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Asachi\", Iasi, Facultatea de Electronica s i Telecomunicatii" }}{PARA 19 "" 0 "" {TEXT -1 43 "Laboratorul de Semn ale, Circuite si Sisteme" }}{PARA 19 "" 0 "" {URLLINK 17 "http://scs4. etc.tuiasi.ro" 4 "http://scs4.etc.tuiasi.ro/scslabs/Simbolice/simbolic e.htm" "" }{TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 16 "Brevia r teoretic" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 338 16 "Scopul lucr arii:" }}{PARA 0 "" 0 "" {TEXT -1 92 "Familiarizarea cu criteriul Nyqu ist de analiza a stabilitatii sistemelor liniare cu reactie." }}{PARA 0 "" 0 "" {TEXT 339 17 "Rezumat teoretic:" }}{PARA 0 "" 0 "" {TEXT -1 92 "In esenta, criteriul de analiza a stabilitatii are la baza teorema Cauchy, enuntata mai jos." }}{PARA 4 "" 0 "" {TEXT -1 14 "Teorema Cau chy" }}{PARA 0 "" 0 "" {TEXT 317 0 "" }{TEXT -1 4 "Fie " }{XPPEDIT 18 0 "F;" "6#%\"FG" }{TEXT -1 1 ":" }{XPPEDIT 18 0 "proc (C) options oper ator, arrow; C end proc;" "6#R6#%\"CG7\"6$%)operatorG%&arrowG6\"F%F*F* F*" }{TEXT -1 50 " o fractie rationala cu coeficienti complecsi, si " }{TEXT 318 1 "C" }{TEXT 319 0 "" }{TEXT -1 90 " un contur inchis in pl anul complex, care nu trece prin nici un pol sau zerou al functiei " } {XPPEDIT 18 0 "F(s);" "6#-%\"FG6#%\"sG" }{TEXT -1 16 ". Daca conturul \+ " }{TEXT 320 1 "C" }{TEXT -1 27 " contine in interiorul sau " } {XPPEDIT 18 0 "Z;" "6#%\"ZG" }{TEXT -1 12 " zerouri si " }{XPPEDIT 18 0 "P;" "6#%\"PG" }{TEXT -1 18 " poli ai functiei " }{XPPEDIT 18 0 "F; " "6#%\"FG" }{TEXT -1 34 ", atunci cand s parcurge conturul " }{TEXT 322 6 "Cauchy" }{TEXT -1 35 " in sens orar, hodograful functiei " } {XPPEDIT 18 0 "F(s);" "6#-%\"FG6#%\"sG" }{TEXT -1 24 " inconjoara orig inea de " }{XPPEDIT 18 0 "Z-P;" "6#,&%\"ZG\"\"\"%\"PG!\"\"" }{TEXT -1 21 " ori in acelasi sens." }}{PARA 0 "" 0 "" {TEXT -1 66 "Sa considera m acum un sistem cu reactie avand functia de transfer:" }}{PARA 257 " " 0 "" {XPPEDIT 18 0 "Hr(s) = K*A(s)/(1-epsilon*K*A(s)*B(s));" "6#/-%# HrG6#%\"sG*(%\"KG\"\"\"-%\"AG6#F'F*,&F*F***%(epsilonGF*F)F*-F,6#F'F*-% \"BG6#F'F*!\"\"F6" }{TEXT -1 1 "," }}{PARA 0 "" 0 "" {TEXT -1 5 "unde \+ " }{XPPEDIT 18 0 "epsilon = 1;" "6#/%(epsilonG\"\"\"" }{TEXT -1 28 " p entru reactie pozitiva si " }{XPPEDIT 18 0 "epsilon = -1;" "6#/%(epsil onG,$\"\"\"!\"\"" }{TEXT -1 25 " pentru reactie negativa." }}{PARA 0 " " 0 "" {TEXT -1 9 "Notam cu " }{XPPEDIT 18 0 "Hd(s);" "6#-%#HdG6#%\"sG " }{TEXT -1 39 " functia de transfer in bucla deschisa:" }}{PARA 257 " " 0 "" {XPPEDIT 18 0 "Hd(s) = K*A(s)*B(s);" "6#/-%#HdG6#%\"sG*(%\"KG\" \"\"-%\"AG6#F'F*-%\"BG6#F'F*" }{TEXT -1 1 "," }}{PARA 0 "" 0 "" {TEXT -1 68 "putem exprima functia de transfer a sistemului cu reactie sub f orma:" }}{PARA 257 "" 0 "" {XPPEDIT 18 0 "Hr(s) = K*A(s)/(1-epsilon*Hd (s));" "6#/-%#HrG6#%\"sG*(%\"KG\"\"\"-%\"AG6#F'F*,&F*F**&%(epsilonGF*- %#HdG6#F'F*!