

u(k)

(d)


Dryingmodel


PID controller



r (k) e (k)

minus

dedt ΔkpΔki Δkd

u(k)

u (k)

f(u Δu)

minus1ku

y (k)dudt






1198961198941015840 (119896) = 1198961198941015840 + Δ1198961198941015840 (119896) 1198961198891015840 (119896) = 1198961198891015840 + Δ1198961198891015840 (119896)

(12)


















119869 = intinfin0

[1199081 |119890 (119905)| + 1199082119906 (119905)2] 119889119905 + 1199083119905119903 (13)



if |119890 (119905)| gt 120575then 119869

= intinfin0

[1199081 |119890 (119905)| + 11990821199062 (119905) + 1199084 1003816100381610038161003816err119910 (119905)1003816100381610038161003816] 119889119905+ 1199083119905119903

(14)




0 10 20 30 40 50 60 70 80 90 100Generation

Fitn

ess v

alue

Best 16448 Mean 27333


100

101

102

103













10 20 30 40 50 60013

015

017

019

021

023

025

027028


Out

put m

oistu

re co

nten

t

The target value

(1)(2)

(4)(3)











utpu

t moi

sture

cont

ent

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018



(a)

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018


Out

put m

oistu

re co

nten

t

(3)

(4)

(2)(1)





(b)










5 Conclusion






Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of















119869 = intinfin0

[1199081 |119890 (119905)| + 1199082119906 (119905)2] 119889119905 + 1199083119905119903 (13)



if |119890 (119905)| gt 120575then 119869

= intinfin0

[1199081 |119890 (119905)| + 11990821199062 (119905) + 1199084 1003816100381610038161003816err119910 (119905)1003816100381610038161003816] 119889119905+ 1199083119905119903

(14)




0 10 20 30 40 50 60 70 80 90 100Generation

Fitn

ess v

alue

Best 16448 Mean 27333


100

101

102

103













10 20 30 40 50 60013

015

017

019

021

023

025

027028


Out

put m

oistu

re co

nten

t

The target value

(1)(2)

(4)(3)











utpu

t moi

sture

cont

ent

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018



(a)

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018


Out

put m

oistu

re co

nten

t

(3)

(4)

(2)(1)





(b)










5 Conclusion






Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





0 10 20 30 40 50 60 70 80 90 100Generation

Fitn

ess v

alue

Best 16448 Mean 27333


100

101

102

103













10 20 30 40 50 60013

015

017

019

021

023

025

027028


Out

put m

oistu

re co

nten

t

The target value

(1)(2)

(4)(3)











utpu

t moi

sture

cont

ent

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018



(a)

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018


Out

put m

oistu

re co

nten

t

(3)

(4)

(2)(1)





(b)










5 Conclusion






Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





utpu

t moi

sture

cont

ent

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018



(a)

95 100 105 110 115 120 125 130 135 140

015

0155

016

0165

017

0175

018


Out

put m

oistu

re co

nten

t

(3)

(4)

(2)(1)





(b)










5 Conclusion






Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






5 Conclusion






Acknowledgments


References
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of











Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Documents

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