课件自控北航400考研873自动控制原理

北航400+考研873自动自控命题人乐之者教育科㠚 ࣟ᧝㘷䈴᧝֒ѐδ⨣㓝㚊㌱䴧%%Chapter IntroductiontoAutomatic

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in im i ᐖਣ䗩䎻Ҿ᧝ェབྷѪᗵᴹ.’ᐖਣ䗩䎻Ҿ䴦Ѫᗵֻ˖ᐢ⸕GsH

s ᧝䀂 G GsHssispi k 䖘䘩ᴹᶑ㓯iiᴹᶑ䘁Step6˖iiᴹᶑ䘁㤕Q!PˈᗵᴹQPᶑ⋯䘁㓯䎻Ҿェ䘌༴ knm N «QPоᇎ䖤 pzᔰ⧟ᶱ⛩ᔰ⧟䴦 n

ᔰ⧟ᶱ⛩ᔰ⧟䴦 k p

nֻ KGsH

nks kk䈅≲ṩ䖘䘩Ⲵ䘁㓯 knmk nmk䴦

piᶱ⛩ M nn䎧᧝䀂ޡ䖝⧟༽⛩к䖘䘩Ⲵ࠶ᯯ᧝о↓ᇎ䖤Ⲵཀྵ䀂DŽ࠶ሴ px px ֻ 䇮㌫㔏ᔰ⧟Ր jj K M 㓸→䀂ޡ䖝ᔰ⧟༽᧝䴦⛩к䖘䘩Ⲵ࠶

GsH ᯯ᧝о↓

䈅㔈㌫㔏ᾲ⮕ṩ䖘䘩 zx zx᧝䀂sHsi

sz i

s k ᔰ⧟䴦⛩˖i p p

z z 6ᒣ䶒к᧝䙷৸・ণ〠 ᙗ䍘 ⛩Ⲵ ⛩〻Ⲵ䀓 ֻ id jdjzipᱟ㌫㔏Ⲵᴹ䲀ᔰ⧟䴦⛩ jķDs_s GsH K ĸdDs

⛩⮕ 䀓˖ṩᦞ㌫㔏ᔰ⧟Ր䙂≲ M

ᔰ༽ᒣ䶒ᶱ⛩Ⲵ䎧᧝䀂

z p↕僔 ↕僔䴦⛩ェ䘌䴦Ĺᇎ䖤кṩ䖘䘩սҾᴹ䲀䴦⛩ˉ1ェ䴦⛩ѻˈഐ↔

pĻĻ M

a a ⛩↔㌫㔏ṩ䖘䘩മ ⛩ മ ˄㠽࠶᧝

Պ䀂˖᧝Պ⛩༴䖘䘩Ⲵ࠶㓯ૂо↓ᇎ䖤ѻ䰤DŽ²DŽ²

l>

md dpjn i dl> d dsj ⌘Ѫ䘋࠶ޕ᧝⛩Ⲵṩ䖘䘩im⌘Ѫ⛩Ⲵ䖘 jiml Ksds s Gi

i

K>KlG n

K>Kl ssdlsi

K> siᱟKKl㌫㔏Ⲵީᆳ䰝

K>siᱟKKl㌫㔏

ᆳ䰝⧟ᶱ⛩ K

K㺕ݵ䈤ķ᧝㌫㔏l䟽ᶱ⛩Ⲵ䎧᧝

*˖⭘ࣣᦞ⺞ᇊˈԔީ⧠ޘ䴦㹼ˈնㅜанਈਧˈ䘉㌫༴ҾѤ⭼っ Z*˖ሶ6MZԓޕ䰝⧟⢩ᖱ〻 Ԕީᇎ䜘ˈ㲊䜘Ѫ䴦ˈ≲Z > d dsd jĸ᧝㌫㔏l䟽䴦⛩Ⲵ㓸→䀂䇑 > d dpdl dli ֻ䇮㌫㔏ᔰ⧟Ր䙂GsGsHs 䈅

䀓˖↕僔ķᴹᶑṩ䖘䘩DŽQ ᶑṩ䖘 䎧 ˄M˅˄M˅˗㓸Ҿェ䘌DŽĹᇎ䖤 ᶑ䘁 a a ⺞䀂 pRpp p ˄㠽

Պ䀂 䀂˖ 䀓 D 䀓 K

മ ˉṩ䖘ss

ĸ䰝⧟⢩ᖱṩѻ〟

ķ䰝⧟⢩ᖱṩⲴѻˈㅹҾ䰝〻ㅜҼ亩㌫aDŽ㤕 m

᧝ᔰ⧟ᶱ⛩ᐢ⺞ᇊнਈⲴ᧝ߥлˈީૂѪᑨⲴn⳺ⲴḀ䰝⧟⛩䶒кૂᐖ〫ࣘ᧝ˈᗵᴹаᶱ⛩ਣ〫ࣘ䘉ṧ᧝㜭䇱ᶱ⛩ѻѪᑨDŽ䘉ሩҾ᧝᧝ṩ䖘䘩Ⲵ䎠DŽṩѻоᔰ⧟ṩ䖘䘩⳺Kǃᶱ⛩ਈ——৲᧝ṩ䖘䘩Ⲵ㔈

D аǃᔰ⧟䴦⛩ਈⲴṩֻ ᐢ⸕䍏侸㌫㔏Ⲵᔰ⧟Ր䙂

ㅹᔰ⧟Ր䙂GsH AP GsHs Tds 䈅 Td ਈⲴ䰝⮕ṩ䖘䘩Ҽǃᔰ⧟ᶱ⛩ਈⲴṩ䇮а䍏侸㌫㔏Ⲵᔰ⧟Ր䙂

Q sമ㔈Ⲵ䲿৲TdਈⲴṩ䖘䘩ྱsമ⽪ֻ 㔏Ⲵᔰ⧟Ր䙂KKGsHKs Ta ⹄ウ ਈⲴṩ䖘䘩 䈅㔈 ‡ㅹᔰ⧟Ր䙂 䰤 ਈⲴṩ䖘䘩 pਈⲴṩ䖘䘩䀓D s Ta ㅹᔰ⧟Ր䙂TsGsH sњᶱ⛩ˈн.ਟ䇑 нњᶱ⛩ˈн.ਟ䇑 н