\"\"F4" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 105 "St abilitatea sistemului cu reactie este data de pozitia in planul comple x a polilor functiei de transfer " }{XPPEDIT 18 0 "Hr(s);" "6#-%#HrG6# %\"sG" }{TEXT -1 79 ". Pentru studiul stabilitati sistemului cu reacti e la modificarea amplificarii " }{XPPEDIT 18 0 "K;" "6#%\"KG" }{TEXT -1 94 " se urmareste determinarea legaturii dintre numarul de poli din semiplanul drept ale functiei " }{XPPEDIT 18 0 "Hr(s);" "6#-%#HrG6#% \"sG" }{TEXT -1 17 " si valoarea lui " }{XPPEDIT 18 0 "K;" "6#%\"KG" } {TEXT -1 25 ", folosind terema Cauchy." }}{PARA 0 "" 0 "" {TEXT -1 28 "In acest scop se noteaza cu " }{XPPEDIT 18 0 "F(s);" "6#-%\"FG6#%\"sG " }{TEXT -1 20 " numitorul functiei " }{XPPEDIT 18 0 "Hr(s);" "6#-%#Hr G6#%\"sG" }{TEXT -1 1 ":" }}{PARA 257 "" 0 "" {XPPEDIT 18 0 "F(s) = 1- epsilon*Hd(s);" "6#/-%\"FG6#%\"sG,&\"\"\"F)*&%(epsilonGF)-%#HdG6#F'F)! \"\"" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT 324 5 "Obs. " }{TEXT -1 32 "Avand in vedere legatura dintre " }{XPPEDIT 18 0 "Hr(s);" "6#-%#Hr G6#%\"sG" }{TEXT -1 4 " si " }{XPPEDIT 18 0 "F(s);" "6#-%\"FG6#%\"sG" }{TEXT -1 28 ", respectiv legatura dintre " }{XPPEDIT 18 0 "F(s);" "6# -%\"FG6#%\"sG" }{TEXT -1 4 " si " }{XPPEDIT 18 0 "Hd(s);" "6#-%#HdG6#% \"sG" }{TEXT -1 32 ", putem spune ca polii functiei " }{XPPEDIT 18 0 " F(s);" "6#-%\"FG6#%\"sG" }{TEXT -1 52 " sunt polii functiei de transfe r in bucla deschisa, " }{XPPEDIT 18 0 "Hd(s);" "6#-%#HdG6#%\"sG" } {TEXT -1 31 ", respectiv zerourile functiei " }{XPPEDIT 18 0 "F(s);" " 6#-%\"FG6#%\"sG" }{TEXT -1 58 " sunt polii functiei de transfer a sist emului cu reactie, " }{XPPEDIT 18 0 "Hr(s);" "6#-%#HrG6#%\"sG" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 48 "Se considera un contur inchis \+ in planul complex " }{XPPEDIT 18 0 "s;" "6#%\"sG" }{TEXT -1 81 " care \+ sa contina toti polii si toate zerourile din semiplanul drept ale func tiei " }{XPPEDIT 18 0 "F(s);" "6#-%\"FG6#%\"sG" }{TEXT -1 40 ", dar ca re sa nu contina polii functiei " }{XPPEDIT 18 0 "F(s);" "6#-%\"FG6#% \"sG" }{TEXT -1 58 " situati pe axa imaginara. Un astfel de contur se \+ numeste " }{TEXT 321 16 "conturul Nyquist" }{TEXT 323 1 "." }}{PARA 4 "" 0 "" {TEXT -1 16 "Conturul Nyquist" }}{PARA 0 "" 0 "" {TEXT -1 122 "Conturul Nyquist este un contur inchis ce inconjoara semiplanul drept al planului complex in sens orar si este format din:" }}{PARA 15 "" 0 "" {TEXT -1 21 "axa imaginara pentru " }{XPPEDIT 18 0 "omega = -infi nity .. infinity;" "6#/%&omegaG;,$%)infinityG!