Semi-Active Suspension Control Design for Vehicles

232 Pages·2010·9.07 MB·English

by  Sergio M. Savaresi

Semi-Active Suspension Control
Design for Vehicles
Semi-Active Suspension Control
Design for Vehicles
S.M. Savaresi
C. Poussot-Vassal
C. Spelta
O. Sename
L. Dugard
AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON(cid:129)NEWYORK(cid:129)OXFORD
PARIS(cid:129)SANDIEGO(cid:129)SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO
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Firstpublished2010
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BritishLibraryCataloguinginPublicationData
Semi-activesuspensioncontroldesignforvehicles.
1.Activeautomotivesuspensions–Design.
I.Savaresi,SergioM.
629.2’43–dc22
LibraryofCongressControlNumber:2010925093
ISBN:978-0-08-096678-6
ForinformationonallButterworth-Heinemannpublications
visitourWebsiteatwww.elsevierdirect.com
Typesetby:diacriTech,India
PrintedandboundinChina
101112 111098 7 65 43 21
Dedication
To Cristina, Claudioand Stefano(S.M.S)
To my Family (C.P-V)
To Daniela(C.S.)
To Isabelle, Corentin and Grégoire(O.S.)
To Brigitte (L.D.)
List of Figures
1.1 Classical scheme ofa wheel-to-chassissuspension in acar......................1
1.2 Filteringeffectofapassive suspension: example ofaroad-to-chassis
frequencyresponse (up),and a road-to-tire-deflectionfrequency
response (bottom). .................................................................3
1.3 The CitroënDS.....................................................................4
1.4 The Lotus Excel. ...................................................................4
1.5 Exampleofa suspension ofa luxurysedan (AudiA8),which integrates
anelectronicallycontrolledgasspringwithload-levelingcapabilities,
anda semi-activedamper. .........................................................5
1.6 Damping-ratiotrade-off............................................................6
1.7 Anexperimentalcomparisonoffilteringperformance(comfort
objective):semi-active strategies;labeled SH-C(forSkyhook),Mix-1
(forMixed Skyhook-ADDwith1 sensor)andMix-2 (forMixed
Skyhook-ADDwith2sensors)versus fixed-dampingconfigurations(c
min
andc ).............................................................................7
max
1.8 Examples ofchassis-to-cabin(bySameDeutz-Fahr)andcabin-to-seat
(bySEARS)semi-activesuspension systems.....................................8
1.9 Examplesofelectronicallycontrolledsemi-activeshockabsorbers,using
threedifferenttechnologies.Fromlefttoright:solenoid-valve
Electrohydraulicdamper(Sachs),Magnetorheologicaldamper(Delphi),
andElectrorheologicaldamper(Fludicon)........................................9
1.10 Examples of“full-corner”vehiclearchitectures:Michelin Active
Wheel©(left)and SiemensVDOe-Corner©(right)............................10
1.11 Bookorganizationandsuggested readerroadmap.Expert readersmay
startdirectlywithstarred(∗)chapters............................................11
2.1 Quarter-carrepresentationofasuspension system in avehicle.................16
2.2 Pictorialrepresentationofthesuspension “passivity constraint”(grey
area).Exampleoflinearcharacteristicsforpassive spring(boldline,left)
andforpassive damper(boldline,right).........................................17
2.3 Exampleofa steel coilspring. ...................................................18
xi
ListofFigures
2.4 Typical deflection-forcecharacteristic(right)ofspringwithnominal
stiffnesscoefficientk =25KNand nominalmaximumdeflectionof
200mm. Steadystatecomputedfora suspended mass of250Kg. .............19
2.5 Schematicrepresentationofa gasspringimplementedwithpneumatic
spring(left)and withhydropneumaticspring(right)............................20
2.6 Typical deflection-forcecharacteristicofanautomotiveairspring.............21
2.7 Concept ofamono-tubepassive shock absorber.................................22
2.8 Diagramofanideal linearpassive characteristicofhydraulicshock
absorber, withandwithoutfriction.The dampingcoefficentis c=2000
Ns/m, thestatic frictionis F =70N. ...........................................22
0
2.9 Graphicrepresentationofsuspension system classification: energy
requestwith respecttothe availablecontrolbandwidth.........................25
2.10 Schematicrepresentationofanelectrohydraulicshock absorber. ..............27
2.11 Idealdampingcharacteristics ofanelectrohydraulicshock absorber
(withnegligiblefriction)..........................................................28
2.12 Left:schematic representationofa magnetorheologicaldamper
behavior:withandwithoutmagneticfield. ......................................29
2.13 Idealdampingcharacteristics ofamagnetorheologicalshock absorber. .......30
2.14 Schematicrepresentationofanelectrorheologicaldamper:with and