ֻ ṩ䖘䘩mKszi

GsHnn55Vˇ*&ᑵ

mK z+ n p䰝⧟⢩ᖱᯯ᧝〻˖'V*V+ GsHs 䘉ቡ䖘䘩〻 ˖GsHssisi 6WHSᇎ䖤к6WHSᇎ䖤кⲴṩ䖘䘩DŽ㤕ᇎ䖤кḀ४⇥ˈਣ䗩䴦ᶱ⛩њ᧝ѻѪ᧝ˈ᧝䈕४ฏᗵᱟṩ䖘䘩Ⲵа䜘Step1:ṩ䖘䘩Ⲵ࠶᧝᧝DŽQStep1:ṩ䖘䘩Ⲵ࠶᧝᧝DŽQ䱦㌫㔏аᇊQtepGsHsszis Step3䖘䘩Ⲵሩ〠ᙗṩ䖘䘩ᴢ㓯ޣҾᇎ䖤ሩ〠ˈᱟ⭡Ҿᡆᇎᡆ䖝༽DŽ⭘ᵜᶑਟ㔈࠶кॺᒣ䶒❦ૂሩ〠⭫࠶лॺ䜘

Step6˖䖘䘩Ⲵ᧝Step4:ṩ䖘䘩Ⲵ䎧⛩㓸䎧 Ⲵ⛩䎧㓸⛩ĺⲴ⛩㓸→Ҿᔰ⧟

㤕Q!PˈᗵᴹQPᶑ⋯䘁㓯䎻Ҿェ䘌оᇎ䖤ཀྵ䀂˖ n «QPоᇎ䖤 pzᔰ⧟ᶱ⛩ᔰ⧟䴦n ᔰ⧟ᶱ⛩ᔰ⧟䴦䎧᧝䀂ޡ䖝⧟༽⛩к䖘䘩Ⲵ࠶ᯯ᧝оm↓ᇎ䖤ⲴཀྵnDŽ࠶ሴ p >d

ds i

jj

jll l 㓸→䀂ޡ䖝ᔰ⧟༽᧝䴦⛩к䖘䘩Ⲵ࠶ᯯ᧝о↓ᇎ䖤Ⲵཀྵ䀂˄ޕ䀂zx zx

dsidpjjil᧝䀂

GsHsszis 䰝⧟䴦⛩⛩Ⲵ⺞

⭘䰝⧟䴦⛩㺘⽪Ⲵ䱦䏳᧝ᓄ㺘䗮䰝⧟Ր䙂 Gs KsG s

H s

GsH

䰝s䰝i䰝⧟Ր䙂

䇮䗃ޕѪঅս䱦䏳˖UWWGs

szi

s

C Ksz GsHsCAnAkspspKKszsCAnAkm

Kgs 䰝⧟䴦j

n s s

ksnsi

Cሶ&V㺘䗮ᔿ䘋㹼 йǃ䰝⧟䴦Cᘛ䙏䰝⧟ᶱ⛩䘌㲊䖤

ྱ ᴹєњᶱ⛩˖ 㤕ˈᶱ⛩ᆀ˖ቡа䶐ᗇᖸ䘁Ⲵ䰝⧟ ӄ⭘ѫ⛩㌫㔏Ⲵᙗ㜭ᖃ□ᖃ□ˈቡਟԕ䇔Ѫskоzᱟаሩሩ㌫㔏䘋㹼ˈቡਟԕሶީᘭ⮕н䇑skമ4-ṩ䖘മ4-ṩ䖘䘩G ᐢ⸕㌫㔏ᔰ⧟Ր䙂G s

s Ks 䈅ᓄ⭘ṩ䖘䘩⌅㌫㔏Ⲵっᇊᙗˈᒦ䇑㇇⧟ѫሬᶱ⛩

ᴹ䱫ቬ∄Ⲵᙗ㜭

↕僔֌㌫㔏Ⲵṩ䖘 Ҽ䱦㌫㔏অս䱦䏳ਧ֌⭘лⲴᙗ㜭ᒣ䶒 Ҽ䱦㌫㔏অս䱦䏳ਧ֌⭘лⲴᙗ㜭V⛩Ⲵḷ䇮Ѫs Vѻޡ䖝Ⲵᶱ⛩Ѫ Ьᐢ⸕㌫㔏㔃ྱമᡰ⽪ ‡㌫㔏ᔰ⧟Ր ЬKሩ㌫㔏ᘱ䗷〻Ⲵᖡ ‡↔㊫ᑖ䴦⛩ⲴҼ䱦㌫㔏Ⲵṩ䖘䘩ˈީ༽Ѫањശˈީ ॺᖴѪ䴦മ മ ‡ሩᓄᔰ⧟ _

_ ᖃᔰ⧟⳺˄ ˅ˈ䰝⧟Ѫєњ䍏⛩ˈ㌫㔏䱦䏳ਧлᓄѪ䶎ᖃᔰ⧟⳺ ˅ˈ䰝⧟Ѫаሩޡ༽ᶱ⛩ˈީ䱦䏳ᓄѪᥟ㦑㺠䗷〻ᖃᔰ⧟ ˈ䰝⧟৸Ѫ䍏ᇎ䗷⛩оṩ䖘 䗷⛩оṩ䖘 ཀྵ䀂Ⲵമ4-

FRV FRV ㌫㌫㔏䱦䏳ᓄީᴹ䖳ྱⲴᒣっˉˉ Kṩ䈅㔈䰝⧟㌫㔏Ⲵṩ䖘䘩ˈྱമ4-മ㓸ᴹєњਣᶱ⛩DŽ䈤ᔰ⧟⳺䇪㤕㌫㔏ѝ䱴ањ䍏ᇎ䴦⛩z1ˈ⭘ᶕழ zമ䱴䴦⛩Ⲵṩ䖘zzമ

㤕䴦 ˈ㌫ণ.ਆԫօ㌫㔏っᖃ.

