Research Article PSO-RBF Neural Network PID...

Research ArticlePSO-RBF Neural Network PID Control Algorithmof Electric Gas Pressure Regulator

Yuanchang Zhong12 Xu Huang1 Pu Meng1 and Fachuan Li1

1 College of Communication Engineering Chongqing University Chongqing 400044 China2 School of Automation Chongqing University Chongqing 400044 China

Correspondence should be addressed to Yuanchang Zhong zyccqueducn

Received 8 April 2014 Accepted 2 June 2014 Published 24 July 2014

Academic Editor Zidong Wang

Copyright copy 2014 Yuanchang Zhong et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The current electric gas pressure regulator often adopts the conventional PID control algorithm to take drive control of the core part(micromotor) of electric gas pressure regulator In order to further improve tracking performance and to shorten response timethis paper presents an improved PID intelligent control algorithmwhich applies to the electric gas pressure regulatorThe algorithmuses the improved RBF neural network based on PSO algorithm tomake online adjustment on PID parametersTheoretical analysisand simulation result show that the algorithm shortens the step response time and improves tracking performance

1 Introduction

With the implementation of the strategy on Western devel-opment and west-east gas transmission project the city gashas developed rapidly How to use gas for higher energysaving and environmental protection and ensure the safetyand reliability of the system has been a key problem and thisbrings opportunity to gas pressure regulating Gas pressureregulating is one of the most important parts of city gaspipeline system and the key technology of highly efficientuse of natural gas resources The gas pressure regulating canensure the output pressure in special range when the pressurereaches a certain value it can be effectively shut off to ensuresafe delivery of gas Currently the accuracy of gas pressureregulators at home and abroad that adopt the traditionaldirect- or indirect-acting regulating principle is not high andsusceptible to external environmental factorsThe accuracy ofgas pressure regulator affects the downstream gas supply sys-tem directly and reduces the efficiency of energy conversionthus resulting in energy waste and environmental pollutionand even possible supply security issues [1 2] In order tosolve the problems of mechanical gas regulator electric gaspressure regulating has become the main direction of thefuture pressure regulating technologyThe focus and difficult

problem of this field is how to improve the precision andstability and shorten the response time [3 4] We had an in-depth study in electric gas pressure regulator under the jointsupport of national innovation fund and Chongqing scienceand technology research project and achieved a series ofresearch results this paper discussed the control algorithmsof electric gas pressure regulator

The current electric gas pressure regulator often adoptsthe conventional PID control mode to take drive control ofthe core part (micromotor) of electric gas pressure regulator[5 6] For piped gas because of the unpredictable changesof downstream load the pipe friction and temperature thesystem is time-varying nonlinear and itrsquos difficult to build aprecise mathematical modelThe parameters of conventionalPID controller set by experts cannot be modified onlinewhich brings much difficulty to achieve the expected effects[7] The conventional PID controller ameliorating is neededto further improve accuracy and stability and to shortenresponse time

Researches show that RBF [8 9] with fast conver-gence speed and strong global approximation capability canapproximate any continuous and nonlinear networks witharbitrary precision and shows better performance in thenonlinear system problem-solving [10ndash12] Compared with

Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2014 Article ID 731368 7 pageshttpdxdoiorg1011552014731368

2 Abstract and Applied Analysis

1

Upstream pressureDownstream pressure

Figure 1 Self-actuated regulator

Control Stepper Transmission Stem Valve

Pressure sensor

Outlet pressure

Drive motor

y(k)

r(k)

minus

Figure 2 The principle diagram of electric gas pressure regulating system

back propagation (BP) neural network radial basis function(RBF) neural network has many advantages faster conver-gence speed less training iteration stronger robustness andno local minimum and so forth [13ndash15] RBF is extremelysensitive to the base-width vector the center vector the radialbasis layer and the selection of the initial value of connectionweights of output layer [16ndash18] If the parameters of thissystem are selected inappropriately the convergence rate ofthe network will be slow and easy to fall into local minima Tothis end we put forward a kind of improved PID intelligentcontrol algorithm which applies to the electric gas pressureregulator The algorithm uses the RBF neural network basedon PSO [19 20] to determine the initial parameters of thenetwork [21] and then makes online adjustment on PIDparameters to improve the control accuracy response speedand tracking performance of the system

2 Electric Gas Pressure Regulating System

The basic principle of traditional pressure regulating ismechanical balance The electric gas pressure regulatingsystem range from simple single stage [22] to more complexmultistage [23] and the principle of operation is the same inall [24 25]The internal structure is shown in Figure 1 Whenthe outlet pressure P2 is stable the upward force P2 acting onthe film is balanced against the spring force If P2 decreases

the spring force is greater than the upward force of the filmThen the spring will move down and pull the valve to moveupward to increase valve opening and the downstream flowthereby increasing the gas outlet pressure until the systemreaches a new mechanical equilibrium Obviously as timegoes on the loss of accuracy of the regulator occurs because ofthe reduced elasticity of the spring and the frictionrsquos damageon diaphragmTherefore we replace the original mechanicalpressure regulating components with stepping motor anddriving system (part 1 of Figure 1) thereof by rebuilding coreparts of pressure regulator The system principle diagramof the improved electric gas pressure regulating is shownin Figure 2 We use the intelligent air pressure sensor arrayand adopts the information fusion algorithm to detect theelectric gas regulatorrsquos inlet and outlet pressure [26] Makingdifferential operation with set pressure value and the resultvalue as the input parameter of controller is to adjust therotation angle of the stepping motor according to the controlalgorithm If the outlet pressure value is less than the setpressure value the stepping motor will rotate forward on thecontrary it will reverse The motor through the driving sys-tem transforms the angle of motor into linear displacementof output shaft which drives the valve rod to control the valveopening and adjust the outlet pressure From the workingprinciple we can draw that the regulator system is a singleinputsingle output closed-loop control system

