Kontrol Sistemlerinin Gecici ve Surekli Hal Davrani lari, Hata ( Sapma) Analizi. 5.3 Ikinci dereceden sistemlere ucuncii kutbun ve sifirin etkisi

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1 Behind Boliim Kontrol Sistemlerinin Gecici ve Surekli Hal Davrani lari, Hata ( Sapma) Analizi 5.1 Zaman yaniti ve test i aretleri 5.2 Birinci ve ikinci dereceden sistemler 5.3 Ikinci dereceden sistemlere ucuncii kutbun ve sifirin etkisi 5.4 Hata ( Sapma) isareti analizi, Surekli hal hatasi 5.5 Bozucu ve giirultii i aretleri analizi 5.6 Gecici hal coziimii kontrolii 5.7 Duyarhk analizi 5.8 Davranis indeksleri 5.9 Tasanm ornekleri

3 Ikinci dereceden sistemlere ucuncii kutbun ve sifirin etkisi 5.

2 5.1 Zaman yaniti ve test isaretleri Siirekli sistemlerin zaman yamti " Konfrol s/sfeffl/erwde. tisa&it dawa/iwwa &/> dâg/^/n/ms qenejjflde sa/aa/f yanrfi i!/2 r/ndw yayj/zr, y/rk i/z Jfa/zM Zamanw fo/ikt/ytm tfordc karsdasardjr. y/rj/rf /Jr/h// da/i o/u&yiajjaj/r ; gedcaaiaa yaa/a/ ve sure/a/ Aa/ yaa/ y^jf) ). SJsiem ya/)/t y/aj=yjb- yji) oaar. (jec/ci ha/ yan/t/, zaata/t J/er/edice,ya/?/A/? i///ra y//a o/arak Amm/awr ; I/a? y//j=o 5>urakl/ AaAya/J/fj m, yasp/frs? <y riye kah/? AvsMok/r. 7a/7 h/rhôl s/saemaer/nde g&da AaA a&r/raa/saar/yaa A&/?>/ Aa/e ms/j/nedey? focz tejzag/? yaa/a/aez zssa&n <u /s/#ras/ $ap/na (hata) Au>nhA aafc/mea/abr. C/kwa sartkk A a/' ya referanz y/r/$j He ayu$/tja/a/y//7/aa at? s/sfanak karar// olu$ur. Jd$ar//r?a/a d&y&r/etfd/r/ne y&)c/\/ sorf&kf/ Aa y/tre yap/hak1ddr Orneksel test isaretleri Tatar/a? proafe/v/fide, aaaa/2 m, ai/ra/vu Ad?y/& at/s/zia/aa, say/da t'ragkw Aesky/r/s /&r<ef/ /Ae yea/j 7d$ar//r?a/a, darraa/z Ar/AerAer/ Aa A?sfA&rÂAer/! cfafaa ve dsa?/x Aa Ar/AerAer jtayatfatfark ^//afe d/j&rjb/i/r*

(jec/ci ha/ yan/t/, zaata/t J/er/edice,ya/?/A/? i///ra y//a o/arak Amm/awr ; I/a? y//j=o 5>urakl/ AaAya/J/fj m, yasp/frs? <y riye kah/? AvsMok/r.

3 Bit /s#ret/er : a) &asamak FfajbsyMU olarak -janm/a/i/r ( rfr) = ft uff)) h) kampa FwksiyMU.) ftarauik Fonh/yon H9 Btd) 2 o -/ (1/z kafsay/s/ has/////: vedav/y/? ejetfh/v/sth Bj/ai/w/

4 5.2 Birinci ve ikinci dereceden sistemler 6/rinci Jtrecede* T/sJ= K/(s+)>) timknak fi/nas/aatiafe, J?/r//n basarnak r(k)=#fk) giris//j ///s/b/) e/k/s, dlttr. T= 1/p s/s/g/h/r? ^a/wan sab/fi'dr. 7~2/?/»a/r zamh/n kikftktoes/ yff) t/k/s. btiyiik/ yii/?ii/i k/2fa smakger/fie is/at/m ydacar. i r^k^> y&ri ys>l hnfre>/ e/i/yian/an seiarak y/k) </hs//j//? /kind d0r c d&? kmlko/ s/s/&n/eri ate, yarar/finarak, 3 vi 2. yum 1 -i t

/»a/r zamh/n kikftktoes/ yff) t/k/s. btiyiik/ yii/?ii/i k/2fa smakger/fie is/at/m ydacar.

5 degerkrine yore y/aj W d/sgf/z/m/ asaq/afa ^A>s farilm/slir. Bis atfyisi/ne. i/ifjhi/t ofieat// Aim/fa/)//nfrrd&rf/ah iw//e&6fir.