withoutelectricfield...............................................................30
2.15 Idealdampingcharacteristics ofanelectrorheologicalshock absorber.........31
2.16 Conceptual blockdiagramofan electronicshock absorber. ....................33
2.17 Diagramoftheelectricdriverina semi-activeshock absorber. ................36
2.18 Stepresponse oftheelectricdriver:open-loop(topline)andclosed-loop
(bottomline). Parametersofthedriverandthecontrollerare:
L =30mH; R =5(cid:2);desiredclosed-loopbandwidthω =100·2π
c
(100Hz); K =500·2π; K =3·2π. ...........................................37
I p
2.19 Block diagramofsemi-active shockabsorberequipped withinternal
controlofelectricsubsystem......................................................38
3.1 Passive quarter-carmodel, generalform(left)and simplifiedform(right).....42
3.2 Eigenvalues ofthepassive quarter-carmodel forvaryingdamping
values. Low damping(rounds),mediumdamping(triangles)and high
damping(dots).....................................................................50
3.3 Frequencyresponse of F (s), F (s) and F (s)forvaryingdamping
z zdeft zdef
valuec. Invariantpoints arerepresentedbythe dots. ...........................51
3.4 Frequencyresponse of F (s), F (s) and F (s)forvaryingstiffness
z zdeft zdef
valuek. Invariantpoints arerepresentedbythe dots. ...........................52
3.5 Simplifiedpassive quarter-carmodel.............................................53
xii
ListofFigures
3.6 Frequencyresponse F (s): comparisonbetweenthequarter-carmodel
z
(dashedline)andits simplifiedversion(solidline)for c=c . ...............55
min
3.7 Half-carmodel(pitchoriented)...................................................56
3.8 Bodediagramofthepitchatthecenterofgravity F (s)(top),thebounce
φ
F (s) atthe centerofgravityand ofthefrontbounce F (s)(bottom)of
z zf
thepitchmodelforvaryingdampingvaluec. ...................................58
3.9 Bodediagrams of F (s) and F (s)forthehalfpitch(solidline)model,
z zf
comparedwithforthe quarter-carmodel(dashedline), forc=c . ..........59
min
3.10 Fullverticalvehiclemodel........................................................61
3.11 Extendedhalf-model. .............................................................63
3.12 Passive (left)andsemi-active (right)quarter-carmodels........................65
3.13 DissipativedomainD(c ,c ,c0) graphicalillustration......................66
min max
4.1 Nonlinearsuspension stiffnessandstrokelimitations...........................75
4.2 IllustrationoftheperformanceobjectivesonBode diagrams. Comfort
orienteddiagram F (top)andRoad-holdingorienteddiagram F
z zdeft
(bottom).Solidline:c , Dashed: c . .........................................77
min max
4.3 Nonlinearfrequencyresponse (FR, obtainedfromAlgorithm1)ofthe
passive quarter-carmodelforvaryingdampingvalues:nominal
c=1500Ns/m(solidline), softc=c =900Ns/m(dashed line)and
min
stiffc=c =4300Ns/m(solidroundedline).Comfortoriented
max
˜ ˜
diagram F (top)androad-holdingorienteddiagram F (bottom)...........82
z zdeft
4.4 Normalizedperformancecriteriacomparisonfordifferentdamping
˜
values. Comfortcriteria– J (lefthistogramset) androad-holding
c
˜
criteria– J (righthistogramset). ...............................................84
rh
4.5 Normalizedperformancecriteriatrade-off({J˜,J˜ } trade-off)fora
c rh
passive suspension system, with varyingdampingvalue
c∈[100, 10,000](solidlinewith varyingintensity).Dots indicatethe
criteriavaluesforthreefrozendampingvalues(i.e.c=c =900Ns/m,
min
c=c =1500Ns/m andc=c =4300Ns/m). .............................85
nom max
4.6 Bumproaddisturbance(top)andits timeandfrequencyrepresentation
(bottomleftandrightrespectively)...............................................86
4.7 Roadbumpsimulationofthe passive quarter-carmodelfortwo
configurations:harddamping(c , solidlines) andsoftdamping(c ,
max min
dashed lines).Chassis displacement(z(t)), tiredeflection(z (t))and
deft
suspension deflection(z (t))....................................................87
def
4.8 Broadbandwhite noiseexample. Time response (left)and itsspectrum
(right). .............................................................................89
xiii
ListofFigures
5.1 Semi-activesuspension optimalperformancecomputationscheme. ...........94
5.2 Illustrationofthe domainD(c , c , c0)modificationas a functionof
min max
c0. Left:c0 =0, right:c0 = cmin+cmax .............................................96
2
5.3 Comparisonofthecontinuousanddiscrete-time(withT =1ms)models
e
˜ ˜
frequencyresponse (Algorithm1).Top: F , bottom: F . ....................97
z zdeft
˜ ˜
5.4 Optimalcomfortorientedfrequencyresponse of F and F obtained
z zdeft
bythe optimizationalgorithm,forvaryingpredictionhorizon N, for
˜
comfortobjective(i.e. cost function J )........................................ 100
c
˜ ˜
