結合順滑模態控制與參考橫擺角速度選取方式於車輛側向控制之研究

୯ ҥ Ҭ ೯ ε Ꮲ

ႝ௓πำࣴز܌

ᅺ γ ፕ Ў

่ӝ໩ྖኳᄊ௓ڋᆶୖԵᐉᘍفೲࡋᒧڗБԄ

ܭً፶ୁӛ௓ڋϐࣴز

Study of combining SMC design and the reference

yaw rate selection in vehicle lateral control

ࣴ ز ғǺֆᄪΓ

ࡰᏤ௲௤ǺఉᝬЎ റγ

่ӝ໩ྖኳᄊ௓ڋᆶୖԵᐉᘍفೲࡋᒧڗБԄ

ܭً፶ୁӛ௓ڋϐࣴز

Study of combining SMC design and the reference

yaw rate selection in vehicle lateral control

ࣴ ز ғǺֆᄪΓ StudentǺRong-Ren Wu

ࡰᏤ௲௤ǺఉᝬЎ റγ AdvisorǺDr. Yew-Wen Liang

୯ҥҬ೯εᏢႝ௓πำࣴز܌

ᅺ γ ፕ Ў

A Thesis

Submitted to Institute of Electrical and Control Engineering College of Electrical Engineering and Computer Science

National Chiao Tung University In Partial Fulfillment of the Requirements

for the Degree of Master in

Electrical and Control Engineering July 2011

Hsinchu, Taiwan, Republic of China

i 

่ӝ໩ྖኳᄊ௓ڋᆶୖԵᐉᘍفೲࡋᒧڗБԄ

ܭً፶ୁӛ௓ڋϐࣴز

ࣴزғǺֆᄪΓ ࡰᏤ௲௤ǺఉᝬЎ റγ

୯ҥҬ೯εᏢႝ௓πำࣴز܌

ᄔ ा

! ! ҁፕЎճҔޔௗᐉᘍΚં௓ڋ ( Direct Yaw Moment ControlǴ

DYC ) מೌ௖૸ًηୁӛ௓ڋϐᛙۓ܄ᆶᏹ௓܄ޑ࣬ᜢ᝼ᚒǶፕЎ

ύ่ӝ໩ྖኳᄊ௓ڋ೛ीᆶୖԵᐉᘍفೲࡋᒧڗޑБԄ٬ୁྖفૈ

ᆢ࡭ӧ৒೚ጄൎϣаᆢ࡭Չًϐᛙۓ܄Ƕ२ӃǴҁፕЎଞჹ 2-DOF

ޑጕ܄ًηኳࠠϩձ೛ीਔᡂᆶߚਔᡂޑୖԵᐉᘍفೲࡋǴኳᔕ่݀

ᡉҢόՠՉًޑᛙۓ܄ёаዴߥǴᏹ௓܄ૈΨёаԖਏޑගϲǶ܌ᕇ

ளޑ่݀ΨᔈҔӧႝηًڀԖྩًठ୏Ꮤࡺምਔϐё᎞ࡋ௓ڋ᝼ᚒǴ

ኳᔕ่݀ᡉҢӧ೽ϩठ୏Ꮤวғࡺምਔً፶ϝёᆢ࡭ځᛙۓ܄ᆶᏹ

௓܄ǶനࡕǴҁፕЎΨ௖૸ًؓՉᎭܭ -split ၡय़ਔճҔ DYC ௓ڋ

БԄޑᛙۓୢᚒǴኳᔕ่݀ᡉҢ܌ග௓ڋ೛ीϐԖਏ܄Ƕ

ii 

Study of combining SMC design and the reference

yaw rate selection in vehicle lateral control

StudentǺRong-Ren Wu AdvisorǺDr. Yew-Wen Liang

Institute of Electrical and Control Engineering

National Chiao Tung University

ABSTRACT

In this thesis, we study the vehicle stability and maneuverability

issues using the direct yaw moment control (DYC) technique. The

proposed scheme employs the sliding mode control (SMC) design and the

reference yaw rate selection approach so that the vehicle not only

maintains its stability but also achieves allowable maneuverability. For a

2-DOF linearized vehicle model, this thesis provides both time varying

and time-invariant reference yaw rates, which are shown from simulation

to be able to realize the maneuverability as better as possible and keep the

vehicle under stable operation. We also extend the results to the reliability

issues when the vehicle experiences actuators’ outage. Besides, the DYC

scheme is also employed to investigate the stability when vehicle drives

on -split road. Simulation results demonstrate the benefits of the

proposed scheme.

iii 

ᇞ ᖴ

! ! ҁፕЎளа໩ճֹԋሡाགᖴࡐӭΓޑᜢЈᆶڐշǶ२ӃགᖴךޑࡰᏤ௲௤ ఉᝬЎറγǴགᖴԴৣ೭ٿԃٰޑಒЈᆶऐЈࡰᏤϷჹךֶֶό॰ޑ௲ᇧǴᡣך ӧၶډ֚ᜤਔࡰᏤך߻຾ޑБӛǴό໻ӧࣴزၸำύڙ੻ؼӭǴЪࡑΓೀ٣ӚБ य़Ԗ೚ӭԋߏǶӕਔךΨाགᖴα၂ہ঩ᄃቺ၈റγǵᎄݯύറγکֺරےറγ ๏ϒࡌ೛܄ޑࡌ᝼ᆶࡰᏤ٬ҁፕЎ׳ᑪֹഢǶ ! ! ௗΠٰǴךाགᖴჴᡍ࠻ޑ৪യ֡Ꮲߏǵ᚟ྍ׊Ꮲߏǵ݅ҥ۝Ꮲߏکᎄԓד Ꮲߏӧךၶډ֚ᜤਔૈ๏ϒ፾ਔޑཀـᆶᔅշǴΨᖴᖴӕᏢඵமǵ։ᇬаϷᏢ׌ һ勃ǵѶᏂکᏢۂ໋໋ޑᔅԆǴᡣךӧྗഢᅺፕޑၸำύளа໩ճǶᖴᖴ 906 ޑӚՏϷҬεᇡ᛽ޑܻ϶ॺǴӢࣁکգॺޑ࣬᛽Ǵᡣךӧٿԃࣴزғఱӭߍӭ࠮ кᅈӣᏫǴؒԖգॺፕЎόёૈ໩ճֹԋǶ നࡕाགᖴךനངޑРᒃǵ҆ᒃᆶۊۊǴҗܭգॺޑεΚЍ࡭ᆶႴᓰǴ٬ך ёаคࡕ៝ϐኁޑӧᏢ཰΢߿۳ޔ߻ǴΨགᖴӧҬε؃ᏢၸำύഉՔ๱ךޑሺ఼Ǵ ᖴᖴգॺǴᙣஒԜፕЎ᝘๏գॺǶ ֆᄪΓ! ᙣ᛽ ύ๮҇୯΋ԭԃΎД ཥԮ! Ҭ೯εᏢ

iv 

Ҟ!ᒵ!

ύЎᄔा... i मЎᄔा... ii ᇞ ᖴ... iii Ҟ ᒵ... iv ߄ Ҟ ᒵ... vi კ Ҟ ᒵ... vii ಄ ဦ ߄... x ಃ 1 ക ᆣፕ... 1 1.1 ࣴزङඳ... 1 1.2 ࣴز୏ᐒ... 3 1.3 ፕЎࢎᄬ... 5 ಃ 2 ക ࣬ᜢࣴز... 6 2.1 ໩ྖኳ௓ڋ... 6 2.1.1 ໩ྖኳ௓ڋϟಏ... 7 2.1.2 ໩ྖኳ௓ڋᏔϐ೛ी... 10 2.2 ̉agic formula ፺जኳࠠ ... 14 2.3 Ѥ፺ً፶୏ᄊኳࠠ... 19 2.3.1 ጕ܄ 2-DOF ًη୏ᄊ ... 20 2.3.2 ߚጕ܄ 7-DOF ًη୏ᄊ ... 22 ಃ 3 ക ୖԵᐉᘍفೲࡋޑᒧڗȐ៾ख़ޑ೛ीȑ... 24 3.1 ୁख़ᏹ௓܄ϐୖԵᐉᘍفೲࡋǺ_{1ሺmaneuverabilityሻ} ... 25 3.2 ୁख़ᛙۓ܄ϐୖԵᐉᘍفೲࡋǺ_{2ሺstablityሻ} ... 29 3.3 ៾ख़Ȑweightingȑޑϟಏ... 33 3.4 ៾ख़ȐweightingȑࣁߚਔᡂᆶਔᡂޑБԄ... 34

v  3.4.1 ៾ख़Ȑweightingȑࣁߚਔᡂ... 35 3.4.1.1 change lane୏բϐኳᔕ... 36 3.4.1.2 ٿԛ change lane ୏բϐኳᔕ... 39 3.4.2 ៾ख़Ȑweightingȑࣁਔᡂ... 42 3.4.2.1 change lane୏բϐኳᔕ... 43 3.4.2.2 ၧᗉምᛖނԶ຾Չ change lane ୏բϐኳᔕ... 46 3.4.2.3 ٿԛ change lane ୏բϐኳᔕ... 50 3.4.2.4 JᙯӛȐJ-turnȑ୏բϐኳᔕ ... 53 ಃ 4 ക ᔈҔ໩ྖኳ௓ڋޑё᎞ࡋ೛ीܭӄًኳࠠ... 57 4.1 ୢᚒඔॊ... 57 4.2 ё᎞ࡋ௓ڋޑ೛ी... 58

4.2.1 ᒡрଓᙫϦԄϯȐOutput Tracking Formulationȑ ... 58

4.2.2 ໩ྖኳᄊ௓ڋޑё᎞ࡋ೛ी... 60

4.2.3 ᒱᇤୀෳᆶບᘐᐒڋȐFDDȑ... 62

4.3 ៾ख़ȐweightingȑޑໆෳБԄ... 62

4.4 ่ӝ໩ྖኳᄊ௓ڋޑё᎞ࡋ೛ीᆶ៾ख़ᢀۺܭӄًኳࠠ... 65

4.4.1 change lane୏բϐኳᔕȐଳၡय़ȑ ... 66

4.4.2 change lane୏բϐኳᔕȐpacked snowၡय़ȑ ... 71

4.5 ໩ྖኳᄊ௓ڋޑё᎞ࡋ೛ीᔈҔܭ-split ၡय़ϐ௖૸ ... 77 ಃ 5 ക ่ፕᆶ҂ٰࣴزБӛ... 82 5.1 ่ፕ... 82 5.2 ҂ٰࣴزБӛ... 82 ୖԵЎ᝘... 83 ߕᒵ... 88

߄ Ҟ ᒵ

߄ 2.1 ًη፺जޑ߯ኧॶa₀~a₈ȐF_z in kN ȑ ... 16 ߄ 2.2 ًηኳᔕୖኧ... 23

vi 

vii 

კ Ҟ ᒵ

კ 1.1! ໩ྖኳᄊ௓ڋޑё᎞ࡋ೛ीϐࢬำკ... 4 კ 2.1! ΢໩ྖय़זᄌޑҢཀკ... 8 კ 2.2! ໩ྖኳᄊҢཀკ... 9 კ 2.3! ϪၢȐchatteringȑ౜ຝҢཀკ... 9 კ 2.4! ໩ྖቫȐsliding layerȑҢཀკ ... 10 კ 2.5! ̉agic formula ୖኧ߄Ԅϐཀက ... 16 კ 2.6! ᕵӛΚ٬Ҕ Magic formula ፺जኳࠠ ... 18 კ 2.7! ୁӛΚ٬Ҕ Magic formula ፺जኳࠠ ... 18 კ 2.8! Ѥ፺ً፶ኳࠠ... 19 კ 2.9! ߚጕ܄ single track ًηኳࠠ ... 20 .. კ 3.1! change lane ኳᔕკ (ɀ_ୢ௦Ҕɀ_ଵ) ... 28 კ 3.2 Mz ኳᔕკ (ɀ_ୢ௦Ҕɀ )_ଵ ... ... 29 ... კ 3.3! change lane ኳᔕკ (ɀ_ୢ௦Ҕɀ_ଶ) ... 31 კ 3.4! ୁྖف(Ⱦ) ... 32 კ 3.5! Mz ኳᔕკ (ɀ_ୢ௦Ҕɀ_ଶ) ... 32 კ 3.6! ՗ෳߚਔᡂ៾ख़܌ሡޑ›_୫ୟ୶ॶ ... 37 კ 3.7 change lane ኳᔕკ (ɀ_ୢ௦Ҕߚਔᡂ៾ख़) ... 37 კ 3.8! Mz ኳᔕკ (ɀ_ୢ௦Ҕߚਔᡂ៾ख़) ... 38 კ 3.9! ߚਔᡂ៾ख़ϐɀ Кၨკ ... 38_ୢ კ 3.10! ߚਔᡂ៾ख़ϐɀ_ୢ܌ቹៜޑୁྖفКၨკ ... 39 კ 3.11! ՗ෳߚਔᡂ៾ख़܌ሡޑ›_{୫ ୶ୟ} ॶ ... 40 კ 3.12! ٿԛ change lane ኳᔕკ (ɀ_ୢ௦Ҕߚਔᡂ៾ख़) ... 41 კ 3.13! ٿԛ change lane ϐ Mz ኳᔕკ (ɀ_ୢ௦Ҕߚਔᡂ៾ख़) ... 41