6 fee/km za/na/7/ Z/ C/k$/a son t/eyer/m %5V we i/hpnsaya ka Ver/esm/ciftirata) za/ha/?/ 7^: son//^/m bm i)r ywewz #e/n?es/ /oo deferis/adzka/aas/fewyecar? za/^anoeki/ok % YifkseJ/ne za/nan/ ~ ' son a/eqerws) %10 'uxdan %9 j/ia ymset y cen za/na/j B>/r_ fanfro/ S/stito//i z/k/s/n/n /basamak g/r/sj /</n ) M he/k say/amas/ /sf&iir : 4) Kaytik as/m b) kdci/k yl/ksg/nie 2a/va/?/ c) k/f^dk gedk/ne 2a/va/)/ of) Kliaiik yer/es/m 2a/na/i/ Bu arada, r(rl- y(/j = /k) l/e kaa/m/aaaa 5a/>/xa yaadkafa kklik ka/masf ama^/annoakkaa//r(3/>-hifarhafa*jnfita//atja9& /fifpgra///?//?m/n/m///n yay>/fotawabr: I=/fe&)ldt Mni/nu/ Uygu/a/vada 7~ yer/es/ne suresi, sonafef&y/f 2% a /y/y/& ka/ tekilde. be/jrlen/r. bu da y*k/auk 0/arak $onaa//w vzrjr. 7~. son deferm s- % V /c/aa/e kafosak sek/zt/ % as//n _ swum a/-**/ (kafazy/s/) kak/a ve. kasakfer/d/k/eri btt/t/ttmak/ad/r. % OSM- Atk/eSX ( /k/sity t/er&z&ifaa s/'s/kav/zr ) f O f 0 0,t 0,7-0,6 0, 0,$ %a?»t O.Z 16 *tk> es #,3 25,*/ S?2

7 AS/JH 0 0,1 0,2.0,1 Of, OS o.c o*.1 Or nek: 3/r hkhl s/shain/n W/- WAV^^/J olarak Vi/ilmMtr. Bir bteaiviak girly/ie. ikd/n, smmsoz fe^tyzr (<ke$a/ tmm/nekaas/, SMU/H era/?/, ohtma 2aman/, O^/M daman/ < awtf ky*) ek^e tf t /(s\2f%s+& ) k/o/ninjen f {*. 1. kazajk) : {tfvntfa 2*/»an/ Z a _il = -A =oss (%z /c/#) Mim(-fye)degerj M (%) *a Xiao = e xioo=2*>,i% Ornek l\[>/ ; s/stern/ni as/m s%, yer/esme za/nam (y#2des/ 2%) 4sanJyen/n st/h/zdaka- /aa?ksek//de fasar/ay/n/z. iukano/ak/ batf/almon, fa'/tt asm/cit f=o t?&?ayyi//?afane/ffir J - 0,7-0?/C)/J ku = l//},?o?=:\kzo/i/r. $Mffc o>/arak / K=w*= 2., yb=2<foij =2 o>//va//okr.

$kazajk) : {tfvntfa 2*/»an/ Z a _il = -A =oss (%z /c/#) Mim(-fye)degerj M (%) *a Xiao = e xioo=2*>,i% Ornek l\[>/ ; s/stern/ni as/m s%, yer/esme za/nam$

8 5.3 Ikinci dereceden sistemlere iicuncii kutbun ve sifinn etkisi t/<u#dt afereceafea k/r s/s/zat/a, m=? Jraffsker kowks/yer?a J/e /aw/v/a/tobym/ i/xra?ya///*/( tv n = i ak/aarak mra?a//e^knkm/s^r). <C<a// a?a's//7da Cjk#?&?f, ktsa/aaan ayka/?a?as/ kaj/ko/e / kcama afeszceak* s/srfe*t, aca/?c# reek kalay? efkk/' /k/va/ e^/jgrek, /k//& afefgzesktf s/sfeate yak Josvk a/arak ab*k tf///?#k;//r( kask/a, ab/n/aa/?k, kaiup ha//). Draek /tkfrak, j- 4 5 /</#, s/skk^/n tin/* /as^a/ak y/r/s/ /k/sk/d <z/k/$/ e-j^e. eak/ecat a/a/za, ^= ak/tataf a/a so/rac/a/va ystk/as/k #/arjrk es/k a/aiaarayao^y/ yfr-a/atitf&rf % w$ h>/ny>/ek$- kakxfikarta r kk/sai/ otkwakfi fa/ta kamn red ka/ay> -i/»*-ij2l.2s?*-awt o/a/*ymd*a yttkaru/ak/ yak/as/k//k kesu/a saj/aaata/m/ikfoa//r. 1 Mo ian (*/x* Iff) (f^^) Of&m 127A ve ojarmasunes//2.%ki~ >(T fe/7 /c/#j saa/ye. o/arm ketay>/a/i/ kukuy>/ar//7 kasha a/ma's/ ka/me,k ^key Offer, zrat/yka, 20% v& Wfu/f&fls okarak J?ek/e#»iekfeya'i. $=0,05 a/eqeri (<f/otfs-=z-zo) /// tir ya /as/k//k o/eyer/o/ap, 20s OfS/at o vee-jfiekffmr.