Abstract and Applied Analysis 3

For static and dynamic analysis of the system we needto model the system that mainly includes drive motor modeltransmissionmodel and regulator valvemodel According tothe pneumatic dynamics the transfer function of controlledobject system of pressure valve [27] can be approximatelyexpressed as

119866119867 (119904) =

11988411198701

11988541199044 + 119885

31199043 + 119885

21199042 + 119885

1119904 + 1198850

(1)

3 PID Controller Based on PSO-RBFNeural Network

31 Parameters Tuning of PID Controller by RBF NeuralNetwork Choose the stepper motor as the operator of theelectric gas pressure regulator and use digital incrementalPID control mode the control algorithm can be expressed bythe following difference equation

Δ119906 (119896) = 119906 (119896) minus 119906 (119896 minus 1)

= 119870119901

Δ119890 (119896) + 119870119894119890 (119896) + 119870

119889 (Δ119890 (119896) minus Δ119890 (119896 minus 1))

(2)

In formula (2) 119870119901 119870119894 and 119870

119889are constant parameters which

cannot be adjusted online and expected control effect isimpossible to get when the controlled system is nonlinear oris with large delay Therefore we adjust PID parameters withRBF neural network online The performance index of PIDparameter is

119864 (119896) =1

2[119903(119896) minus 119910(119896)]

2=

1

2119890(119896)2 (3)

In formula (3) 119903(119896) is the set value of outlet pressure 119910(119896) isthe actual output value of system and 119896 is the sampling timeIn order to minimize the 119864(119896) 119870

119901 119870119894 and 119870

119889are sets via the

gradient descent method Consider

Δ119870119901

= minus120578120597119864

120597119896119901

= minus120578120597119864

120597119910

120597119910

120597Δ119906

120597Δ119906

120597119896119901

= 120578119901

119890 (119896)120597119910

120597Δ119906[119890 (119896) minus 119890 (119896 minus 1)]

(4)

Δ119870119894

= minus120578120597119864

120597119896119894

= minus120578120597119864

120597119910

120597119910

120597Δ119906

120597Δ119906

120597119896119894

= 120578119894119890 (119896)

120597119910

120597Δ119906119890 (119896)

(5)

Δ119870119889

= minus120578119889

120597119864

120597119896119889

= minus120578120597119864

120597119910

120597119910

120597Δ119906

120597Δ119906

120597119896119889

= 120578119889119890 (119896)

120597119910

120597Δ119906

times [119890 (119896) minus 2119890 (119896 minus 1) + 119890 (119896 minus 2)]

(6)

To find Δ119870119901 Δ119870119894 and Δ119870

119889in (4) (5) and (6) respectively

we must figure out 120597119910120597Δ119906 which can be approximately gotby Jacobian matrix of RBF neural network The radial basis

function is 119867 = [ℎ1 ℎ2 ℎ

119898] and it is usually expressed by

Gauss function Consider

ℎ119895 (119883) = exp(minus

10038171003817100381710038171003817119883 minus 119862

119895

10038171003817100381710038171003817

21198872

119895

2

) 119895 = 1 2 119898 (7)

In formula (7) 119883 = 1199091 1199092 119909

119899119879 is the 119870-dimensional

input layer vector 119862119895is the central value of 119895 node and

119861 = [1198871 1198872 119887

119898]119879 is basis-width vector of the network

119882 = [1199081 1199082 119908

119898]119879 is weight vector of the network so

the output layer can be expressed as 119910119898

= 1199081ℎ1

+ 1199082ℎ2

+ sdot sdot sdot +

119908119898

ℎ119898 The performance index function of RBF is

119869 =1

2[119910 (119896) minus 119910

119898 (119896)]2 (8)

In formula (8) 119910(119896) is the actual output of the controlledobject after 119870 iterations In order to make 119869 minimumaccording to the gradient descent method the iterativealgorithm of output weights center vector and basis-widthvector parameters is shown as follows

Δ119908119895

= [119910 (119896) minus 119910119898 (119896)] ℎ

119895

119908119895 (119896) = 119908

119895 (119896 minus 1) + 120578Δ119908119895

+ 119886 [119908119895 (119896 minus 1) minus 119908

119895 (119896 minus 2)]

Δ119888119895119894

= [119910 (119896) minus 119910119898 (119896)] 119908

119895

119909119895

minus 119888119895119894

1198872

119895

119888119895119894 (119896) = 119888

119895119894 (119896 minus 1) + 120578Δ119888119895119894

+ 120572 [119888119895119894 (119896 minus 1) minus 119888

119895119894 (119896 minus 2)]

Δ119887119895

= [119910 (119896) minus 119910119898 (119896)] 119908

119895ℎ119895

10038171003817100381710038171003817119883 minus 119862

119895

10038171003817100381710038171003817

1198873

119895

119887119895 (119896) = 119887

119895 (119896 minus 1) + 120578Δ119887119895

+ 119886 [119887119895 (119896 minus 1) minus 119887

119895 (119896 minus 2)]

(9)

In (9) 120578 is the learning rate and 120572 is the momentum factorSince the online identification ability of neural networks inJacobian matrix (sensitivity of output versus input change) ispowerful when the neural network identifier can approachthe object we can use 119910