viii  კ 3.14 change lane ኳᔕკ (ɀ_ୢ௦Ҕਔᡂ៾ख़) ... 44 კ 3.15! ៾ख़ᒿਔ໔ޑᡂϯკ... 44 კ 3.16 Mz ኳᔕკ (ɀ _ୢ௦Ҕਔᡂ៾ख़) ... 45 კ 3.17! ਔᡂ៾ख़ϐɀ _ୢޑКၨკ ... 45 კ 3.18! ਔᡂ៾ख़ϐɀ_ୢ܌ቹៜޑୁྖفКၨკ ... 46 კ 3.19! ኳᔕၧᗉምᛖނԶ௦Ҕޑًೲ (-5m/s) ... 47 კ 3.20! ၧᗉምᛖԶ຾Չ change lane ޑኳᔕკ (ɀ_ୢ௦Ҕਔᡂ៾ख़) ... 47 კ 3.21! ၧᗉምᛖԶ຾Չ change lane ޑ៾ख़ᡂϯკ... 48 კ 3.22! ၧᗉምᛖԶ຾Չ change lane ޑMzኳᔕკ (ɀ_ୢ௦Ҕਔᡂ៾ख़) ... 48 კ 3.23! ၧᗉምᛖԶ຾Չ change lane ϐɀ ޑКၨკ_ୢ ... 49 კ 3.24! ၧᗉምᛖԶ຾Չ change lane ϐɀ_ୢ܌ቹៜޑୁྖفКၨკ ... 49 კ 3.25! ٿԛ change lane ኳᔕკ (ɀ_ୢ௦Ҕਔᡂ៾ख़) ... 50 კ 3.26! ٿԛ change lane ޑ៾ख़ᡂϯკ... 51 კ 3.27! ٿԛ change lane ޑMzኳᔕკ (ɀ_ୢ௦Ҕਔᡂ៾ख़) ... 51 კ 3.28! ٿԛ change lane ϐɀ _ୢޑКၨკ ... 52 კ 3.29! ٿԛ change lane ϐɀ_ୢ܌ቹៜޑୁྖفКၨკ ... 52 კ 3.30 J-turn ᙯӛϐኳᔕკ (ɀ_ୢ௦Ҕਔᡂ៾ख़) ... 53 კ 3.31! J-turn ᙯӛޑ៾ख़ᡂϯკ ... 54 კ 3.32! J-turn ᙯӛޑMzኳᔕკ (ɀ_ୢ௦Ҕਔᡂ៾ख़) ... 54 კ 3.33 J-turn ᙯӛϐɀ ޑКၨკ_ୢ ... 55 კ 3.34! J-turn ᙯӛϐɀ_ୢ܌ቹៜޑୁྖفКၨკ ... 55 კ 3.35! J-turn ᙯӛϐ X-Y ০኱კ ... 56 კ 4.1! change lane ୏բϐ߻፺ᙯӛف... 64 კ 4.2! ՗ෳډޑ៾ख़!)ɐ ൌͲǤͷ͸ͳͺ* ... 64 კ 4.3! change lane ኳᔕკ (ɐ ൌ ͲǤͷ͸ͳͺ) ... 65

ix  კ 4.4 change lane ܭ҅த(ଳ)ၡय़ϐ FDD კ ... 67 კ 4.5 change lane ܭ҅த)ଳ*ၡय़ǴѰࡕ፺ठ୏Ꮤ 1.5 ࣾࡺም... 68 კ 4.6! ӧ҅த(ଳ)ၡय़ޑًೲКၨკ ... 68 კ 4.7! ӧ҅த(ଳ)ၡय़ޑ໩ྖᡂኧȐsliding variableȑКၨკ ... 69 კ 4.8! ӧ҅த(ଳ)ၡय़ޑ፺ηڋ୏/០୏סΚКၨკ ... 69 კ 4.9! ӧ҅த(ଳ)ၡय़ޑ፺ηᙯೲКၨკ ... 70 კ 4.10! ӧ҅த(ଳ)ၡय़ޑ X-Y ০኱კ ... 70

კ 4.11! change lane ܭ packed snow ၡय़ϐ FDD კ ... 72

კ 4.12! change lane ܭ packed snow ၡय़ǴѰࡕ፺ठ୏Ꮤ 1.5 ࣾࡺም ... 73

კ 4.13! ӧ packed snow ၡय़ޑًೲКၨკ ... 73

კ 4.14! ӧ packed snow ၡय़ޑ໩ྖᡂኧȐsliding variableȑКၨკ ... 74

კ 4.15! ӧ packed snow ၡय़ޑ፺ηڋ୏/០୏סΚКၨკ ... 74

კ 4.16! ӧ packed snow ၡय़௦Ҕ៾ख़ޑ RSMC ϐ፺ηڋ୏/០୏סΚ ... 75

კ 4.17! ӧ packed snow ၡय़ޑ፺ηᙯೲКၨკ ... 75

კ 4.18! ӧ packed snow ၡय़௦Ҕ៾ख़ޑ RSMC ϐ፺ηᙯೲ ... 76

კ 4.19! ӧ packed snow ၡय़ޑ X-Y ০኱კ ... 76

კ 4.20! ՉᎭܭ-split ၡय़ǴѰࡕ፺ठ୏Ꮤ 0 ࣾࡺም ... 78

კ 4.21! ӧ -split ၡय़ޑًೲКၨკ ... 78

კ 4.22! ӧ -split ၡय़ޑ໩ྖᡂኧȐsliding variableȑКၨკ ... 79

კ 4.23! ӧ -split ၡय़ޑ፺ηڋ୏/០୏סΚКၨკ ... 79

კ 4.24! ӧ -split ၡय़ޑ፺ηᙯೲКၨკ ... 80

კ 4.25! ӧ -split ၡय़ϐѤঁ፺ηޑୁӛΚКၨკ ... 80

კ 4.26! ӧ -split ၡय़ޑ X-Y ০኱კ ... 81

಄ဦ߄!

!

P! _{፺जᆶӦय़ϐነᔔ߯ኧ!} Pˆ! ፺जᆶӦय़ϐነᔔ߯ኧޑ՗ෳॶ! xi f ! _{ಃ i ঁ፺जϐᕵӛነᔔΚ!} yi f ! _{ಃ i ঁ፺जϐୁӛነᔔΚ!} z F ! ፺ज܌ڙϐ҅ӛΚ! O! ፺जྖ౽౗! D! _{፺जྖ౽ف!} f D ! _{߻፺ϐ፺जྖ౽ف!} r D ! ࡕ፺ϐ፺जྖ౽ف! i Z ! ಃ i ঁ፺जϐفೲࡋ! i G ! ಃ i ঁ፺जϐᙯӛف! i T ! _{ಃ i ঁ፺जϐڋ୏0០୏סΚ!} z I ! _{ًηޑᙯ୏ᄍໆ!} w I ! ፺जޑᙯ୏ᄍໆ! w R ! ፺जъ৩! E! _{ًηϐୁྖف!} Eˆ_{! ًηϐୁྖفޑ՗ෳॶ!} J ! _{ًηϐᐉᘍفೲࡋ!} d J ! ًηϐୖԵᐉᘍفೲࡋ! z M ! _{ᚐѦౢғޑΚં!} y F ! _{ًηୁӛΚϐᕴک!} v! _{ًη߻຾ೲࡋ!} x v ! ًηᕵӛೲࡋ! y v ! _{ًηୁӛೲࡋ!} x 

y a ! _{ًηޑѦ೽уೲࡋ!} f C ! _{߻፺፺जϐᐉӛࠂࡋ!} r C ! _{ࡕ፺፺जϐᐉӛࠂࡋ!} f l ! _{ًηύЈᗺډ߻፺ືϐࠟޔຯᚆ!} r l ! ًηύЈᗺډࡕ፺ືϐࠟޔຯᚆ! t l ! _{߻፺ືຯ܈ࡕ፺ືຯϐ΋ъ!} l! ߻፺ືډࡕ፺ືϐࠟޔຯᚆ! W ! _{ਔ໔தኧ!} m! _ًη፦ໆ! xi 

1

ಃ 1 ക

ᆣፕ

1.1

ࣴزङඳ

җܭ౜ӧًؓמೌޑ຾؁ǴًηޑՉᎭೲࡋΨόᘐޑගϲǶਥᏵ಍ीǴ܌ Ԗޑ٣ࡺύԖຬၸ 40%ࢂӢࣁًೲϟܭ 80km/hᆶ 100km/hԶ೷ԋًηวғୁྖ Ȑspin outȑޑཀѦǴԶًೲӧ 160km/hа΢܌วғޑཀѦ൳Я೿ࢂҗܭୁྖ܌ Ꮴठޑ [1]ǶӢԜǴӵՖගϲًؓՉᎭޑӼӄ܄ࢂ౜ӧًؓख़ाޑࣴزፐᚒǶ

ୁྖȐspin outȑޑౢғࢂӢࣁًᡏޑୁྖفȐside-slip angleȑၸεǴ຾Զ ٬ًيѨ௓Զр౜Ѻᙯ܈ត౽ޑՉࣁǶ྽ًೲၸזǵՉᎭӧነᔔΚၨեޑၡय़ [2] ܈ࢂӧ΋٤੝ਸ௃ݩǴٯӵǺᆙ࡚ᗉምǵՉᎭܭρ-splitၡय़Ǵࣣ཮٬ୁྖفᡂ εԶ೷ԋًηόᛙۓǴ܌аჹᙯӛޑᛙۓࡋԶقǴୁྖفޑελࢂ΋ঁࡐख़ा ޑୖԵ٩ᏵǶӧSAEЎ᝘ [3]ύගډǴჹ΋૓ᎯᎭޣԶقǴૈඓ௓ޑୁྖفӧ 2 ±ѰѓǴԶ஑཰ޑᎯᎭޣ߾ё৒೚ӧ 4±аΠǶՠࢂୁྖفޑज़ڋځჴ཮ᒿၡय़ ރݩԶׯᡂǴ৒೚ᛙۓޑୁྖفനεॶ٠όӵ΢य़܌ॊ೭ሶᝄदǴӧAVECЎ ᝘ [1]ගډǴӧଳၡय़΢Ǵୁྖفޑज़ڋӧ 10±ߕ߈ǴऩຬၸԜज़ڋǴًηёૈ ཮഼Ѩ௞ᏹ௓܄Զ٬ځѨ௓Ǵӧ፰፯ၸޑഓӦȐpacked snowȑ΢Ǵୁྖفޑज़ ڋӧ 5±ѰѓǶ! ! ྽ًᡏᛙۓ܄ѨᑽਔǴऩԖ΋ঁЬ୏Ԅޑس಍ૈϷਔٛЗً፶Ѩ௓ǴჹᎯ

ᎭޣԶقࢂߚதख़ाޑǶҗܭABSȐAnti-lock Braking SystemȑǵTCSȐTraction Control Systemȑϩձӧ෧ೲǵуೲޑਔংω೸ၸ௓ڋᕵӛྖ౽౗Ȑslip ratioȑ ٰߥ᛾ڋ୏ᆶ០୏ਔᕵӛ୏ΚᏢޑ܄ૈǴ໔ௗޑ௓ڋ෧ೲǵуೲਔୁӛޑᛙۓ

2

܄ǴՠࢂӧᙯӛޑၸำύǴऩ܌ڙޑୁӛΚௗ߈፺जکӦय़ߕ๱ޑཱུज़Ǵ߾ؓ ًஒԖёૈ཮Ѩѐᏹ௓܄ᆶᛙۓ܄Ƕӧ 1980 ԃжǴVehicle Stability ControlȐVSCȑ س಍೏ว৖٠ᔈҔܭׯ๓ًηޑᛙۓ܄ૈǴځҞޑࢂߥ࡭ًηӧނ౛ज़ڋޑ߻ ගΠϝᏱԖځᏹ௓܄ [4]ǶฅԶǴόӕًؓቷ୘ჹᛙۓ܄௓ڋس಍ԖόӕޑӜᆀǴ ٯǺVehicle Stability ControlɡVSCȐTOYOTA, LEXUSȑǵDynamic Stability

ControlɡDSCȐBMW, MazdaȑǵElectronic Stability ProgramɡESPȐAudi, Chrysler, Mecedes, VWȑǵStabiliTrakȐBUICK, CadillacȑǵAdvanceTracȐFord, LINCOLNȑǵVehicle Dynamics ControlɡVDCȐNISSANȑ[5]฻Ǵځ่ᄬᆶф ૈᜪ՟Ǵӧ೭ϐύΞаBosch!ගрޑElectronic Stability ProgramȐESPȑനԐ ୘཰ϯ [6]ǶҁፕЎࣁΑБߡଆـǴ಍΋ᆀբESPǶ!