\"\"F'" }{TEXT -1 103 " \+ mai putin in apropierea polilor de pe axa imaginara care sunt ocoliti \+ fiecare cu un semicerc de raza " }{XPPEDIT 18 0 "r0;" "6#%#r0G" } {TEXT -1 2 " (" }{XPPEDIT 18 0 "proc (r0) options operator, arrow; 0 e nd proc;" "6#R6#%#r0G7\"6$%)operatorG%&arrowG6\"\"\"!F*F*F*" }{TEXT -1 78 ") cu centrul in polul de pe axa imaginara, semicerc situat in s emiplanul drept" }}{PARA 15 "" 0 "" {TEXT -1 63 "conturul se inchide c u un semicerc in semiplanul drept de raza " }{XPPEDIT 18 0 "R0;" "6#%# R0G" }{TEXT -1 2 " (" }{XPPEDIT 18 0 "proc (R0) options operator, arro w; 0 end proc;" "6#R6#%#R0G7\"6$%)operatorG%&arrowG6\"\"\"!F*F*F*" } {TEXT -1 21 ") centrat in origine." }}{PARA 256 "" 0 "" {TEXT -1 28 "P ractic, alegerea valorilor " }{XPPEDIT 18 0 "R0;" "6#%#R0G" }{TEXT -1 4 " si " }{XPPEDIT 18 0 "r0;" "6#%#r0G" }{TEXT -1 26 " se face in felu l urmator:" }}{PARA 15 "" 0 "" {XPPEDIT 18 0 "R0;" "6#%#R0G" }{TEXT -1 78 " trebuie sa fie mult mai mare decat modulul tuturor singularita tilor functiei " }{XPPEDIT 18 0 "F(s);" "6#-%\"FG6#%\"sG" }{TEXT -1 3 ", (" }{XPPEDIT 18 0 "proc (R0) options operator, arrow; infinity end \+ proc;" "6#R6#%#R0G7\"6$%)operatorG%&arrowG6\"%)infinityGF*F*F*" } {TEXT -1 2 ")." }}{PARA 15 "" 0 "" {XPPEDIT 18 0 "r0;" "6#%#r0G" } {TEXT -1 101 " trebuie sa fie mult mai mic decat distanta dintre orica re doua singularitati distincte ale functiei " }{XPPEDIT 18 0 "F(s);" "6#-%\"FG6#%\"sG" }{TEXT -1 3 ", (" }{XPPEDIT 18 0 "proc (r0) options \+ operator, arrow; 0 end proc;" "6#R6#%#r0G7\"6$%)operatorG%&arrowG6\"\" \"!F*F*F*" }{TEXT -1 2 ")." }}{PARA 256 "" 0 "" {TEXT -1 6 "Notam:" }} {PARA 15 "" 0 "" {XPPEDIT 18 0 "P;" "6#%\"PG" }{TEXT -1 29 " numarul d e poli ai functiei " }{XPPEDIT 18 0 "F(s);" "6#-%\"FG6#%\"sG" }{TEXT -1 22 " din semiplanul drept;" }}{PARA 15 "" 0 "" {XPPEDIT 18 0 "Z;" " 6#%\"ZG" }{TEXT -1 54 " numarul de zerouri din semiplanul drept ale fu nctiei " }{XPPEDIT 18 0 "F(s);" "6#-%\"FG6#%\"sG" }{TEXT -1 1 "." }} {PARA 0 "" 0 "" {TEXT -1 68 "Se alege un sens de referinta de exemplu \+ sensul orar. Se noteaza cu " }{XPPEDIT 18 0 "N;" "6#%\"NG" }{TEXT -1 60 " numarul de inconjururi pe care le face hodograful functiei " } {XPPEDIT 18 0 "F(s);" "6#-%\"FG6#%\"sG" }{TEXT -1 61 " in jurul origin ii in sensul de referinta fixat, atunci cand " }{XPPEDIT 18 0 "s;" "6# %\"sG" }{TEXT -1 117 " parcurge o singura data conturul Nyquist in ace lasi sens. Dar numarul de inconjururi pe care le face hodograful lui \+ " }{XPPEDIT 18 0 "F(s);" "6#-%\"FG6#%\"sG" }{TEXT -1 84 " in jurul ori ginii este acelasi cu numarul de inconjururi pe le face hodograful lui " }{XPPEDIT 18 0 "Hd(s);" "6#-%#HdG6#%\"sG" }{TEXT -1 20 " in jurul p unctului " }{XPPEDIT 18 0 "1/epsilon;" "6#*&\"\"\"F$%(epsilonG!