cylinders是什么意思inders在线翻译读音

LongkeWang

e-mail:@

e-mail:@

s

e-mail:s@

ffSchool

ofMechanicalEngineering,

GeorgiaInstituteofTechnology,

Atlanta,GA30332

AHydraulicCircuitforSingle

RodCylinders

Thispaperproposesanovelhydrauliccircuitforasinglerodcylindercontrolledbya

cuitarrangementnotonlygivesthesystemhigh

energyefficiencybutalsoimprovesuponth外国著名诗人有哪些 einternalinstabilityoftraditionalcircuits.

Stabilityis

motivations,derivations,andproofsofthesystemdynamicalstabilitiesarepresented.

Controlalgorithmsincludingstabilitycontrolandslidingtothedesiredworkingregion

mentsareconductedtoverifythecircuit,andresultsshowthatthe

circuithasgoodperformance.[DOI:10.1115/1.4004777]

1Introduction

Hydraulicsystemsarewidelyusedinindustrialapplications

becauseoftheirhighpowerdensity,flexibility,andhighstiffness.

Applicationscanbefoundinagriculture,mining,construction,

r,theefficiencyoffluidpowerisrela-

tivelylowwhencomparedwithmethodsoftransmittingpower

creasingconcernsaboutfuel

pricesandemissionregulations,theefficiencyoffluidpowerhas

becomeanimportantissue.

Valvecontrolledsystemsdominateintoday’shydraulic

ofavalvecontrolledsystemseemstobea

straight-forwardsolutionwheresystemsuseapressurecompen-

satedorload-sensingpumptosupplyindividualvalvesthatcon-

ignlookssimple,buttherearesome

disadvantages:highinstallationcost,highcomponentcosts,and

lowenergeticefficiencyduetothrottlinglosses[1].Displacement

controlledhydrostatictransmissionsusuallycanbefoundin

smallermobilemachinesandareusedaspropulsiondrives.

Energyefficiencyimprovementusuallyisevaluatedbycompar-

ingwithfuelconsumptionwhenthesameworkingroutinesare

conducted,forexample,a3-mindiggingcycleisrepeated10

majoradvantageofapumpdisplacementcontrolledactuatoris

thatitprovideshigherenergyefficiencybecausethereareno

throttlinglosseswithinthemainpowerlinesoftheactuatorsand

becausethepumpisabletoregenerateenergyfrompotentialand

brakingenergyfromotherfunctionunitsbymechanicallysharing

thepumps’ncipleofpowerregenerationissimilar

tothatusedinelectricalsystems,wherepartoftheenergythat

feedstoelectricmotorsonthesamepowergridisregenerated

tly,thereare

manyvehicles,includingexcavators,cranes,andsomerobots,

usingmultiplelinearandrotaryhydraulicactuatorssimultane-

ously;theabilitytorecoverenergywillbeanecessarypartofnew

generationhydraulicmobilemachines.

Oneimmediateproblemforpumpdisplacementcontrolledsys-

temsisthatthemostcommonactuatorsusedbytheindustryare

pleistheboomstructureusedin

ingasinglerodcylinderinapumpdisplace-

mentcontrolledcircuit,anappropriatecircuitarrangementisnec-

essaryinordertobalanceunequalflowratesenteringandleaving

thecylindervolumesbecauseofthedifferentialareasofthe

cylinder.

Severalapproachescanbefoundinliteraturetosolvethedif-

r[2]andLodewyks[3,4]intro-

ducedahydraulictransformerforunequalflowcompensations.

Thehy眩组词 draulictransformer,whichissimilartoanelectricaltrans-

former,iscapableofconvertinganinputflowatacertainpressure

leveltoadifferentoutputflowattheexpenseofachangeinpres-

ransformerratioisthesameasthearearatioofa

givencylinder,theunequalflarbutmore

innovativeproductisdevelopedbyINNAS[5],basedonthebent

ainsthreeports,wherethecontrolofthevol-

umeflowtotheindividualportsisachievedbycontrollingthe

ansformercanonlybeusedforasinglerodcyl-

inderinfourquadrantoperationstogetherwithanadditionalhigh

r[2]alsoproposedtousetwovariabledis-

placementpumps,whosedisplacementratioisadaptedtothearea

ratioofthesinglerodcylinder,tocompensatedifferentialflows.

Besidesclosedloopcircuitsolutions,Heybroek[6]proposedan

openloopcircuitsolutionbyimplementingasetofH-bridgecon-

cuitextendsthemaximumspeedatwhich

thesinglerodcylindercanbeoperated.

In1994,aconceptforclosedcircuitdisplacementcontrolwas

patentedbyHewett[7]basedonavariabledisplacementpump

andalowpressurechargelineforcompensatingthedifferencein

volumetricfl-positionthree-way

valvewasusedtoconnectthelowpressuresideofthecylinderto

cuitwassuccessfullyimplementedon

amobileforestrymachine[8].Asimilarconcept,whichusestwo

pilotoperatedcheckvalves,wasdevelopedbyRahmfeld[9]and

RahmfeldandIvantysynova[10].Fuelsavingsof15%overa

load-sensingweredemonstratedbyexperimentsusingprototype

antagesofsuchsolutionsinclude:(1)throt-

tlinglossesareeliminated;(2)thecostofthecircuitislowcom-

paredwithothersolutions;(3)energyrecoveryispossible

becausethepumpssharethesameinputshaft.

Thehydrauliccircuitneedstobeoperatedinfourquadrant

modesinordertorecoverenergyfromotherfunctionunits.A

reportedproblemforthiskindofcircuitispumposcillationunder

somecircumstances[11].Moreexplicitly,thepressuresonthe

capsideandrodsidesometimesuncontrollablyoscillate;corre-

spondingly,thecylindervelocityoscillatesandchangesrapidly

eventhoughitiscontinuousbecauseofmassinertia;thesystem

hasfastoscillationsbetweenpumpingmodeandmotoringmode.