! ESPࢂ΋ᅿЬ୏ԄޑӼӄس಍ǴѬх֖ΑABSᆶTCS٠уΕΑᐉᘍΚં௓

ڋȐYaw Moment ControlȑǴவڋ୏ǵ០୏аϷᙯӛޑ௃ݩࣣჹًؓޑᛙۓ܄Ԗ ΑࡐεޑфҔǶځ୷ҁচ౛ϩࣁٿ೽ϩǴಃ΋೽ϩࢂॉၞߥ࡭ޑᏹ௓܄ୢᚒǴ җًηޑᐉᘍفೲࡋȐyaw rateȑٰඔॊǴќ΋೽ϩ߾ࢂᛙۓ܄ޑୢᚒǴёҗً η፦Јޑୁྖفٰඔॊ [5]Ƕ೸ၸ௓ڋًηޑᐉᘍفೲࡋᆶୁྖفٿঁᡂኧٰ௖ ૸ًᡏޑᏹ௓܄Ϸᛙۓ܄ࢂESPЬाޑБԄǴՠҗܭٿঁᡂኧӸӧ๱ጠӝޑᜢ ߯ǴΨ೷ԋ௓ڋ΢ޑᜤࡋǶ ᐉᘍΚં௓ڋȐYaw Moment Controlȑё࿶җቹៜ ߻ࡕືୁӛΚޑѳᑽ܈ৡ୏ڋ୏ΚȐdifferential brakingȑٰౢғᛙۓޑᐉᘍΚ ંǶ[5], [7]-[8]΋૓ԶقԖǺ

1.Ь୏ᙯӛس಍ȐٯӵǺЬ୏߻፺ᙯӛǵЬ୏ࡕ፺ᙯӛǵ4WSȑ!

2. DYCȐDirect yaw controlǴޔௗᐉᘍΚં௓ڋȑǺ௓ڋًη០୏کڋ୏Κ Ь୏ᙯӛس಍ӧୁӛуೲࡋၨλޑ൯ࡋϣǴ௓ڋΚၰڗ،ܭᆶБӛዬᙯفԋК ٯޑ፺जୁୃΚǴՠҗܭًيޑज़ڋǴӧଯୁӛуೲࡋਔǴୁୃΚόӆᆶБӛ ዬԋКٯǴ຾ԶᏤठၸӭᙯӛǶԶ DYC ߾ࢂ྽ًᡏόᛙਔǴᙖҗჹѤঁ፺η ޑ០୏ᆶڋ୏܌ౢғޑᕵӛΚǴᚐѦౢғ΋ঁёᛙۓޑᐉᘍΚંǴԜБԄΨ೏

3 ESPس಍ቶݱᔈҔǴࣁҞ߻ਏ݀ࡐӳޑᛙۓБԄϐ΋ǴҁፕЎௗΠٰΨࢂ೸ၸ ԜБԄٰׯ๓ًηޑᏹ௓܄ᆶᛙۓ܄Ƕ

1.2

ࣴز୏ᐒ

ჹًηѦ೽୏ᄊԶقǴً፺ޑᙯӛفऩ໻җᎯᎭޣᒡΕǴ߾ёעѬຎࣁ΋ ঁόё௓ޑϡનǶԶ೸ၸ፺η០୏ǵڋ୏܌ᚐѦౢғޑᐉᘍΚંӧԜךॺёע Ѭ྽բ΋ঁ௓ڋᒡΕǴவ࣬ჹ໘ኧޑᢀۺԶقǴ΋ঁ௓ڋᒡΕ໻ѝૈ௓ڋ΋ঁ ᡂኧǴ܌аךॺόૈӕਔ௓ڋᐉᘍفೲࡋᆶୁྖفٿঁᡂኧ [8]-[10]ǶӧҁፕЎ ύǴᐉᘍΚં௓ڋȐYaw Moment Controlȑࢂ௦Ҕჹᐉᘍفೲࡋѐ଺௓ڋǴ٠ ೸ၸ໩ྖኳᄊ௓ڋȐSliding Mode ControlǺSMCȑ٬ჴሞޑᐉᘍفೲࡋȐactual value of the yaw rateȑᆶୖԵޑᐉᘍفೲࡋȐreference yaw rateȑϐ໔ޑᇤৡᡂ λǴӢԶၲډؼӳޑё௓܄Ƕ

җܭѝჹᐉᘍفೲࡋբ௓ڋǴᗨߥԖόᒱޑᏹ௓܄Ǵՠًηޑᛙۓ܄߾ค ݤዴߥǴԶ൩ᆉߥԖᛙۓ܄ǴёૈΞ཮഼Ѩ௞ًηޑᏹ௓܄ǶࣁΑׯ๓೭٤ୢ ᚒǴҁፕЎ೸ၸᒧڗୖԵޑᐉᘍفೲࡋȐreference yaw rateȑБԄǴӧόѨᛙۓ ܄ޑ௃ݩΠǴϝёߥԖόᒱޑᏹ௓܄ǴԜ೽ϩ཮ӧಃΟക၁ॊϐǶ

ќ΋Бय़Ǵҗܭ߈൳ԃҡϯૈྍޑ෧ϿϷεৎჹᕉნԦࢉޑख़ຎǴૈྍؓ ًޑว৖Ԗځᓬ༈ᆶॐϪ܄ǶҁፕЎӧಃѤകԵቾаႝηًȐElectric VehiclesǺ EVsȑޑኳٰࠠ྽բ௓ڋჹຝǴ࣬ჹܭ໺಍ϣᐯЇᔏȐinternal combustion engineǺ ICEȑǴႝηًȐEVsȑޑᓬ༈׳ӭ [11]Ƕӧ [12]-[13]ЎകύǴᕴ่рᏱԖаΠ ᓬᗺǺ(1)ଭၲౢғޑᙯંࡐזΨࡐᆒዴǵ(2)ଭၲёаӼးӧѤঁ፺η΢ǵ(3) ёаࡐᆒዴޑޕၰଭၲޑᙯંελǴ೭٤ᓬ༈٬ளႝηًȐEVsȑКଆ໺಍ICE ࠠޑًηёа׳ᇸܰޑ՗ीၡय़ޑ௃ݩǴΨҗܭѤঁଭၲࣣёᐱҥޑѐ០୏܈ ڋ୏ǴჹКܭϣᐯЇᔏȐICEȑٰᇥǴᐉᘍΚં௓ڋȐYaw Moment Controlȑё аගٮ׳ӭޑБԄٰᆢ࡭ESPس಍ޑᛙۓǶ

4

ନԜϐѦǴ྽ႝηًȐEVsȑޑ୏Κس಍܈གᔈᏔȐsensorȑวғό҅தރ ݩȐࡺም܈ࢂԴϯ฻౜ຝȑǴٯӵǺ྽ً፺ޑଭၲࡺምਔǴऩόϷਔჹس಍௦ڗ ௛ࡼǴ߾཮࠶ુډᎯᎭޣᆶ४࠼ޑғڮӼӄǶӢԜǴךॺ཮ӧಃѤക࿯ޑ೽ϩԵ ቾё᎞ࡋޑୢᚒǴ٠೸ၸ໩ྖኳᄊ௓ڋޑё᎞ࡋ೛ीБԄȐSMC Reliable designȑ[14]Ǵӆу΢ᒧڗӝ፾ޑୖԵᐉᘍفೲࡋȐreference yaw rateȑޑགྷݤǴ ٬ளًηӧวғރݩࡕϝёᆢ࡭҅தᛙۓޑՉᎭЪၲډ୷ҁޑ܄ૈǶԜѦǴӧಃ Ѥകޑࡕъࢤךॺ཮ଞჹՉᎭܭޔጕޑρ-splitၡय़ѐ଺ϩ݋ᆶ૸ፕǴӕኬޑ೸ၸ SMCޔௗჹᐉᘍفೲࡋѐ଺௓ڋǴ൩ᆉՉ࿶ρ-splitၡय़ޑၸำύวғᐉᘍفೲࡋ کًᡏୁྖفၸεԶᏤठًᡏѺᙯޑ౜ຝǴΨૈԖਏޑ٬ᐉᘍفೲࡋکًᡏୁྖ فӧอਔ໔ᡂλԶ٬ᛙۓ܄ૈዴߥǶനࡕǴךॺΨ཮ӧኳᔕޑ೽ϩԵቾՉ࿶ρ-split ၡय़ਔً፺ଭၲࡺምޑё᎞ࡋୢᚒǴ೸ၸSMCޑё᎞ࡋ೛ीΨૈԖόᒱޑԋਏǶ ё᎞ࡋ௓ڋޑࢬำკӵΠǺ d

J

J

f

G

ˆ _{, ˆ}

E P

Z

კ 1.1 ໩ྖኳᄊ௓ڋޑё᎞೛ीϐࢬำკ  ᚒǴ೸ၸSMCޑ Ǻ

5

1.3

ፕЎࢎᄬ

! ҁፕЎӧࡕុޑക࿯ጓ௨ӵΠ܌ॊǺಃΒകϟಏ໩ྖኳᄊ௓ڋ౛ፕک

Magic formula፺जኳࠠаϷѤ፺ًη୏ᄊኳࠠȐጕ܄ 2-DOF ًηኳࠠǵߚጕ ܄ 7-DOF ًηኳࠠȑǶಃΟകӃᇥܴୁख़ᏹ௓܄ޑୖԵᐉᘍفೲࡋȐreference yaw rateȑаϷୁख़ᛙۓ܄ޑୖԵᐉᘍفೲࡋϐᢀۺᆶᓬલᗺǴௗ๱ӆЇΕ៾ख़ ޑᢀۺٰׯ๓ୖԵޑᐉᘍفೲࡋ٬ًηޑᛙۓ܄ёаᕇளׯ๓Ƕӧ೭ϐύǴך ॺவጕ܄ 2-DOF ޑًηኳࠠύǴ՗ෳрߚਔᡂޑ៾ख़ǴՠΨӢࣁѬόᒿਔ໔ᡂ ୏ޑલᗺǴനࡕࣁΑ಄ӝჴሞᔈҔԶ೛ीр΋ঁёᒿًೲǵ߻፺ᙯӛفԶᡂ୏ ޑ៾ख़٠ᔈҔܭጕ܄ޑᙁϯኳࠠ٬ளًηӧߥԖᛙۓ܄ޑ߻ගΠΞёᏱԖόᒱ ޑᏹ௓܄ǶಃѤക߾ᔈҔ໩ྖኳᄊ௓ڋޑё᎞ࡋ೛ीБԄ٠่ӝ៾ख़ޑᢀۺܭ ߚጕ܄ޑӄًኳࠠύǴ௖૸ӧًೲၸז܈ՉᎭܭեነᔔΚၡय़аϷՉᎭӧޔጕ ޑρ-split ၡय़ਔǴ፺ηྩًסΚวғࡺምϐё᎞ࡋୢᚒѐ଺ϩ݋ᆶ૸ፕǶಃϖ ക଺่ፕᆶ૸ፕ҂ٰёࣴزϐБӛǶ! ! !

6

ಃ 2 ക

࣬ᜢࣴز

!

!

2.1

!໩ྖኳᄊ௓ڋ!

Ҟ߻ςԖεໆЎ᝘௦ڗ໩ྖኳᄊ௓ڋȐsliding mode controlǴSMCȑٰှ، ӚԄӚኬޑ௓ڋୢᚒǴځচӢόѦЯѬᏱԖаΠᓬᗺǺϸᔈזೲǵჴ౜৒ܰǵ ჹόዴۓ܄Ȑuncertaintiesȑ܈ѦӧυᘋڀԖம଼܄ȐRobustnessȑ[15]-[21]Ƕӧ ߚጕ܄ё᎞ࡋ௓ڋ೽ϩǴҞ߻ԖΟᅿ௓ڋБԄǴ٩ׇࣁጕ܄Βԛፓ࿯ȐLinear quadratic regulationǴLQRȑǵ _{[22]-[24]ᆶ໩ྖኳᄊ௓ڋȐsliding mode controlǴ}

SMCȑ[20]ǴԶ߻य़ٿᅿБԄ೿ሡाଞჹΒԛԋҁڄኧȐquadratic cost functionȑ ೛ीрന٫௓ڋࡓǴࡺόёᗉխޑ໪ाѐှHamilton-JacobiБำԄ܈ό฻Ԅޑ ୢᚒǶ౲܌ڬޕǴှHamilton-JacobiБำԄߚதό৒ܰǴ܌аLQRᆶ_೛ीБ

Ԅӧჴ౜΢Ԗځ֚ᜤ܄Ƕόၸ೸ၸճҔჿભኧȐpower seriesȑБݤ [25]Ǵёа ளډHamilton-JacobiБำԄޑ߈՟ှǴՠԜБݤ٠ؒԖԵቾᛙ଼܄ȐRobustnessȑ ޑୢᚒǴऩس಍Ӹӧόዴۓ܄Ȑuncertaintiesȑ܈ࢂѦӧυᘋਔǴس಍ёૈ཮ڙ ډቹៜԶόᛙۓǶฅԶǴ೸ၸ໩ྖኳᄊ௓ڋȐsliding mode controlǴSMCȑޑБ ԄǴό໻ёаှ،ё᎞ࡋୢᚒǴԶЪSMCᗋ৒ה๱س಍όዴۓ܄܈ჹѦӧυᘋ ޑᛙ଼܄ȐRobustnessȑǴ׳όѸѐ؃ှHamilton-JacobiБำԄ܈ό฻ԄޑှǴ ӢԶεε෧Ͽीᆉ΢ޑॄᏼΨቚу௓ڋࡓჴ౜ޑёՉ܄Ǵ܌аҁፕЎࣣ௦ڗ໩ ྖኳᄊޑ௓ڋБԄǶӧҁ࿯ךஒϟಏ໩ྖኳᄊ௓ڋ٠ᙁॊځ௓ڋᏔޑ೛ीБԄǴ ԶSMCޑё᎞ࡋ೛ी೽ϩךॺ཮੮ډಃѤകଞჹߚጕ܄ޑё᎞ࡋ௓ڋୢᚒӆ ѐ௖૸Ƕ

7

2.1.1

!໩ྖኳᄊ௓ڋϟಏ!