\"\"" } {TEXT -1 8 ", adica " }{XPPEDIT 18 0 "-1+I*0;" "6#,&\"\"\"!\"\"*&%\"IG F$\"\"!F$F$" }{TEXT -1 36 " (-1,0) pentru reactie negativa sau " } {XPPEDIT 18 0 "1+I*0;" "6#,&\"\"\"F$*&%\"IGF$\"\"!F$F$" }{TEXT -1 31 " (1,0) pentru reactie pozitiva." }}{PARA 0 "" 0 "" {TEXT -1 32 "Hodogr aful functiei de transfer " }{XPPEDIT 18 0 "Hd(s);" "6#-%#HdG6#%\"sG" }{TEXT -1 7 ", cand " }{XPPEDIT 18 0 "s;" "6#%\"sG" }{TEXT -1 38 " par curge conturul Nyquist se numeste " }{TEXT 326 16 "diagrama Nyquist" } {TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 32 "Avand in vedere teorema \+ Cauchy, " }{XPPEDIT 18 0 "N = Z-P;" "6#/%\"NG,&%\"ZG\"\"\"%\"PG!\"\"" }{TEXT -1 7 ", deci " }{XPPEDIT 18 0 "Z = N+P;" "6#/%\"ZG,&%\"NG\"\"\" %\"PGF'" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 325 5 "Obs. " }{TEXT -1 32 "Avand in vedere legatura dintre " }{XPPEDIT 18 0 "Hr(s);" "6#-%#HrG6#%\"sG" }{TEXT -1 4 " si " } {XPPEDIT 18 0 "F(s);" "6#-%\"FG6#%\"sG" }{TEXT -1 28 ", respectiv lega tura dintre " }{XPPEDIT 18 0 "F(s);" "6#-%\"FG6#%\"sG" }{TEXT -1 4 " s i " }{XPPEDIT 18 0 "Hd(s);" "6#-%#HdG6#%\"sG" }{TEXT -1 17 ", putem sp une ca " }{XPPEDIT 18 0 "P;" "6#%\"PG" }{TEXT -1 91 " reprezinta numar ul de poli din semiplanul drept ai functiei de transfer in bucla desch is, " }{XPPEDIT 18 0 "Hd(s);" "6#-%#HdG6#%\"sG" }{TEXT -1 6 ", iar " } {XPPEDIT 18 0 "Z;" "6#%\"ZG" }{TEXT -1 98 " reprezinta numarul de poli din semiplanul drept ai functiei de transfer a sistemului cu reactie, " }{XPPEDIT 18 0 "Hr(s);" "6#-%#HrG6#%\"sG" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 327 32 "Criteriul de s tabilitate Nyquist" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 328 0 "" } {TEXT -1 0 "" }{TEXT 329 0 "" }{TEXT -1 87 "Un sistem cu reactie este \+ stabil daca diagrama Nyquist inconjura punctul de referinta (" }{TEXT 341 6 "(-1,0)" }{TEXT -1 26 " pentru reactie negativa, " }{TEXT 340 6 "(+1,0)" }{TEXT -1 29 " pentru reactie pozitiva) de " }{XPPEDIT 18 0 " P;" "6#%\"PG" }{TEXT -1 35 " ori in sens antiorar, atunci cand " } {XPPEDIT 18 0 "s;" "6#%\"sG" }{TEXT -1 55 " parcurge o singura data in sens orar conturul Nyquist." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 "Expresia matematica a criteriului de stabilitat e Nyquist este " }{XPPEDIT 18 0 "N = -P;" "6#/%\"NG,$%\"PG!