Atthisstage,thesystemlosescontrollabilityorisunderweak

.11,anobserverisdesignedtopredictwhen

suchpressureoscillationsoccurinordertointroducecontrol

y,largeoscillationsofactua-

torpressureandvelocityareundesirableandmaybedangerous.

Thelossofcontrollabilityorweakcontrollabilityispotentially

unacceptableforindustryapplications.

Inthispaper,anovelflowcontrolcircuitfordifferentialflow

ratesispresentedandverificeptis

developedfromHewett’sstructure[7].Newcomponentsand

ContributedbytheDynamicSystemsDivisionofASMEforpublicationinthe

JOURNALOFDYNAMICSYSTEMS,riptreceived

May27,2010;finalmanuscriptreceivedMay14,2011;publishedonlineDecember

6,:LuisAlvarez.

JournalofDynamicSystems,Measurement,andControlJANUARY2012,Vol.134/011019-1

CopyrightVC2012byASME

ributionsubjecttoASMElicenseorcopyright;see/terms/Terms_

单杆液压缸

cuitinheritsadvan-

tagesofHewett’sdesign,buttheprinciple,theworkingpoint

analyses,andtechnicalfocusaretotallydifferentfromHewett’s.

Thecircuitnotonlypreservesenergyefficiencybutalsoelimi-

re,trackingperformancecan

beadjustedasdemanded.

2TheFlowControlCirc七言古诗词 uitWithDynamical

Compensations

TheproposedclosedloophydrauliccircuitisshowninFig.1.

Thecircuitconsistsofapairofcheckvalves(3a,3b),apairof

flowcontrolvalves(4a,4b),apairofreliefvalves(5a,5b),a

three-positionthree-wayshuttlevalve(6),twopressuresensors,

stheproposedcircuit,thewholesystem

includesadisplacement东坡肉的做法 controlledpump(1),achargepump(2),

andasinglerodcylinder(7).Thedifferentialvolumeandvolu-

metriclossesarebalancedthroughoneofthecheckvalvesorthe

shuttlevalvetothelowpressurepowerlinewhosepressureis

closetothechargepressuredependingonthecharacteristicsof

trollerdynami-

callyadjuststheflowcontrolvalvestoallowthecircuittobecom-

itycompensationisaccomplishedbyusinga

small,controlledleakagesuchthatthepressureoscillationsare

onalcompensationcanbeissuedbythecontroller

ief

valves,whichdonotoperateinnormalworkingsituations,pro-

videapressuresafetyprotection.

Thecircuitworksinallfourquadrantoperationsasshownin

itivedirectionisdefinedasthedirection,which

makesthecylinderextendunderpumpingmodeasshowninFig.

2(a)Thatis:thedifferentialpressureonthepumpisdefinedas:

PP

a

P

b

,pumpflow,Q,isdownwardonthepump,thecylin-

derdisplacement,x,erP;Qhave

samesign,thepumpisinpumpingmode,whichmeansthepump

istransferringenergytothecylinder;otherwise,thepumpisin

themotoringmodewhichmeansthecylinderfeedsenergybackto

0;P0,thepumpneithergivesenergynor

absorbsenergyandthemovementofthecylinderismainly

hercase,whenP%0;Q0,

thereisnolargeenergyexchangebetweenthepumpandthecyl-

inder;noticethatthecylinderismovinginthiscase,forexample,

whenitisextending,mostofenergyexchangeisbetweenthecyl-

inderandthechargepump.

Whenthecylinderisextending,themainflowinthecircuitin

Fig.1iscounterclockwise(portB!pump!portA).Inthiscir-

cumstance,(1),P>0;Q>0;_x>0,

rgyis

-

thattheextraflow(usually

referredtoascooloil)iscomingthroughthecheckvalve3b,

whichisconnectedtothechargepumpwherethepressureislow-

(2),P0;

_

x>0,therodisbeingpulledup

thiscase,thehighpressureflowpassesthroughthevariabledis-

,thepumpcouldrecoverthisenergy.

Noticethistimethatthecooloilisenteringthesystemthrough

checkvalve3a.Thearrangementofcheckvalvesinthesystem

firstistoensurethecooloilalwaysenters

secondistoreplenishtheoillostduetoleakagesandtoregulate

theminimumpressuretopreventcavitations.

Whenthecylinderisretracting,themainflowinthecircuitis

clockwiseinFig.1(portA!pump!portB).Therearetwo

(1),P<0;Q

<0;

_

x<0,thepumppushesthecyl-

hepressureatportBishigherthanthe

pressureatportA,thethree-wayshuttlevalveconnectsthepower

lineatportBtothechargepumpsuchthattheextraflow(usually

referredtoashotoil)canbereleasedtothetank=accumulator.

SinceP;Qhavethesamesign,thesystemisunderpumping

(2),P>0;Q<0;

_

x

pushingthecylinderdown;thus,thepressureatportAishigher

thanthepressureatportB,thenthethree-wayshuttlevalve

switchessothatthehotoilisreleasedthroughthethree-way

angementoftheshuttlevalveinthesystemisto

ensurethatthehotoilisalwaysreleasedfromthelowpressure

sidetoensurethecircuit’senergyrecoveringabilities.

3StationaryStabilityAnalysis

am-

icscanbedescribedas

m

€

xb

_

xA

1

P

a

A

2

P

b

mgF(1)

wheremisthemassconsistingoftheloadsandtherodofthecylinder,

bisthelinearfrictioncoefficient,A

1

istheareaofthepistonside,A

2

istheannulusareaoftherodside,gisthegravitationalacceleration.

Fig.1Hydrauliccircuitforasinglerodcylinder

Fig.2(a)Positivedirectiondefinition,(b)Fourquadrantworking

domain

Fig.3Singlerodcylindermodel

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单向阀作用

换向阀6的

作用，热交

换

,

externalloadforce,coulombfriction,nonlinearfrictionetc.