മᡰ⽪䱦䏳ᓄᱟ㺠ᥟ㦑Ⲵˈфᥟ㦑仁

䲿.Ⲵབྷ㘼 䱴䴦⛩Ⲵṩ䖘 ˈ䱴 Ⲵ䴦⛩㌫㔏ṩ䖘䘩ӽᴹєᶑ㓸սҾsᒣ䶒Ⲵਣॺ䜘

ㅜഋㄐ --ぜτ∅ぜτ∅ˉӾ䟼ਦ 䟼ˉ仁ˉර⧟㢲Ⲵ仁ˉ㌫㔏Ⲵᔰ⧟仁ˉ仁⦷っᇊˉ㌫㔏䰝⧟仁⦷⢩ᙗо䱦䏳ᓄⲴޣˉᔰ⧟仁⦷⢩ᙗо㌫㔏䱦䏳ᓄⲴޣ䔄 䛽1.仁⦷⢩ᙗⲴสᵜᾲᘥ

ਟ⭘䟼ਦ㓗⽪є䟽㾱仁⦷⢩ᙗᴢ㓯৺㔈⭘仁⦷⢩ᙗሩ㌫㔏䘋㹼˖

f

n˄˅ྱ∿ᦞ˗˄2˅ࣘᘱ૱䍘Ⲵ

TT˄3˅っᘱ䈟T

e

a

TftFRVntGT TTftVLQntGT

ਟᗇઘᵏ Ⲵᑵᓖ仁䉡ˈྱ ᡰ⽪Ⲵ᧝ս仁䉡ྱ ᡰ⽪Af AVLQnt n nDUFWDQan ᑵᓖ仁 ս仁к䘠ઘᵏਧⲴ仁䉡ᴹྱ䉡㓯⋯仁⦷ 䉡㓯ѻ䰤ㅹ䐍ᐳˈє䛫䉡㓯ѻ䰤Ⲵ䐍ㅹҾส⌒⦷ˈԫєᶑ䛫䉡㓯ѻ䰤нਟ ⧠ީԆⲴ

f n

⦷䟿ሩҾ䶎ઘᵏਧˈਟԕ䇔Ѫᱟઘᵏਧઘᵏ䎻ҾབྷⲴᶱ䲀л䶒ݸሶઘᵏਧⲴ)RXULHU㓗ኅᔰᔿ㺘⽪ᡀл

ft Mn TMn⧠ n ʌ ˅ਟԕ㺘⽪nf n

ʌ ʌ ftHMntGtʌ

ԔF

ftHʌftHMntGt f

Fʌn

ʌ

ʌ

˄ ˅˄ ˅ᡀҶ䶎 ਧ ftᦒf ftHMtGt ૂ)RXULHU䘶ʌ ftⲴ)RXULHUਈᦒਟԕ㺘⽪ lim FnHMnt ʌn F ftFRVtGt ftVLQ lim 5HFnHMnta b ʌ

F

ʌ f FnHMnt limn n

ʌF FnVLQntnʌ ʌn DUFWDQк䘠㺘䗮ᔿ䈤ˈ䶎ઘᵏ

anbnftҏਟԕ䀓Ѫェ

ਟ⸕ˈн䇪ᱟઘᵏਧ䘈ᱟઘᵏਧˈਟԕⴻᡀᱟ⭡ェཊњ↓ᕖਧⲴˈնнҾઘᵏਧⲴᖒˈ䘉䟼↓ᕖਧⲴ䀂⦷ᱟ䘎㔝ਈⲴˈሩҾ仁⦷ѪnⲴ↓ᕖਧˈީFnʌѪҶ᧿䘠仁䉡䘎㔝ᐳⲴߥˈ䘉䟼ᕅޕঅս仁ᑖⲴ仁䉡²²仁F ቡ〠Ѫ f Ⲵ仁䉡ᇶᓖ

ᕖ Ⲵ㔃䇪ᱟީᴹ аǃ仁rtRic

r RVLQRs dc iC

C RCdctctr

tedc c eԔTRC

ctr

ԕRC㖁㔌 G䗉

OLPct

VLQttgOLPct

VLQttg ਟԕਟԕⴻˈ↓ᕖؑਧ֌⭘лˈ䟿ᱟ䗃ޕ仁⦷Ⲵ↓ᕖؑっаǃ仁㓯ᙗᇊᑨ㌫㔏ˈ↓ᕖؑਧ֌⭘лˈ䗃ⲴっᘱоޕⲴ༽∄ˈ〠Ѫ㌫㔏Ⲵ仁⦷⢩ᙗ˄ণѪᑵ⢩ᙗㆰ〠

仁⦷⢩ᙗਟ⭡Ր䙂മйǃ仁 മᑻ仇⢯ᙝȽ仇⢯ᙝȽᑻ GM GM AHM A aѪ㌫㔏Ⲵᑵ仁 a Ѫ㌫㔏Ⲵ⴨仁ሯ᧝ᯯ仇ሩ᧝仁⦷⢩ᙗᴢ㓯৸〠仁仁㓯ሩ᧝ᑵ仁LL JAaമ5ˉ5RCⲴᑵ⢩ᙗᴢ