\"\"" } {TEXT -1 33 " si este echivalenta cu conditia " }{XPPEDIT 18 0 "Z = 0; " "6#/%\"ZG\"\"!" }{TEXT -1 80 " (sistemul cu reactie sa nu aiba poli \+ in semiplanul drept, adica sa fie stabil)." }}{PARA 0 "" 0 "" {TEXT 330 0 "" }}{PARA 0 "" 0 "" {TEXT -1 80 "Trasarea diagramei Nyquist ple aca in principiu de la diagrama polara a functiei " }{XPPEDIT 18 0 "Hd (I*omega);" "6#-%#HdG6#*&%\"IG\"\"\"%&omegaGF(" }{TEXT -1 206 ", deoar ece o parte a conturului Nyquist (cea mai semnificativa) este situata \+ pe axa imaginara. Diagrama Nyquist este simetrica fata de axa reala de oarece conturul Nyquist este simetric fata de axa reala si " } {XPPEDIT 18 0 "Hd(conjugate(s)) = conjugate(Hd(s));" "6#/-%#HdG6#-%*co njugateG6#%\"sG-F(6#-F%6#F*" }{TEXT -1 14 " pentru orice " }{XPPEDIT 18 0 "s;" "6#%\"sG" }{TEXT -1 53 " complex (pentru sisteme realizabile practic functia " }{XPPEDIT 18 0 "Hd(s);" "6#-%#HdG6#%\"sG" }{TEXT -1 24 " are coeficienti reali)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 331 96 "Studiul stabilitatii sistemului cu react ie la variatia amplificarii utilizand criteriul Nyquist." }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 73 "In principiu se pleaca de la diagra ma Nyquist trasata pentru amplificare " }{XPPEDIT 18 0 "K;" "6#%\"KG" }{TEXT -1 67 " unitara. Daca se modifica valoarea amplificarii, modulu l functiei " }{XPPEDIT 18 0 "Hd(s);" "6#-%#HdG6#%\"sG" }{TEXT -1 27 " \+ se rescaleaza cu valoarea " }{XPPEDIT 18 0 "K;" "6#%\"KG" }{TEXT -1 135 ", dar argumentul ramane neschimbat. Din acest motiv alura diagram ei Nyquist ramane neschimbata dar se contracta sau se dilata dupa cum \+ " }{XPPEDIT 18 0 "K < 1;" "6#2%\"KG\"\"\"" }{TEXT -1 5 " sau " } {XPPEDIT 18 0 "1 < K;" "6#2\"\"\"%\"KG" }{TEXT -1 63 ". Acest lucru fa ce posibila deducerea numarului de inconjururi " }{XPPEDIT 18 0 "N;" " 6#%\"NG" }{TEXT -1 184 " (in jurul punctului de referinta), la diferit e valori ale amplificarii, din pozitia relativa a punctului de referin ta in raport cu diagrama Nyquist trasata pentru amplificare unitara." }}{PARA 0 "" 0 "" {TEXT -1 98 "In functie de caracterul sistemului la \+ variatia amplificarii se poate face urmatoarea clasificare:" }}{PARA 15 "" 0 "" {TEXT -1 15 "un sistem este " }{TEXT 332 19 "conditionat st abil " }{TEXT -1 4 "sau " }{TEXT 337 20 "conditionat instabil" }{TEXT -1 25 " daca exista doua valori " }{XPPEDIT 18 0 "K1;" "6#%#K1G" } {TEXT -1 4 " si " }{XPPEDIT 18 0 "K2;" "6#%#K2G" }{TEXT -1 2 " (" } {XPPEDIT 18 0 "0 < K1;" "6#2\"\"!%#K1G" }{TEXT -1 3 " , " }{XPPEDIT 18 0 "0 < K2;" "6#2\"\"!%#K2G" }{TEXT -1 55 "), astfel incat sistemul \+ cu reactie este stabil pentru " }{XPPEDIT 18 0 "K = K1;" "6#/%\"KG%#K1 G" }{TEXT -1 20 " si instabil pentru " }{XPPEDIT 18 0 "K = K2;" "6#/% \"KG%#K2G" }{TEXT -1 1 "." }}{PARA 15 "" 0 "" {TEXT -1 15 "un sistem e ste " }{TEXT 333 19 "neconditonat stabil" }{TEXT 334 0 "" }{TEXT -1 27 " daca pentru orice valoare " }{XPPEDIT 18 0 "K;" "6#%\"KG" }{TEXT -1 2 " (" }{XPPEDIT 18 0 "0 < K;" "6#2\"\"!