໩ྖኳᄊ௓ڋ(sliding mode controlǴSMC)Ǵ܈ޣᆀᡂ่ᄬ௓ڋȐvariable structure controlǴVSCȑǴӧ 1960 ԃжҗ߮୯Γ Filippov ౗Ӄගрޑߚጕ܄௓ڋ ݤ߾Ƕځ੝ᗺӧܭճҔόೱុޑ௓ڋᒡΕǴ٬س಍നಖ཮೏ज़ڋӧ΋ঁႣӃ، ۓޑ໩ྖय़Ȑsliding surfaceȑ΢ǴԶڙ௓س಍ޑՉࣁ߾ࢂҗ໩ྖय़ٰೕጄǶ྽ ໩ྖڄኧࣁ႟ਔǴ߄Ңس಍΢ډΑ໩ྖय़ǴԜਔރᄊॉၞݮ๱໩ྖय़ྖՉޑၮ ୏БԄךॺᆀϐࣁ໩ྖኳᄊȐsliding modeȑǴ܌а໩ྖय़ޑᒧڗБԄӧ SMC ޑ ೛ी΢൩ᡉளߚதख़ाǶ! ჹ΋૓س಍ԶقǴ໩ྖڄኧёૈࢂጕ܄܈ߚጕ܄ޑǴ೭ᜐךॺᒧ᏷ጕ܄ޑ ໩ྖڄኧ׎ԄӵΠǺ! ! s x( ) Cx! (2.1) ځύǴ

x

߄Ңس಍ރᄊᡂኧǶ! ௗ๱ǴࣁΑ٬ᡣس಍ёа΢໩ྖय़Ǵ܌аѸ໪٬೛ीޑ௓ڋᏔᅈىΠӈచҹǺ! !

s s

T



d 

K

s

₂

,

 ൐

K

0

! (2.2) ځύ ˜ _pж߄p-ጄኧȐp-normȑ[26]Ƕ! Զ (2.2)ԄΞᆀࣁ#ډၲచҹȐreaching conditionȑ#[27]ǴΠय़ךॺჹ#ډၲచҹ Ȑreaching conditionȑ#଺Α΋٤ှញӵΠǺ 1 ( ) 2 T d T dt s s s s ! ! ! ! ! 2 2 1 ( ) 2 d dt s ! ! ! ! ! 2 2 d dt ˜ s s ! (2.3) ϐࡕע (2.3)Ԅޑ่݀஥Ε (2.2)ԄǴёள (2.4)Ԅ! ! 2 2 2 d dt

K

˜ d  s s s ! (2.4) !

8 ע (2.4)Ԅ᏾౛ࡕǴӵ (2.5)Ԅ܌ҢǺ! ! d ₂ dt s d 

K

(2.5) ! җ΢य़ޑ௢ᏤǴёว౜

s(x

( ))

t

₂ჹਔ໔ޑᡂϯ౗೿λܭ܈฻ܭ

K

Ǵ೭Ψ߄Ң! ( ))t s(x Ԗज़ਔ໔཮ᡂԋs(x( ))t 0ǴΨསҢ๱ ( )x t Ԗज़ਔ໔཮΢໩ྖय़΢ǶନԜ ϐѦǴ྽

K

ຫεǴރᄊ΢ډ໩ྖय़ޑೲࡋΨ཮ຫזǴ܌а

K

ஒࢂቹៜॉၞ΢໩ ྖय़זᄌޑޑᜢᗖǴӵკ 2.1 ܌ҢǶ! ! ! კ 2.1! ΢໩ྖय़זᄌޑҢཀკ! ! ԖΑ (2.2)ԄԜచҹǴёߥ᛾Һ΋ރᄊঃऩӧ໩ྖय़΢Ǵ߾ځॉၞѸ཮ᖿ߈໩ྖ य़ǴΨ҅ӢӵԜǴ྽س಍຾Ε໩ྖኳᄊȐsliding modeȑࡕǴځ୏ᄊ཮ڙ௓ܭ໩ ྖय़Ǵӵკ 2.2 ܌ҢǶ! !

9 ! კ 2.2! ໩ྖኳᄊҢཀკ! ! ՠჴሞ΢ǴԐයޑ໩ྖኳᄊ௓ڋҗܭ٬Ҕ sgn ڄኧٰ೛ीǴӢԶ೷ԋރᄊӧᖿ ߈໩ྖय़ޑၸำύڙډόೱុ௓ڋᒡΕޑቹៜǴ٠ό཮ֹӄပӧ໩ྖय़΢ǴԶ ࢂӧ໩ྖय़ߕ߈ٰӣᡂ୏ǴԶ೭Ψ೷ԋ໩ྖኳᄊ௓ڋऩӧଯᓎ଺Ϫඤޑ୏բਔ ཮Ԗ#ϪၢȐchatteringȑ#౜ຝǶԜ౜ຝନΑ཮ౢғόѸाޑૈໆ੃઻ѦǴᝄख़ ߾཮ᐟว΋٤س಍ወӧܭଯᓎޑ҂ኳ೽ϩȐhigh frequency unmodeled partsȑ຾ Զ٬س಍όᛙۓǴӵკ 2.3 ܌ҢǶ! ! კ 2.3! ϪၢȐchatteringȑ౜ຝҢཀკ! ! ฅԶǴϪၢ౜ຝᗨคݤᗉխՠځελёҗ௓ڋᒡΕޑำࡋԶۓǴӧ [28]ගр໩ ྖቫȐsliding layerȑޑཷۺǴځ໩ྖቫޑҢཀკӵΠǺ! Ψ೷ԋ໩ྖኳᄊ ຝǶԜ౜ຝନΑ཮ౢғό ଯᓎ que ܌ high fre Α཮ౢ gh ǶԜ౜ຝନΑ཮ౢғ ᓎ eq ܌Ң gh ϩȐhi Ƕ! ޑ҂ኳ೽ϩȐ ନΑ ϩȐ Α ೽ϩ ຝନ ೽ϩ Ԝ౜ຝ ҂ኳ೽ኳ೽ ҂

10

! კ 2.4! ໩ྖቫȐsliding layerȑҢཀკ!

!

ځБԄࢂ೸ၸႫکڄኧȐSaturation FunctionȑǵᅶᅉڄኧȐHysteresis Functionȑ ǵᅶᅉ.ႫکڄኧȐHysteresis Saturation Functionȑٰڗжচٰޑ಄ဦڄኧȐSign

FunctionȑǴԶ೭٤БԄᔈҔܭჴሞس಍ύǴΨዴჴёаᕇளԖਏޑׯ๓Ƕ

2.1.2

໩ྖኳᄊ௓ڋᏔϐ೛ी!

໩ྖኳᄊ௓ڋᏔޑ೛ीЬाϩԋΒঁ؁ᡯ [27], [29]-[31]ǴӵΠǺ! ؁ᡯ΋Ǻᒧڗ፾྽ޑ໩ྖय़٬س಍ޑॉၞӧ໩ྖኳᄊਔૈྖӛ௓ڋҞ኱ᗺǶ! ؁ᡯΒǺ೛ीӝ፾ޑ௓ڋᏔ٬س಍ૈӧԖज़ਔ໔ϣ΢ډ໩ྖय़! аΠךॺԵቾ΋ߚጕ܄୏ᄊس಍ӵ (2.6*.(2.7*ԄǺ!! ! x f x +_o( ) G_o( )x u˜ ! (2.6) ! 1 2 y y ª º « » ¬ ¼ y ! ! (2.7) ځύ n R  x ࣁރᄊᡂኧǴ m R  u ࣁ௓ڋᒡΕǴ 2 R  y ࣁس಍ᒡрǴ ( ) n o R f x Ϸ ( ) nxm o G x R ࣁςޕޑѳྖڄኧǶ!

11 ௗ๱ۓကس಍ᒡΕ.ᒡрᜢ߯ԄȐjoqvu.pvuqvu!sfmbujpo!frvbujpoȑӵΠǺ! ! ( ) 1 ( ) 2 ( ) ( ) p q y G y ª º  ˜  « » ¬ ¼ f x x u d (2.8) ځύ 1 2 ( ) ( ) ( ) f f ª º « » ¬ ¼ x f x x !ǵ! 1 2 ( ) ( ) ( ) G G G ª º « » ¬ ¼ x x x ک 1 2 d d ª º « » ¬ ¼ d Ƕ! 1 y ᆶy2ϐ࣬ჹ໘ኧȐrelative degreeȑϩձࣁpᆶqǴ 2 : n R oR f Ϸ 2 : n xm G R oR Ƕ ԜѦǴჹ܌ԖxԶقǴךॺଷ೛ ( )G x ࣁӈᅈજȐfull row rankȑǶ d ࣁѦӧυᘋ Ȑexternal disturbanceȑ܌೷ԋޑᘋ୏Ǵ٠ଷ೛

d

₂

d

U

,

!Ъ

U

!0Ƕ! ! ௓ڋࡓ೛ीޑҞ኱Ǻ׆ఈ೸ၸ௓ڋࡓ٬س಍ᒡрଓᙫډୖԵᒡрȐreference outputȑǴऩଷ೛y_dࣁୖԵᒡрǴځҞޑ൩ࢂ׆ఈyoy_dǶќѦǴךॺۓကᒡр ᇤৡᆶ໩ྖय़ϩձࣁ (2.9*ᆶ (2.10*Ԅ;! ! 1 2 d e e ª º _ « » ¬ ¼ e y y _! (2.9) ! ( 1) ( 2) 1 ( 1) 1 2 1 1 1 1 ( 1) ( 2) 2 ( 1) 2 2 2 1 2 2 p p p q q q e a e a e a e s e b e b e b e s       ª     º ª º « » « » _{«     »} ¬ ¼ ¬ ¼ s !  0  !   (2.10) ځύa_i !0_Ǵi 1,!, (p1) ᆶ bj ! Ǵ0 j 1,!, (q1) ฅࡕךॺԵቾ೛ी௓ڋࡓӵΠ܌ҢǺ 0 1 u u u (2.11) 0 u ޑҞޑӧ٬ރᆢ࡭ӧ໩ྖय़΢ǴԿܭu₁߾ࢂ٬س಍ރᄊૈӧԖज़ਔ໔΢ډ໩ ྖय़΢ǶԶu₀ჹᔈޑచҹǴךॺёаҔ (2.12)Ԅٰ߄Ң! ! s 0_! (2.12) !