5.5 Optimalroad-holdingfrequencyresponse of F and F obtainedby
z zdeft
theoptimizationalgorithm,forvaryingpredictionhorizonN, for
˜
road-holdingobjective(i.e. cost function J ). ................................ 101
rh
5.6 Normalizedperformancecriteriacomparisonforincreasing prediction
horizonN: comfortcriteria−whencost functionis J˜ (lefthistogram
c
set)and road-holdingcriteria− whencost functionis J˜ (right
rh
histogramset).................................................................... 102
5.7 Normalizedperformancecriteriatrade-off({J˜ ,J˜ } trade-off)fora
c rh
passive suspension system, withdampingvaluec∈[c ;c ](solid
min max
linewithvaryingintensity)andoptimalcomfort/road-holdingbounds,
withα ∈[0;1](dashdottedline). .............................................. 102
5.8 Bumptest responses ofthe optimalcomfortorientedcontrol(solidsmall
roundsymbol),optimalroad-holdingoriented(solidlargeround
symbol)andpassive withnominaldampingvalue(solidline). Fromtop
tobottom:chassis displacement(z), chassis acceleration (z¨)andtire
deflection(z )................................................................. 105
deft
6.1 Skyhookidealprincipleillustration. ........................................... 108
6.2 Comfortorientedcontrollaw frequencyresponse F (top)and F
z zdeft
(bottom).......................................................................... 112
6.3 Normalizedperformancecriteriacomparisonfordifferentcomfort
˜
orientedcontrolstrategies: comfortcriteria– whencost functionis J
c
˜
(lefthistogramset) androad-holdingcriteria–when costfunctionis J
rh
(righthistogramset)............................................................. 114
6.4 Road-holdingorientedcontrollawfrequencyresponse F (top)and F
z zdeft
(bottom).......................................................................... 115
6.5 Normalizedperformancecriteriacomparisonforthe different
road-holdingorientedcontrolstrategies: comfortcriteria–when cost
˜
functionis J (lefthistogramset) androad-holdingcriteria– whencost
c
˜
functionis J (righthistogramset). ........................................... 116
rh
xiv
ListofFigures
6.6 Normalizedperformancecriteriatrade-offforthe presentedcontrol
algorithms,comparedtothepassive suspension system, withdamping
valuec∈[c ;c ](solidlinewithvaryingintensity),optimalcomfort
min max
androad-holdingbounds (dashdottedline).................................... 116
˜ ˜
7.1 Frequencyresponse of F and F ofthemixed SH-ADDwithrespect
z zdeft
tothepassive car(withminimaland maximaldamping)...................... 123
7.2 Normalizedperformancecriteriacomparison:comfortcriteria– J (left
c
histogramset)androad-holdingcriteria– J (righthistogramset).
rh
SH-ADDcomparisonwith respecttocomfortorientedalgorithms........... 124
7.3 Normalizedperformancecriteriatrade-offforthe presentedcomfort
orientedcontrolalgorithmsandMixed SH-ADD,comparedtothe
passive suspension system, with dampingvalue c∈[c ;c ](solid
min max
linewithvaryingintensity), optimalcomfortandroad-holdingbounds
(dashdottedline). ............................................................... 124
˜ ˜
7.4 Frequencyresponse of F and F ofthemixed1-sensorSH-ADDwith
z zdeft
respectto thepassive car(withminimalandmaximaldamping)............. 126
7.5 Normalizedperformancecriteriacomparison:comfortcriteria– J (left
c
histogramset)androad-holdingcriteria– J (righthistogramset).
rh
SH-ADD1-sensor comparisonwithrespectto comfortorientedalgorithms.127
7.6 Normalizedperformancecriteriatrade-offforthe presentedcomfort
orientedcontrolalgorithmsand1-sensor mixedSH-ADD,comparedto
thepassive suspension system, withdampingvaluec∈[c ;c ](solid
min max
linewithvaryingintensity), optimalcomfortandroad-holdingbounds
(dashdottedline). ............................................................... 127
7.7 Pictorialanalysis oftheinequality(7.4)........................................ 129
7.8 Function |D+(ω)| (innormalizedfrequency). ................................... 129
T
7.9 Exampleofevolutionoftheautonomoussystems z¨(t)=αz˙(t) and
z¨(t)=−αz˙(t) (startingfromz˙(0)>0). ....................................... 130
7.10 Sensitivitytothe parameterα ofthe mixedSH-ADDperformances......... 131
7.11 Time responses ofsoftdampingsuspension (c ),harddamping
min
suspension (c ),SH, ADD, andmixed-SH-ADDto threepure-tone
max
roaddisturbances:2.1Hz (top),4Hz (middle)and 12Hz (bottom)........... 132
7.12 Time responses ofsoftdampingsuspension (c ),harddamping
min
suspension (c )and1-Sensor-Mixed(1SM)tothreepure-toneroad
max
disturbances:2.1Hz (top),4Hz (middle)and 12Hz (bottom). ............... 134
7.13 Acceleration(top)and tiredeflection (bottom)responses toatriangle
bumpontheroadprofile:passive softdamping(c ),harddamping
min
(c ),SH, ADDand mixedSH-ADD. ........................................ 136
max
xv