119898(119896) instead of the actual output of

the controlled object in the system 119910(119896) The Jacobian matrixalgorithm of neural network is

120597119910 (119896)

120597Δ119906 (119896)=

120597119910119898 (119896)

120597Δ119906 (119896)=

119898

sum

119895=1

119908119895ℎ119895

119888119895119894

1198872

119895

(10)

In formula (10) 1199091

= Δ119906(119896) Δ119906(119896) = 119906(119896) minus 119906(119896 minus 1) TakingJacobian information of the RBF neural network into (4) (5)and (6) three parameter variations (Δ119870

119901 Δ119870119894 Δ119870119889) of PID

can be obtained Although RBF neural network can adjustPID parameters online the selection of the initial parameters


of RBF network will affect the performance of PID controldirectly so we use the particle swarm algorithm to optimizeRBF neural network to determine initial parameters of thenetwork

32 Realization of Particle Swarm Algorithm to Optimize RBFNeural Network Suppose there are m particles in a swarmthe information of 119894th particle is expressed by 119863 vectorso its position and velocity are expressed respectively as119883119894

= (1199091198941

1199091198942

119909119894119889

) and 119881119894

= V1198941

V1198942

V119894119889

After eachiteration every particle updates its position and velocityaccording to individual extremism (pbest) and groupextremum (gbest) which are shown as follows

V119894119889 (119896 + 1)

= 120582V119894119889 (119896)

+ 11988811199031

(119901119894119889 (119896) minus 119909

119894119889 (119896)) + 11988821199032

(119901119892119889 (119896) minus 119909

119894119889 (119896))

(11)

119909119894119889 (119896 + 1) = 119909

119894119889 (119896) + V119894119889 (119896) (12)

In formula (11) 1198881and 119888

2are learning factors 119903

1and

1199032

sub (0 1) are random variables 120582 is the inertia factor and 119896

is an iteration number A large number of experiments showthat with the algorithm iteration performing 120582 decreaseslinearly improving the convergence of the performance ofthe algorithm significantly [28] Consider

120582 = 120582max minus119896 times (120582max minus 120582min)

120582max (13)

In formula (13) 120582max and 120582min are the maximum andminimum values of 120582 and 119896max is the total number ofiterations and make 120582max = 09 and 120582min = 04 The PSOalgorithm convergence is quick but easy to fall into localoptima This paper makes individual mutate at a certainprobability by using genetic algorithm variation theory Thespecific steps of center vector basis-width vector and outputweights of RBF neural network optimized by particle swarmoptimization are as follows

(1) particle swarm initialization determine the numberof particle swarm the initial position speed individ-ual extremum and swarm extremum

(2) map each individual component to the RBF networkparameters and put them into the neural network tocalculate the fitness value

(3) identify individual extremum and swarm extremumaccording to fitness value

(4) update the particlersquos velocities and positions accord-ing to formulas (11) and (12)

(5) if the number of iterations reaches a predeterminedmaximum or meet the performance requirements ofminimum error stop the iteration and output currentswarm extremum as initial parameters of the RBFneural network or return to Step (2)

Electricregulator

Feedback

PID

PSO-RBF

r(k) e(k)

minus

minus

y(k)u(k)

link

controller

Figure 3 The PID control block diagram set by PSO-RBF online

33 PID Controller Design of PSO-RBF Neural Network RBFneural network-based PID control algorithm can solve theshortage problem of conventional PID control and PSOalgorithm can solve the problem of the initial parameters ofRBF network The structure of PID controller of PSO-RBFneural network is shown in Figure 3

The controller is composed of two parts the classic PIDcontroller with 119870

119875 119870119894 and 119870

119889modified by PSO-RBF online

and PSO-RBF network firstly it uses PSO algorithm toinitialize the output weights the node center and the basis-width of the RBF neural network and secondly it utilizesthe gradient information of RBF neural network onlineidentification to adjust three parameters of PID controlleronline control electric regulator valve opening and adjustthe downstream outlet pressure quickly and accurately Thesteps of PID intelligent controller algorithm of PSO-RBFneural network are as follows

(1) select RBF structure initialize the input layer nodenumber 119899 the hidden layer node number 119898 thelearning rate 120578 and the momentum factor 120572

(2) determine the output weights center node and initialvalue of node basis-width vector of RBF neural net-work algorithm by using particle swarm algorithm

(3) take the Jacobian information into formulas (4) (5)and (6) obtain PID parameter increments Δ119896

119875 Δ119896119894

and Δ119896119889 and correct 119896

119901 119896119894 and 119896

119889online

(4) make 119896 = 119896 + 1 and return to Step (3) until it reachesthe cycle index or meets the performance index

4 Simulation Results and Analysis

The function of electric gas pressure regulator system canrefer to formula (1) with the following values 119885

1= 5327 times

1041198852

= 1135times1061198853

= 81931198854

= 105711988411198701

= 1328times

109 and 119885

0= 8688 times 10

8 then discretize it considering thesampling period 119879 = 0001 s and get the 119885 transform

119866119867 (119911) = (523 times 10

minus71199113

+ 575 times 10minus6

1199112


119911 + 575 times 10minus7

)

times (1199114

minus 3991199113

+ 5981199112

minus 399119911 + 100)minus1

(14)

41 Step Response To test the ability of the system responseto a step input RBF network structure is chosen as 3-6-1


0 10 20 30 40 50 600

02

04

06

08

1

12

Time (s)