%\"KG" }{TEXT -1 48 ") a am plificarii sistemul cu reactie este stabil" }}{PARA 15 "" 0 "" {TEXT -1 15 "un sistem este " }{TEXT 335 22 "neconditionat instabil" }{TEXT 336 0 "" }{TEXT -1 27 " daca pentru orice valoare " }{XPPEDIT 18 0 "K; " "6#%\"KG" }{TEXT -1 2 " (" }{XPPEDIT 18 0 "0 < K;" "6#2\"\"!%\"KG" } {TEXT -1 51 ") a amplificarii sistemul cu reactie este instabil." }}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 12 "Mod de lucru" }}{PARA 0 "" 0 "" {TEXT -1 133 "In afara de functiile incluse in libraria standard Maple , in aceasta lucrare vor fi utilizate cateva functii din libraria adit ionala " }{TEXT 288 7 "SCSlib." }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 74 "Pentru trasarea diagramei polare a functiei de transfer i n bucla deschisa:" }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " }{TEXT 291 69 "Bode[polara] \+ " }{HYPERLNK 17 "help" 1 "..\\Help\\Helpfile.mws" "Functia Bode [polara]" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 92 "Pentru reprez entarea conturului si diagramei Nyquist corespunzatoare unui sistem cu reactie:" }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " }{TEXT 289 15 "Nyq uist[contur]" }{TEXT -1 54 " \+ " }{HYPERLNK 17 "help" 1 "..\\Help\\Helpfile.mws" "Functia Nyquist[contur]" }{TEXT -1 1 " " }}{PARA 15 "" 0 "" {TEXT -1 8 "funct ia " }{TEXT 290 16 "Nyquist[diagram]" }{TEXT -1 51 " \+ " }{HYPERLNK 17 "help" 1 "..\\Help\\H elpfile.mws" "Functia Nyquist[diagrama]" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "Pe parcursul lucrari i, vom folosi urmatoarele notatii:" }}{PARA 15 "" 0 "" {XPPEDIT 18 0 " Hd(s);" "6#-%#HdG6#%\"sG" }{TEXT -1 69 " pentru functia de transfer in bucla deschisa a sistemului cu reactie" }}{PARA 15 "" 0 "" {XPPEDIT 18 0 "K;" "6#%\"KG" }{TEXT -1 47 " pentru amplificare (intervine in ex presia lui " }{XPPEDIT 18 0 "Hd(s);" "6#-%#HdG6#%\"sG" }{TEXT -1 1 ") " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "libname: =\"../SCSlib\",libname:" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 3 "Exe" }{TEXT 26 0 "" }{TEXT -1 9 "mplul III" }}{PARA 0 "" 0 "" {TEXT -1 80 " Fie un sistem cu reactie pentru care functia de transfer in bucla desc hisa este:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "Hd:=K*(s+10)*( s-10)/(s*(s^2+1)*(s^2+s+100)):" }}}{PARA 0 "" 0 "" {TEXT -1 299 "Exist a un pol in origine care va fi ocolit de catre conturul Nyquist si alt e doua perechi de cite doi poli complex conjugati situati in semiplanu l sting, poli care vor fi in exteriorul conturului. Reprezentarea diag ramei poli zerouri a functiei de transfer in bucla deschisa si a contu rului Nyquist:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "Nyquist[co ntur](eval(Hd,K=1),repere=[-1,1],compresie=[6,1],tipgrafic=static);" } }{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "64-%'CURVESG6%7\\ ju7$$!