Error en Estado Estable

 

LZZEZ L@ L]XKHE L]XKJCL

 

–Lrrer l` Lstkhe Lstkjcl—

Lc k`ëcasas y haslûe hl sastldks hl me`trec sl me`ml`trk l` trls lsplmagamkmae`ls9 ;) Zlspulstk trk`saterak. :) Lstkjacahkh. =) Lrrerls l` lstkhe lstkjcl. L` lc haslûe hl u` sastldk hl me`trec lxastl u` medpredase l`trl ck rlspulstk trk`saterak hlslkhk, lc lrrer l` lstkhe lstkjcl y lc rlqulradal`te hl qul lc sastldk slk lstkjcl.

 

Hlga`amae`ls y l`trkhks hl pruljk Lc lrrer l` lstkhe lstkjcl ls ck haglrl`mak l`trl ck l`trkhk y cckk skcahk pkrk u`k l`trkhk hl pruljk prlsmratk me`gerdl t⟷∐. Ck saoual`tl tkjck dulstrk cks l`trkhks hl pruljk ldpclkhks pkrk lc k`ëcasas y haslûe hlc lrrer l` lstkhe lstkjcl.

 

Kpcamkmaý` k sastldks lstkjcls ^ulste qul lstkdes a`tlrlskhes l` ck haglrl`mak h aglrl`mak l`trl ck l`trkhk y ck skcahk hl u` sastldk hl me`trec rltrekcadl`tkhe hlspuás qul sl bkyk kcmk`zkhe lc lstkhe lstkjcl, `ulstre k`ëcasas sl cadatk k sastldks lstkjcls, he`hl ck rlspulstk cajrl sl

kprexadk kmlre k dlhahk qul t⟷∐. Ces sastldks a`lstkjcls a`ls tkjcls rlprlsl`tk` ck párhahk hl me`trec l` lstkhe lstkjcl

y `e hljl` uskrsl l` kjsecute, per ce mukc, sl hljl vlragamkr ck lstkjacahkh hlc sastldk muk`he sl rlkcaml lc k`ëcasas y haslûe hl lrrer l` lstkhe lstkjcl.

 

Lrre Lr rerr l` ls lstkh tkhe e lstkj lstkjcl cl pkrk pkrk sastl sastldk dkss me me` ` rltr rltrek ekca cadl dl`tk `tkma maý` ý` u` u`at atkr krak ak    

Gao.k) ]astldk rltrekcadl`tkhe u`atkrakdl u`atkrakdl`tl `tl

 

  ; 

Gao.j) Gu`maý` hl trk`sglrl`mak l` ckze mlrrkhe

Me`sahlrl lc sastldk rltrekcadl`tkhe rltrekcadl`tkhe hl ck Gao. k), pkrk bkcckr L(]), lc lrrer

l`trl ck l`trkhk, Z(]), y ck skcahk M(s), lsmrajades9

     √ 

 

     √ 

Hava Havaha hal` l`he he ls lstk tk lx lxpr prls lsaý aý` ` l` l`tr trll Z( Z(s) s),, sl ta tal` l`ll

;          √      ; √      ;    √     ;   ( ሶ ;  ;    ( ሶ  

^er ce tk` k`tte, lc lrr lrrer l` ls lstk tkhe he ls lsttkj kjcl cl,, L( L(]) ]),, k` k`tl tl ck l` l`tr trkh khkk Z( Z(]) ]),, l` tárda árda`e `ess hl Ck Ckpc pckm kml, l, ls 9   

;     ;  

Hl lstk ùctadk gýrduck pehldes ejslrvkr qul lc lrrer l` lstkhe lstkjcl hlpl`hl hl9

•

Lc tape hl sastldk (Ls hlmar, sastldk tape >, sastldk tape ;, sastldk tape :, ltm).

•

Hl ck l` l`tr trkh khkk kc sa sast stld ldkk (L (Lsm smkc kcý` ý`,, rkdp rkdpk, k, pk pkrë rëje jeck ck). ).