Forconvenience,newvariablesaredefinedas

a

A

2

A

1

~

P

a

P

a

P

0

~

P

b

P

b

P

0

m

c

g1aA

1

P

0

Fm

€

xFmgb

_

x

(2)

whereaisthepistonarearatio,P

0

isthechargepressure(which

usuallyislow,forexample,150psi),m

c

gisthecriticalmassforce

(m

c

isreferredtoasthecriticalmassinthefollowingandgis

gravitationalacceleration),whichisequaltothenetforcepro-

videdbythecylinderwhenbothside描写七夕节的古诗有哪些 softhecylinder’spressure

equalP

0

.Thus,Eq.(1)canbewrittenas

Fm

c

gA

1

~

P

a

a

~

P

b

(3)

ThehydrauliccircuitshowninFig.1worksinallfourquadrant

operationsandcanregenerateenergyfrompotentialenergyand

frombrakingenergyappliedbyotherfunctionunits,theseobser-

vationsleadtofollowingresults:

(1)

~

P

a

;

~

P

b

arealmostnonnegative.

(2)Atleastoneof

~

P

a

,

~

P

b

isclosetozeroundernormalworking

conditions.

(3)Thesystemisunderpumpingmodeif

Fm

c

gand

_

xhave

thesamesign;otherwise,itisinmotoringmode.

(4)If

Fm

c

gisclosetozero,thecylinderismainlypowered

bythechargepump.

Result1isduetothepressureinbothportsofthecylinderbeing

heckvalveswereideal

components,theywouldpreventpressurefromfallinglowerthan

tice,thereisalwayssomeinternalflow

resistanceinthevalve,andacrackingpressureisrequiredtooper-

atethevalve,butthesekindsofpressuredropsthroughvalvesare

,itdoes

notpreventusfromasserting

~

P

a

;

~

P

b

arepositivemosttimes.

Result2comesfromensuringenergyefficiencyandenergy

erthecylinderisextendingorretracting,the

cooloilorhotoilshouldbealwaysconductedtooneofthepower

linesatthechargepressurethatisregulatedbythecheckvalves

s3and4canbelearned

frompreviousdiscussions.

Figure4isapressureplanegraphofpressuresatportAand

sults1and2,thedesiredpressureworkingregions

ofenergyefficientcircuitsshouldlieintheregionsapproximately

rtoobtainthesedesiredworkingregions,

threekindsofcircuitarrangementswillbecomparedconsistingof

(a)idealpilotoperatedcheckvalves,(b)commonpilotoperated

checkvalves,and(c)theproposedhydrauliccircuitinthispaper.

Sincethemainfocusofthissectionistocomparestationarysta-

bilityregionsandcost,withoutlossofgenerality,thecracking

pressureofvalves,whichisusuallydeterminedbystaticvalve

springs,isassumedtobezero;thevalvedynamicsareneglected.

5showsacircuit

usedforvariabledisplacementcontrolledactuatorsproposedby

Rahmfeld[9],RahmfeldandIvantysynova[10],andWilliamson

andIvantysynova[11].Apairofpilotoperatedcheckvalveshas

beenimplementedtobalancedifferentialflperated

checkvalves(alves),arecheck

,

alvesblockflowsinonedirection,likestandard

checkvalves,butcanbereleasedonceanadequatepilotpressure

flowisallowedinthereversedirection.

alvesinpopularusein

firstsuchvalve’soperationistriggeredwhen

P

1

>P

reference

,whereP

reference

usuallyisaconstantpressureinde-

pendentofthevalveitselfandP

1

isthepilotoperationpressure

pleofthistypeisvalvemodel

herkindof

alve,operationistriggeredwhenP

1

P

3

=a>P

2

,

whereP

1

isthepilotoperationpressure,P

2

isinletportpressure,

P

3

istheoutletportpressure,aisanarearatioofthevalvecore,

andapleismodel

terkindofvalvehas

ven-

ience,ndthe

nthispaper.

areshowninFig.6.

Valve(A)showninFig.5operatesinthecrosshatchedarea

IfP

a

jP

a

>P

01

g,Valve(B)showninFig.5takeseffectin

crosshatchedareaIIfP

b

jP

b

>P

01

eckvalvesare

closedintheareaIIIIIIwithconstraints

~

P

a

>0;

~

P

b

>

showninFig.6,IIIisnonempty.

Weclaim:itisimpossibleforP

01

tocollapsetoP

0

.P

0

isthe

P

01

P

0

(orP

01

%P

0

),

IIIthenwillcovermostworkingregions;thismeansthatboth

portsofthecylinderarealwaysconnectedtothechargepump.

Obviously,thecircuitlosesefficientcontrolorhasextremelyinef-

fectivecontrolinthesenseofenergyeffiacontra-

,P

01

P

0

alsoleadstosomeproblems.(1)Besidesthechargepressure,the

systemneedsanotherreferencepressure,thusthewholecostof

thecircuitwillincrease.(2)AhighboundofP

01

P

0

will

decreasethecircuit’senergyefficiency,butalowboundcannot

ensurethesystemiscontrollable.(3)RegionIIIisaninternally

equilibriumworkingpointinthisareadoomsthesystemtobe

unstablebecausetherearealwaysextraflowsintooroutofthe

cylinder,andthesteadyworkingpointcannotremainthereifthe

enthecylinderhappenstobe

Fig.4DesiredworkingregionsinthepressureplaneFig.5Thecircuitusingpilotoperatedcheckvalves

JournalofDynamicSystems,Measurement,andControlJANUARY2012,Vol.134/011019-3

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回路失去了有

效地控制，或

者说在节能方

面显得非常无

用

stationary,adeviationwouldexcitealimitcyclewhichwillbe

eabovediscussion,weconcludethat

isnotagoodsolutionforsinglerodcylin-

dercontrolcircuits.

.

Valve(A)showninFig.5operatesinthecrosshatchedarea

IfP

a

;P

b

jP

a

P

b

=3>P

0

(B)showninFig.5oper-

atesincrosshatchedareaIIfP

a

;P

b

jP

b

P

a

=3>P

0

checkvalvesareclosedintheareaIII

IIIwithconstraints

~

P

a

>0;

~

P

b

>ninFig.7,IIIisnonempty.

