Report Control System - Chibum Lee:3. A block diagram 0 1' a servo system for Illotion control is...

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< Report > Control System Homework 6 L Ohtain the se tìme peak time , maxÎU1UUl overs Ìloot , aJlCl the settlìng time in the unÎì step response of a dosed 100p gíven by 1' (8) R( .s) + + :36 = .ì_ j = 36 = = \ 6' e_c '--' Wd ;:$1(_ G) M f = e - = 0 ‘s- gg _2_i( r

Transcript of Report Control System - Chibum Lee:3. A block diagram 0 1' a servo system for Illotion control is...

Page 1: Report Control System - Chibum Lee:3. A block diagram 0 1' a servo system for Illotion control is 8ho、vn Ín t.he Fìgure below: D(s) rτ뀐r깐깐원'h씩l“뻐e쩌때}까깨센따p)짜뻐1;

< Report >

Control System Homework 6

L Ohtain the rÌse tìme ‘ peak time, maxÎU1UUl oversÌloot , aJlCl the settlìng time in the unÎì step response

of a dosed 100p sy잉tmn gíven by

1'(8) 3상

R(.s) s강 + 깅.5 + :36

_}ζ띠씨 = .ì_ j ω 'ý).J_ = 36

ω Yì =b ) ~=끌 • ωd=ω짜=환 =J꿇 11

CDtγ= 뜯뷰 = χ←뀔녕 = 0 껴츄 ξec ~V나 ~ J엎드

(3')十,...,==- 주드==: --;:죠- 디‘];.3 \ 6' e_c '--' '-γ Wd ,, ) 2,료

;:$1(_

G) Mf = e -Jl-딪퓨 = 0 ‘s-gg

않늄은£뚫 =4 않ζ 훤양 _2_i( αa샘ói/l

뇨잊꿇 r £ rηζ }、。 f 틀 사 앙j 씌 bνq

Nscl
텍스트 상자
4
Nscl
스티커 노트
Nscl에 의해 설정된 Unmarked
Page 2: Report Control System - Chibum Lee:3. A block diagram 0 1' a servo system for Illotion control is 8ho、vn Ín t.he Fìgure below: D(s) rτ뀐r깐깐원'h씩l“뻐e쩌때}까깨센따p)짜뻐1;

Stsp Re,s:p:onse 1 ξ

0.\5

‘ 2:

원 그 른 다 g갖

o 찢

0.2

용 1) 2' ~

..,.."J ;; .5 r、

℃‘

τïme (s:ec)

Picture 1. problem 1; the step response & Transient-Response Specifications

( ‘ ι

Page 3: Report Control System - Chibum Lee:3. A block diagram 0 1' a servo system for Illotion control is 8ho、vn Ín t.he Fìgure below: D(s) rτ뀐r깐깐원'h씩l“뻐e쩌때}까깨센따p)짜뻐1;

4상 l ξ 헌\ 1 먹 l석 휴I젓L 8}ε+ε꺼 펴fY영S:F()Y)Q드슬 」꺼프숭 ~션 /'01다

:S C d σVWl Vv1.완 γ-o.+-lD) 7• 。 이 l져 l자。1 향으효 (/v'V\de;vφVW\(fε건 &>ε봐n 의 름영즐

동앤쏟수해각 규TJWl혹BV\누 V'eSFYìSE려~ OVI아납LùOt* 二ìj)__ !흐수쩔꺼기~~,

LVd:::j똥=ζ‘익 Ib ycJ/S위 쟁수 즉/ 1 ‘ oμ8eC위추71흐 깅황뜯 혐e까 야싼ct­O\I6'V야하71- 용 뺑 ↓규능e 과Yle(七사。 I 비파갖 때냥 깃흔 불 4- Zlq-련! l즘 통화111 l;W\d?x-d뼈Fd 당ß~켜 얘ne-do씨(À(/I'\히|썩 응흉록영를 .É,~격돈츄 %입마 뽕11이써 쉰l갤납받 빠w!E;(c싹:_Ye.뺀ý).훈 뿌eεr감하융Y)S 즉/ γ=rse 十싸,ε4- peOvk: -}-ι11ζ )'V)(Î\)짜ηψY}y Ò vc;?;γ&'hò。十 씩ll. 0하f) 야끼깝 +과le 을

