A Bandwidth Allocation Strategy based on Multirate Sampling Method in Networked Control System.docx

A Bandwidth Allocation Strategy based on Multirate Sampling Method in Networked Control System.docx

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ABandwidthAllocationStrategybasedonMultirateSamplingMethodinNetworkedControlSystem

ABandwidthAllocationStrategybasedonMultiMateSamplingMethodinNetworkedControlSystem

ZhiwenWang,HongtaoSun2

Abstract.Consideringoftheresourceconstraint,abandwidthallocationstrategywithmultiratesamplingmethodisproposedtoachievethecontrolandschedulingco-designofnetworkedcontrolsystem（NCS）.Theproposedbandwidthallocationstrategyintegratesstaticschedulingmethodwithdynamicschedulingmethodandthefinalbandwidthofeachclosedloopisdeterminedbythreesteps.First,thebasicsamplingperiodisselectedbasedonthemaximumavailablebandwidthofnetwork.Then,theinitialbandwidthallocationmethodisgivenonthebasisofthesamplingperiodwhichisdeterminedbythedifferentcharacteristicsofeachclosedloop,andthecentralbandwidthcanbeobtainedinthisstep.Atlast,thefinalbandwidthcanalsobeadjusteddynamicallyonthebasisofthestatechangeofeachplant.Inordertoverifythevalidityofthisbandwidthallocationstrategy,thestabilityofcontrolsystemandthebandwidthutilizationofnetworksystemareshownthroughsimulationexperiments.

Keywords:

networkedcontrolsystem;co-design;bandwidthallocation;multiratesampling

1Introduction

Recently,theresearchofnetworkedcontrolsystem（NCS）whichsensors,controllersandactuatorsareconnectedthroughthecommunicationnetworkhasattractedincreasingattention[1].ThereisacommonviewthattheperformanceofNCSnotonlycorrelatedwiththecontrolalgorithmsbutalsowiththenetworkresourceallocation.InordertoresolvetheproblemsthatcausedbyQoPandQoSmutuallyinfluenceandrestrictedeachother,Steo[2]putforwardthethoughtofcontrolandschedulingco-designforNCSwhichadoptaneffectiveinformationschedulingschemetoachieve aminimum utilization of networkresourcesagainstthebackgroundofguaranteeing thecontrolperformance.

Inthecontrolandschedulingco-designofNCS,controlsystemandnetworksystemshouldbeconsideredatthesametime.Fortunately,thesamplingperiodestablishestherelationshipbetweentheQoPandQoS.Ashortersamplingperiodcansupplyabetterperformanceforcontrolsystemthatmeansbiggerbandwidthoccupancyandalongeronecansupplyasubprimperformanceforcontrolsystemthatmeanssmallerbandwidthoccupancy.Inordertoprovideanappropriatebandwidthforeachcontrollooponthebackgroundofbandwidthlimitation,anappropriatesamplingperiodshouldbedetermined[3,4].Aboutresearchonco-designofnetworkedcontrolsystem,mostworksdevoteitselftothecontrollerdesignonthecontextofthetimevaryingsamplingperiodwhichmainlyfocusesontheQoP[5].Buttheseworkswouldattachmoreimportanttothe“combination”ratherthanthe“co-design”.Bandwidthmanagementisconsideredasafeasiblewaytoachievetheco-designofNCSbecauseittakesthedifferentcharacteristicsofeachsingleclosedloopintoaccount.Anoptimalbandwidthallocationstrategywhichdeterminethesamplingperiodaccordingtothestatefeedbackofeachaxisispresentedin[6].AQoS-adaptiveisdesignedin[7]whichallocatethebandwidthtoeachcontrolloopbymeasuringthenetworkQoSparameters.Ultimately,thebandwidthallocationstrategyisstillfocusontheadjustmentofsamplingperiods.Infact,distributionandvastscalearetheinvariablepropertyofNCS,itisimpossibletoadoptaconstantsamplingperiodtoachievetheexpectedperformance.Sothemultiratesamplingmethodistheinevitablechoiceinthecontrolandschedulingco-designofNCS.Inaddition,therationalarrangementofsamplingperiodprovidesafeasiblewaytoallocatethenetworkbandwidth.

Thispaperisaimtoelaboratetheideaofmultiratesamplingmethodweproposedandorganizedasfollows.TheNCSmodelandrelateddescriptionaregiveninsection2.Thebandwidthallocationstrategyofinitialallocationandredistributionwhichbasedonthemultiratesamplingmethodisgiveninsection3.Thesimulationresultsisshowntoillustratetheabovetwomethodsinsection4andsomeconclusionsareobtainedinsection5.

2TheNCSModelandProblemDescription

TheNCSconsideredhereconsistingofacollectionofLTIplants.Eachsubsystemcommunicateswithitscontrollerviaasharedcommunicationnetwork,asshowninFig.1.

Thecontinuous-timestate-spacemodelofthe

plantcanbedescribedbythefollowingstandardform:

（1）

where

isthestateofplant

iscontrolinputforloop

isthetimedelayofthe

closedloop,

arerealmatrixandwithappropriatedimensions.

Fig.1TheNCSmodel

Inordertoillustratethebasicproblemsaboutsamplingperiodindetail,someassumptionsaregivenasfollows.