Thedrawbacksofthisarrangementarethat:(1)SinceIIIis

nonempty,therearecases,whereifthecylindermovesfastand

thefluidresistanceofthereturninglineisalsohigh,bothvalves

,thecylinderlosescontrolinthesenseof

energyefficiency.(2)InareaIII,ys-

tem’ssteadyworkingpointshappentolieinthisarea,thesystem

cannotbestable.(3)Simulationresultsshowtheareaofthis

regionisimportanttodynamicstability.

ternativetotheabovecircuits,

theworkingregionsoftheproposedcircuitinthispaperaremuch

,

thewholepressuredomainisdividedintothreeregions,fI;I0;Ng,

whereIfP

a

;P

b

jP

a

>P

b

g,I0fP

a

;P

b

jP

a

b

g,and

NfP

a

;P

b

jP

a

P

b

sly,II0;,andthetheoretical

measureoftheset,N,iszero(thickness).Situationswherebothof

,stationarysta-

bilityisnolongeranissue.

Evenconsideringcomponentimperfections,thisadvantagestill

tice,itispossiblethattheworkingpointliesnearthe

setofNwhenconsideringvalvedynamics,nonidealvalveflow

case,aslidingsurfacecanbeformed,

Sf

~

P

a

;

~

P

b

jA

1

~

P

a

a

~

P

b

s;

~

P

a

>0;

~

P

b

>sical

e

aidoftheflowvalvecontrol,whichwillbediscussedinthenext

sections,theworkingpointsslideonthesurfaceuntilitarrivesat

dingsurfacesatisfies

tanb1=,anypossibleineffective

workingpointsnolongerexist.

4DynamicStabilityAnalysis

ThesystemasshowninFig.1involvesloaddynamics,valve

dynamics,variabledisplacementpumpdynamics,andfluiddy-

npurposesofthispaperaretoanalyzewhenand

howpressureoscillationsaretriggeredbythecircuititselfand

,the

valvedynamicsareneglected,andtheinputtothecircuitis

assumedtobetheflproxi-

mationleadstoaconservativeconclusion,butthenumericalsim-

ulationsaresimplifiedbecauseerroraccumulationsareminimized

inthediscontinuoussystemdynamics.

Experimentsshowthatthesepressureoscillationsseldomoccur

llbecomeclearattheend

ofthissection,sothefollowinganalysisfocusesonthecasein

venience,thestatevaria-

blesaredefinedas

~

xx

1

;x

2

;x

3

T

_

x;P

a

;P

b

itive

plifieddynamicsare

describedinEq.(5)usingdefinitionEq.(4).

e

V

=

b

(4)

m_x

1

aAx

3

Ax

2

bx

1

mgF

e

_

x

2

FlowAx

1

Cx

2

x

2

R

on

x

3

>x

2

e_x

3

FlowaAx

1

Cx

3

x

3

R

on

x

2

>x

3

(5)

whereFlowisthefluidratesuppliedbythevariabledisplacement

pump,misthemassconsistingoftheloadandtherodofthecyl-

inder,Aistheareaofcylinderdefinedpreviously,aistheareara-

tiooftherodsidetothecapside,bisthelinearfriction

coefficient,Fisthetotalforceexcludingthoseexplicitly

expressedintheequations,Cisthefluidleakagecoefficient,and

R

on

isthefl

that,theoretically,R

on

shouldbeanonlinearmappingrelatingthe

valvecore’spositionandthedifferentialpressurethrough

.(5),afirstordermodelisusedtoapproximatethe

shuttlevalve’scharacteristics(tomakethisapproximationbetter,

wehaveselectedalargecapacityratedvalve).[cond]isa

Fig.8Workingregionsoftheshuttlevalve

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本文主要的目

的是分析回路

本身的压力波

动是何时以及

如何被触发的

ratoroutputis1whencondistrue,

otherwise,bulkmodulusofthefluidused,Vis

thevolumeofthefluidchamberwhichincludestwoparts.

VV

line

V

c

t(6)

whereV

line

referstothevolumeofthefluidpipeline,V

c

trefers

tothevolumeofthecylinderchamber,,

itdependsonthepositionoftherod).Therodsidevolumeisdif-

ferentfromthecapsidevolumebecausethecylinderisasingle

oughthecylindervolumeislimited,thebulk

portedthattheeffectivebulkmodu-

lusofanaverageworkingfluidisatthelevelof200,000psi(1.38

MPa)[12],andMerritt[13]haspointedoutthat100,000psi(0.69

MPa)er-

agevolumeofbothsidesisusedtocalculateeinEq.(4)instead

ofusingtwodistinctvaluesfore

1

;e

2

inEq.(5).

Thefirstcaseconsidersequilibriumpointsontheset

Ifx

2

;x

3

jx

3

>x

2

;x

2

2<;x

3

2

tionsm;F;flow,(suchequilibriumpointsdoexist;forexample,

letmgFgotoalargenegativevalueinEq.(5)).Aroundthe

equilibriumpoint,thesystemis

_

~

x

b

m

A

m

aA

m

A

e

C1=R

on

e

0

aA

e

0

C

e

2

6

6

6

6

6

4

3

7

7

7

7

7

5

~

x(7)

where

~

xisthevector

~

xdefinedinEq.(5)withacoordinateorigin

changedtotheequilibriumpointcorrespondingtoagiveninputset.

ilibriumpointonIfx

2

;x

3

jx

3

>x

2

;

x

2

2<;x

3

2

Proof.

ThesystemdescribedbyEq.(7)ck

diagramofthesystemaroundtheequilibriumpointisshownin

Fig.9wherethetransferfunctionsare

Tf1s

1

msb

Tf2s

A

esC1=R

on

Tf3s

aA

esC

(8)

SinceTf2;Tf3arestrictlypassive,theirparallelcombinationis

asymptoticallystablebutTf1isalsostrictlypassive,thusthe

,alloftherealparts

ofthesystemeigenvaluesarelessthanzerosincethesystemis

mpletestheproofofpart(1).From(1),thedetermi-

nantofsystemmatrixisnonzero,thusthematrixisaonetoone

mapping;therefore,theequilibriumpointisunique.

(Q.E.D)

OntheotherhalfofthepressureplaneinFig.8,transferfunc-

tionscanbedefinedas

Tf1s

1

msb

Tf2s

A

esC

Tf3s

aA

esC1=R

on

(9)

Usingthesamearguments,wearriveatLemma2.

eisanequilibriumpointonanysideofthe

linefx

2

;x

3

jx

3

x

2

;x

2

2<;x

3

2

(1)exponentiallystableand(2)uniqueoneachsideoftheline.

Arethereanyequilibriumpointsonthesetfx

2

;x

3

j

x

3

x

2

;x

2

2<;x

3

2

theorigin.

sonlyoneequilibriumpointifx

2

x

3

and

theequilibriumpointisstable.

Proof.

Whenpressuresonthecylinderportsareequal,theshuttle

valveliesinthecenterposition,R

on

!1,theleakageofcylinder

Cisverysmall;thusfromEq.(5),

Ax

1

%FlowandFlow%aAx

1

)x

1

%0

Cx

3

FlowandFlowCx

2

)x

2

x

3

0

Thestabilitycanbeprovenusingthepreviouspassivitymethod.

(Q.E.D)

Sofar,wehaveexaminedthepossibleequilibriumpointsinthe

temdescribedbyEq.(5)isdrivenbythe

Flowandmgputisvelocity;P

a

;P

b

-

ever,thisdoesnotnecessarilymeanthatthemappingfrominput

ly,whenatsteadystateandwhen

x

2

x

3

jj

isverysmall,itispossiblethattherearetwoequilibrium

ursunderthe

mainreasonforthiscomesfromthefriction,whichisproportional

yspeaking,theratioofsteadyvelocitiesat

ferenceofnetforcescausedbyfric-

tionhappenstomovetheequilibriumpointfromonesidetoother

thisonlyhappenswhenequilibriumpointsarenear

rgydissipatedorregener-

atedisverysmallcomparedwiththeenergydissipatedbythe

chargepump,sothatanyequilibriumpointinwhichthesystem

willstayisacceptable.

Theseequilibriumpoints,whichareneartheorigin,aretrivial

,wewillfocusonthestabilityof

theequilibriumpointslyingfartherfromthex

2

x

3

thattheexponentialstabilityoftheequilibriumpointsoneach

sideofthelinedoesnotnecessarilyleadstothestabilityofthe

continuityoftheoperatoroperationdefinedinEq.

(5)cantriggerthesystem’slimitcycleevenwhenthesystemhas

ervationisthat,if

x

2

;x

3

donottouchinthepressureworkingplanethenthethree-

,thereisnoswitchingin

Eq.(5),andbecauseofthestabilityproveninLemma2,thepres-

themotivationofthestabil-

itystrategy.

ontroleffortsensurex

2

x

3

aftersystem

enterstheregionwheretheequilibriumpointexists,thesystemin

Eq.(5)isstable.

Proof.

Foranyinputset(Flow,mgF),thesystemhasthepropertiesFig.9Blockdiagramaroundtheequilibriumpoint

JournalofDynamicSystems,Measurement,andControlJANUARY2012,Vol.134/011019-5

ributionsubjecttoASMElicenseorcopyright;see/terms/Terms_

x

1

jj

Flow

aA

x

2

jjl

Flow

C

x

3

jj

l

Flow

C

,thestatespace,

~

x,fora

retwocasestoconsider.

Thefi-

ondiswhenthesystementersalimitcycle.

Ifthesystemdoesnotenteralimitcycle,thenthesystemmust

r,byLemma2,theequilibrium

pointisstableandunique;therefore,thesystemwillstayatthe

,theproofisdoneforthecaseofnolimit

cycle.

Nowsupposesystemhaslimitcycle,wecanfindtheupper

boundsofx

1

;x

2

;x

3

alsoknowx

2

x

3

atsometime(otherwise,thesystemisstable).

Withoutlossofgenerality,assumex

2

t

1

x

3

t

1

,x

2

t

1

>

x

3

t

1

atsometimet

1

,andthereisanequilibriumpointsatisfying

x

2

>x

3

.Becausethecontroleffortsensurex

2

x

3

bytheassump-

tion,thesystemwillgototheequilibriumpointbecauseofthesta-

bilityoftheequilibriumpointbyLemma2.

Fromanotherviewpoint,thestabilityproblemworkslikeazero

inputresponseproblemifalimitcyclehappensandwetakethe

the

worstinitialstatesareboundedbecausethelimitcycleisbounded.

Toensurex

2

x

3

whent>t

1

,x

2

x

3

shoulddecayfastenough

toitssteadystate.

Thesystem,describedbyEq.(5),isalineartimeinvariantsys-

temduringthetimeintervalofconsecutivetimeeventswhenthe

systempassesthroughthepressurelinex

2

x

3

.Withoutlossof

generality,thesystemcanbedescribedinEq.(10)inthe

fx

2

;x

3

jx

3

2

;x

2

2<;x

3

2

m

_

x

1

aAx

3

Ax

2

bx

1

e

_

x

2

Ax

1

Cx

2

e

_

x

3

aAx

1

Cx

3

x

3

R

on

(10)

where

~

xx

1

;x

2

;x

3

Tisdefinedwithreferencetotheequilibrium

isverysmall,asdiscussedintheprevioussections,

singularperturbationtheoryisapplied[14,15].C,theleakagecoef-

ficient,isverysmall,butR

on

istheflowresistance,whichis

designedtobeverysmallwhenthevalveisoperated;thusthethird

equationofEq.(10)achievessteadystateinthetwotimescales

2

;x

3

arebounded,theslowmanifoldsatisfies

x

3

aAR

on

x

1

(11)