쥬적을 통해 일ξ g밟 J..)1I몬띠에 일웅 강똘 ~1ii2챔gL더이 장형l μt용없다 ζ}한 _çe;뮤l쩌폐e려 용운 수적증 8VIV9l댁==>-PCA끼C+lC>Yî으흐분분1 승4시칸강~6\~71 램이| 쐐흥 장에석 쭉e혈 활!강 낌1;zj:z~ 다-i ~\7 1--- 해껴야기 ðtÀ\안 P빡£쇼쩔:쳐-0)0)꺼 혐흉파억l 혜행吃 짧1.7t- _2!씨프 장애써 썽l 0Yi녕@η 빙회 에뇨 응후。l 할11C 關슬 표훤경r1 <9L↑형 I z,야씩을 후 ~ 호까l 영첼둥 쥬~\ 않풍 갯。Izr~ ~녔을 찾능쥬 갖~다 ,

「‘ J

Page 4: Report Control System - Chibum Lee:3. A block diagram 0 1' a servo system for Illotion control is 8ho、vn Ín t.he Fìgure below: D(s) rτ뀐r깐깐원'h씩l“뻐e쩌때}까깨센따p)짜뻐1;

2. COIlsider (l system wÌ1Îch Îs described by thc transfer fUllction

G{s) = 1 (잔 + :J8 + 2)(s2 + 1008 + 100(1 ) ‘

(a) Find the order of the s랜t잉m

(b) vVrÍte down thc m st two dorninaut m패es λ1 and 서 of the sysr ern ‘

(c) Lct us approxÌI빠o the tra때31' function G( s) hy 01 (s) = (S 시;9 A2) where A1 mld λ:2 a"따ho

two 따minant Illod잇 없1d C 싫 야}C써en such tl떼 0 1 (.10) = (;ω0). UsÎI웹 't\1ATLAB, find the step

responses of G(8) and 01 (8) ‘ ( 치:>mparc t hc plots and conllne따 on t henl ‘

4깨Om7h얘ηy : (<s휴δS十l) l<s노[(}ì)<s十 (rJOül )

뻐뻐e_ ~빡뀐뺑heSt-하S앙← po。ω써0y- \!ìI) 1바~늄h벼e 어 eγ까!)I'r'ν빼’ ‘ 터승) ~ 4배 Oydeγ S썩-:eMî

(s휴농-r-l)(S뇨 lõlJs 十 /00이)==- (s十 I)CÇ十_J_)(ç十bO-86. G1Ó)(하SD十 86 ,{y Id)

“ pc>te{?) = -) _) -lJ-to土 8~.bl서

융 J싸v\αtt\- po \없 -μ -; [ ‘ 나ìe n8αvY8콰 +-Wo po\es 서 나ιJω 않)

: λ l二 -l l λ_:)_= -1 (ay λ = -~ . Àl= -\ )

GI(S) = • C; I (")D) = 두 Cs十 1)(5+까 ι ._.L

~(J이= 주길g = G ‘(00)= 중

C

l. \ ‘ C 二 -

_2_() O야 167Jl) I ”

l~) 츄

λ :::.-}_ (þ) λ :::.-) , )\;:;__:::. ,- ' .J

y\(jD이 α) G , c성 二 (S-H) Cs十괴

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Page 5: Report Control System - Chibum Lee:3. A block diagram 0 1' a servo system for Illotion control is 8ho、vn Ín t.he Fìgure below: D(s) rτ뀐r깐깐원'h씩l“뻐e쩌때}까깨센따p)짜뻐1;

Fα ’ 6-ZeTÛ' MB.p ↑양양 r 4''\: ~.앙 ’ ‘ ’ -"- - - ~-

f、、 --“‘ ι _[.t짧 :ι ‘- --호강8- --o:;Z O.1f! 0폈 , eo f- -' ---•,; .. ,\.-.、、‘、 、、 ’、 : 성g;

---_ &'~. '::--

영〉까찢

-(」πt-@mE

셔흉8 •’‘ - 지:← i ‘"‘- - 、~ - ,’- - - - --ι-- --L- -」’ 꼈()~ _ c. - ')0、、“

캘꿇ι l ’. -1} 짧:、- ‘젠챔 o강 G.12 0α§ .. -,f - _ __ ’ -_ .1

-ε양 -정쳤 -3Ð -2앙

.Reial .ÄXÎs

-10 양 -Hl

Picture 2. problem 2- (8); The Pole-Zero Map & Dominant Poles

F h ‘ )

Page 6: Report Control System - Chibum Lee:3. A block diagram 0 1' a servo system for Illotion control is 8ho、vn Ín t.he Fìgure below: D(s) rτ뀐r깐깐원'h씩l“뻐e쩌때}까깨센따p)짜뻐1;

x ζ

d ‘

Step ReSipOflSe

앙 !S

L ‘ cιι

‘‘

3

흑르<D εg Q.

흘 “2'

i S

() & ? ',. : ‘; ö

~

?