12 ӧόԵቾѦӧυᘋޑ௃ݩΠǴٰ؃ளu₀Ȑзu u₀ȑǶځ௢ᏤӵΠǺ! २ӃǴჹ໩ྖय़༾ϩ! ! !!!!!! 1 2 s s ª º « » ¬ ¼ s    ! !!!!!!! ( ) ( 1) 1 ( 1) 1 2 1 1 1 ( ) ( 1) 2 ( 1) 2 2 2 1 2 p p p q q q e a e a e a e e b e b e b e     ª     º « _{   } » « » ¬ ¼   !   !     ! !!!!!!! ( ) ( 1) 1 1 0 1 ( 1) 1 2 1 1 1 ( ) ( 1) 2 2 0 2 ( 1) 2 2 2 1 2 ( ) ( ) ( ) ( ) p p d p q q d q f G y a e a e a e f G y b e b e b e     ª  ˜      º « _{ ˜     } » « » ¬ ¼ x x u x x u   !   !     ! !!!!!!! ( ) ( 1) 1 1 ( 1) 1 2 1 1 1 0 ( ) ( 1) 2 2 ( 1) 2 2 2 1 2 ( ) ( ) ( ) p p d p q q d q f y a e a e a e G f y b e b e b e     ª      º  ˜ « _{    } » « » ¬ ¼ x x u x   !   !     ! !!!!!!! 0 ёள ( ) ( 1) 1 1 ( 1) 1 2 1 1 1 0 ( ) ( 1) 2 2 ( 1) 2 2 2 1 2 ( ) ( ) ( ) p p d p q q d q f y a e a e a e G f y b e b e b e      ª      º  _{˜ « »}      « » ¬ ¼ x u x x   !   ! (2.13) ځύ 1 ( ) T( ) [ ( ) T( )] G x G x ˜ G x ˜G x  ࣁG x( )ޑpseudo inverseǶ! ฅԶǴރᄊӧᖿ߈໩ྖय़ޑၸำύǴёૈ཮ᎁڙډѦ೽ᚇૻޑυᘋԶ٬ރᄊᚆ ໒໩ྖय़ǴӢԜךॺѸ໪ӆ೸ၸ΋ঁόೱុޑ௓ڋࡓu₁עᚆ໒໩ྖቫޑރᄊ௢ ӣ໩ྖय़΢Ƕu₁ჹᔈޑచҹࣁ(2.2)Ԅ!

s s

T



d 

K

s

₂

,

 ൐

K

0

Ǵځ௢ᏤၸำӵΠǺ! !! ( ) ( 1) 1 ( 1) 1 2 1 1 1 ( ) ( 1) 2 ( 1) 2 2 2 1 2 p p p T T q q q e a e a e a e e b e b e b e     ª     º ˜ « _{   } » « » ¬ ¼ s s s !     !     ! !!!!! ( ) ( 1) 1 1 0 1 1 ( 1) 1 2 1 1 1 1 ( ) ( 1) 2 2 0 1 2 ( 1) 2 2 2 1 2 2 ( ) ( ) ( ) ( ) ( ) ( ) p p d p T q q d q f G y a e a e a e d f G y b e b e b e d     ª  ˜        º ˜ « _{ ˜       } » « » ¬ ¼ x x u u s x x u u   !   !     ! ! ! ! ( ) ( 1) 1 1 ( 1) 1 2 1 1 1 0 1 ( ) ( 1) 2 2 ( 1) 2 2 2 1 2 ( ) ( ) ( ) ( ) p p d p T T T q q d q f y a e a e a e G f y b e b e b e     ª      º ˜_{« »} ˜ ˜   ˜      « » ¬ ¼ x s s x u u s d x   !   !     ! ! !

13 ע(2.13*Ԅޑu₀஥Ε΢ԄࡕǴёள! ! !!!!! ( ) 1 T T T G ˜ ˜  ˜ s s s x u s d_! !!! !!!!!! ( ) 1 _{2 2} T T G d ˜s x u˜  s ˜ d ! !!! !!!!!! ( ) 1 ₂ T T G U d ˜s x u˜  s ! ! ȐӢࣁ

d

2

d

U

Ъ

U

!0ȑ! ࣁΑᅈى(2.2*ԄǴךॺ೛ीu₁ӵ(2.14)܌Ң 1 1 2 ( + ) sgn(s ) ( ) ( + ) sgn(s ) G U K U K  ª ˜ º  _{˜ « »} ˜ ¬ ¼ u x (2.14) നࡕё٬ள !!!! !! 1 2 1 ₂ 2 T T s s U K U U K ˜ ª º d  ª_{¬ º «¼ »} ˜ ¬ ¼ s s  ሺ ൅ ሻ •‰ሺ• ሻ s ሺ ൅ ሻ •‰ሺ• ሻ ! ΞӢࣁ T _˜sgn( ) _˜s1 sgn( )_{s1  ˜s2} sgn(_s2) _{s1  s2 s 1} s s ϷӛໆጄኧȐopsnȑό฻ Ԅ s ₁! s ₂Ǵࡺךॺёע΢Ԅ᏾౛ӵΠǺ !! !!!! !! 2 2 2 2 2 T _{d } U K _U T _ U K _U _{d }K s s ሺ ൅ ሻ s s ሺ ൅ ሻ s s s ! ࡺനࡕ௓ڋࡓu u₀u₁ӵ(2.13*ᆶ(2.14*Ԅ܌ҢǶ

14

2.2 Magic formula

፺जኳࠠ!

፺जޑ่ᄬᆶΚᏢ੝܄،ۓΑًؓޑ܄ૈǴځ܌ڙޑቹៜٯӵǺᕵӛΚǵୁ ӛΚǵࠟޔΚ฻ࣣޔௗቹៜًηӧՉ຾ύޑᏹ௓܄ᆶᛙۓ܄Ƕҗܭ፺जޑፄᚇ่ ᄬᆶځߚጕ܄ޑΚᏢ੝܄Ǵ܌аӵՖᒧ᏷፺जኳࠠჹً፶୏ΚᏢޑү੿מೌԶق ቹៜࣗεǶ೭ᜐךॺᒧҔ΋ঁъ৩ᡍࠠޑ#Magic formula፺जኳࠠ#[32]-[36]ٰඔ ॊൂપᕵӛȐpure longitudinalȑޑነᔔΚኳಔǴൂપᐉӛȐpure lateralȑޑነᔔ ΚኳಔǶ

(1) ፺जᕵӛነᔔΚǺ

1 1

1 1 1 1 1 1

( )

sin(

tan (

(

tan (

))))

xi i i i i

f

O

D

C



B

O



E B

O





B

O

(2.15) ፺जᕵӛነᔔΚύޑӚୖኧीᆉБԄǺ 1 0 C a (2.16) 2 1 1 z 2 z x0 z D ˜a F  ˜a F P ˜F (2.17) 5 2 1 1 1 ( 3 4 ) a F_z z z B C D a F˜  ˜a F ˜e ˜ (2.18) 1 1 1 1 1 1 B C D B C D (2.19) 2 1 ( 6 z 7 z 8) E a ˜F  ˜ a F a (2.20) ځύF_zࣁ፺ज܌ڙϐ҅ӛΚǴ

P

_x0ࣁ(ᜪ՟)നεᕵӛነᔔ߯ኧǴࢂMagic Formula ϣ೽ޑ΋ঁதኧǴOࣁ፺जޑྖ౽౗Ȑslip-ratioȑǶќѦǴa ~₀ a₈ࣁ ๏ۓϐୖኧ[32]-[33]Ǵځኧॶӵ߄2.1 ܌ҢǶ΋૓ᇡࣁǴ੿҅ޑᕵӛነᔔ߯ ኧࣁ xi x z f F

P

(2.21)

15 Ψ൩ࢂǴ

1 1

1 1 1 1 1 1

( ) sin( tan ( ( tan ( ))))

xi i i i i z z f D C B E B B F F

O



O

_

O

_ 

O

! 1 1 0 1 1 1 1 1

( _{x z}) sin( tan ( _i ( _i tan ( _i))))

z

F C B E B B

F

P

_{˜ ˜} 

O

_

O

_ 

O

! ! ! 1 1

0 sin(C1tan (B1 i E B1( 1 i tan (B1 i))))

P _˜  O _ O _  O ! ! !

P O

_x( )_i ܌аёว౜

P

_x0ࢂ

P O

_xi( )_i ޑനεॶǶௗ๱ǴճҔa ~₀ a₈؃рD₁ࡕǴҔD₁ѐନ аF_zջё؃ள

P

_x0ǴΨ൩ࢂᇥ

P

_x0ࢂ΋ঁёа؃ޑۓॶǶ! ! (2) ፺जᐉӛነᔔΚǺ 1 1 2 2 2 2 2 2

( )

sin(

tan (

(

tan (

))))

yi i i i i

f

D

D

C



B

D



E B

D





B

D

(2.22) ፺जᐉӛነᔔΚύޑӚୖኧीᆉБԄǺ 2 0 C a (2.23) 2 2 1 z 2 z y0 z

D

˜

a F

 ˜

a F

P

˜

F

(2.24) 1 2 2 2 3 4 5 sin tan Fz B C D a a a  § § ·· ˜ _¨¨ ˜ _{¨ ¸¸¸} © ¹ © ¹ (2.25) 2 2 2 2 2 2 B C D B C D (2.26) 2 2

(

6 z 7 z 8

)

E

a F

˜

 ˜ 

a F

a

(2.27) ځύFzࣁ፺ज܌ڙϐ҅ӛΚǴPy0ࣁ(ᜪ՟)നε(ᐉӛ)ነᔔ߯ኧǴࢂ Magic

formula ϣ೽ޑ΋ঁதኧǴD ࣁ፺जޑྖ౽فȐslip angleȑǶӵӕᕵӛΚ΋૓Ǵ ёаว౜Py0ࢂP Dyi( i)ޑനεॶǶќѦǴa ~0 a8ځኧॶӵ߄2.1܌Ң (ߕຏǺᆶ

16 ࡕǴҔD2ѐନаFzջё؃ளPy0ǴԜਔޑPy0Ψࢂ΋ঁёа؃ޑۓॶǶ 0 a a₁ a₂ a₃ a₄ a₅ a₆ a₇ a₈ , x F N 1.65 -21.3 1144 49.6 226 0.069 -0.006 0.056 0.486 , y F N 1.30 -22.1 1011 1078 1.82 0.208 0.000 -0.354 0.707 ߄ 2.1Ǻًη፺जޑ߯ኧॶa₀~a₈ȐF_z in kNȑ ! ԜѦǴᕵӛΚȐ fxiȑᆶୁӛΚȐ fyiȑޑ Magic formula ነᔔΚኳಔύޑ!

Bǵ C ǵDکE٩ׇࣁখ܄ӢηȐstiffness factorȑǵ׎ރӢηȐshape factorȑǵ ঢ়ॶȐpeak valueȑکԔ౗ӢηȐcurvature factorȑ[34]Ǵӵკ 2.5Ƕ

კ 2.5! Magic formula ୖኧ߄Ңϐཀက ! ૸ፕόӕၡय़ޑነᔔΚኳಔǺ ၡय़ነᔔΚ߯ኧόӕΨ཮೷ԋᕵӛΚᆶୁӛΚޑׯᡂǴ܌аӧௗΠٰޑ೽ ϩךॺଞჹၡय़ރݩόӕਔǴځMagic formulaነᔔΚኳಔ߄ҢБԄ଺ΑаΠޑ ᇥܴǶҗܭMagic formulaǴځࣁ΋ঁъ࿶ᡍࠠޑነᔔΚኳಔǴԶࢂଷ೛ӧଳၡ य़Πޑ௃ݩΠ܌ว৖рٰޑነᔔΚኳಔǴӢԜόፕᕵӛ܈ୁӛΚځ߯ኧa0~a8 Ψࢂଞჹଳၡय़܌ुۓǶঃऩךॺགྷճҔMagic formulaٰ߄Ңόӕၡय़ޑᕵӛ

17

Κ܈ୁӛΚਔǴӢςޕ΋ಔ߯ኧa ~₀ a₈Ǵځ߄Ңޑࢂଳၡय़ΠޑୖኧȐߕຏǺ ߚଳၡय़ޑ߯ኧa ~₀ a₈ךॺ٠คவளޕȑǶ[36]ךॺଷ೛፺जޑᕵӛࠂࡋ Ȑlongitudinal stiffnessȑکᐉӛࠂࡋȐcornering stiffnessȑࣁۓॶǴаϷ፺जޑ ҅ӛΚȐnormal forceȑࣁۓॶǴѝԵቾඤ

P

_x0ᆶPy0ࢂёᡂޑȐi.e.,

P O

x( )ᆶP Dy( )

ޑനεॶࢂ཮ᒿ๱όӕၡय़ᡂޑȑǶඤѡ၉ᇥǴӧѝᏱԖȐଞჹଳၡय़ȑςޕޑ ߯ኧa ~₀ a₈ǵک࣬ჹᔈ؃ளޑ

P

_x0ᆶPy0ȐځύPx0 Py0 P0ȑǴ೸ၸځගٮޑБ ݤٰඔॊ྽

P

₀ʈ

P

ȐςޕޑॶȑਔǴ߾΢΋ঁ೽ҽ܌ගрޑ

f

_xi

(

O

_i

)

܈ f_yi(

D

_i)཮ ӵՖᡂϯǶ ᡂϯБԄӵΠǺჹᔈଳၡय़ޑ

P

₀аϷ߯ኧa ~₀ a₈ࣁךॺςޕǴଷ೛ჹᔈཥၡय़ ޑ

P

ΨࣁςޕǶۓကӵ(2.28)ԄǺ 0 : R P P (2.28) ྽

P

₀ʈ

P

Ǵ߾ (1) ፺जᕵӛነᔔΚ( f_xiሺ ሻO_i ʈ fxi̵ሺ ሻO )i Ǻ ' 1 1 1 1 1 1 1 1

( )

sin(

tan (

(

tan (

))))

xi i i i i

f



O

˜

R D

C



B

O



E B

O





B

O

(2.29)

(2) ፺जᐉӛነᔔΚ(

f

_yi

ሺ ሻ

D

_i ʈ

f

yi̵

ሺ ሻ

D

i )Ǻ

1 1

2 2 2 2 2 2

( )

sin(

tan (

(

tan (

))))

yi i i i i

f

̵

D

˜

R D

C



B

D



E B

D





B

D

(2.30)

18 კ 2.6 ᆶკ 2.7Ǵځ fxࣁᕵӛΚ(ൂՏǺN )Ǵ

O

ࣁ፺जྖ౽౗Ȑslip-ratioȑǴ fyࣁ ୁӛΚ(ൂՏǺN )ǴD ࣁ፺जྖ౽فȐslip-angleȑǴࠟޔΚF_z 3.188 (kN)Ƕ კ 2.6! ᕵӛΚ٬Ҕ Magic formula ፺जኳࠠ! კ 2.7! ୁӛΚ٬Ҕ Magic formula ፺जኳࠠ! ! ᕵӛӛ ٬Ҕ MMagic foMag ua፺

19

2.3

Ѥ፺ً፶୏ᄊኳࠠ!