 

He`hl lc tape hl sastldk val`l hltlrda`khe k pkrtar hl ck gu`maý` hl trk`sglrl`mak l` ckze kjalrte mede sl dulstrk k me`ta`ukmaý`9

 

    +  + ⋥ +    + + ⋥ +

He`h He `hll @, hl hlttlrda lrda`k `k lc ta tape pe hl sas sastl tld dk    >         >    ;        ;    :         e e:

 

Ejtl`maý` hlc lrrer l` lstkhe lstkjcl l` tárda`es hlc taldpe Kpcacamk Kp mk`h `he e lc tler tlerld ldkk hlc hlc vkc kcer er ga ga`k `kc, c, sl ta tal` l`l9 l9    cad (ሶ ↚

 

 

⇚

   cad  ↚

; ; 

K`kcazk`he lstk ùctadk gýrduck gýrduck pkrk9 haglrl`tls l`trkhks (lsmkcý` rkdpk y pkrëjeck) y tapes hl sastldk (tape >, tape ; y tape :)

   

 

XKJCK ;.-GÝZD\CK] ;.-GÝZD\ CK] ^KZK MKCM\CKZ CE] LZZEZL] L@ L @ L]XKHE L]XKJCL L]XKJCL (  ) Q ]\] ZL]^LMXAWK] L`trkhk

ME@XK@XL] HL LZZEZ L]XËXAME (  ,  y  ) Mtls hl lrrer lstëtame Lrrer l` lstkhe lstkmae`krae

Lsmkcý` u`atkrae

   cad (ሶ

Zkdpk u`atkrak

   cad (ሶ

^krëjeck u`atkrak

↚



↚

   cad   (ሶ ↚

;

  

   

   

Fp4Mt 4Mtll hl lrrer lrrer lstëtame hl pesamaý`.

;   ;  ; 

XKJCK ;4 tkjck hl gýrducks

4Mtll hl lrr lrrer er Fv4Mt lstëtame hl vlcemahkh Fk4Mt 4Mtll hl lrrer lrrer lstëtame hl kmlclrkmaý`

 

L` ck Xkjck : sl dulstrk lc lrrer l` lstkhe lstkjcl K`tl l`trkhks 9 Lsmkcý`, rkdpk y pkrëjeck ^krkk sastldks9 Xape >, Xape ; y Xape :. ^kr XKJCK :.-LZZEZ L@ L]XKHE L]XKJCL L`trkhk

Xape >

Xape ;

Xape:

Lsmkcý` u`atkrae

Mtl

>

>

mtl

>

Zkdpk u`atkrak

^krëjeck u`atkrak

 

∐

 

∐

XKJCK :4tkjck hlc lrrer

∐

mtl

 

Lilrmamae 9 L`mul`trl ces lrrerls l` lstkhe lstkjcl pkrk l`trkhks hl ( >(  :ሶ (  =ሶ =ሶ( (  8ሶ

L` ck Gu`maý` hl trk`sglrl`mak l` ckze kjalrte, ejslrvkdes qul9 Lc sastldk ls tape >

 

^kse =

\tacazkdes ck XKJCK : hl ck saoual`tl gerdk9

Mede lc sastldk ls tape mlre, l`dkrmkdes l` reie ck mecud`k Xape Xap e > y l`dkrmkdes l` kzuc k ck l`trkhk lsmkcý` bkstk a`tlrmlptkr me` ck mecud`k reik. L` ck a`tlrslmmaý` a`tlrslmmaý` hl lstks hes dkrmks lstk ck pkckjrk mtl l a`tlrprltkdes ksä9 •

\` sastldk tape mlre k`tl u`k l`trkhk lsmkcý` prlsl`tk u` lrrer l` lstkhe lstkjcl, mtl, ls hlmar 9 lss4Mtl

XKJCK :.-LZZEZ L@ L]XKHE L]XKJCL L`trkhk Xape > Xape ; Xape: Lsmkcý` u`atkrae Mtl Zkdpk u`atkrak   ∐ ^krëjeck u`atkrak

∐

> mtl ∐

> > mtl

Kberk l`dkrmkdes l` vlrhl k ck l`trkhk rkdpk bkstk A`tlrmlptkrck me` ck mecud`k mecud`k reik. L` ck a`tlrslmmaý` a`tlrslmmaý` hl lstks Hes dkrmks lstk lc sädjece ∐ l a`tlrprltkdes ksä9 \` sastldk tape mlre k`tl u`k l`trkhk rkdpk prlsl`tk u` lrrer hlma mar9 r9 lss4 ∐ l` lstkhe lstkjcl, ∐, ls hl •

Zlpltades l`dkrmk`he l` derkhe derkhe k ck l`trkhk pkrëjeck pkrëjeck bkstk A`tlrmlptkrck me` ck mecud`k mecud`k reik. L` ck a`tlrslmmaý` a`tlrslmmaý` hl lstks hes dkrmks lstk lc sädjece ∐ l a`tlrprltkdes ksä9 •

\` sastldk tape mlre k`tl u`k l`trkhk pkrëjeck prlsl`tk u` lrrer l` lstkhe lstkjcl, ∐, ls hl hlma mar9 r9 lss4 ∐

L`te`mls pehldes hlmar qul 9 \` sastldk tape mlre mlre prlsl`tk prlsl`tk u` lss4 Mtl Mtl k`tl u`k l`trkhk l`trkhk lsmkcý` lsmkcý` y

lss4

∐ k`tl l`trkhks rkdpk y pkrëjeck

 

Hlspuás hl bkjlr utacazkhe uta cazkhe ck XKJCK: XKJCK: medpcldl`tkdes utacazk`he cks gýrducks hl ck XXKJCK KJCK ; XKJCK ;.-GÝZD\CK] ^KZK MKCM\CKZ CE]  Q CK] ME@XK@XL]9  ,  Q  L`trkhk

Mtls hl lrrer lstëtame    cad (ሶ ↚

Lsmkcý` u`atkrae Zkdpk u`atkrak

Lrrer l` lstkhe lstkmae`krae   

;  

   cad (ሶ ↚

  

;  

   cad  (ሶ ↚

   

 



 

Fv4Mtl hl lr lrrer rer lstëtame hl vlcemahkh

; 

^krk l`trkhk rkdpk 9   

Ces lrrerls l` lstkhe lstkjcl ( ) k`tl l`trkhks9 lsmkcý` , rkdpk y pkrëjeck, ksä mede cks me`stk`tls hl lrre lrrerr lstëtame 9

  ∐

Mede yk skjäkdes lc vkcerhltlrda`kr hlc lrrer lrrer,, l`te`mls, l`te`m ls,hl per me`slmul`mak pehldes lc vkcer

Fk4Mtl hl lrr lrrer er lstëtame hl kmlclrkmaý`

F p, F v ,

y

Fk

^krk l`trkhk lsmkcý` 9 >



^krëjeck u`atkrak

;

Fp4Mtl hl lrr lrrer er lstëtame hl pesamaý`.

L` u` sastldk tape >

   cad    cad ↚

   

↚

< ;  



< ;:>

;:>( ;:> (  :ሶ

;:>(:ሶ

   (  =ሶ( =ሶ(  8ሶ (=ሶ(8ሶ >

 

>

< :;

   

   :>

Wkcer Mtl

Lrrer Mtl

@ýtlsl qul sl mkdjae lc ; per < l` ck gýrduck pkrk mkcmuckr  yk qul kc A`amae hlc lilrmamae sl a`hamý qul ck l`trkhk lsmkcý` ls hl kdpcatuh ( >(  :ሶ            :ሶ   ;:>( ;:>(  :ሶ ;:>( ;: >(  ;   ;   

 

r(t) <

Z  

  

Gao. L`trkhk lsmkcý` hl kdpcatuh <

  

M(]) ;:>   :    ;:? :?  :   :

;:>   :    ;:? ;:?  :.: >.;< >.;

>.>< >.>;

>.>:

>.>=

>.>8 >.>8<

t (slo)

Gao. L`trkhk rkdpk hl kdpcatuh <

M(]) ;:>   :    ;:? ;:?  :