τíme {scec ,Ì

Picture 3. problem 2-(C); The step responses of G(s) and Gl(s)

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Page 7: Report Control System - Chibum Lee:3. A block diagram 0 1' a servo system for Illotion control is 8ho、vn Ín t.he Fìgure below: D(s) rτ뀐r깐깐원'h씩l“뻐e쩌때}까깨센따p)짜뻐1;

;< 1g i Step Re.s:pcnse

찢용6?

4.98깡g

1---.---_._ - --

월 4 繼§융

f; •----εL

를 ." 4 ,00옳# |=;l 4,9862

4.~

6.SS7E >3.557B 6.65:5 ê 용5.&2 6.5ε84 6‘B500 5 .6ξæ 6.S-58 B.S당'1;i.

Ti01e (sec)

Picture 3- 1. problem 2-(C) ; The step responses of G(s) and G 1(s)

」낌 3익에 GCs) 1J누Gt센킥 와'er 파\PUvt며 에캉 둥힘ο 1 fJ,짝 81"*,향증

앙수 잉다 를위 _;z\에총 3기 증)핵 합ζ{/\한 4째프7~ 7) 2'63-\ cl아 _ì.~δ-\ 익|역 릎수 %동。 l 증텅 κ|경띠| 혜한 G,Cs)와 GICS)박 _:l기채 l7!--

ζ↓12특 O‘000.2. x 10펴 컸정짧애 아지 않황

증/ 운껴능 과차 지스e잉 ~섭능 ι0~/~짧 GìICS)'Ö:호 용념t역 생ZS찾L춘 %Al야

6J, C정능 옆σ1에 doVYWVì때+ po\es훌 껴~1 .2. -t잉한 8)<5-I-twvJ 0 \아 (!:~μl dose-LÖOp 8)εtE?JVVl 의 +γ<NV\S'{e-싸 Y양PQÝ)ôe- beVlOV1.Xσγσ11 do pì vnovvf fol eS커 영똥이 치8'V(앙셔눈 찢등 효컨L철수 akζγ

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Page 8: Report Control System - Chibum Lee:3. A block diagram 0 1' a servo system for Illotion control is 8ho、vn Ín t.he Fìgure below: D(s) rτ뀐r깐깐원'h씩l“뻐e쩌때}까깨센따p)짜뻐1;

:3. A block diagram 0 1' a servo system for Illotion control is 8ho、vn Ín t.he Fìgure below:

D(s )

rτ뀐r깐깐원'h씩l“뻐e쩌때}까깨p센따)1짜뻐1;

、찌、、Y‘{앙앙 、will dütflrτ1mn안 the‘ 、v(λ써11tH‘es of‘ k, kl and kd

(a) DetenllÍIπ the trans엎feαr’ func떠:

(h매) Deh‘ern‘nl너1Ìne the tn‘~(.t씨t

E(드.) = ~(s) - \C5:) _ -,

다ι〕 二 κ\l~)e(s) 二 κ,(;드) \ R(~) - y(_ç)이 까ls) = 다(&) 十 Dζ) - k_)_~)‘,\cζj

= \<\(s) ~ (S) - [\<1 C의十ιιjJ \G=_)十 Dc~) Ycs-) = 61설〕 ‘ UtLS)

= G\Cs). k\ c&"} \<[9 - Gt~) [κlC~)+ 타(s:)그 h드) 十 6)(,ζj -Dc온)

YCS) = Gì(5) \<,(-. RC0 +ìc'* ‘ Dc캉 1+ G,(ç)k,여+6야 μs) \十 G)(S) μ ci) -t ~(S) ~.L(s)

T(l,,} :::: 효?- = G@μ c>) ~~/ f\여 l十GCSJμ~十G,U)k1강

브κl

s~ζ1<<s+( j_十없)$악드ι| ν

"CCc안 k, C킹 -k여 = ---; =

R잉 \+허양 ~(꾀허)(~~C9

klSff 그εrS

흙$h;:κι홉~)s-+st~ 1 ι

[

Page 9: Report Control System - Chibum Lee:3. A block diagram 0 1' a servo system for Illotion control is 8ho、vn Ín t.he Fìgure below: D(s) rτ뀐r깐깐원'h씩l“뻐e쩌때}까깨센따p)짜뻐1;

(c샤‘) De야t(:쩌n:n비lnü샤t,he c써‘.:11a써u:ac샀1'18쩨t’; 1G‘ po야’

y퍼) . A이{뱅i섭ju얀였s았‘;t t he pa값nuneter않s k , k나 and ktt 80 that the characteristic polynomial 0 1' the dosed loop

sv션tem Ìs

,,3 ÷ 2혜8+2ω삶 + 쇄

(d) DctcrmÍne the cont떠 pa.rameters for ω0 = 5‘

( e ) S illlulate USiI앵 MATLAB , the step respoIlse 0 1' the open and closed loop systerns (Hillt : You mi얄ht

need to use the funetiolls stcp, 'f, and plot. You can 삼 n셔 씨bout them by typing help .step, help ~f

anι1 hclp plot at. thc MATLAB prompt)

、 드~\ 1(5) 二

ι ‘s육퇴ζ능-t-(ì션μdfiL.十흐μ!