! Եቾୃૐѳय़Ȑyaw planeȑޑ୏ᄊ٠Եቾ߻፺ᙯӛفࣁG_fǴԶࡕ፺ᙯӛف ࣁ႟Ƕௗ๱٩ׇჹጕ܄2-DOF ᆶߚጕ܄ 7-DOF ޑًη୏ᄊ଺ϟಏǴךॺޑѤ ፺ً፶ኳࠠӵკ2.8܌ҢǺ!

f

l

r

l

t

l

f

G

x

v

y

v

v

J

E

1 x

f

4 x

f

2 x

f

3 x

f

1 y

f

2 y

f

3 y

f

4 y

f

t

l

_G

_f

x

y

კ2.8! Ѥ፺ً፶ኳࠠ Ѥ፺ًޑύЈᗺࣁًηޑख़ЈȐCGǺcenter of gravityȑǹаύЈࣁଆᗺǴًᓐБ ӛࣁ҅ӛޑ x ০኱ǴًηѰᜐБӛࣁ҅ӛޑy০኱ǹv ࣁًη߻຾ޑೲࡋǴԶv_x ᆶvy߾ϩձࣁًηೲࡋӧ x ০኱ᆶy০኱΢ޑϩໆǹ

J

ࣁᐉᘍفೲࡋȐyaw rateȑ;

E

ࣁୁྖفȐside-slip angleȑǹlf ᆶlrϩձࣁًηύЈᗺډ߻፺ືᆶࡕ፺ືϐࠟ ޔຯᚆǴl_t߾ࣁ߻፺ືຯ܈ࡕ፺ືຯϐ΋ъǶӧҁፕЎύۭ኱ޑኧӷ

1,2,3,4

٩ ׇࢂ߄Ң߻Ѱ፺Ȑfront-leftȑ,߻ѓ፺Ȑfront-rightȑ, ࡕѓ፺Ȑrear-rightȑ, ࡕѰ ፺Ȑrear-leftȑǶ

E

f

2 8! Ѥ፺ً፶ኳࠠ x

v

E

f

Ѥ፺ً 3 x

f

_x

JJ

20

2.3.1

ጕ܄ 2-DOF ًη୏ᄊ!

! Եቾ2-DOFޑsingle trackኳࠠ[37]Ǵӵკ2.9܌ҢǶҗܭѬࢂҗ΋ঁ߻፺ᆶ ΋ঁࡕ፺܌ಔԋޑኳࠠǴ܌а೭ᜐךॺଷ೛Ѥ፺ًѓୁᆶѰୁޑኳࠠ࣬ӕࣣࣁ single trackኳࠠǶவ၀ኳࠠёаᏤр(2.30)ᆶ(2.31)Ԅ[38]Ǻ! !

ma

_y

¦

F

_y! (2.31) ځύ

¦

F

_y

2

f

_xf

sin

G

_f



2

f

_yf

cos

G

_f



2

f

_yr< ! !

I

_z

J



(2

f

_xf

sin

G

_f

)

l

_f



(2

f

_yf

cos

G

_f

)

l

_f



(2

f

_yr

)

l

_r



M

_z! (2.32) z M ǺᚐѦౢғޑΚં! y a ǺࣁًηޑѦ೽уೲࡋȐlateral accelerationȑ! ! კ2.9! ߚጕ܄single trackًηኳࠠ ! җܭךॺ೭ᜐѝଞჹѦ೽୏ᄊѐ଺૸௖Ǵ܌аଷ೛ًηаvxࣁۓॶޑБԄ߻຾Ƕ

ௗ๱೸ၸଷ೛Gf ࡐλȐi.e., sinGf Gf ک cosGf ȑکόԵቾᕵӛΚޑቹៜа1

Ϸעၮ୏ᏢۓကޑୁӛуೲࡋȐ

a

yȑ߈՟ԋ

a

y

|

v

x

(

E J





)

ޑБԄǴ߾ёаע(2.31) Ԅᆶ(2.32)ԄᙁϯӵΠǺ!

21 1 (2 _yf 2 _yr) x f f mv

E

  

J

(2.33) 1 (2 _{yf f} 2 _{yr r z}) z f l f l M I J ˜  ˜  (2.34) ௗ๱ךॺ٬Ҕֽ೽୔ୱޑ߈՟БԄǴ೸ၸ฻ਏޑ፺जᐉӛࠂࡋȐtire cornering stiffnessȑעԄ (2.33)ک (2.34)Ԅᙁϯԋ฻ਏޑጕ܄ 2-DOFኳࠠǶ፺जᐉӛࠂࡋ ޑۓကӵΠԄǺ! ! C )፺जᐉӛࠂࡋ* fy D (2.35) ځύ fyࣁᐉӛነᔔΚǴ

D

ࣁ፺जྖ౽فǶ! ! ܌а߻፺ᐉӛነᔔΚȐfyf ȑᆶࡕ፺ᐉӛነᔔΚȐ fyrȑёҔΠԄ߄ҢǺ! ! yf f( x f f) x v l f C v E J G    (2.36) ! ( x r ) yr r x v l f C v

E



J

 ! (2.37) നࡕǴ೸ၸ(2.35)ԄޑۓကǴךॺёаᙁϯԋጕ܄ޑ2-DOF୏ᄊ[38]Ǵځ୏ᄊ ߄Ңӵ(2.38)ԄǺ 2 2 2 (2 2 ) 2 2 2 2 2 2 Ǧ ͳ f r r r f f x x r r f f f f r r z z x C C l C l C mv mv l C l C l C l C I I v

E

E

J

J

  ª _{ } º « » ª º _{« »}ª º « » _{«    »¬ ¼}« » ¬ ¼ « » « » ¬ ¼   ! ! ! ! ! 2 0 1 2 f x f z f f z z C mv M l C I I

G

ª º ª º « » « » « » _{« »  « »} « » « » ¬ ¼ « » ¬ ¼ ! (2.38) ځύC_f کC_rϩձࣁ߻፺ᆶࡕ፺ޑ፺जᐉӛࠂࡋǶ! ! !

22

2.3.2

ߚጕ܄ 7-DOF ًη୏ᄊ!

! Եቾ7-DOFًηኳࠠӵკ2.8ځًη୏ᄊӵΠ[39]Ǻ! ! 4 1 0 0 0 0 0 1 0 xi i yi i xi i yi i i z zi mv c s f c f s mv s c f s f c mv I M E E G G E E E G G J J  ª º ª º ª º ª º « » « _ »_˜ « _ » «_ » « » « » « » « » « » « » « » « » ¬ ¼ ¬ ¼ ¬ ¼ ¬ ¼

¦

   (2.39) ! i w xi i, 1,..., 4 w R f T i I Z  (2.40) ځύM_zi l_xi(f c_xi G_i f s_yi G_i)l_yi(f s_xi G_i f c_yi G_i), 1,.., 4i Ƕ! !

೭ᜐǴ c ᆶ s ٩ׇࣁcosineᆶsineڄኧȐٯӵǺ

c

E

cos

E

ǵs

G

i sin

G

iȑǴ m ࣁ ًη፦ໆǴI_zᆶI_wϩձࣁًηᆶ፺जޑᙯ୏ᄍໆȐthe moment of inertiaȑǴR_wࣁ ፺जъ৩ǴZǵGᆶT٩ׇࣁ፺जفೲࡋȐwheel angular speedȑǵ፺जᙯӛف Ȑsteering wheel angleȑک፺जޑڋ୏0០୏סΚȐbrake/drive torqueȑǴf_xiᆶ f_yi

ϩձࣁ፺जکၡय़ϐ໔ޑᕵӛᆶୁӛነᔔΚǶ೭ᜐךॺଷ೛G G1 2 Gf Ǵ

3 4 0

G G

Ǵl_x1 l_x4 l_tǴl_x2 l_x3 l_tǴl_y1 l_y2 Ǵl_f l_y3 l_y4 l_r[39]ǶԶᕵӛ

ΚȐ f_xiȑᆶୁӛΚȐ f_yiȑޑ߄ԄБԄǴךॺ௦Ҕ(2.15)ک(2.22)ԄޑMagic formula

ነᔔΚኳಔӵΠǺ!

!

f

_xi

( )

O

_i

D

₁

sin(

C

₁

tan (

1

B

₁

O

_i



E B

₁

(

₁

O

_i



tan (

1

B

₁

O

_i

))))

1 1

2 2 2 2 2 2

( )

sin(

tan (

(

tan (

))))

yi i i i i

f

D

D

C



B

D



E B

D





B

D

! !

ԜѦǴ(2.15*Ԅک(2.22)ԄύޑOǵD ϩձࢂ፺जޑྖ౽౗Ȑwheel slip-ratioȑᆶ ፺जޑྖ౽فȐwheel slip-angleȑǴځۓကӵΠ[39]Ǻ!

23 ! !

^

`

, 1,.., 4 max , w i i w i v R i v R

Z

O

Z

 ! _(2.41) ! 1 1 tan ( ) , 1, 2. tan ( ) , 3, 4. f f i f l v s i v c l v s i v c

J

E

G

E

D

J

E

E

   ˜ ­   ° _˜ ° ® _{ ˜} ° ° _˜ ¯ ! (2.42) ߕຏǺ

O

_i 0߄Ңಃiޑ፺η҅ӧуೲȐaccelerationȑ<! !!!!!!

O

_i !0߄Ңಃiঁ፺η҅ӧ෧ೲȐdecelerationȑǶ! ! ߕຏǺಃΟകϷಃѤകޑًηኳᔕୖኧӵΠ[40]Ǻ ୖኧ)ൂՏ*! ಄ဦ! ኧॶ! ًη፦ໆȐkgȑ! m ! 1300 ًηύЈᗺډ߻፺ືϐࠟޔຯᚆȐmȑ! lf ! 1.25 ًηύЈᗺډࡕ፺ືϐࠟޔຯᚆȐmȑ! lr! 1.25 ߻፺ືډࡕ፺ືϐࠟޔຯᚆȐmȑ! l! 2.5 ߻፺ືຯ0ࡕ፺ືຯϐ΋ъȐmȑ! lt! 0.8 ፺जъ৩Ȑmȑ! Rw! 0.3 ًηޑᙯ୏ᄍໆȐ‰ଶȑ! Iz! 2000 ፺जޑᙯ୏ᄍໆȐ‰ଶȑ! Iw! 0.6 ߻፺፺जϐᐉӛࠂࡋȐN/radȑ!

C

f ! 54053 ࡕ፺፺जϐᐉӛࠂࡋȐN/radȑ! Cr! 54053 ߄2.2Ǻًηኳᔕୖኧ! ! !