Thereducedordersystemcanbesimplifiedto

m

_

x

1

a2A2R

on

bx

1

Ax

2

e

_

x

2

Ax

1

Cx

2

(12)

Thesimplifiedsystemcanbeviewedasafeedbackconnectionof

twosubsystemsdescribedbythefollowingtransferfunctions:

A

esC

A

msba2A2R

on

(13)

Thus,thecharacteristicequationofthesimplifiedsystemcanbe

derivedas

ms2

ba2A2R

on

mC

e

s

Cba2A2R

on

A2

e

0

(14)

SinceC;eareverysmall,thesecondtermisdominatedby

mC

=

e

in

Eq.(14),andthethirdtermisdominatedby

A2

e

.Thus,thedamping

coefficientfortheabovethesecondordersystemcanbederivedas

n

C

ffiffiffiffi

m

p

2A

ffiffi

e

p

(15)

Asmentionedabove,weareinvestigatingthezeroinputresponse

ofthesystem;on

(15)showsthatthedampingcoefficientwillincreasewiththe

leakagecoeffiansthepressurewilldecayfaster

nceptledtoadditionof

theflowcontrolvalvestothesystemasshowninFig.1tostabi-

elopeofthepressureresponse

willdecayatthespeed

e

nx

n

t

e

ba2A2R

on

mC

e

t

(16)

Figure10isasimulationofthesystemdescribedbyEq.(5)by

varyingleakagecoefficientswiththe[cond]operatordisabledin

ssures

arereferencetothechargepressureandtheequilibriumpointis

selected(bycombinationofthemassandthepumpdisplacement)

hepressureP

b

isalmostequal

tothechargepressurethusonlyrelativeP

a

figure

showsthatwhenleakageincreasestothreetimeslargerthanthe

originalleakage,thesystempressuresareboundedinonesideof

thepressureplaneandgoestosteadystate.

Theaboveanalysisfocusesonthecasewhenthecylinderis

extending,butitisalsovalidforthecasewhenthecylinderis

etractingcase,thesystemhasalargersafetymar-

reasonablebecause

oneport’spressureislowerthanthechargepumppressuredueto

theinternalflowresistanceofthecheckvalveandtheshuttlevalve,

whiletheotherport’spressureishigherthanthechargepumppres-

ore,thetwopressuresarenotequalsothereisno

switchinginthesystem’temgoestosteady

statebecauseofthestabilityoftheequilibriumpoints.

Isthecircuitstillenergyefficient?Twoflowcontrolledvalves,

shownas(4a)and(4b)inFig.1,

begintoworkonlywhenpressureoscillationscouldpossibly

ediscussionabove,onecanseethatthepressure

Fig.10Responsewithvaryingleakagecoefficient

011019-6/Vol.134,JANUARY2012TransactionsoftheASME

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oscillationsoccurwhenatasteadystatex

2

x

3

g,wheregis

someupperboundwhichcanbedeterminedbyexperimentsor

throughexperience,forexample,20PSI(0.14MPa).

Whentheequivalentleakagehasbeenincreased;thesystem’s

overallenergeticefficiencywillbeloweredatfi-

ever,thechangeinoveralleffi,

x

2

x

3

goccursonlywhentheforceexertedbythecylinder

isclosetothecriticalmassforceasdefinedinEq.(2).Inpractice,

theforceonthecylinderfromstructuralweight,suchasboom

structuresofanexcavator,isalreadymuchgreaterthanthecritical

re,innormalworkingsituations,thecylinderis

usedtoliftheavyloadsortopullsomeobjectrequiringlarge

,thecompensationalgorithmistriggeredonlyfora

-

ond,whenthecompensationistriggered,thedissipatedenergyis

boundedbygQ

l

,重阳席上赋白菊古诗赏析 whereQ

l

istheleakageflthistime,

theenergydissipatedbythechargepumpwhichisconstantly

workingisP

0

Q

0

,whereQ

0

isthechargepumpfl

P

0

>>g;Q

0

>>Q

l

,thustheenergydissipatedbytheleakage

compensationcanbeneglected.

5CompensationAlgorithmsfortheFlowControl

Valves

Thecompensationalgorithmsareimplementedusingtheflow

reatleasttwokindsof

compensationsinthecircuit:pressureoscillations,quotientgroup

sliding;andoneoptionalcompensationforthetrackingperform-

ance(Thedetailsoftrackingperformancecompensationscanbe

foundinWangetal.[15,16]).Sincethecircuithassymmetry,the

controleffortsforthevalve(4a)showninFig.1aretheexample

forthefollowingdiscussions;thecontrolofvalve(4b)isjusta

mirroredalgorithm,soitisomittedinthispaper.

Thecontrolsignalfortheflowcontrolvalveisdefinedas

uu

p

u

s

u

t

(17)

whereu

p

referstocontroleffortsofcompensationforpressure

oscillations,u

s

isthepartforformingquotientgroupsliding,u

t

is

theparttoimprovethetransientresponseoftrajectorytracking

problems.

u

p

isthenecessarypartbecausethepressureoscillationsinher-

entlyexistinthecircuitduetothecircuit’sdiscontinuousswitch-

ing.u

t

partofu

t

ensuresgoodtracking

performance,butitalsosacrificespartofthewholesystem’s

energyeffipplication’stransientresponseisnot

criticalorifthenaturaltransientresponsehasalreadybeensatis-

fied,hereare

alwayssomeimperfectionsonthevalve’sdynamicsanditsflow

resistance,thesystemwillattimesbeoutofthedesiredworking

regions.u

s

ensuresthattheworkingpointslidestothedesired

hispartneversacrificessystemenergyeffi-

ciency,itisrecommendedtokeepthiscompensation.

Theinputstothealgorithmarepressuresonthecylinderports.