흥t-~+(마s\'셋확드kí:= 응S十 ll(b칸S十 4띠sε \- 띠i녁 4누 강}김 = .. 2JÅ)o / 료\<-:::-_lωζ/ 효k\ 二 ω암

.td-二 울 (ω。 -l ) J k= 융ωζ l κ1= 숨「 ωf y

7믿/ ω。=-5 .1 -t-hEWì \<(닌 = 도 l κ =- lD ) ιl::: ~료 4

\<-C~)

\O\C)SB -=

-r lopÐV\

l 十 T=re;이

Tcl~e. l그뇨

'ícsj

\ll ’‘ T "r- \- T니~e - S휴l넓표ζ十↓£ 냥xξ ‘S욕~l 밟슨누~

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(/

Page 10: Report Control System - Chibum Lee:3. A block diagram 0 1' a servo system for Illotion control is 8ho、vn Ín t.he Fìgure below: D(s) rτ뀐r깐깐원'h씩l“뻐e쩌때}까깨센따p)짜뻐1;

St~ Res:p.onse " ι ‘

양던를-a ξt

1.8

1.6

1 쩍 --- c싸s'e-locpSy‘§ 연c)

-- open-:I。δp Sys (To)

+ y =lr“’. LapJaceπ'o'Ul 1 ε

‘J.8

0.6

1.5 2 2,5 3 -‘

i g

{ Y V i .., -4 ,5 -ι

‘ r

τìOle {s:ecì

Picture 4. problem 3-(e); The step responses

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Page 11: Report Control System - Chibum Lee:3. A block diagram 0 1' a servo system for Illotion control is 8ho、vn Ín t.he Fìgure below: D(s) rτ뀐r깐깐원'h씩l“뻐e쩌때}까깨센따p)짜뻐1;

4낌때|적 퍼면 디。흥'-\ÕOf ~혔B'V1I1픽 S궐fYQS뿌일슬 함ζ)량수 하아 yTst:_ t과y\e_ 0 l 잭 0 ↑호 정한12 , P효oJ-_ +τ애e ð \ 얘 l 초가풍。|썩 α@파。0+능 ζ4↑짝 10;." 렁흐려 十YQv'v허eνl十 릉/성풍 냥。1 0\ I 역 l -t접해7년 기Qξ 휠잉강1'%4

뺀I DpBlv1- \öof> ~γs닝v1 즉/ 우eed \。σck- c I 없fι 쟁객싹l -r찾1- S썩0yv\허 S껴f YßSpo~se승 밟올 얘 특정굉1/0")\ 수경ò}슨; 찢'\ ó~~十 πwvp환쯤1영 특강거룡7놓 7vl1?_ 전행갖으흐 증7(승}승 헝Eν1조 니당싼ι 깅냥'"\ ~d←을 형용,vr..-z\ 앓연 Sys하”ξ RePeγ9r1ce 형 nα4를 강싹껴 흥하i 됐해써성흔 양수 껴~~까 a싸?치 악 용츄능 d∞ξ4∞y (;。이.~Qy라-etv얻을L킬껴懶1 싸짧능 깃。l 찍책항효 강 츄 ~q-

아한/ 찾7t커 으{ξ쳐*중 씨AT버g쥐1<1 ’~+er l황수슬샤용쐐 <s+er V@ÇfDVlse효

화잉해등wv) ~Q"ëvl+ 특성01 핸싸깃l 찮았다 μ1.0슬옮끼 ξ렴 깨VO/XSξ 냐F‘@ ₩vY1S.~ðψ키 4깜Vle-dovYì에힘써 。썩끼_[∞P~ε녕1에킥 낭낭r ~빡1잉슬 휴þ! p\o뷰a、11핵뀔양아 6 \ 체능 초I 0ιO. j__탑호싸|머쩌 +γM리ént 록엉아 뻐V야오 ~ 01류흐능 ti형깅ξ흐 썽냥뜰 강f짧아 4셔요 '-s;+ep철수슬 자청f켜 랩느 결쐐화 θjJEö벼 o‘4줬흐 ζ↓1밤~j_링 특성듬 과양아 양영| 등링캉 씬E흥힘슐 p!。뀌l썽을칸깃양G1\ 1-꺼 }<\--o 17~ 뱉j갱、높| 의용kι「

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