Ideal positionOnly PID

RBF-PID PSO-RBF-PID

ydy

Figure 4 The step response of three kinds of algorithms

Suppose 120578 = 050 120572 = 005 120578119901

= 120578119894

= 120578119889

= 015and 119896

1199010= 1198961198940

= 1198961198890

= 01 Individual information ofparticle swarm consists of 30 dimension vectors which aremapped to the RBF network parameters and its evaluationstandard is the minimum error of RBF neural network PIDcontroller The population size of PSO algorithm is 20 andthe number of iterations is 100 119888

1= 1198882

= 2 and individualmutation probability is 004 In RBF network without beingoptimized by PSO its initial value is 119862

119895= 9 times rands(3 6)

119861 = 9timesrands(3 6) and119882 = 9timesrands(6 1)The conventionalPID parameters 119870

119901= 119870119894

= 119870119889

= 01 The step responseof three kinds of algorithms in Figure 4 shows that the stepresponse curve time of the system is 24 s and is in a stablestate under the adaptive control of PID parameter by PSO-RBF While without using PSO to optimize RBF or adoptingconventional PID control the curve reaches a steady state in12 s and 32 s respectively The conclusion is that PSO-RBF-PID has the shortest response time and the minimum error

The parameters adaptive tuning curve of PSO-RBF neuralnetwork PID controller is shown in Figure 5 it is set finallythat 119870

119901= 0280 119870

119894= 1290 and 119870

119889= 0001

The minimum error evolution of PSO-RBF neural net-work is shown in Figure 6 The minimum error changesobviously in the early stage and reaches an optimal value at63th iteration RBF network parameters optimized after 100times are as follows

119862119895

= [

[

032 011 002 minus021 037 055

minus036 minus013 030 minus003 minus030 minus006

minus035 016 001 003 minus021 020

]

]

119861 = [021 011 030 032 036 048]119879

119882 = [minus039 016 038 minus037 minus057 045]119879

(15)

42 Tracking Performance According to the actual needs ofthe regulator electric pressure regulator will be formulatedaccording to the input pressure fast regulate valve openingand make the outlet pressure stable in the range of errors Sowe need to test the tracking performance of the control sys-temThe tracking curves of three kinds of control algorithms

0 10 20 30 40 50 600

02

04

Time (s)

0 10 20 30 40 50 60Time (s)

0 10 20 30 40 50 60Time (s)

0

1

2

0

02

04

kp

ki

kd

Figure 5 The adaptive tuning curve of PSO-RBF neural networkPID controller

0 20 40 60 80 100200

300

400

500

600

700

Iterations

Min

imum

erro

r

Figure 6 The minimum error evolution of PSO-RBF neuralnetwork

are shown in Figure 7 It shows that electric gas pressureregulator which adopts the PSO-RBF-PID has good dynamicperformance and higher control precision

5 Conclusion

An in-depth research has been conducted on the mechanismof electric gas regulator about its nonhigh control precisionand stability and a longer response time It shows that theexisting electric gas regulators widely use conventional PIDcontrol mode for it is simple and easy to be implementedHowever it is difficult to establish a precise mathematicalmodel given that the pressure regulating system is time-varying and nonlinear Meanwhile the conventional PIDcontroller parameters usually set in line with human expe-rience cannot be modified online So it is hard to achievethe expected control effect to use conventional incrementalPID control mode Therefore on the basis of the original


0 05 1 15 2Time (s)

Ideal positionOnly PID RBF-PID

PSO-RBF-PID

ydy

1

05

0

minus05

minus1

Figure 7 The tracking curves of three kinds of control algorithm

incremental PID control mode the RBF neural networkbased on PSO optimization is utilized to determine the initialparameters of the network and then again set PIDparametersonline thus an improved PID intelligent control algorithmsuitable for electric gas pressure regulator is establishedTheoretical analysis and experimental results demonstratethat the algorithm improves the control accuracy responsespeed and tracking performance of electric gas pressureregulator and can be widely applied to the field of electric gaspressure

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This paper was supported by the National Natural ScienceFoundation of China (no 10C26215113031) and the Scientificand Technological Project of Chongqing (no CSTC2010gg-yyjs40010)

References

[1] C Gongjian S Fengbin W Lili et al ldquoAnalysis on natural gaspressure regulator design principle and itrsquos influence factorsrdquoNatural Gas and Oil vol 29 no 3 pp 67ndash71 2011

[2] F Liang J Di and L Shuhui ldquoStudy on dynamic model ofsingle-stage self-operated gas regulatorrdquo Gas and Heat vol 29no 2 pp B10ndashB13 2009

[3] C Yudong W Yong and L Yanjun ldquoOverview of control valvetechnologyrdquo Control and Instruments in Chemical Industry vol39 no 9 pp 1111ndash1114 2012

[4] Z Xiaomu and Z Mingjun ldquoOptimum configuration in pres-sure regulation system at delivery station in gas pipelinerdquoNatural Gas and Oil vol 23 no 4 pp 27ndash29 2005

[5] Z Rongrong Z Shiwen and S Guohua ldquoThe design ofan intelligent controller for use with electric valve-actuatorsrdquoIndustral Instrumentation Automation no 4 pp 26ndash28 2005

[6] L Zhiguo L Jian and X Lixin ldquoElectric pressure regulatingvalve and self-reliance type pressure regulating valve of combi-nation stationrdquoOil-Gas Field Surface Engineering vol 31 no 11p 108 2012

[7] L Wang W F Li and D Z Zheng ldquoOptimal design ofcontrollers for non-minimum phase systemsrdquo Acta AutomaticaSinica vol 29 no 1 pp 135ndash141 2003