+VV5)[%!#>$!+#o:#)=#!\"*7$$!+vGe&[%F*$!+N2QW F*$!+/F#Q;#F-7$$!+u6]NWF*$!+M&oD;#F-7$$!+ee!GV%F*$!+3WDh@F-7$$!+8/KIWF *$!+2E/g@F-7$$!+q$GwU%F*$!+x+te@F-7$$!+:(>[U%F*$!+#pgt:#F-7$$!+4WOAWF* $!+'ejh:#F-7$$!+u;q>WF*$!+X`'[:#F-7$$!+q(QpT%F*$!+m#=N:#F-7$$!+\\QA9WF *$!+#e%>_@F-7$$!+hce6WF*$!+6$34:#F-7$$!+#=V'3WF*$!+yOZ\\@F-7$$!+_s)fS% F*$!+a(y\"[@F-7$$!+F)QJS%F*$!+z**yY@F-7$$!+Tja+WF*$!+!*f_X@F-7$$!+e&*p (R%F*$!+:!QT9#F-7$$!+1*3]R%F*$!+jh#G9#F-7$$!+$y$=#R%F*$!+[([99#F-7$$!+ ;\"4%*Q%F*$!+Of4S@F-7$$!+E3\\'Q%F*$!+)4t'Q@F-7$$!+2qm$Q%F*$!+=jHP@F-7$ $!+Xdw!Q%F*$!+#y\")e8#F-7$$!+\"*[(yP%F*$!+?BZM@F-7$$!+?k?vVF*$!+$GrJ8# F-7$$!+yO8sVF*$!+SJnJ@F-7$$!+UAPpVF*$!+xnKI@F-7$$!+mTTmVF*$!+TX))G@F-7 $$!+C%pNO%F*$!+gv\\F@F-7$$!+w]RgVF*$!+z)\\f7#F-7$$!+.HjdVF*$!+cJgC@F-7 $$!+\\D[aVF*$!+tr1B@F-7$$!+dqf^VF*$!+E.m@@F-7$$!+7]U[VF*$!+nP6?@F-7$$! +'oucM%F*$!+?Gx=@F-7$$!+:r_UVF*$!+%>Qs6#F-7$$!+26ZRVF*$!+5#[d6#F-7$$!+ *f,kL%F*$!+W;D9@F-7$$!+2yKLVF*$!+))Hv7@F-7$$!+V+OIVF*$!+GgI6@F-7$$!+1` 8FVF*$!+zPt4@F-7$$!+dd/CVF*$!+TuA3@F-7$$!+Kpx?VF*$!+'pLm5#F-7$$!+fC!yJ %F*$!+lM=0@F-7$$!+()y\\9VF*$!+\"HsN5#F-7$$!+IbJ6VF*$!+/2--@F-7$$!+%*R7 3VF*$!+VYY+@F-7$$!+l@x/VF*$!+F/$))4#F-7$$!++$o;I%F*$!+6rJ(4#F-7$$!+AFZ )H%F*$!+y!fd4#F-7$$!+OW#\\H%F*$!+z!HS4#F-7$$!+MMp\"H%F*$!+vPX#4#F-7$$! +-4P)G%F*$!+WQ$34#F-7$$!+IG(\\G%F*$!+%3x\"*3#F-7$$!+5@$=G%F*$!+)zXw3#F -7$$!+-eYyUF*$!+CX+'3#F-7$$!+;h5vUF*$!+zkO%3#F-7$$!+v5\\rUF*$!+KRg#3#F -7$$!+,DGoUF*$!+k&R53#F-7$$!+'peXE%F*$!+))RAz?F-7$$!+dz%F*$!+o(Gr/#F-7$$!+^Tt%>%F*$!+//=X?F-7$ $!+.O7\">%F*$!+\\+UV?F-7$$!+Er\"o=%F*$!+(Q?8/#F-7$$!+)p)=$=%F*$!+:8bR? 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Functia de \+ transfer in bucla deschisa are " }{XPPEDIT 18 0 "P = 0;" "6#/%\"PG\"\" !" }{TEXT -1 90 " poli in semiplanul drept, deducem ca numarul de zero uri din semiplanul drept al functiei " }{XPPEDIT 18 0 "F(s);" "6#-%\"F G6#%\"sG" }{TEXT -1 6 " este " }{XPPEDIT 18 0 "Z = 1;" "6#/%\"ZG\"\"\" " }{TEXT -1 3 ". (" }{XPPEDIT 18 0 "Z = N+P;" "6#/%\"ZG,&%\"NG\"\"\"% \"PGF'" }{TEXT -1 37 "). Sistemul cu reactie pozitiva este " }{TEXT 343 23 "neconditionat instabil " }{TEXT -1 32 "avand 1 pol in semiplan ul drept." }{TEXT 344 0 "" }{TEXT -1 0 "" }}}}}{MARK "6 10 6 4" 80 } {VIEWOPTS 1 1 1 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }