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Transkript

1 b) wej(jh-h'n.afuncliol'l ~ O-nSWG" I tedponse.. 0+ ~ ß(js\.e.rY) C9 tl a. Cdvi rclc.-) 1\'VI rt.<.b> e... a SInpcd c) e;eenvotue... af Q 8~.'1 i ~ d.d- ( ;\ i r -A) ( ~ 0 ~ of Q e.~. bcs)", o/so - s~: A F.i..8 lv ~QYl..- Öf' a.., ch.o..füc~l ;rf5+i c.. e.9 ~'ö ~ :w ()..f1.. Q)Ef'Lvo1.ue.. ) bt.-d 0_o+.QG..Ch e..lt.f-''/vo.-e.ue. i.5 <L f4.

2 d) l'di~ -.s~ <Di#er-en-ha1 9)...LcdifYL ~Ti yt- ~ y.f- ~.. k ' (cu., +-7; Q;.) 'Iro.nsfr Foh'OrL. ~1:2J 5 2. ~ +.~ S Y +y ~ t< (<1J..,.;-1; S 'I.u ) 6=f;::> (T Jb S'L ht) ~ -0:.J( ( A+ TDS) 'kj, _, Li Ls) k. (A.+7n5) U (s) :::D b(s) ==- ~ = e) ~ let1ö - S!fkm 1 S 2. +-=r;; ~ t--1 ~ ) X ~ ~ Ax+ B'tv ~ ::;: Cx+ D ').v XA (ß)) Li ) J fwls{.e.r fwlc:tiorl XeS) :. ; (. X n (S) 5.X(s) ~ A ~'X(5) + J3~~L[S) &>':> (s I -A) X(6):. ß -1LLs) A c~) ~(&) '= (sr -Ar 3.-\L(s) ~ ~ (s) :. C [ Csr -At..-l ß ;-- DJ ttlls) ü-i.) ~~ v~ cur.d J2Jee-n~ ~v Ai ~v Vi \ d6t' (/)i:t -A) ::0 ( Ai I - A ) Vi ~ 0 1

3 dlffh-e.nno..t ~.ucdiorl 'pit3-6(ft-em -=P 13 lr + T G q + G; ~.~ t{ 0< k [ 'U, t-.~ [1.vtc:)d~ ] a 'b.,.,. ~1Ct-C.Q.. h-a.ngfbr~of) -I> '13 s:3y +- T2. '2? Y t- 11 s y + y - k' [ 1L + ~ - ~~] 3.c:Ji=:I/ (T T'2. s 2. +'~ S +-..A) Y ~ (k + ~~) ~ y(s) u(s) /' ( ) K' +- '1:5 ={>~S~ r ~ 3 -,-2.-r 1 ' 'ZS +'/ b) damrih'ö k' D ~ c..os ( 0,;4:ili1, o L D L.- 1

4 d) ;ta-p ICLc.o- h-a.xlsfof-rno.t-prl '00 06 ff (-I:)} = [-f' Ct) e:- St dt (j Diru-c. ~ ~ rnfub:>e.. &(i;) ~~ [A (-b) - A ( -l: -ob ) ] ) ob ~o 06 {öli:)j -:- f esel) e- t-oll; 'impu.-lt>e..fcom [-0) 1-0] rt) e - C> +0.t- 0. f~o A JI ()OJ eil 0 -Si, = <1 L-L) ~-- dt +- e;m; ~ f 0lt) cl-/:; -C) e 1

5 .-) cli~6cl-nce. ~ fu.nct>ön _ N~ ~NG Gs - b2,ls) = NR; N.s. ~~ r ~.1 'r brj bs G-~ C;s Go :::::.--- ~ &fo 's A ~ ) Kz. (;f + 01I, os ) (-1 t- Tr:1 5 '!l:-~----~-i----:-_-...:::;...a...~---~ ( T~S) f K2. (/f +- ~ ) (.-1 -I- 1 ) ;cl 1.1:1 0 6~te.n1 "6 ~ -6+a..b~.. (,p~ ~ 5:=0)

6 0) GlS) J:!> G es) = :L 6,.,..1 -'-'-; s. e... <t:j.. k ~10 i 'T~ = i ~ ~O. b - {~~.t-'4-.) s e.. 2. Go (s) e. 1-i-S 1 _1~6 b -. --c.- C1.+ s )(1+-V e.

7 a) '&d.- - Djnara-m IGIcl.ß ~~~: J)eod.41 rne. ) -9cf --.2:f ~b) ~e.10 Lt t- k ~ ~ ~ ~~ff~'~ A ~ [0-1. ] -K ~ [4] = [~ ~ ] [:] + [~ ] U Ci) Y= [~ 0 ]