[8] Y D Song Q Cao X Du and H R Karimi ldquoControl strategybased on wavelet transform and neural network for hybridpower systemrdquo Journal of AppliedMathematics vol 2013 ArticleID 375840 8 pages 2013

[9] A Zhang C Chen and H R Karimi ldquoA new adaptive LSSVRwith online multikernel RBF tuning to evaluate analog circuitperformancerdquo Abstract and Applied Analysis vol 2013 ArticleID 231735 7 pages 2013

[10] X Dong Y Zhao H R Karimi and P Shi ldquoAdaptive variablestructure fuzzy neural identification and control for a class ofMIMO nonlinear systemrdquo Journal of the Franklin Institute vol350 no 5 pp 1221ndash1247 2013

[11] C C Chuang J T Jeng and P T Lin ldquoAnnealing robustradial basis function networks for function approximation withoutliersrdquo Neurocomputing vol 56 no 1ndash4 pp 123ndash139 2004

[12] J K Sing D K Basu M Nasipuri and M Kundu ldquoFace recog-nition using point symmetry distance-based RBF networkrdquoApplied Soft Computing Journal vol 7 no 1 pp 58ndash70 2007

[13] H Liu S Wang and P Ouyang ldquoFault diagnosis in a hydraulicposition servo system using RBF neural networkrdquo ChineseJournal of Aeronautics vol 19 no 4 pp 346ndash353 2006

[14] Z A Bashir and M E El-Hawary ldquoApplying wavelets to short-term load forecasting using PSO-based neural networksrdquo IEEETransactions on Power Systems vol 24 no 1 pp 20ndash27 2009

[15] C Zhang M Lin and M Tang ldquoBP neural network optimizedwith PSO algorithm for daily load forecastingrdquo in Proceedingsof the International Conference on Information ManagementInnovation Management and Industrial Engineering (ICIII rsquo08)vol 56 pp 82ndash85 December 2008

[16] K Meng Z Y Dong D H Wang and K P Wong ldquoA self-adaptive RBF neural network classifier for transformer faultanalysisrdquo IEEE Transactions on Power Systems vol 25 no 3 pp1350ndash1360 2010

[17] G Li Q Zhang and Y Liang ldquoGA-based PID neural networkcontrol for magnetic bearing systemsrdquo Chinese Journal ofMechanical Engineering vol 20 no 2 pp 56ndash59 2007

[18] W Lianghong W Yaonan Z Shaowu and T Wen ldquoDesign ofpid controller with incomplete derivation based on differentialevolution algorithmrdquo Journal of Systems Engineering and Elec-tronics vol 19 no 3 pp 578ndash583 2008

[19] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of IEEE International Conference on NeuralNetworks pp 1942ndash1948 December 1995

[20] M Barari H R Karimi and F Razaghian ldquoAnalog circuitdesign optimization based on evolutionary algorithmsrdquo Math-ematical Problems in Engineering vol 2014 Article ID 59368412 pages 2014

[21] M Sheikhan R Shahnazi and S Garoucy ldquoSynchroniza-tion of general chaotic systems using neural controllers withapplication to secure communicationrdquo Neural Computing andApplications vol 22 no 2 pp 361ndash373 2013

[22] R Mooney ldquoPilot-loaded regulators what you need to knowrdquoGas Industries vol 34 no 1 pp 31ndash33 1989

[23] AKrigmanGuide to Selecting Pressure Regulators InTech 1984


[24] A E Rundell S V Drakunov and R A DeCarlo ldquoA slidingmode observer and controller for stabilization of rotationalmotion of a vertical shaft magnetic bearingrdquo IEEE Transactionson Control Systems Technology vol 4 no 5 pp 598ndash608 1996

[25] N Zafer and G R Luecke ldquoStability of gas pressure regulatorsrdquoApplied Mathematical Modelling vol 32 no 1 pp 61ndash82 2008

[26] Y Zhong F Wang L Zhang and C Tao ldquoThe informationfusion algorithm on gaspressure regulator inletoutlet detec-tionrdquo Journal of Computational Information Systems vol 10 no5 pp 2145ndash2153 2014

[27] W Zhi Study on Dynamic Characteristic and Control of ElectricControl Valve Shan Dong University 2013

[28] Y H Shi and R C Eberhart ldquoEmpirical study of particle swarmoptimizationrdquo in Proceedings of the Congress on EvolutionaryComputation pp 1945ndash1950 Piscataway NJ USA 1999

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1

Upstream pressureDownstream pressure

Figure 1 Self-actuated regulator

Control Stepper Transmission Stem Valve

Pressure sensor

Outlet pressure

Drive motor

y(k)

r(k)

minus

Figure 2 The principle diagram of electric gas pressure regulating system

back propagation (BP) neural network radial basis function(RBF) neural network has many advantages faster conver-gence speed less training iteration stronger robustness andno local minimum and so forth [13ndash15] RBF is extremelysensitive to the base-width vector the center vector the radialbasis layer and the selection of the initial value of connectionweights of output layer [16ndash18] If the parameters of thissystem are selected inappropriately the convergence rate ofthe network will be slow and easy to fall into local minima Tothis end we put forward a kind of improved PID intelligentcontrol algorithm which applies to the electric gas pressureregulator The algorithm uses the RBF neural network basedon PSO [19 20] to determine the initial parameters of thenetwork [21] and then makes online adjustment on PIDparameters to improve the control accuracy response speedand tracking performance of the system