Pressuresaredetectedbythepressuresensorswhosebandwidthis

requiredtobegreaterthan让心归零的说说 thepump’mmer-

ollow-

ing,P

a

referstothepressuredetectedonthepowerlinewhich

connectstothecylinderportofthesinglerodcylinderandP

b

is

thepowerlineconnectedtotherodsideofthecylinder.

Fig.11Hydraulicliftertestbed

Fig.12Controlstructure

Fig.13(a)Pressureresponse;(b)positionandvelocity

response

JournalofDynamicSystems,Measurement,andControlJANUARY2012,Vol.134/011019-7

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Alowpassfilterf

s

withtimeconstantsisdefinedintransfer

functionform

f

s

s

1

ss1

(18)

Lettheoperatorf

s

:

systemf

s

.Themeanvaluesoftwopressuresareevaluatedas

P

a

f

s1

P

a

P

b

f

s1

P

b

(19)

withatimeconstants1,forexample,s1

1

=

20p

litude

ofthepressureoscillationsduringaperiodoftransientresponseis

evaluatedas

DP

a

f

s2

P

a

P

a

jj(20)

wheres2isatimeconstant.

ThepressureoscillationsoccurwhenP

a

P

b

isclosetozero.

WewillturnonthistypeofcompensationwhenP

a

P

b

falls

belowsomebound,P

os

,thengraduallyturnitoffinordertomain-

udocodeforthepressureoscillation

compensationisasfollows:

If

P

b

P

a

jj

>2P

os

u

p

0

Elseif

P

b

P

a

jj

>P

os

u

p

gain2

P

b

P

a

jj

P

os

Else

u

p

gain

Endif

Fig.14(a)Pressureresponsewithoscillations;(b)position

andvelocityresponsewithoscillations

Fig.15Oscillationsareinhibitedbyincreasingleakage

Fig.16Experimentresponses(M50Kg)

Fig.17Experimentresponses(M561.2Kg)

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wheregainisaconstantvaluecorrespondingtotheflowvalve’s

percentageopening.

AtleastoneofeitherP

a

orP

b

shouldbeclosetothecharge

pressurewhenthecircuitisinthedesirableworkingcondition.

Abnormalsituationsoccurwhentheshuttlevalveisnotfully

flow

controlvalve,inthiscase,willbefullyopenedtoletthesystem

fi,thecompensa-

tionisdescribedby

If(

P

b

>P

error

)

u

s

FullOpen

Else

u

s

0

Endif

whereP

error

isaboundofmaximalpressuredropontheshuttle

Openisacontrolvoltage

tofullyopentheflowcontrolvalve.

Pressuresurg杜牧清明创作背景 esduringtrackingperiodsindicatethattheaccel-

erationofthecylinderisnotsmooth(Noticethatthepressureon

othersideofthecylinderisalmostaconstantvalue).Thecompen-

sationisproportionaltothepressureoscillation’,

thecompensationisdescribedas

u

t

jD

P

a

wherejisaconstant.

Themaincomputationloadfortheentirealgorithmisdecided

byfourfirst-orderequations(thesecanbemergedintothreeequa-

tions).Sincethefilterbandwidthisverylow,say,lessthan5Hz,

mostcommercialDigitalSignalProcessorsorMicroprocessors

cancompletethisalgorithm.

6SimulationsandExperiments

Experimentsandsimulationswereconductedtovalidatethe

ed,whichisillustratedschematicallyin

Fig.1,glerodcylinderhasa

meteroftherodandthepistonare

0.0254mand0.038m,nnelironplatform

eceofthe

venoftheseweightscanbe

alvesusedinthecircuitarecho-

senfromSunHydraulicsCorporation’iable

displacementpumpisaSauerDanfossH1axialpistonpump.

pis

c-

tricmotoralsodrivesasmallchargepumptoprovidethecharge

pressure,whichisregulatedbyareliefvalveat150psi(1MPa).

Thehosesusedinthecircuitcansustainover3000psi(20.6

MPa).Thereliefvalvesareadjustedto1500psi(10.3MPa)for

ssuresensors,madebyHydacTechnologyCorpo-

ration,areratedto3000psi(20.6MPa)andareinstalledasshown

orithmsarerunontheMATLABxPCTargetreal

mandsforpumpdisplacements

andtheelectricmotorcontrolsuseaCANBUSnetworktoconnect

thetargetcomputer,thevariabledisplacementpump,andthe

nalInstrumentsPCI-6052

A=D&D=Acardisusedtocollectpressuresignalsanddrivethe

fllowpassfiltersisalsousedtofilter

theinterferencenoisefromtheelectricalmotorandactasanti-ali-

asingfiplacementsensor,madebyMTSSystemsCor-

poration,isusedtomeasurethecylinder’sposition.

Thealgorithmspresentedintheprevioussectionareimple-

epropor-

tionalcontrolisdesignedtobetheoutercontrollooptotrack

loopdesignstructureis

duetothecylinderlengthlimitationsandnonlinearfrictionchar-

acteristicsduringcylinderretractingandextending;however,the

-

resentsthecom-

resentstheexperimentalresults

withoutimplementingthispaper’

Cshowstheexperimentalresultswiththecompensations

implemented.

6.1PartA:strateandsolvepressureos-

cillationproblems,-

rametersusedbythecodeapproximatedthoseusedinthe

13showsasetofsimulationresults

whentheoscillationshavenotoccurred.

Fig.18Experimentresponses(M5142.8Kg)

Table1Experimentalresultswithoutcompensations

Mass(Kg)PressureoscillationEnergyefficiency

0NoGood

20.4NoGood

40.8YesNotacceptable

61.2YesNotacceptable

81.6YesNotacceptable

102YesNotacceptable

122.4NoGood

142.8NoGood

Fig.19SimulationresultwithM560.2Kg

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InFig.13,duringtimeinterval,0

that,thepumpchangesthesignofthedisplacementsothatthe

13(a)showspressureschangeswith

respondingpositionandvelocityinforma-

tionareshowninFig.13(b)

samesetofparametershavebeenusedasinthesimulationinFig.