ሩ᧝᧝仁aമˉമˉሩḷ5-65-7GA喎GA喎ᑵ仁 ሩ᧝仁⦷⢩ᙗᴢ㓯ሩ᧝ᑵ仁⢩ OJA

仁ሩᑵ L OJሩ᧝᧝仁⢩ മ5ˉ7∄ֻ⧟㢲Ⲵ仁⦷⢩ᙗᴢ

⧟ᑵ仁仁മ5ˉ8〟⧟㢲Ⲵᑵ仁ǃ仁ǃᑵ⢩ᙗᴢ

മ ⧟

G G MʌG MG GHMDUFWDQ L OJATDUFWDQOJTDUFWDQ ᙗ⧟㢲Ⲵᑵ仁ǃ仁ǃᑵ⢩ᙗᴢ

TᖃLTTՐ䙂 G

s മ ᙗ⧟㢲Ⲵሩ仁⦷⢩ᙗᴢ

G 仁 nM仁nn Mᑻ仇⢯ᙝȽ仇⢯ᙝȽᑻ

䉀ᥟ仁 䉀മ䉀ᥟ仁䉀 മ ᥟ䉀ᥟ仁䉀 nn ⧟G

ሯ᧝ᯯ仇GMGMᑵ仁 ᔦ䘏⧟㢲䗃ޕ䗃ޣ࠶㌫Rc rtRG HA A L喎㈫㐏⮴ᐰ⣟䷁ ㌫㔏ᔰ⧟ᑵ仁о ⢩ᙗᴢ LiiLL䇮㌫㔏ᔰ⧟Ր䙂⭡㤕ᒢީLiiLLs sGGᔶ⧥ᑻമ Qമ5ˉ22㌫㔏ᔰ⧟ᑵ⢩ᙗᴢ 㔏ᔰ⧟ᑵ⢩ᙗᴢ

㌱㔕ᔶ⧥ᑻⲴᔰ⧟ᑵᔰ⧟Ր䙂〟⧟㢲ˈᔰ⧟Ր䙂〟⧟㢲ˈķᖃ仁ɒˈީ

⧟〟ĸᖃ仁

ˈ㤕n>mˈG(jʘ)䀂Ѫ(mͲn)ʋ/2DŽĹ㤕ѝᆀਜ਼ᴹsഐᆀ⧟㢲ˈީG(jʘ)ᴢĺG(jʘ)ᴢ㓯о䍏ᇎ䖤ⲴӔ⛩ˈᱟањޣ䭞 ㌫㔏ᔰ⧟ሩᑵ仁оሩ仁㺘䗮

ֻ㌫㔏ᔰ⧟Ր䙂GL JG

OJGi

JGi 㔈㌫㔏ᔰ⧟ሩᑵ仁о仁⢩ᙗᴢ㓯㌫㔏ᔰ㌫㔏ᔰ⧟ሩᑵ仁ㅹҾ⧟㢲Ⲵሩᑵ仁ѻˈㅹҾ⧟㢲仁ѻG ֻˉG ᔰ⧟⭡йњީර⧟㢲㓴ᡀˈ⇿њ⧟㢲Ⲵሩᑵ仁о仁⢩ᙗᱟᐢ⸕ⲴDŽሶ⧟㢲Ⲵሩᑵ仁о仁ᴢ㓯 ণᗇ㌫㔏Ⲵᔰሩᑵ仁৺仁

s s 123s փ㌱߉ᡀީර⧟㢲ѻ〟 ⧟㢲Ⲵ䘁㓯䖜ᣈ仁⦷༴↓䘁㓯ᗇ⧟㢲ᴢ㓯ሶ⧟㢲ᴢ аǃྱྱ⢩っ

ᔰ⧟ՐGsH MsMNsNMN䰝MN G MsNGsH NsN MsMNNsԔFGsHNsNMsM 侸᧗㌫ NsNnsF nsL䖵䖵ࣙF(s)ީᴹྱķީ⛩ ᱟ䰝⧟ᔰ⧟Ⲵ⢩ᖱṩDŽĸީ⛩Ⲵњоᶱ⛩Ⲵњ

䗆䀈ྱ᧝ሱ䰝ᴢ㓯ss᧝ˈF(s)ᴢ㓯㔅᧝⛩䘶䪸䖜Z㤕RѪ䍏ˈ㺘⽪F(s)ᴢ㓯㔅᧝⛩亪䪸䖜sz F:ྱྱ᧝⢩っ F GsH NsNs MsMNsN nsnF nsL

sFsF亪䪸Fs a L F s L F s sᔰ⧟ᑵ仁⢩ᙗᴢ᧝䲀བྷণ_s_GsHsF GsH F P

ণ᱐ሴѪFsᒣ䶒 F GjHjᒣ䶒 GjHjᴢ㓯 䗆䀈ྱ᧝ሱ䰝㓯s࠶ᴹZњF(s)Ⲵ ྱ ⛩Pњ)Ⲵ⛩࠭᧝PᐞণZ

䰝⧟㌫㔏っᇊⲴ࠶ݵᗵ㾱 ਈૂᯯ᧝ˈᔰ⧟ᑵ᧝⢩ᙗGMHMᴢ㓯㔅 M⛩䘶䪸䖜䗷Ⲵസ᧝R┑䏣˖ ྱ 䰝⧟㌫㔏っᇊⲴ࠶ݵᗵ㾱

ֻ‡ᐢ⸕㌫㔏ᔰ⧟ՐKᖃ Ӿ0᧝ ᙗ Gs sGMHMᴢ㓯 M⛩䘶䪸Ⲵസ᧝N=R/2┑䏣

䈅ᓄ⭘ྱ K=0.5 ⢩ᙗᴢ䰝⧟㌫㔏нっ䰝⧟㌫㔏っ

ǃ⧟䙂ਜ਼ᴹ〟࠶⧟㢲 sֻ仈5- Gs

㤕ᔰ⧟㌫㔏っᇊ˄p=0˅ˈ䰝⧟㌫㔏っ LGB仁⇥࠭ˈ

↓䍏ク 㓯 ⌘ ᔰ⧟ሩᑵ仁⢩ᙗབྷҾ䴦Ⲵ仁⇥ ⌘˖ᔰ⧟ሩᑵ仁⢩ᙗབྷҾ䴦Ⲵ仁⇥ ク䎺DŽ1Ѫ䍏ク䎺⅑᧝DŽ

仁⢩ᙗᴢ㓯 ク ሩ᧝仁⦷っ ֻ㌫㔏䰝⧟っᔰ⧟ሩᑵ仁JGMⲴ仁⇥

‡ᐢ⸕㌫㔏ᔰ⧟Րᔰ⧟ሩ仁⢩ᙗᴢ㓯 e㓯Ⲵ↓ǃ䍏ク GsH NN ZP

䈅 䰝⧟っ䀓˖㔈 ㌫㔏⧟仁DŽ⭡ᔰ⧟Ր

ֻ‡ᐢ⸕㌫㔏ᔰ⧟ՐN GsH s P‡䈅 䰝⧟っ䀓˖㔈㌫㔏ᔰ⧟ሩ仁ྱമ

J 䍏ク

ᡰԕˈL OKO G% N䍏1ˈ↓0ˈN=0-1=- 䰝⧟⢩ᖱ ˄⁑˅っᇊ㼅 GMH Ⲵ䟿о䍏ᇎ䖤Ⲵཀྵ䀂ᖃ ḷമкOJ GMHGMHᔰ⧟ᑵ᧝ᴢ㓯ሩ᧝ᑵ仁ᴢhdB

GMcH㌫㔏っ ㌫㔏っ ㌫㔏っᇊ˄ሩᴰሿս㌫㔏喎㈫㐏䬝̾䭦䋳 മ⭡ _OA_PA

hAᑵhAᑵᇊ㼅ᇊ㼅ᇊ㼅hOJh G%‡മ⽪‡മ⽪ 侸㌫㔏Ⲵ䰝⧟Ր䙂G ᡰ⽪㌫㔏Ⲵᔰ⧟仁ਟᗇ䰝⧟ᑵ仁⢩ᙗᴢMķ䴦仁 ᧝᱐㌫㔏᧝Mਧ֌⭘лᱟ᧝ᆈ᧝䶉ĸ䉀ᥟጠMm᧝᱐㌫㔏ⲴᒣbᙗDŽĹᑖᇭ仁᧝᱐㌫bⲴᘛ䙏ᙗDŽĺ䰝bM᱐㌫㔏ᣇ儈仁ᒢᢠⲴ㜭喎ᐰ㈫㐏䭦䋳

ք仇⇫䙊 Ⲵ४⇥ˈ䘉а⇥Ⲵ⢩ᙗᆼޘ⭡〟⧟㢲ᔰ⧟മˉᔰ⧟ሩᑵ仁䘁⢩ᙗᴢ

㌫㔏ᔰ⧟ሩᑵ仁儎仇⇫Ⲵᑵˈⴤ᧕᱐Ҷሩ䗃ޕ儈仁㌫㔏ᔰ⧟ሩᑵ仁儎仇⇫Ⲵᑵˈⴤ᧕᱐Ҷሩ䗃ޕ儈仁ᒢᢠ䔄䔄പᱜ1.єᑨ⭘ṑ↓㻵㖞

㈫㐏ᵑₓ䃮䃑ǃ㜭䎵䈳䟿%䈳㢲ᯯ᧝tsкॷᯯ᧝䰤t っᘱ䈟⧟ㅹDŽᡚ→仁 っᇊ㼅 ⁑っᇊ㼅

˖v=Ⲵ㌫ ᑖᇭ仁

䉀ᥟ仁⦷ 侸㌫㔏රаǃҼ䱦㌫㔏Ⲵᙗ㜭ḷˈ䘉⌅ݵ䘀⭘䘉Ӌ㔃ˈሶ㔉ᇊ㔃ᶴㅹѪᐢ⸕Ⲵީර㔃ᶴ㹼ሩ∄ˈ䘉ṧᖰᖰ֯䎵䀂Ⲵ䎵䀂Ⲵᴰབྷ䘉аᴰབྷ⭏ሩ仁⦷⢩ᙗᴢ㓯Ⲵօѝᗳ༴ˈሩᓄⲴ䀂仁 മ6ˉ4㌫㔏ⲴѢ㚄

˄ˉ Lǃ᧝ս @䘁㓯OJaTOJaTGcL JȦമ

a²ਟ㿱ˈṑ↓֌⭘Ⲵѫ㾱⢩⛩ᱟᨀ↓Ⲵ〫ˈ〠ս䎵 marcWDQaTarcWDQ U Gm m

U Z

RCsaTaTOJ OJ T

R R ᧝єњ䖜ᣈ仁

RR RRCsRR

᧝Ⓚᗞ࠶

VLQa

VLQ VLQ

RRR

RRCRR㔃䇪˖᧝䀂ĀⲴণ䎵᧝Ⲵˈᴹаབྷ᧝䀂ĸᴰབྷ 䀂ᴹɠ GRc

a aGRc

aa

aTL OJG OJ OJ

㔃䇪Ⓚ࠶᧝བྷ᧝T b └ṗ↙㻻㖤ਥԛ䙐䗽сഴⲺⓆ㖇㔒R G Uc R

⭘Ҷ㖁㔌Ⲵ儈仁㺠⢩ᙗˈሿ㌫㔏Ⲵᡚ→仁⦷ˈӾ㘼っᇊ

RR

ᓖབྷˈ䇱Ҷっᇊᙗᥟ㦑ᙗⲴழDŽĸ⢪⢢ᘛ䙏ᙗᶕᦒਆᇊᙗழᥟ㦑⌘⭡Ҿṑ↓⧟㢲Ⲵ᧝ս┎ૂѫ㾱ૂ⭏᧝վ仁⇥ˈ⇥Ⲵ᧝⢩ᙗᴢ㓯മ6ˉ10ǃ┎ˉ䎵⭡മਟ㿱ᒦ᧝վ仁⇥Ⲵ᧝⦷оᓖ᧝っᘱ㋮ᓖᒦᵚ⭡Ҿ┎ૂṑ↓㘼┎࠶䙊䗷᧝⧟བྷ㌫仁४ᑵ仁⢩ᙗ儈ᓖⲴਟ㜭

ѪҶޘ䶒ᨀ儈㌫㔏Ⲵࣘᘱ૱䍘ˈ֯っᘱ㋮ᓖǃᘛ䙏ṑ↓Ⲵ䖜ᣈ仁⦷ᓄ䘹᧝㌫㔏Ⲵվ仁੄—䎻Ѣ㚄ṑ↓ⲴՐ䙂Ⲵа㡜Gcab

bT aTT T

Ր䙂GTGTa aT aT R Rᇎ⧠ⲴⓀ㖁മ

Tb aⲴ৸〠∄ֻͲᗞṑ↓ಘˈީՐ⌒⢩৸〠∄ֻͲᗞṑ↓ಘˈީՐGc Kds

Gc

ᖃҾ ᖃҾⲴ䎵p

T〦²〥²ᗤṗ↙ಞθީՖT ᖃҾ┎ṑ↓㻵㖞৲Ⲵਸ⨶䘹㌫㔏ᔰ⧟⳺Ⲵ䝽ਸᱟ䶎ᑨ䟽㾱ֻˈ㤕ሶ䎵ṑ↓⧟㢲Ⲵ৲䇮㖞㌫㔏Ⲵվ仁४ˈቡ䎧нᨀ儈っᇊ㼅ᓖⲴ֌⭘DŽ⨶㤕ሶ┎ṑ↓⧟㢲Ⲵ৲䇮㖞ѝ⭊㠣֯㌫㔏нっ

喎͢㖄⤶䃪䃮䃑ǃѢ㚄ṑ↓Ⲵ仁‡仁⦷ฏ䇮䇑 һ㔉ᇊ㌫㔏㔃ᶴമമ6Ͳ14ᡰ⽪

䀓 UDG R 䘹 ս䎵 മ䇮䇑Gc

UDGっᇊ㼅 c

Tṑ↓ᔰ⧟Ր䙂GcsG

s っᇊ㼅

മ䎵ṑ↓മ ㌫㔏ⲴѢ㚄┎

ǃѢ㚄ṑ↓Ⲵṩ䖘䘩DŽ䰝⧟Ⲵ૱䍘䙊ᑨᱟ䙊䗷䰝⧟ѫሬᶱ⛩ᶕഐ↔䇮䇑ᔰˈ䴰㾱ᢺሩ䰝⧟ᙗ㜭ḷⲴ㾱≲ˈ䙊䗷䖜㌫ᔿˈ䘁լൠ⭘䰝⧟ѫሬᶱ⛩༽ᒣ䶒кⲴս㖞ᶕ㺘⽪ֻ䇮㌫㔏Ⲵ㔃ᶴമമ6Ͳ17ᡰ⽪

䇮ṑ↓㖁㔌ⲴՐ䙂G s M䘹M↔ ਆ˖ ⺞ᇊᶱ⛩ս㖞ˈ֯ᗇᵏᵋᶱ⛩┑䏣䀂㾱≲䇮䇑Ѣ㚄䎵ṑ↓⧟㢲ˈᗇ㌫㔏䱦䏳ᓄ┑䏣

R 㾱≲ˈ䎵䈳䟿 ˈ䈳㢲

p ṑ↓㌫㔏ᔰ⧟Ր䙂

ᯯ亸GsG K s ⁑〻䇑㇇

G

GGsHമ ṑ↓㌫㔏Ⲵṩ

ᱮ❦ˈᕅ䘋H(s)Ⲵ֌⭘ᱟᐼᵋGs֯њ䰝⧟㌫㔏Ⲵ૱䍘ᗇ亸 侸ਈተ䜘㔃

ǃ⭘侸䜘㔃ķ⭘ս㖞᧝侸वത〟࠶⧟㢲KGs Hs G K 侸

֯㌫㔏Ⲵᐞᓖл䱽ˈ ĸ⭘䙏ᓖ᧝侸ത᧝ᙗૂᯯ᧝བྷ⧟㢲

Ĺ⭘䙏ᓖ᧝侸वതањሿ䱫ቬⲴҼ䱦ᥟ⧟㢲ૂᯯ᧝བྷ⧟㢲 GG Ҿᘛ䙏ޕ䙏ᓖ侸 Ҷ䱫ቬˈᕡҶሿ䱫⧟㢲Ⲵнᖡĺ䙏ᓖ᧝侸ਧ࠶㓿䗷T KTT KTs>TTs TKK

᧝⭘᧝ ᕡ䶎㍐ᴰީරⲴֻᆀᱟ G⭡G ⳺нਈˈᐞᓖнਈ˗ᨀ儈っᇊᓖǃᣁ ⳺нਈˈᐞᓖнਈ˗ᨀ儈っᇊᓖǃᣁಚǃᇭ仁᧝侸ਟᨀ儈 • о侸ṑ↓ṑ•ṑമ ⭘侸ǃ᧗᧝⭘Ⲵ᧝᧝㖞

ᐼᵋ㌫㔏䗃ᆼޘ༽⧠᧗䗃Ԕ㌫㔏䰝⧟Ր

E RsCE R C GsGcsRGCRG>Gcs G

മ 㖞

G KKnnttr࠶ᐞՐ䙂E GsGsasnasn

㐃䃪 R G sasnasna asnasnasKGE snasnnasnanKr

ഐ↔㋮ᓖ㾱≲儈Ⲵᘛ䙏䲿ࣘ㌫㔏ˈ㓿ᑨ䟷⭘᧝㖞asnasnasK sssasnasnaKa

䟷⭘䱴 㖞᧝ᇎ䍘っっ䈟Ⲵ≲asKG G KK

࠶᧝ᶕ㘳㲁ֻ㌫㔏ྱമ6Ͳ28ᡰ⽪

ㅹՐമമѝ ᱟ䱴Ⲵ㖞ṑ↓DŽ㌫㔏ㅹ䙏മӽਚᴹањ〟⧟㢲DŽሶമ6-⽪㌫㔏Ѫമ6-29ᡰ⽪Ⲵㅹঅս䍏侸Ⲵީර

ㅹঅս䍏侸㌫㔏ᔰ⧟CGCGcGGRG

മ ㅹ㌫ǃሩᢠⲴ 㺕ሩҾᢠⲴ㺕᧗ 㖞֌⭘ᴹᒢᢠⲴ㌫㔏㔃ᶴമമ²ᡰമ ᒢᢠⲴ㖞

GG G˄cঅ㓟࠶䶐എ䐟Ⲵ䇮䇑ᶕ䗮ഠ᧝⭘ Ⲵᒢᢠ㺕㻵㖞⧠ᢠ㔏䗃࠶Ⲵн 䶎⌅ֻᒢᢠ䘋㹼㺕Ⲵ㌫㔏㔃ྱമˉᡰ⽪മЬᇊ᧝ᶕⲴ䰝ਸഎ䐟Ⲵ⢩ᖱཊ亩ᇊᶑ⧠㾱≲䇮䇑Gcsˈᢠ䘋㹼㺕