2 Electric Gas Pressure Regulating System

The basic principle of traditional pressure regulating ismechanical balance The electric gas pressure regulatingsystem range from simple single stage [22] to more complexmultistage [23] and the principle of operation is the same inall [24 25]The internal structure is shown in Figure 1 Whenthe outlet pressure P2 is stable the upward force P2 acting onthe film is balanced against the spring force If P2 decreases

the spring force is greater than the upward force of the filmThen the spring will move down and pull the valve to moveupward to increase valve opening and the downstream flowthereby increasing the gas outlet pressure until the systemreaches a new mechanical equilibrium Obviously as timegoes on the loss of accuracy of the regulator occurs because ofthe reduced elasticity of the spring and the frictionrsquos damageon diaphragmTherefore we replace the original mechanicalpressure regulating components with stepping motor anddriving system (part 1 of Figure 1) thereof by rebuilding coreparts of pressure regulator The system principle diagramof the improved electric gas pressure regulating is shownin Figure 2 We use the intelligent air pressure sensor arrayand adopts the information fusion algorithm to detect theelectric gas regulatorrsquos inlet and outlet pressure [26] Makingdifferential operation with set pressure value and the resultvalue as the input parameter of controller is to adjust therotation angle of the stepping motor according to the controlalgorithm If the outlet pressure value is less than the setpressure value the stepping motor will rotate forward on thecontrary it will reverse The motor through the driving sys-tem transforms the angle of motor into linear displacementof output shaft which drives the valve rod to control the valveopening and adjust the outlet pressure From the workingprinciple we can draw that the regulator system is a singleinputsingle output closed-loop control system



119866119867 (119904) =

11988411198701

11988541199044 + 119885

31199043 + 119885

21199042 + 119885

1119904 + 1198850

(1)



Δ119906 (119896) = 119906 (119896) minus 119906 (119896 minus 1)

= 119870119901

Δ119890 (119896) + 119870119894119890 (119896) + 119870

119889 (Δ119890 (119896) minus Δ119890 (119896 minus 1))

(2)

In formula (2) 119870119901 119870119894 and 119870



119864 (119896) =1

2[119903(119896) minus 119910(119896)]

2=

1

2119890(119896)2 (3)


119901 119870119894 and 119870



Δ119870119901

= minus120578120597119864

120597119896119901

= minus120578120597119864

120597119910

120597119910

120597Δ119906

120597Δ119906

120597119896119901

= 120578119901

119890 (119896)120597119910

120597Δ119906[119890 (119896) minus 119890 (119896 minus 1)]

(4)

Δ119870119894

= minus120578120597119864

120597119896119894

= minus120578120597119864

120597119910

120597119910

120597Δ119906

120597Δ119906

120597119896119894

= 120578119894119890 (119896)

120597119910

120597Δ119906119890 (119896)

(5)

Δ119870119889

= minus120578119889

120597119864

120597119896119889

= minus120578120597119864

120597119910

120597119910

120597Δ119906

120597Δ119906

120597119896119889

= 120578119889119890 (119896)

120597119910

120597Δ119906


(6)

To find Δ119870119901 Δ119870119894 and Δ119870






ℎ119895 (119883) = exp(minus

10038171003817100381710038171003817119883 minus 119862

119895

10038171003817100381710038171003817

21198872

119895

2

) 119895 = 1 2 119898 (7)

In formula (7) 119883 = 1199091 1199092 119909



119861 = [1198871 1198872 119887


119882 = [1199081 1199082 119908



= 1199081ℎ1

+ 1199082ℎ2

+ sdot sdot sdot +

119908119898


119869 =1

2[119910 (119896) minus 119910

119898 (119896)]2 (8)


Δ119908119895

= [119910 (119896) minus 119910119898 (119896)] ℎ

119895

119908119895 (119896) = 119908

119895 (119896 minus 1) + 120578Δ119908119895

+ 119886 [119908119895 (119896 minus 1) minus 119908

119895 (119896 minus 2)]

Δ119888119895119894

= [119910 (119896) minus 119910119898 (119896)] 119908

119895

119909119895

minus 119888119895119894

1198872

119895

119888119895119894 (119896) = 119888

119895119894 (119896 minus 1) + 120578Δ119888119895119894

+ 120572 [119888119895119894 (119896 minus 1) minus 119888

119895119894 (119896 minus 2)]

Δ119887119895

= [119910 (119896) minus 119910119898 (119896)] 119908

119895ℎ119895

10038171003817100381710038171003817119883 minus 119862

119895

10038171003817100381710038171003817

1198873

119895

119887119895 (119896) = 119887

119895 (119896 minus 1) + 120578Δ119887119895

+ 119886 [119887119895 (119896 minus 1) minus 119887

119895 (119896 minus 2)]

(9)




120597119910 (119896)

120597Δ119906 (119896)=

120597119910119898 (119896)

120597Δ119906 (119896)=

119898

sum

119895=1

119908119895ℎ119895

119888119895119894

1198872

119895

(10)

In formula (10) 1199091


119901 Δ119870119894 Δ119870119889) of PID





= (1199091198941

1199091198942

119909119894119889

) and 119881119894

= V1198941

V1198942

V119894119889


V119894119889 (119896 + 1)

= 120582V119894119889 (119896)

+ 11988811199031

(119901119894119889 (119896) minus 119909

119894119889 (119896)) + 11988821199032

(119901119892119889 (119896) minus 119909

119894119889 (119896))

(11)

119909119894119889 (119896 + 1) = 119909

119894119889 (119896) + V119894119889 (119896) (12)