24

ಃ 3 ക

ୖԵᐉᘍفೲࡋޑᒧڗ (៾ख़ޑ೛ी)

ࣁΑᡣًηӧᙯ៻ޑၸำύǴёаߥԖؼӳޑᏹᕵ܄ૈ٬ளًηԖ߈՟ύ

܄ᙯ៻ޑ੝܄ࢂࡐख़ाޑǶ[11]྽Եቾًηۓೲࡋ٠аڰۓޑᙯӛъ৩ޑచҹ

ΠՉᎭǴךॺёаᆀԜՉࣁύ܄ᙯӛՉࣁȐneutral steer behaviorȑǶًηୖԵޑ ᐉᘍفೲࡋȐreference yaw rateǺ

J

_dȑӵΠ߄Ң

x d f v l

J

G

(3.1) x v ࣁًηᕵӛೲࡋǴlࣁًη߻ࡕ፺ޑືຯǴG_f ࣁ߻፺ޑᙯӛفǶ

ฅԶჴሞᐉᘍفೲࡋȐactual value of the yaw rateǺ

J

ȑࢂցεܭ܈λܭୖԵޑ ᐉᘍفೲࡋȐreference yaw rateǺ

J

_dȑёа଺ࣁղᘐًηࢂցೀܭត౽Ȑόى ᙯӛȑ܈ѺᙯȐၸࡋᙯӛȑޑ௃ݩǶ܌а྽

J J

 _dޑৡॶຫλǴ཮Ꮴठًη߈՟ ύ܄ᙯӛޑՉࣁǴ೭Ψཀښ๱ًηޑᏹᕵ܄ૈࡐӳǶՠε೽ϩޑًηࣁΑӼӄ ଆـࣣ೏೛ीӧόىᙯӛޑՉࣁȐunder-steering behaviorȑǴନΑϿ೽ϩࣁΑᝡ ᖻޑً፶೏೛ीӧၸࡋᙯӛޑՉࣁȐover-steering behaviorȑǴऩ೛ीӧύ܄ᙯӛ ޑՉࣁǴ߾ًηࡐ৒ܰӢࣁѦӧυᘋԶᏤठًηᡂԋၸࡋᙯӛӢԜวғӒ ᓀ [41]Ǵࡺךॺሡा׳ӳޑᏤӛ܄٬ًηૈௗ߈ύ܄ᙯӛаߥԖؼӳޑᏹ௓܄ ૈǶ

25

3.1

ୁख़ᏹ௓܄ϐୖԵᐉᘍفೲࡋǺ

઻

_{૚ሺܕ܉ܖ܍ܝܞ܍ܚ܉܊ܑܔܑܜܡሻ} ӧ[42]ගрޑБݤǴࢂаጕ܄2-DOFًηኳࠠޑ୷ᘵΠǴ௢ள΋ঁӧᏹᕵ ܄΢ᏱԖόᒱ߄౜ޑୖԵᐉᘍفೲࡋȐ

J

dȑǶጕ܄ًηኳࠠޑރᄊޜ໔߄Ң Ԅ[38]ӵϦԄ(3.2)܌ҢǺ ! ! 11 12 1 21 22 2 d d f d d a a b a a b E E _G J J ª º ª ºª º_ª º « » « »« » « » ¬ ¼¬ ¼ ¬ ¼ ¬ ¼   (3.2) ځύ 11 12 2 1 (2 2 ) 2 2 2 1 f r r r f f f x x x C C l C l C C a a b mv mv mv      ΓΔʳʳʳ ΓΔʳʳʳ 2 2 21 22 2 2_{r r} 2 _{f f} 2 _{f f} 2_{r r} 2 _{f f} z z x z l C l C l C l C l C a a b I I v I    ΓΔʳʳ ΓΔʳʳ (3.3) ߻፺ޑᙯӛفډୖԵᐉᘍفೲࡋޑᙯ౽ڄኧ೏௢ᏤӵΠǺ २ӃǴஒϦԄ(3.2)ᙯԋ܎ද܎ථᙯඤȐLaplace transformȑ 11 12 1 d d d f s˜E a ˜E a ˜J  ˜b G (3.4) 21 22 2 d d d f s˜J a ˜E a ˜J  ˜b G (3.5) ځύ s ࣁ܎ද܎ථᡂኧȐLaplace variableȑǶ! ฅࡕǴע(3.4)Ԅ᏾౛ӵΠ! ! 12 1 11 1 ( ) ( ) d a d b f s a

E

˜ ˜  ˜

J

G

 (3.6) ! ௗ๱ע(3.6)жΕ(3.5)Ǵёள 21 22 12 1 2 11 ( ) ( ) ( ) d d f f a s a a b b s a

J

J

G

G

 ˜ ˜ ˜  ˜  ˜  ! עځ᏾౛ࡕǴӵΠ! 2 11 22 11 22 21 12 1 21 2 11 2

[

(

)

(

)] (

)

d

s

a

a

s

a

a

a

a

b a

b a

b s

f

J

˜







˜



˜

˜

 ˜ 

˜

G

_!

26 ӆ೸ၸ౽໨᏾౛ԋ(3.7*Ԅ! ! 2 2 1 21 2 11 11 22 11 22 21 12 ( ) ( ) ( ) ( ) ( ) d f s b s b a b a s s a a s a a a a

J

G

 ˜  ˜    ˜  ˜ (3.7) നࡕёע(3.7*ԄǴԜΒ໘س಍ׯቪԋΠԄǺ! 2 1 21 2 11 1 21 2 11 2 11 22 11 22 21 12 11 22 21 12 11 22 21 12 1 ( ) ( ) ( ) ( ) 1 ( ) ( ) 1 ( ) ( ) d f b s s b a b a b a b a a a s a a a a _{s s} a a a a a a a a J G  ˜  ˜ _˜ ˜  ˜  ˜  ˜ _{ } ˜  ˜ ˜  ˜ ! ࣁΑБߡǴךॺע΢ԄᙁϯԋϦԄ(3.8)ǴӵΠ܌ҢǺ 2 ( ) 1 ( ) 1 ( / ) (1/ ) d R R A A A s T s G s T D s D s

J

G

   (3.8) ځύ R 1 21 2 11 A b a b a G D  (3.9) 2 1 21 2 11 R b T b a b a (3.10) 11 22 A T a a (3.11) 11 22 12 21 A D a a a a (3.12) ௗ๱ǴӆעϦԄ(3.9)-(3.12)ᙁϯӵΠǺ 1 21 2 11 2 2 ( ) 2     x   x R r r f f A us x x f r v v b a b a G m l C l C D l k v l v lC C     ˜ ! ȐЪ

l



l

f

l

rȑ! 2 2 11 22 (2 2 ) (2 2 )    f r  f f r r  A x z x C C l C l C T a a mv I v    ʳ   2 2 11 22 12 21 4 2 ( )     f r x r r f f A z x C C l mv l C l C D a a a a I m v    ԶЪGRࣁΒ໘س಍ޑᛙᄊॶȐsteady stateȑ

27 җܭT_AࣁॄॶǴऩD_Aࣁεܭ႟Ǵ߾Ԝጕ܄ޑًηኳࠠࢂᛙۓޑ 0 A D ! ! Î! ( ) 2 0 2 r r f f x f r m l C l C l v lC C   ˜ ! ΨསҢ๱Ǻ 2 0 us x lk v ! (3.13) ځύ 2 f r us f r l l m k l C C § ·  ¨ ¸ ¨ ¸ © _¹ (3.14) ж߄όىᙯӛఊࡋȐunder-steer gradientȑ[43]Ƕ ऩk_us !0ࣁόىᙯӛǴk_us 0ࣁύ܄ᙯӛǴk_us 0ࣁၸࡋᙯӛǶ΋૓ԶقǴऩ ًηӧόىᙯӛޑ߻ගΠk_usຫεǴًηӧଯೲՉᎭ཮׳Ӽӄᛙۓ[11]ǶԖᜢό ىᙯӛఊࡋޑۓကᆶᢀۺҁക࿯൩όᙧॊǴፎୖԵࡕय़ߕᒵǶ ! ! ฅԶ[44]-[47]ගрǴऩᐉӛೲࡋȐlateral velocityȑԏᔙԿ႟Ǵךॺёаע ᐉᘍفೲࡋȐyaw rateȑޑៜᔈঅ҅ࣁ΋໘ۯᒨس಍ǴӵΠǺ 1 ) ( ) 1 ሺmaneuverability d s s J J W  (3.15) ! 1( ) 2 x maneuverability f us x v l k v

J

˜

G

 ! 2 ( ) 2 x f r r f f x f r v m l C l C l v lC C G ˜   (3.16)

W ࣁਔ໔தኧȐtime constantȑǴ s ࣁ܎ද܎ථᡂኧȐLaplace variableȑǶ

! ! ೭ኬޑঅ҅БԄନΑёаቚуًηᛙۓ܄ޑज़ڋΞёаᗉխ߻፺ᙯӛفჹ Β໘س಍܌ౢғޑ᎜ᕏǶ೸ၸᒧڗJ_{1 (}maneuverability₎྽բୖԵޑᐉᘍفೲࡋȐ

J

dȑǴ ךॺёаዴߥًηӧᙯӛਔёаၲډؼӳޑᏹ௓܄ૈǶՠࢂǴ྽ᗉምǵًೲၸ ז܈ӧեነᔔΚၡय़ՉᎭ฻௃ݩΠǴًᡏޑୁྖفȐside-slip angleȑ཮೴ᅌቚ εǶၸӭޑୁྖف཮ᏤठᎯᎭΓᙯӛޑᒡΕӧᐉᘍၮ୏ό௵གǴӢԶ೷ԋᐉӛ

28 ᛙۓޑൾϯǴ٬ளًηӧᐉӛޑՉࣁᡂޑόᛙۓǶΠय़ךॺኳᔕୖԵᐉᘍفೲ ࡋᒧҔ

J

₁ޑБԄӧًೲࣁ25m/sȐ90km/hrȑ຾Չchange laneޑ୏բǴځ߻፺ᙯ ӛفGf ӵკ 3.1(a)๏ۓǶவკ 3.1(b)ᆶ 3.1(d)ёว౜J Ԗଓᙫډ

J

d٠ЪᒿGf Զ ᡂ୏Ǵനεॶऊࣁ0.8rad/secǶՠΨว౜٬Ҕ

J

1ޑБԄ཮٬ளًᡏޑୁྖفຬၸ ୁྖف৒೚ޑനεॶȐߕຏǺಃΟകޑ೽ϩǴךॺԵቾКၨᝄᙣޑБԄӵSAE Ў᝘[3]ϣ܌ॊǴ

E

_max q2 Ǵऊ 0.0349/sec ٰ྽բୁྖفޑज़ڋȑǴӵკ3.1(c)Ƕ ܌аǴऩѝ௦ڗJ1 (maneuverability)ޑБԄܭًηୁӛ௓ڋǴᗨᏱԖόᒱޑᏹ௓܄Ǵՠ ًηޑᛙۓ܄ךॺคݤඓඝѬǶკ3.2ࣁ௓ڋᒡΕMzǴᙯ୏Κંऊ5000Nmа ϣǶ ! კ3.1! change laneኳᔕკȐ

J

d௦Ҕ

J

1ȑ

29 ! ! კ3.2! MzኳᔕკȐ

J

d௦Ҕ

J

1ȑ

3.2

ୁख़ᛙۓ܄ϐୖԵᐉᘍفೲࡋǺ઻

_{૛ሺܛܜ܉܊ܔܑܜܡሻ} ߈൳ԃǴӧ [9]-[10]္ගрΑќ΋ᅿୖԵᐉᘍفೲࡋȐ

J

dȑޑБԄǴךॺ ᆀࣁJ_{ʹ stability( )}ǶࣁΑ٬ًᡏޑୁྖفᆢ࡭ӧ΋ঁӝ౛ޑλ୔ୱϣǴךॺሡाׯ ๓ًηޑᐉӛᛙۓǶԵቾߚጕ܄2-DOFًηޑѦ೽୏ᄊӵ(3.17)܌ҢǺ 2 cos( ) 2 2 cos( ) 2 yf f yr x f yf f r yr z F F mv l F l F M

G

E

J

J

G

 ­ _{ } ° ® ° ˜  ˜  ¯   (3.17) ଷ٬೸ၸMz٬ள

J

ଓᙫډ

J

dǴךॺёаעE ୏ᄊׯቪԋ(3.18)ԄӵΠǺ 2 _yf cos( _f) 2 _yr d x F F mv

G

E

  

J

 (3.18)

30 ௗ๱ǴךॺעୖԵޑᐉᘍفೲࡋȐ

J

_dȑۓကӵ[10]܌ॊǺ ( ) 2 cos 2 ʹ yf f yr stability x F F k mv

G

J

E

  (3.19) ೸ၸԜୖԵᐉᘍفೲࡋ(

J

_d)ޑᒧڗǴསҢ๱ًᡏޑୁྖف཮ᅌ຾ԏᔙԿ႟Ǻ k

E

 

E

Γ (3.20) ځύk Ѹ໪ࣁᝄ਱҅ኧȐstrictly positiveȑǶ ӧ [9]္य़ǴΨӵӕ΢य़ޑཷۺǴவጕ܄ 2-DOFًηኳࠠ [38]ύפډΑӝ፾ޑ ( ) ʹ stability J ǴځགྷݤӵΠǺ२ӃǴԵቾΠӈጕ܄2-DOFًηኳࠠǴӵ(2.38)_Ԅ! 2 2 2 (2 2 ) 2 2 2 0 1 2 2 2 2 2 Ǧ ͳ f r r r f f f x x x f z f f r r f f f f r r z z z z x C C l C l C C mv mv mv M l C l C l C l C l C I I I I v

E

E

_G

J

J

  ª _{ } º ª º ª º « » « » ª º _{« »}ª º_{« » « »} « » _{«    »}« » _{« » « »} ¬ ¼ ¬ ¼ _{« » « » « »¬ ¼} « » « » ¬ ¼ ¬ ¼   ! ٠ଷ೛ ) ( ) 1 ʹሺstability d s s J J W  (3.21) 2 ) 2 2 2( ) ሺ f x stability f x f f r r C v mv l C l C J ˜G   (3.22) ೸ၸM_zȐᚐѦౢғޑᙯ୏ᄍໆȑ٬ள