䀓㺕ᇊᒢᢠѪ䱦䏳֌⭘ˈਚ㾱ਆቡਟԕ䗮っᘱ㺕DŽᒢᢠᡰᕅ䎧Ⲵっᘱ䈟ᐞѪ䴦eNeNぜ⟦⾪ ∅㓿⟦ᔱ⾪䬤㓿

ѫ㾱⣦ᘱ侸⣦ᘱ㿲⍻ಘᴹ⭼䗃ޕǃᴹ⭼䗃Ⲵっᇊᙗᵾ䳵䈪ཛㅜҼ⌅ǃ⣦オ䰤 i x it x i x it C R L L LeR Rx cRcRLL ec C а㡜ᖒ˖ Xമ9-7㌫㔏㔃

ሿ㔃˖ķᢺ䗃ޕ᧝䗃࠶Ⲵ᧗᧝䗷〻࠶ᡀҶєњ⭧ᗤ࠶ᯯ᧝ぁ≸⣬ᘷグ䰪㺞䗴㤕 W y ǃ«ǃy

x utt ቡਟ⺞ᇊ㌫㔏Ⲵ㹼 a ax 䘹ਆ⣦ᘱਈn y y yn

˄9-Ǻ ㌫㔏㔃മമ⽪üü㜭᧗ᖒ

㌫㔏Ⲵ㔃മѝਚᴹ⌅ֻಘᆼޘ⭡䇑⁑ഐ ৸〠Ѫ䇑ynay a ay x

һ㘳㲁⭘л᧝ᑨᗞ࠶ᯯ᧝〻᧿䘠Ⲵ㌫ xny ay ay

na

nay yaxna anxanx x 䗃ޕѪXˈ䗃࠶Ѫ\ x

X 䈅≲㌫㔏Ⲵ⣦ x

üü㜭㿲㿴㤳䀓 x y y x

x x

xx മ9-4ֻ9-3㌫㔏Ⲵ㔃

ynay a a x

an aann

ay * Y

X x U a ansan

bY snaa

asU y y Y U

YsbY xsnasn as

x

Y bY X xynay a a

y X

üü㜭᧗㿴㤳 x ሩ䀂ᖒ⣦ᘱオ䰤㺘䗮 x

b bsX G x an asa

* ky X

s s ssީѝ˖kiLGsssiީ x Ԕ˖; usѪㅜiњᘱਈⲴਈᦒ x

ss ণਆX

; us x s ax sX sX u ; us sX sX us y sXn snXns ;