In formula (11) 1198881and 119888


1and

1199032




120582max (13)







Electricregulator

Feedback

PID

PSO-RBF

r(k) e(k)

minus

minus

y(k)u(k)

link

controller




119875 119870119894 and 119870






119875 Δ119896119894

and Δ119896119889 and correct 119896

119901 119896119894 and 119896

119889online




1= 5327 times

1041198852

= 1135times1061198853

= 81931198854

= 105711988411198701

= 1328times

109 and 119885

0= 8688 times 10


119866119867 (119911) = (523 times 10

minus71199113


1199112


119911 + 575 times 10minus7

)

times (1199114

minus 3991199113

+ 5981199112

minus 399119911 + 100)minus1

(14)



0 10 20 30 40 50 600

02

04

06

08

1

12

Time (s)


RBF-PID PSO-RBF-PID

ydy


Suppose 120578 = 050 120572 = 005 120578119901

= 120578119894

= 120578119889

= 015and 119896

1199010= 1198961198940

= 1198961198890


1= 1198882


119895= 9 times rands(3 6)


119901= 119870119894

= 119870119889



119901= 0280 119870

119894= 1290 and 119870

119889= 0001


119862119895

= [

[

032 011 002 minus021 037 055


minus035 016 001 003 minus021 020

]

]

119861 = [021 011 030 032 036 048]119879


(15)


0 10 20 30 40 50 600

02

04

Time (s)

0 10 20 30 40 50 60Time (s)

0 10 20 30 40 50 60Time (s)

0

1

2

0

02

04

kp

ki

kd


0 20 40 60 80 100200

300

400

500

600

700

Iterations

Min

imum

erro

r



5 Conclusion



0 05 1 15 2Time (s)


PSO-RBF-PID

ydy

1

05

0

minus05

minus1





Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119866119867 (119904) =

11988411198701

11988541199044 + 119885

31199043 + 119885

21199042 + 119885

1119904 + 1198850

(1)



Δ119906 (119896) = 119906 (119896) minus 119906 (119896 minus 1)

= 119870119901

Δ119890 (119896) + 119870119894119890 (119896) + 119870

119889 (Δ119890 (119896) minus Δ119890 (119896 minus 1))

(2)

In formula (2) 119870119901 119870119894 and 119870



119864 (119896) =1

2[119903(119896) minus 119910(119896)]

2=

1

2119890(119896)2 (3)


119901 119870119894 and 119870



Δ119870119901

= minus120578120597119864

120597119896119901

= minus120578120597119864

120597119910

120597119910

120597Δ119906

120597Δ119906

120597119896119901

= 120578119901

119890 (119896)120597119910

120597Δ119906[119890 (119896) minus 119890 (119896 minus 1)]

(4)

Δ119870119894

= minus120578120597119864

120597119896119894

= minus120578120597119864

120597119910

120597119910

120597Δ119906

120597Δ119906

120597119896119894

= 120578119894119890 (119896)

120597119910

120597Δ119906119890 (119896)

(5)

Δ119870119889

= minus120578119889

120597119864

120597119896119889

= minus120578120597119864

120597119910

120597119910

120597Δ119906

120597Δ119906

120597119896119889

= 120578119889119890 (119896)

120597119910

120597Δ119906


(6)

To find Δ119870119901 Δ119870119894 and Δ119870






ℎ119895 (119883) = exp(minus

10038171003817100381710038171003817119883 minus 119862

119895

10038171003817100381710038171003817

21198872

119895

2

) 119895 = 1 2 119898 (7)

In formula (7) 119883 = 1199091 1199092 119909



119861 = [1198871 1198872 119887


119882 = [1199081 1199082 119908



= 1199081ℎ1

+ 1199082ℎ2

+ sdot sdot sdot +

119908119898


119869 =1

2[119910 (119896) minus 119910

119898 (119896)]2 (8)


Δ119908119895

= [119910 (119896) minus 119910119898 (119896)] ℎ

119895

119908119895 (119896) = 119908

119895 (119896 minus 1) + 120578Δ119908119895

+ 119886 [119908119895 (119896 minus 1) minus 119908

119895 (119896 minus 2)]

Δ119888119895119894

= [119910 (119896) minus 119910119898 (119896)] 119908

119895

119909119895

minus 119888119895119894

1198872

119895

119888119895119894 (119896) = 119888

119895119894 (119896 minus 1) + 120578Δ119888119895119894

+ 120572 [119888119895119894 (119896 minus 1) minus 119888

119895119894 (119896 minus 2)]

Δ119887119895

= [119910 (119896) minus 119910119898 (119896)] 119908

119895ℎ119895

10038171003817100381710038171003817119883 minus 119862

119895

10038171003817100381710038171003817

1198873

119895

119887119895 (119896) = 119887

119895 (119896 minus 1) + 120578Δ119887119895

+ 119886 [119887119895 (119896 minus 1) minus 119887

119895 (119896 minus 2)]

(9)




120597119910 (119896)

120597Δ119906 (119896)=

120597119910119898 (119896)

120597Δ119906 (119896)=

119898

sum

119895=1

119908119895ℎ119895

119888119895119894

1198872

119895

(10)

In formula (10) 1199091


119901 Δ119870119894 Δ119870119889) of PID





= (1199091198941

1199091198942

119909119894119889

) and 119881119894

= V1198941

V1198942

V119894119889


V119894119889 (119896 + 1)

= 120582V119894119889 (119896)