Assumption1:

Thesensorsaretimedriven;controllersandactuatorsareeventdriven.Thesamplesignalandthecontrolsignalisholdbythezero-order-holder（ZOH）.

Assumption2:

thedataofeachnodeissinglepackettransmissionandnopacketdropoutoccurred.

Assumption3:

[8]Inordertoguaranteethestabilityofeachclosedloop,themaximumallowdelaybound（MADB）whichdenotesas

isgivenatfirst.Ifthesamplingperiod

isbiggerthan

thestabilityofcontrolsystemwillbenotguaranteed.Theaboveconditioncanberepresentedas

（2）ifthecontrolsystemisstable:

（2）

Assumption4:

Therelationshipbetweenthequalityofperformanceandbandwidth

ofthe

closedloopcanberepresentedas:

（3）

Thetimedelaywhicharisesfromtheintroductionofnetworkisanimportantfactorwhichshouldbeconsideredanditcandegradetheperformanceofcontrolsystem.Thesampledatawhichisdefinedasthestatesignal

arrivesatthecontrolleraftersometimedelayswhicharecalled

.Then,thecontrollercomputesthecontrolsignal

bythedatawhichisreceivedfromthesensorsanditwouldgenerateanthertimedelaywhichiscalledthecomputationdelay.However,itcanbeincludeinthenetworkdelay.Thecontrolsignalissentbythenetworkfromthecontrollerandarisestheadditionalthetimedelayswhichcalled

.After,thecontrolsignalisarriveattheactuatorandholdbytheZOHtoo.However,thetimedelayismainlymadeupwiththedelay

fromthesensortocontrollerandthedelay

fromcontrollertoactuatorforsimplicity.Thetotaltimedelayofeachclosedloopcanbeobtainedby（4）andthedetailisshowninFig.2.

（4）

Fig.2Thetimedelayofeachclosedloop

Generally,theabovesamplingcontrolsystemisadiscretesystemandcalculatesitscontrolvalvebasedoninputvalveateachsampleperiod.So,Shanonsamplingtheoryisthebasicoftheanalysis.Samplingsystem

（1）with

canberepresentedasfollowsifthetimedelay

isconsidered:

（5）

where

，

and

isthesamplingperiodofthe

controlloop,

isthesameas

（1）.

The

controlloopsareconnectedvianetworkthatthemassdataneedtobetransmittedthroughitandthebandwidthlimitationshouldbeconsidered.Becauseofthedifferentcharacteristicofeachclosedloop,theamountofdatathatneedtobetransmittedisalsodifferent.Inaddition,thebandwidthrequirementisalsodifferentwhenthestateofplantischangingatdifferenttimes.Obviously,itwouldleadtothewasteofbandwidthandbadperformanceofNCSifaconstantoraveragesamplingperiodisadopted.Hence,themainproblemwhichneedstobedealtwithinnetworkistodeterminethesamplingperiodforeachsingleclosedloop.Therearetwoproblemstobesolvedinthispaper.Oneisthemethodtodeterminetheinitialsamplingperiodwhichbasedonthecharacteristicforasingleclosedloopandanotheristhemethodtoadjustthesamplingperioddynamicallywhichbasedonthestatechangeofplant.

3BandwidthAllocationwithMultirateSamplingMethod

Inthissection,themethodofmultiratesamplingperiodisillustratedandthebandwidthallocationstrategywhichbasedonmultiratesamplingmethodisgiven.Theessenceofthemultiratesamplingistoallocatearationalbandwidthforeachclosedloopfromdifferentperspectives.Itmakessensethatthestabilityisguaranteedforcontrolsubsystems.Inthefollowing,thedetailofbandwidthallocationstrategywhichbasedonthemultiratesamplingmethodisgiven.

3.1TheInitialBandwidthAllocation

Themainpurposeoftheinitialbandwidthallocationistodeterminetheroughbandwidthbasedonthedifferentcharacteristicsofeachclosedloop.Here,thebandwidthwhichdeterminedbytheinitialallocationiscalledthecentralbandwidthanditcanvaryinsomeextent.However,thecondition

（2）ismetthroughtheinitialbandwidthallocationandallclosedloopcanbestabilizedsimultaneously.Atthesametime,thetimedelaycanbereducedtothecondition（6）.

（6）

Fromtheperspectiveofnetworksystem,thetotalbandwidthwhichdenotesas

isinvariableandthedefinitionisgivenbelow.

Definition1:

Denotethetotalbandwidth

ofnetworkisthemaximumamountofdatacanbetransmittedinunittimewhichisrepresentedas:

（7）

where

istheminimumthesamplingperiodwhichcalledthebasicsamplingperiod.Here,thetotalbandwidth

ismainconsiderationinviewofthenetworksystemanditistinydifferentfromthebandwidthwhichcombinethecontrolsystem.

Then,thebandwidthofeachclosedloopwhichcombinesthecontrolsystemcanbedefinedasbelow[9].

（8）

where

isthetimespentonmessagingrequiredtoperformoperationanditisassumedtoaconstantforeachclosedloop.

However,thebandwidthsummationofeachclosedloopshouldnotexceedthetotalbandwidthanditcanberepresentedas（9）.

（9）

Inordertodeterminethebandwidthofeachclosedloopwithana