ss

us∿ sX

Ѯֻ.䇮㌫㔏ⲴՐ䙂sX GX s 䀓⭡⢩ᯯ᧝〻XnsnXn

x x x x G

kOLPGs

kLGs

n

nn ysGsu

kOLPGsx x u yk k s

X X y n

yk

axaxanxnbubཊ䗃ޕͲཊ䗃㌫ axaxaxbubn pxnanxanxannxnbnuമ9Ͳ6ཊਈ䟿㌫

uupyy

Ѫ⣦ᘱਈ䟿˗Ѫ䗃ޕ䟿˗Ѫ䗃aabnbnaabnbnnn

䗃࠶ਈ䟿〻ycxcxcnxndupupycxcxcnxndud&yx=P&yx=Px=Ax+x= d & qഋǃ䙂࠶᧝⸙㌱㔕⣬ᘷᯯ᧝

X BUY >C DU ᇐѿՖ䙈⸟䱫 G C

sI

˄9-GsCDGMsIABDCDGMsIABsI

һ‡䇮㌫㔏Ⲵࣘᘱ〻Axxu⢯ᖷぁ x x uy x y x䈅≲䈕㌫㔏ⲴՐ䙂⸙䱥sss䀓 G CsIAsss CP>P(VIAP

һ䇮㌫㔏Ⲵ⣦ᘱᯯ᧝〻

䀓㌱㔕ぁ A b _sIA_det 䈅≲㌫㔏Ⲵ⢩ᖱᯯ᧝

_sIA_ һo ѻ㌫㔏䘋㹼ḷo㌫

䀓

xx x x

䈅≲ਈᦒ㌫㔏Ⲵ⢩ᖱ〻⢩ᖱӄǃ㓯ᙗᇊᑨ㌫㔏⣦ᘱᯯ᧝〻Ⲵx b bb⢩ᖱ ˈˈx b bb⢩ᖱ ˈˈ Ak HAtѪQhQ⸙䱥ˈ〠⸙䱥DŽҾᱟ⅑⣦ᘱᯯ᧝〻Ⲵ䀓

x ˄9-∿䘶ਈᦒxH$tx L> xH$t

≲䀓-

H > Ax Ax ˄9-sI L> sI L> Akt ᴰ㓸ᗇ ⣦䖜〫䱥

ᴹԕлᙗ䍘xH$xH$tt

ttt оа䀓⌅ᡰᗇ㔃а㠤

>t ᙗ䍘 䇮㌫㔏Ⲵ⣦ᘱᯯ᧝〻x x

x മ9-8⣦ᘱ䖜〫

䈅≲⣦ᘱ䖜〫⸙䱥䀓 A Akt

һ䇮㌫㔏⣦ᘱᯯ᧝〻k A t tt

ਥԛߏぁ䀙

xt t

䈅≲⣦ᘱᯯ᧝〻Ⲵ䀓xt

䀓 ⭞᧝≅᧝ᦘ≸䀙Ⱦݾ≸࠶⸟䱫ሼрᕅ䘑㺂᧝≅䘼sIA HAtL>sIA@

HtH HtHts H H H H sIsIADGMssI

ete

ete s

xteAt e e e et 䶎喀⅑⣦ᘱᯯ᧝

tHAtHAtx HAIJBuGx Axx Ax Bux Ax Bu

⭞H ᐜҎрᕅњxHAttHxHAttHAtBu t(9- x ĭt BuGxtHAt HAtxtHAt HAtIJIJG VxV Ax Bu x VIA᧝≅䘼

VIABu ᴶx />VIA />VIABuVᴶ HA />V ⭧ভ〥t

x HAt HAIJBu IJGL>s Bus HA(tIJ)BuGһ

䀓

>VI

x LsIA᧗᧝䟿Ѫ䱦 HtH HtHtH H H Ht H HtHAIJBu G H H

㏯ᕗ㈫㐏⮴टᣗᕗ়ट㻲ぁᶛ㺞⽰ H HW ⣬ᘷグ䰪⌋ѣθሯ㌱㔕Ⲻᨅ䘦ਥ⭧⣬ぁᶛ㺞⽰x W

HWH ⣬ᘷぁᱥᨅ䘦⭧䗉ޛခ⣬ᘷᡶᕋ䎭Ⲻ⣬ᘷⲺχ䗉ぁᱥᨅ ⭧ӄ⣬ᘷ㙂ᕋ䎭䗉 ခ⣬ᘷѰ䴬 H Htx HtH

ੜ㜳᧝᧝⣬ᘷⲺ᧝ૂĆĆć⣬ᘷⲺ᧝ૂ㜳ੜ⭧䗉࠶ૂ᱖࠶ᶛĆĆ䘏њ䰤从аǃྱ䇶

㊩ቊ亵+DPLOWRQ&D\OH\&D\OH\ 䇴$ᱥQhQ⸟ [ᱥQh䠅喆⅗ぁ

af a˄9-

n㤕 㤕

˄9-˄˄9-ᓄ⭘&D\OH\+DPLOWRQ aa a k 䀓A A A ᶕ㺘⽪ ⸙䱥$Ⲵ⢩ᖱཊ亩

HA

A ˄9-k

_ A A

UDQN>b

A Anb@ A A ᵢ从

Ⲻ࠶ݻᗻ㾷ᶗԬᱥφᆎ᧝t

˄9- 䶔ྱᔸȾ䘏䠂$hQEQhҼǃ㓯ᙗ㌫㔏Ⲵ⇿њ᧝᧝⣦ᘱxt䖜〫᧝ttfⲴਖаԫ⣦ᘱt᧝〠↔㌫㔏

Ҽ㔤㌫㔏⣦ᘱ䖜〫䗷〻ྱമᡰമ9-㤕ሩԫ᧝⣦ᘱxt᧝ањᴹ tftૂമ9-䟿utˈ㜭᧝tfᯯ᧝᧝ሶ⣦ᘱx 䖜᧝᧝↔㌫㔏 ঋ䠅㓵ᙝᇐᑮ㌱ A b ˄9- c d ˄9- 㤕 ᡀ・᧝䶒߶ྱ⸕䇶Ⲵ⨶W!ˈ֯ W⸙䱥䶎ྱᔲਆWѣ$QhQE hQ Ⲵ WI㌱㔕ਥⲺݻᗻ㾷

u bTHAT t

>xHAtfx(9-

ሶX (9-IJIJ%X

ᗵ㾱ခᇐ㌱㔕⭧Ա᧝᧝⣬ᘷ㻡᧝᧝᧝䴬⣬ᘷθ᧝IခtH$t H$tIJ%XIJGx HAt HAtb^bT t>xHAtxtHAtxHAtHAbbTHA tfxG

t HAbu ˄9-tHAtHAbbTHA tfHAtxG

ṯᦤ HAtxHAt HAtHAt

t

A

mu㌱㔕

A t muG t Ambu ㌫㔏

x

uuᴹ b Abᴹu

PcbAbA ㌫㔏㓖ᖃරᯯ᧝〻⭧䶘䇞䇰ਥ⸛θㅿԭᦘуਥᙝȾ

ଙନݨ ķа⢩ᖱሩᓄⲴ㓖ᖃඇਚᴹаඇˈণ㓖ᖃඇⲴ⢩ᖱнDŽĸ⇿а㓖ᖃඇᴰа㹼ˈᡰሩᓄⲴEѝⲴݳ㍐нѪ䴦DŽ䘉аݵᗵ㾱ᶑԦ৸〠Ѫঅ䗃ޕ㌫㔏㓖ᖃᖒ〻Ⲵਟ᧗ᙗ 䀓㌫㔏⣦ᘱᯯ᧝ ഐѪ$䱥ᴹєњ㓖

ⲴEѝⲴݳ b

EE᧝нѪ䴦ഐ↔㌫㔏ྱ ᙝ⸟䱫Ⲻྱ ᙝ⸟䱫Ⲻ⌋ b b

EE䈅⺞ᇊ㌫㔏

ᓄ┑䏣жѠ䗉ޛ㌱㔕

ሩҾа㡜Ⲵঅ䗃ޕQ㔤ᘱEX㌱㔕жᇐਥл䶒㔉ਈᦒ⸙䱥ķ䇑㇇ਟ᧗ᙗ⸙䱥ĸ䇑㇇S-1ˈᒦ䇠S-1Ⲵᴰа㹼ѪKDŽĹᶴ䙐Pĺһ

㤕Q㔤অ䗃ޕ㌫㔏ਟ᧗ˈᆈਟ䘶㓯䀓ݸਟ᧗ᙗˈ䇑㇇ਈᦒ⸙䱥ˈሶ⣦ᘱ[SGAbA䈅ሶ㌫㔏⣦ᘱ〻 аᇊਟሶᆳ↔ḷ߶ᖒѝⲴ㌫㔏⸙䱥Ⲵᴰа㹼㌫ቡᱟ$ A= h P b=Pb ㌫㔏ᯯ᧝ਟ᧗ᙗ䘋㹼࠶㌫㔏ਟ᧗ˈਟ䙊䗷ਟ䘶㓯

Ⲵਟ᧗ᙗ⸙ ˅ˈᆈ 䱥3ˈ֯ᗇਈᦒⲴ㌫㔏〻⧠⹄ウнਟ᧗Ⲵߥˈ䘉