+ 11988811199031

(119901119894119889 (119896) minus 119909

119894119889 (119896)) + 11988821199032

(119901119892119889 (119896) minus 119909

119894119889 (119896))

(11)

119909119894119889 (119896 + 1) = 119909

119894119889 (119896) + V119894119889 (119896) (12)

In formula (11) 1198881and 119888


1and

1199032




120582max (13)







Electricregulator

Feedback

PID

PSO-RBF

r(k) e(k)

minus

minus

y(k)u(k)

link

controller




119875 119870119894 and 119870






119875 Δ119896119894

and Δ119896119889 and correct 119896

119901 119896119894 and 119896

119889online




1= 5327 times

1041198852

= 1135times1061198853

= 81931198854

= 105711988411198701

= 1328times

109 and 119885

0= 8688 times 10


119866119867 (119911) = (523 times 10

minus71199113


1199112


119911 + 575 times 10minus7

)

times (1199114

minus 3991199113

+ 5981199112

minus 399119911 + 100)minus1

(14)



0 10 20 30 40 50 600

02

04

06

08

1

12

Time (s)


RBF-PID PSO-RBF-PID

ydy


Suppose 120578 = 050 120572 = 005 120578119901

= 120578119894

= 120578119889

= 015and 119896

1199010= 1198961198940

= 1198961198890


1= 1198882


119895= 9 times rands(3 6)


119901= 119870119894

= 119870119889



119901= 0280 119870

119894= 1290 and 119870

119889= 0001


119862119895

= [

[

032 011 002 minus021 037 055


minus035 016 001 003 minus021 020

]

]

119861 = [021 011 030 032 036 048]119879


(15)


0 10 20 30 40 50 600

02

04

Time (s)

0 10 20 30 40 50 60Time (s)

0 10 20 30 40 50 60Time (s)

0

1

2

0

02

04

kp

ki

kd


0 20 40 60 80 100200

300

400

500

600

700

Iterations

Min

imum

erro

r



5 Conclusion



0 05 1 15 2Time (s)


PSO-RBF-PID

ydy

1

05

0

minus05

minus1





Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












= (1199091198941

1199091198942

119909119894119889

) and 119881119894

= V1198941

V1198942

V119894119889


V119894119889 (119896 + 1)

= 120582V119894119889 (119896)

+ 11988811199031

(119901119894119889 (119896) minus 119909

119894119889 (119896)) + 11988821199032

(119901119892119889 (119896) minus 119909

119894119889 (119896))

(11)

119909119894119889 (119896 + 1) = 119909

119894119889 (119896) + V119894119889 (119896) (12)

In formula (11) 1198881and 119888


1and

1199032




120582max (13)







Electricregulator

Feedback

PID

PSO-RBF

r(k) e(k)

minus

minus

y(k)u(k)

link

controller




119875 119870119894 and 119870






119875 Δ119896119894

and Δ119896119889 and correct 119896

119901 119896119894 and 119896

119889online




1= 5327 times

1041198852

= 1135times1061198853

= 81931198854

= 105711988411198701

= 1328times

109 and 119885

0= 8688 times 10


119866119867 (119911) = (523 times 10

minus71199113


1199112


119911 + 575 times 10minus7

)

times (1199114

minus 3991199113

+ 5981199112

minus 399119911 + 100)minus1

(14)



0 10 20 30 40 50 600

02

04

06

08

1

12

Time (s)


RBF-PID PSO-RBF-PID

ydy


Suppose 120578 = 050 120572 = 005 120578119901

= 120578119894

= 120578119889

= 015and 119896

1199010= 1198961198940

= 1198961198890


1= 1198882


119895= 9 times rands(3 6)


119901= 119870119894

= 119870119889



119901= 0280 119870

119894= 1290 and 119870

119889= 0001


119862119895

= [

[

032 011 002 minus021 037 055


minus035 016 001 003 minus021 020

]

]

119861 = [021 011 030 032 036 048]119879


(15)


0 10 20 30 40 50 600

02

04

Time (s)

0 10 20 30 40 50 60Time (s)

0 10 20 30 40 50 60Time (s)

0

1

2

0

02

04

kp

ki

kd


0 20 40 60 80 100200

300

400

500

600

700

Iterations

Min

imum

erro

r



5 Conclusion



0 05 1 15 2Time (s)


PSO-RBF-PID

ydy

1

05

0

minus05

minus1





Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 10 20 30 40 50 600

02

04

06

08

1

12

Time (s)


RBF-PID PSO-RBF-PID

ydy


Suppose 120578 = 050 120572 = 005 120578119901

= 120578119894

= 120578119889

= 015and 119896

1199010= 1198961198940

= 1198961198890


1= 1198882


119895= 9 times rands(3 6)


119901= 119870119894

= 119870119889



119901= 0280 119870

119894= 1290 and 119870

119889= 0001


119862119895

= [

[

032 011 002 minus021 037 055


minus035 016 001 003 minus021 020

]

]

119861 = [021 011 030 032 036 048]119879


(15)


0 10 20 30 40 50 600

02

04

Time (s)

0 10 20 30 40 50 60Time (s)

0 10 20 30 40 50 60Time (s)

0

1

2

0

02

04

kp

ki

kd


0 20 40 60 80 100200

300

400

500

600

700

Iterations

Min

imum

erro

r



5 Conclusion



0 05 1 15 2Time (s)


PSO-RBF-PID

ydy

1

05

0

minus05

minus1





Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 05 1 15 2Time (s)


PSO-RBF-PID

ydy

1

05

0

minus05

minus1





Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article PSO-RBF Neural Network PID...

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