#k;//r( kask/a, ab/n/aa/?k, kaiup ha//). Draek /tkfrak, j- 4 5 /</#, s/skk^/n tin/* /as^a/ak y/r/s/ /k/sk/d <z/k/$/ e-j^e.

9 S/sfejft//? ~fr~a/r$k#r -koaksjyoaamsmka $/kr ka/aaafar/t d& afavra/?/<> kz?/k//k/k yuker c# kr< He a/enll $o/?las/k etk/n httylata yah* /s&, z/fir/an/i efk/s/k kzabr k&zk? s/ kaabr, Bu /tzal&ak / fa$a/7a?/t?a'a k/r J>'a s/tzyee k kal/m/larak #fk/s/ka!ea karka/ua/vas/ y/>/a/ra ytitk ; (PI) * G6) Yes) klaraia samz/ C2%kr/fer/ id*) ASs ve asm ekatakssfomz S/sit/n/a kaca/kaaa?aa isfea$/a. ^i/jz #k//7^^k t/a/sa (a&w yauas/jt o/arak 4-%)< ^kjy^ nya/?/*3t, & *far. [w A s ). bavrew/? ira/rsk*r ke/jkvyma T&, m rr kk fi s^x X ) /fs + A^S ^ ) i/d/h/aaf&l/k s%k z = +2fas+<V*=* J*+ f6s+122 e&w/yi uyay/a^a i K 2 m ize, K ^ 1b a/arott 6e//rUh)r. B/f duramda T ^, %Gt&X*+& filmak/aj/r.. o/arak 6ed/ecek tkvrsa aia 7?s)* o/ur(dc fazaaa 1). 6pCs)*1 Ian a&ai 21% darak 6d/hka/Hev/?e kar&a, ka$j/2y c kalianfkntito hal/adz, bu a/eyer, Meaal/y/ U2&-&, A

ea karka/ua/vas/ y/>/a/ra ytitk ; (PI) * G6) Yes) klaraia samz/ C2%kr/fer/ id*) ASs ve asm ekatakssfomz S/sit/n/a kaca/kaaa?aa isfea$/a. ^i/jz #k//7^^k t/a/sa (a&w yauas/jt o/arak 4-%)< ^kjy^ nya/?

10 5.4 Hata ( Sapma ) isareti analizi, Surekli hal hatasi Sek/Jdekj negaf/f yar/hes/ajvaj/ s/s/eat &/e a//aj//?. f*)* R(s) r Yts) /-//*)=* 1 tc/h /h/rim g&r/kesfesn e// $/'$fkjn) saaaca ayars/yca, RCs) " 1+ GC*) fo* Afs)_ Gfo Mrs) Fro- R(s) zomcaaa var/f/r. Ba $MUC ESs) /sarefia/a fife) y/r/s/a/a J>/c V& stsieai -forifay MUM bay// o/dagaaa gfofyf77?ej5fa//r. Gc>2&/>fi4/?iin tz >oo -i&s? s///r o//naya/?/>//& sarek// ha/ha/as/ p/arah aa, /aaa//n//r. 5a/7 o/&yer fa/m l/ni e(/) * Im se/$) yaz/iah///r.5o>/?a<0/am/:. efa>)=e ^//ai. ss s^o o/a?a&/aabr Ba dt/nt/nda, or/jek ojarak fcfs)^j_ y/r/s/ae ///sh//? fb/r/a? samakyy/r/$i) saretft'hat' ha/as/, i e = l/m. o/ar. * 1+66)

Ba $MUC ESs) /sarefia/a fife) y/r/s/a/a J>/c V& stsieai -forifay MUM bay// o/dagaaa gfofyf77?ej5fa//r. Gc>2&/>fi4/?iin tz >oo -i&s? s///r o//naya/?