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13 pno~~ S ~ (1) a) ~ (~) ::: *C\ (-\,) (\) lg\ ppc\ce ~91~~S~{)J( ~ (\) Y(s L:: l. L Q (S) -::b G(s) =- ~($l.::: ----'-1_ f\ 2> ~($) 14- S B1. PT11 - e~ l'v?t: tij5):= \< l\+.}) -::: \< (\ -t.) (\..,.us) (\+S) fn e~c\~i'je ~eed ~ck ~ R t(cj ~) y(. (s) -V S r HjS), ~ GCs) 1 $) I Open -~oop b~ s4etr\: \-11 (s). G{s) ~ - COl (S) COILS) ::: k( I+}). \ \<: ( ~\-\-~) _ K~ ( \+s) f\s _. As( S4 I} - f\s2~ COl (s L::- k ~S2 _. fr<oo\fdoj$ (!)~ CoILS) -)(- ~o Res. R" 2 == o ~ VJ:::: 2 )t'- +-he91e Q9te Vlo "ZmDs =p m:so. If- ~'t1 -;: ('191-\}-rr :::- ('2?1-IJ 1'1 ; 91;: t,2. Y'l-IT) 2. Cfn ::= :+ ~

14 Posi.\l\le fead back: \Xl s) (<;) V+ f \..h(s) I GCS) s) O?eVl -e,dp s~s~em ~ C02 (s) ~ \\(\4- -t-).l - - \( l \ 1'S ) 14 'b - f\s 2. Roo-\ JOoJsof C62(SJ ~ _ popes: r\7 z :;;: 0.;:p. Y\ ~ 2 J«, d? 91 -:= _'2911f - ~ J ~ Tf. ::: 911'\ ) 11 "S' l., 2. VI-/\') 2 ~11 := -\0-11

15 2 PDlI- ~ehi : \..h (s) -= k f'l e~c\~\'\je ~(11 s) (s) -y f~ed ~c~: ~ds) (\)(s) (\ -t ToS) (\ ",T\5) - ~ Ges) - QpeV)-foop ~~Jovn \'b~ (03= \-\2.(S). GtS)=-!«\-\lDS~).J.- C D CJ (\+\1 $) p.,s 3:= I< ('+2$) ~ \( ( \-'\ 2S) f\;>(\-ts) ~ls1..-+s) Roo+ lows or Coo: ~ - 'Lenos: XI ~ - \/"2. -:=:? rn :=!. ~ ~ot'es ~ (4S ( S+I) =- c> ~ ~1 ~ 0 ~ P2.::- - \ -d> Y;.$ 2. ~ _ Cf'" -:::: l'2?1-111l -;:: ('2}'t -lj-n s (' I) 1'1' ; 91:s I 'V')-rn 2-~ L?91 ~ 1\

16 -J. 2. Hs) ~(») \~'2(SJ ~~. ~ 6(S) 'jl$)., O~e~ -rddp e;us-lem: C~4;:: 1~2(S). QLs) -: k\\-t105).~ o (\+Ti5) As ~~;::- \('( \+25) f.\ls2~s) R'0oiJoGllS ~ C6Q: ~ - Leno ~ t 2', -== -1 J2 -) In -1 u x,- po fes ~ S 2 ~s -;::; 0 -::::) 'be ~.T\ J ~ 0 $') Pr ;::- Cl ~ f2:;--i ~ h.:; Z. K- CfJ1 -:: 2 911'\ ~ Q 911'1 j 91 $ 1 -=h l' ()Jt ~ 211 h -1/1 \..).

17 \ me b~s..\em CQVi ~e CI Si)mp-b.\\c Oh~ \Ni~1-t PDT;-e11?trl<'ht C\vx::\ Y\-e'6G\~{\Je f.e~d bt1<:j$. 1'091 lk >0{

18 C) PC) \ S,_ b(s) ~ --I k \ ':(($) ~ (s Li r;~ttj( Sil)., UlS) c.(s) = ~'l CCs) C (5) -::----:::-;::-_--::-k _ S3+ 6S?.+IIS+ 6+K ChQHqC~..e-'911~J,k eiuc\~\o kl:. S S '2 + '1 ~ '(.:::-0 ~ Clo $1. ~ ch = 6' II.; ofi\ I} C\ 3". is -1-1<,;,-\k >- os t61:"s" \ai\ :5 \ >0 \ \\ 6-1-k )0 \ ~ 60- k>o ~ K <'6 0 \-6 <\< <6 0

19 d) OpeV?-Roo~ ~4en;. C.(s,> ~ \( j f( ~ b (b-\r\)( s-t2)(~-t3j CCS) ~ - (, (s'\- \) (~-+ 2) (~4?' ) No 7eJto<:> ~?oj,(s: p\ =0 - \ y Pl :0"- 2. p p~_. 6 CCs) ~ ~ ~ ( \ 4- ~) (\+ b)( \+ &) \ L '3 C(s)::: \ (\~ ~)(\~~)(\4~J WO \ =! J'1",d ISeG ~ Wo 2 ~ 2 'I1"J /gee ~ W03' 3JI..d,i,.,c;,".;'" ;-- r~~~~~{~~;~s"o~c~~l~'~i~1~~;:tr~~1~~~;i~~31w~i~i~~~lt8-~f'?i.~~rti.i~~;trti':'?"~l0;1~b2.et;''-:{;~f:;:::ow:;;;2r~~;;;:~~~~~;:::i}~f;s;:~lfi;::i;~t~(fl' _... ~:.::.~,,- ~;";.O'~,'- 3: C!S~.. ;,-,

20 60 c i c,, "H", ' C,.. ". ".\,. '" -".~. """'-".,.,.,.,.,.",,--r-rr=l -90 ".,1. "~..-J-..,!..u.u.cl--~".," Kreisfrequenz [r~1

21 l -j ~4..J...:..!J.J.l;L_J.'R"''':''u.u...._...l..~..Lll!L..-J..._WJ.Jj:.J.J,._,_;;.!.lU...._i.._i_Ll.Ui.iL.._J...i..L.!..U/.. ~. J._.I Ll.U~iL....L~.:..LJ.l,ll.!L_...i,. ;..,.ljji.l.\...)...i-'-l.l,lul.._.,...;.~;.lll,..~ 1~-~ 1(Y'-"1 ~O'D ~i)"1 ~0"'2 ~Oftequency~)'~ ~1Y'5 HJ"i ~!Y<I ~Y:l 1(;":0 HY~ I e) OR ~S; ~~ St St~""'fltt.'S Jo.h'1f eo~ t~t' 11.. tj~"j~.- 2~? 5" ~ 'ß ~ /1 (J C 111, (;., Ci. /1) CV-<_ AO GUt i. [;0 G I/e (e"l-"... o~ dc...'("j.)

22 +) (20 r i j.----_+,+-"01./ IV ~.. (J AO -( ()-r------r--t ~~!!!!!!!!!!!!!!!~~----+ b 4_~~ -20r---~~--=...: ~':7:h.;; ~~--- +_ Bode Diagram Cl ~ :ä Q) -5 'e Cl cu ::i: ;.. :.. "." "."" Cl Q) -45 ~ Q) -90 Vl cu.s:: CL -135 ", ' ,. :,. '." :..::.::::: :.::::::: :.~~'--.;--:.:::::: ::.::::::.:::;;.:.:."::::...~.. V'( ~ o.. ""';'~... ~~..,.,~~~"-... ::::::::::::::::.:: ::r:r:-::::::~~:::::::::: :::::::... " '----''--'--'-,--,-,-"ll.--'--'-l-l.ujul--'---l-'--'-ljw1---'--j'-i..j..1.l.ll '-.l-.l..ul.llll---l...l-l..l..u.ul----i---'-l.ju..lllj------'----'-'-..llj..!jll.-j...l...;u..lj.l.ll..-.j-j...lll1llj Frequency (rad/sec)

23 ttf Imaginärteil 3 Realteil Wl = 10 [r~j -3-4 'h) Ye S I i I is dc.l. Le- i ( - -1 J 0 ~ ) i~ 0'-_ JLe ~~ t.irh Q f JLeeet t V. { r ('.t.-~. # tor: K L t" tvy1g<t"r ~ ). Dr - C>l

24 i) j) Bode Diagram A~ I k) Tl~ CorVler +~~t( tr..c te S Wtc<~"'J L... allt c1wf {Pd. it ~~ l!

25 Ir- g.lc...".:/" ~ ~ ~~e-. Bode Diagram ~ 70 Q) -g 65 ~ lijl 60 : Cl Q) ~ Q) 11l '".c c ~=:::::L::.:------'----'--'-----'----.1~~_----'-_'---L...J..--'--J'--'-'-~_----'-_~";;-'-----'--.L-L...J~_----'-_...L..-...L..-,----,--,-,-J Frequency (rad/sec)

26 o~ Lu 0 o e

27 Re 1f)e s'j5iely) CqV) be OlS~mpto+\c. Oh %W \~~?Dt _ er~e~i qnd h~det\\v~ ~ee-dkck fo'1 \r->ö I ~

28 '-),,'-~~ ) Y;:J k --- Cs) (SL... t;s; t)(stij c(s)::;". \< t~/+s-.5+6)(5-h) \ -+. \( \. ~2. 4..t5~ -t6)(b+\) CCs) =: _-.:: ~ CCS) Ces) -= K S~ \1 S-+ 6+K ChCl.1!Qd.e911 'i>~ k e'l UcA~ {Cl ko : S 3 -+ t $ 2 +- H'& \( =0 '2~. aos\ a\s'2. -I- Cl2::' + Cl3 :=0 j -. I oos-\. ~ Cl\:=6 ~ Clz.:11 ~ Q376+k~)k>'6 L\:s- \ct\\ ~ \ >0 0\0, \< '/0 ~ 60- k>o ~ \( <"6 0 -nie s';\s~vn \s $\0 ~fe Rö'lt W<K <

29 d) OpeVJ-koof &&s4bn: C(s) :: \( ( b-\\ )( ~~ 2 ) (.~-\ 3J i CGs) ::: ( ~~\) (ß-t 2) (~-t~) No 7mos ~ po-&s: ~\:;;_.\ 9 Pt~-2 ~ P-$-'~' CCs) ~ ~ Af( \4- th1+ ~)(\+~) ces) == \, (\~ t)(\","~)(\4~j WO\ = 1. 7' /sec ~ Uh2. -::- 2 '11c.1J.J~ec. ~ Wl\3 ~ '3J1~Ei