J

ёаଓډ

J

_dǴӢ٬ךॺёע

J

࣮՟ d

J J

٠஥Εًᡏୁྖف୏ᄊȐside- slip angle dynamicȑϣǶനࡕǴёว౜(3.23)

Ԅᆶ(3.20)Ԅ࣬ӕǴًᡏୁྖفࣣ཮ԏᔙԿ႟Ǵ຾ԶዴߥًηޑᛙۓǶ (2 _f 2 _r) x C C mv

E

  

E

(3.23) Πय़ךॺኳᔕୖԵᐉᘍفೲࡋᒧҔ

J

2ޑБԄӧًೲࣁ 25m/sȐ90km/hrȑ຾Չ

change laneޑ୏բǴځ߻፺ᙯӛفG_f ӵკ3.3(a)๏ۓǶவკ3.3(b)ᆶ3.3(d)ёว ౜J Ԗଓᙫډ

J

_d٠ЪᒿGf Զᡂ୏Ǵځനεॶࣁ0.26 rad/secǴ࣬ჹܭკ3.1(b)ύ

31 J നεॶ0.8 rad/secλࡐӭǴΨཀښ๱٬Ҕ

J

₂ޑБԄ཮٬

J

_dၨλǴᏹ௓܄ૈၨ ৡǶՠࢂǴךॺΨว౜٬Ҕ

J

₂ޑБԄǴًᡏޑୁྖف߈՟ܭ႟Ǵᇻλܭ

E

_maxǴ ӵკ 3.3(c)ᆶკ 3.4Ƕ܌аǴऩѝ௦ڗJʹ maneuverability( )ޑБԄܭًηୁӛ௓ڋǴᗨ ёа٬ًᡏޑୁྖفࡐλԶᆢ࡭ӧୁྖف৒೚ޑനεॶϣ຾Զዴߥځᛙۓ܄Ǵ ՠӢࣁ

J

_dࡐλǴค׎ύًη཮഼Ѩࡐӭޑᏹ௓܄Ǵ٬ᎯᎭޣคݤᒿЈ܌టޑᏹ ௓ًηՉ຾ޑБӛǴऩၶډ߻БԖᆙ࡚ރݩёૈӢࣁᙯӛޑ൯ࡋόεԶ೷ԋཀ ѦวғǶკ3.5ࣁ௓ڋᒡΕMzǴᙯ୏Κંऊ8000NmаϣǶ ! კ3.3! change laneኳᔕკȐ

J

d௦Ҕ

J

2ȑ

32

! კ3.4! ୁྖف(

E

₎

! ! კ3.5! MzኳᔕკȐ

J

d௦Ҕ

J

2ȑ

E

33

3.3

៾ख़Ȑweightingȑޑϟಏ

வ3.1ک3.2࿯ϩձගډٿᅿୖԵޑᐉᘍفೲࡋȐ

J

dȑǴ΋ᅿࢂJ1 ( maneuverability) ќ΋ᅿࢂJʹ stability( )Ƕᒧ᏷J1 ( maneuverability)ёаளډؼӳޑᏹ௓܄ૈǴՠёૈ཮Ӣࣁ ՉᎭޑރݩԶᏤठًᡏޑୁྖفȐside-slip angleȑᡂεǴԶ഼Ѩًηޑᛙۓ܄Ƕ ᒧ᏷J_{ʹ stability( )}ёа٬ளًηޑᛙۓ܄ૈ٫٠ዴߥًη๤፾܄ᆶӼӄ܄Ǵՠځલ ᗺࢂ཮഼Ѩ௞೚ӭޑᏹ௓܄Ǵ٬ᎯᎭޣӧᏹ௓΢όӵႣයǶ வ [13]ύǴගрΑ೸ၸًᡏୁྖفޑελٰ،ۓᒧڗJ_{1 (maneuverability)}܈ࢂ ( ) ʹ stability J ޑБԄǶځۓကӵΠǺ 1( ) (1 ) 2( ) d maneuverability stability J ˜V J  V J˜ _! (3.24) ځύ 0d d ǶV 1 ྽ୁྖفࡐλਔǴV ᒧ᏷ 1ǹ྽ୁྖفࡐεਔǴV ᒧ᏷ 0ǴՠԜБԄёૈ ཮೷ԋ៾ख़ȐweightingȑࢂόೱុޑރݩǴӧ0ᆶ1ϪၢǶҗܭ៾ख़ޑϩ݋ᆶ ่݀ӧ߈යޑЎ᝘ύ૸ፕࣗϿǴӧу΢฽ޣᇡࣁԜБԄዴჴёаӧًηᙯӛޑ ᏹ௓܄ᆶᛙۓ܄ԖΑ׳ӭޑԾҗࡋǴࡺҁፕЎௗ๱཮ӧࡕុޑക࿯ύ૸ፕ៾ख़ БԄ܌஥ٰޑᓬ༈Ǵ٠Եቾ៾ख़ࣁߚਔᡂᆶਔᡂٿᅿБԄǶനࡕǴע៾ख़БԄ ᔈҔܭًηᙁϯኳࠠӧόӕޑᎯᎭ௃ݩȐٯӵǺًೲၸזǵᆙ࡚ᗉምȑǶԜѦǴ ಃѤകޑ೽ϩךॺΨ཮ע៾ख़ᢀۺ஥Εߚጕ܄ޑӄًኳࠠύǴ௖૸ӧόӕޑၰ ၡރݩΠȐ-splitၡय़ǵlow-ၡय़ȑ៾ख़܌஥ٰޑᓬ༈٠଺ϩ݋ᆶ૸ፕǶ

34

3.4

៾ख़ȐweightingȑࣁߚਔᡂᆶਔᡂޑБԄ

ךॺޑགྷݤࢂӵՖ೸ၸ៾ख़ȐweightingȑᒧڗޑБԄ٬ளًηӧᛙۓ܄ё аᆢ࡭ޑ߻ගΠΞёаᏱԖόᒱޑᏹ௓܄Ƕ೸ၸΠय़ጕ܄ޑ 2-DOFًηኳࠠǴ ӵ(2.38)ԄǺ 2 2 2 (2 2 ) 2 2 2 0 1 2 2 2 2 2 ͳ f r r r f f f x x x f z f f r r f f f f r r z z z z x C C l C l C C mv mv mv M l C l C l C l C l C I I I I v

E

E

_G

J

J

   ª _{ } º ª º ª º « » « » ª º _{« »}ª º_{« » « »} « » _{«    »}« »_{¬ ¼ « » « »} ¬ ¼ _{« » « » « »¬ ¼} « » « » ¬ ¼ ¬ ¼   ྽

J

ёଓᙫډ

J

_dਔǴךॺёаעE ୏ᄊҔΠԄ߄ҢǺ 2 (2 2 ) 2 2 ( 1 ) f r r r f f f d f x x x C C l C l C C mv mv mv

E

  

E

   

J



G

(3.25) ࣁΑБߡीᆉǴךॺଷ೛ 1 k1 f J ˜G (3.26) 2 k2 f J ˜G (3.27) 3 2 _f d f x C k k mv

E

  ˜  ˜ 

E

J

˜

G

(3.28) ځύ (2 f 2 r) x C C k mv  (3.29) 1 2 2 2 2 2 ( ) f r x x us x f r x r r f f lC C v v k lk v l C C mv l C l C (3.30) 2 2 2 2( ) f x x f f r r C v k mv  l C l C (3.31) 3 2 2 1 r r f f  x l C l C k mv    Ζ (3.32) ߕຏǺ k ǵk₁ǵk₂ǵk₃ࣣࣁًηᕵӛೲࡋ(v )_x ޑڄኧ

35 ௗ๱ע(3.24)Ԅ஥Ε(3.25)ԄޑE ୏ᄊϣǴёள 3 1 2 2 [ (1 ) ] _f f _f x C k k k k mv

E

  ˜  ˜ ˜   ˜

E

V

V

˜

G

 ˜

G

3 1 2 3 2 2 [ ( ) f ] _f x C k k k k k k mv

E V

G

 ˜  ˜    ˜ җܭ 3 2 2 f x C k k mv  ǴࡺE ୏ᄊёᙁϯӵΠԄǺ 3

(

1 2

)

f

k

k k

k

E



 ˜  ˜

E V



˜

G

(3.33) ࣁΑБߡϩ݋Ǵӆз h k k₃( ₁k₂) f

k

h

E



 ˜  ˜ ˜

E V

G

(3.34) ௗ๱Ǵךॺӧࡕय़ޑ3.4.1࿯ᆶ3.4.2࿯൩ଞჹ(3.34)ԄޑE ୏ᄊѐ଺៾ख़ޑ௢ ᏤǴ຾Զϩ݋рߚਔᡂ៾ख़ᆶਔᡂ៾ख़ޑٿᅿБԄ٬ًᡏޑୁྖفό཮ຬၸୁ ྖفޑज़ڋǶ

3.4.1

៾ख़Ȑweightingȑࣁߚਔᡂ

྽Եቾ៾ख़ࣁۓॶਔǴё؃рE ޑॶӵΠԄǺ ( ) 0 (0) t ( ) ( ) k k t f e E h e W d h y t E  _˜E _{ ˜ ˜}V   _˜G W _˜ W V _{˜ ˜}

³

(3.35) җܭًηۘ҂ᙯӛ߻Ǵୁྖف߃ۈॶё࣮՟႟Ǵࡺз

E

(0) 0жΕ(3.35)ԄǴځ ่݀ӵ(3.36)Ԅ܌ҢǺ ( ) 0 ( ) ( ) t _{k t} f h e W d h y t E V _{˜ ˜}   _˜G W _˜ W V _{˜ ˜}

³

(3.36) ځύ ( ) 0 ( ) t k t _f( ) y t

³

e W ˜G W ˜dW ǴךॺёҔΠӈ୏ᄊ؃рǴӵ(3.37)Ԅ

36 ( ) f y  ˜ k y G t (3.37) ࣬ჹᔈޑᙯ౽ڄኧӵ(3.38)Ԅ ( ) 1 ( ) f Y s s s k G  (3.38) ӢࣁךॺԵቾ៾ख़ࣁۓॶǴΞу΢Ѹ໪ዴߥًηӧᙯӛޑၸำύࢂᛙۓޑǴࡺ ًᡏޑୁྖفሡᅈىԜచҹǺ

E

_max d d

E E

_maxǶ ฅԶୁྖف཮ᒿ๱߻፺ᙯӛ فGf( )t ޑׯᡂԶᡂεǴ܌аӧ՗ෳ៾ख़ਔǴךॺाԵቾ

y t

( )

max

y

maxǶԖΑа ΢ޑଷ೛ᆶచҹǴ៾ख़ёаճҔΠԄ՗ෳрٰǺ max max h y E V ˜ (3.39)

3.4.1.1 change lane

୏բϐኳᔕ

Πय़ኳᔕୖԵᐉᘍفೲࡋᒧҔ៾ख़ࣁۓॶޑБԄܭًೲ 25m/sȐ90km/hrȑ ຾Չchange laneޑ୏բǴځ߻፺ᙯӛفGf ӵკ3.7(a)๏ۓǶ೸ၸϦԄ(3.37)ޑ୏

ᄊё؃ளy_maxǴӵკ3.6Ƕௗ๱עᆉрٰޑ h ॶȐh 6.6737ȑᆶ

E

_max 0.0349а Ϸy_max 0.01094஥ΕϦԄ(3.39)Ǵ຾ԶෳрV 0.478Ƕځ่݀ӵკ3.7(b)ᆶ3.7(d) ܌ҢǴJ Ԗଓᙫډ

J

_d٠ЪᒿG_fԶᡂ୏Ǵځനεॶࣁ0.52 rad/secǶԶკ3.7(c)Ψ ᡉҢୁྖف҅ӳပӧEmax΢य़ԶؒຬၸѬǶკ3.8ࣁ௓ڋᒡΕMzǴᙯ୏Κંऊ 6000NmаϣǶவკ3.9ᆶკ3.10׳ёаว౜ډ٬Ҕ៾ख़ޑБԄ࣬ჹܭѝ٬Ҕ

J

₁ ܈

J

₂Ǵୁྖفό཮ຬၸځ৒೚നεॶȐዴߥᛙۓ܄ȑǴΞૈᅰёૈޑගϲୖԵ ᐉᘍفೲࡋ٬ளᏹ௓܄ૈ׳ௗ߈

J

₁ޑБԄǶ

37

! კ3.6! ՗ෳߚਔᡂ៾ख़܌ሡޑy_maxॶ

! კ3.7! change laneኳᔕკȐ

J

d௦Ҕߚਔᡂ៾ख़ȑ

38

! ! კ3.8! MzኳᔕკȐ

J

d௦Ҕߚਔᡂ៾ख़ȑ

კ3.9! ߚਔᡂ៾ख़ϐ

J

dКၨკ