11 f geribedme//' dstma/e. stm rm/>ay/r/s/he /'k/kk/k krf 10% okaa?k sek/kafe k( afey&k/?/' J/u/a/wz. ksu - ///n s fc)=* ///* s KCs+9) zzlim ^ = _je «o/#n HafitoM 1&Vo tifoiau it/fide, oj =JEQ e&mjpk uyamca, $0M/c#/?a vara J/r. J(= 500 Btritn-geribeslme// a/may*/? s/si^/enje (k.seb/deyprji/dky ayar/nca k&fa a/?ak/-z/ y#y>/ktk/'k/k. 6fs) Rfi) 6&) Yrsj

12 Bti a/uru/nah stire/c//ha/ Ziafas/ e, ss o/a&? //r. Or/iek : = f*q, //C$) = (s+s) a/ay? /?eaak/ yar/kesjeate// sssfgyrjz/e., h/r//n hafa/^ak y/r/s//?e /J/x/ya 5Ut k// ha/ ha/as//?/ ha/aaaz. Est/oyer sjsfe/r?, fa) Gfs) b/4//w/7al ofaza/rfrr. 6 /s) ve //Os) yer/er//?& faaa/arsa, &/*),., too s?+110s+400 darake/t/e aa#//r. 1/s o/u(, a = l/nt 5 * ^/ s a ^ -Og S^0 1 + "00 1+0,25 ' s* 110S /r s/suoi/n saraju/ /?#/ hafe$/ e s/s/aat//? &/s) ya/>/$/aaj l^a/ai: Skton 71/,/ : Gfs) /wh/ytauaaa s=a'da/://a/a/>/a~ r/a//i say/s/ $/sfa» //hi /t/arak a///aaa//r///r(, K(4+2$) 3 /?/>/ s/ ^#?y

& faaa/arsa, &/*),., too s?+110s+400 darake/t/e aa#//r.

13 _55 ^ ^*,. > /// ff 4+(j($) a/ar. 0 f/pj s/sfaaide. 4-h 6(9)

14 5.5 Bozucu ve giiriiltii isaretleri analizi 3u k^z zeki/ckek/ h//)k dyayyra/w /node// kk km/to/0/w/? 3 #/ri<>// hjrj/71 genhesketne/i skskejn^ &k. ahs//). fe) Y& kk>l harefker/.s/rasiyka. kozaca ve auru/fu isaref/irm _ karsm Jhmektidir. k o n t m l 5 r w ko/iirof etfkm s/sfem EJs) \. Gc(s) G(s) 1 + 6h)6(s) 1+ 6d)6fo 1+G/s)5ft

$k o n t m l 5 r w ko/iirof etfkm s/sfem EJs) \.$

15 zdhatma vanl/r. T^fe) k>02ua/ ve Nfs) giri/fi isareheri s/ /sardine p/tiftisuz. eft yen /zarel/er o/maklad/r. kukanda verilen E/s) ha/a /sard Rh)=Nfc)=o ia/j yazj/irsa, /$)= T/s) olur. SSrulJigu 0iLi Lis) - 6(s) bavik Mukw^fc) Mrehnin hata kardinddriol/jmsuz e/tkki azallk Mkte. kt)2vat isaretler aleak kreka/xlid/n Ba nedznke &/s) ko/iirdlorti/iufi kf^rmnda c i/(1+ B c fogfc)) c/uyahigjnm akak Irzkans/arda kuci/k ahasma dikkat edilmel/dlr. Ormk : r>ekiueki fapat cevr/mlj hiz bnfrd sisiemino. ilitkin l?hk diagram fc a/m/a. 11 T t (s) O KuvvetJenc/lrfQ Ka. Km 7s7B l</(s) t >- Takometre. Bu djyayrasn sekddek/ gene/ bicimz. sokulab'ilir (Y(f)^.Wfs),Nti^o) 'HQ Rfs) 6Js) ^klfs) 1 Gfs) z 66)- KgKtn / /y= L,m=K,+ Ts+b Rfc)=o i cm Tj (s) 'in Els) hkta ka refine, e/h'si ek cr/mw.

kt)2vat isaretler aleak kreka/xlid/n Ba nedznke &/s) ko/iirdlorti/iufi kf^rmnda c i/(1+ B c fogfc)) c/uyahigjnm akak Irzkans/arda kuci/k ahasma dikkat edilmel/dlr.

16 Si^kanda vzrilefi 6Mudar tfy#r//?ca, Em= 7 &L- 7;rs) yazjlob'dit l H <Mrfi/r»win Jiim kreka/is> bolgesinde. 1 J de/l bkiyiij oltnas/ kialinde., R($)~D ic/n, l/\jf$ 9 72) uyamw, GJs), 6k) V 1. 2 Jffc) yerferine konarak, <z/de edlkzcek pkursa, dde. tdihr. 7,fs) = yak momanii'kin, surekl, hal diwrnu y swdkyer feormi uyarjnca, limu/(i) = Jim swfs)^ -1 b olur. Kmeklendind bmcinin yukekilm/ halinda de>, sonottuna vanl/r.

$, R($)~D ic/n, l/\jf$ 9 72) uyamw, GJs), 6k) V 1. 2 Jffc) yerferine konarak, <z/de edlkzcek pkursa, dde.$

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