13exceptthemassischangedtobeclosetothecriticalmassas

definedintheprevioussections(Eq.(2)).Almostnooscillation

occursduringextending,butoscillationsdooccurwhilethecylin-

tinuitiesandalimitcyclecanbeeasily

identifiedinthisfigure.

UsingthesameparametersasinFig.14,theequivalentleakage

coeffiultis

thatpressureisstabilizedafterthetwo

,itcanbeseenthattheproposed

algorithmissomewhatconservativebecausethezeroinput

responseproblemdoesnotalwaysencountertheworstcase.

6.2PartB:一年级必背20首古诗 ExperimentalResultsWithout

experimentswereconductedwiththe

compensationdeactivatedinordertoverifytheinternalstabilities

ollowingtests,themassis

referredtoastheweightsmountedonthechannelironplatform.

Thetotalmassistheaddedweightsplusthemassoftheplatform,

erimentsstartatzeroadded

tof20.4Kgisaddedforeachsuccessiveexperi-

s16–18

showtheresultsforthreeoftheseexperiments.

Intheaboveresults,thecircuitisshowntoworkwellwhenthe

loadisfarfromthecriticalmassasshowninFigs.16and18.

Whentheloadisnearthecriticalmass(M68Kg),neithercyl-

inderportisconsistentlyconnectedtothechargepressure,and

thereareseriouspressureoscillationsinthecircuitasshownin

sultsfordifferentloadscanbeseeninTable1.

Theresultsshowthatthecircuitisinheritablystablewhenthe

-

ise,

theperformanceisnotacceptableeitherfromanenergyefficiency

vieworsystemsafetyviewbecausethetestbedmakesnoiseand

vibrationswhenthisoccurs.

Aseriesofsimulationsatdifferentloadsalsohasbeencon-

ductedtocomparethesimulationresultswithexperimental

ationexampleisshowninFig.19usinganadded

rrespondstotheexperimentalresult

timeinterval,0

isextending;afterthatthecylinderisretracting.

Simulationresultsatdifferentloadsareconsistentwiththeex-

perimentalresultsatthecorrespondingloadsanddisplacement.

Theresultsmatchwellwhenpressureoscillationsdonotoccur.

Thesimulatedpressurevalueisalittlelowerthantheexperimen-

fferencemaybedueto

turbulentflow,whichisnotconsideredinthesimulation,orthe

Fig.21Experimentresponseswithcompensations(M561.2

Kg)

Fig.22Experimentresponseswithcompensations(M5142.8

Kg)

Fig.23Experimentresponseswithcompensations(critical

mass)

Fig.20Experimentresponseswithcompensations(M50Kg)

011019-10/Vol.134,JANUARY2012TransactionsoftheASME

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r,thepredictionofpressureoscil-

lationsbysimulationsisveryaccurate.

6.3PartC:ExperimentalResultsWith

hesameparametersasinpartB,the

wholesetofexperimentswasrepeatedwithcompensationsturned

s20–22showtheexperimentalresultswhentheadded

weightsare0,61.2,and142.8Kg,respectively.

Figure20showsthecylinderisworkinginpumpingmode

normalbecausetheload

issosmallthatthepumponlyneedstoovercomesomefrictionto

eseenthatoneofportsisconsistentlyconnectedto

.22,alargeloadisaddedtothecylin-

der,sothepumpisunderpumpingmodewhentheloadislifted

upandisundermotoringmodewhenthecylinderisretracting

inderportontherod

sideisalwaysconnectedtothechargepressure.

Thingsbecomecriticalwhentheloadisclosetothecritical

mass;thepumpworksinpumpingmodeinboth为有暗香来是哪首诗 directionsas

ssuredifferencewhenthecylinderis

retractingissmall(around10psi(69KPa)).Noticethatoscilla-

tiondoesnotoccurasseeninthesimulationsandtheexperiments

situationwillhappen

ifweaddasmallamountofweightonthecylindertoapproach

ecylinderis

retracting,pressuresonbothcylinderportsareexactlyidentical;

however,lsetofresultsis

listedinTable2.

Theresultsalsoshowthereareno“undesirableworking

region”heportsisalwaysreliablyconnected

ustnessofthecircuitalsohasbeen

testedbyvaryingtrajectoryprofiles,forceimpulseonthecylinder,

ases,thecircuitworks

well.

7Conclusion

Thispaperpresentsanovelflowcontrolcircuitwhichissuita-

bleforsinglerodcylindersinvariablecontrolleddisplacement

temmodelhasbeenderivedand

sationalgorithms

havebeendevelopedtostabilizethesystemandtoimprovethe

cuitisenergeticallyefficientand

reoscillationshavebeeneffec-

ngperformancecanbeimprovedif

cuitinheritsadvantagesoftraditionaldesignsbut

cuitisvalidatedbyhardware

experimentsandshowsgoodrobustness.

Acknowledgment

ThisworkissupportedinpartbyCenterforCompactandEffi-

cientFluidPower,aNationalScienceFoundationEngineering

ResearchCenterfundedundercooperativeagreementnumber

hors

gratefullyacknowledgethesupport.

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trolConceptsforDisplacementControlledActuators,”ower,6(2),

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[3]Lodewyks,J.,1993,“Differentialzylinderimgeschlossenenhydrostatischen

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ofHydraulicExcavators,”4thInternationalSymposiumonExperimental

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[12]Yu,J.,Chen,Z.,andLu,Y.,1994,“TheVariationofOilEffectiveBulkModu-

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Control:AnalysisandDesign(Academic,NewYork,1986).

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Table2Experimentalresultswithcompensations

Mass(Kg)PressureoscillationEnergyefficiency

0NoGood

20.4NoGood

40.8NoGood

61.2NoGood

68.2NoGood

81.6NoGood

102NoGood

122.4NoGood

142.8NoGood

JournalofDynamicSystems,Measurement,andControlJANUARY2012,Vol.134/011019-11

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