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Asachi\", Iasi, Facultatea de Elect ronica si Telecomunicatii" }}{PARA 19 "" 0 "" {TEXT -1 43 "Laboratorul de Semnale, Circuite si Sisteme" }}{PARA 19 "" 0 "" {URLLINK 17 "http ://scs4.etc.tuiasi.ro" 4 "http://scs4.etc.tuiasi.ro/scslabs/Simbolice/ simbolice.htm" "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 16 "Breviar teore tic" }}{PARA 0 "" 0 "" {TEXT -1 62 "Chestiuni teoretice sunt descrise \+ in Partea I a laboratorului." }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 46 "R eguli de trasare rapida a locului radacinilor" }}{PARA 0 "" 0 "" {TEXT -1 49 "Consideram functia de transfer in bucla deschisa " } {XPPEDIT 18 0 "Hd(s) = K*A(s)*B(s);" "6#/-%#HdG6#%\"sG*(%\"KG\"\"\"-% \"AG6#F'F*-%\"BG6#F'F*" }{TEXT -1 5 " cu " }{XPPEDIT 18 0 "P;" "6#%\" PG" }{TEXT -1 14 " poli, notati " }{XPPEDIT 18 0 "p[k],k = 1 .. P;" "6 $&%\"pG6#%\"kG/F&;\"\"\"%\"PG" }{TEXT -1 4 " si " }{XPPEDIT 18 0 "Z;" "6#%\"ZG" }{TEXT -1 17 " zerouri, notate " }{XPPEDIT 18 0 "z[l],l = 1 \+ .. Z;" "6$&%\"zG6#%\"lG/F&;\"\"\"%\"ZG" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 56 "Sunt reamintite pe scurt formulele importante de cal cul." }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 16 "Reactie negativa" }} {PARA 0 "" 0 "" {TEXT -1 50 "Functia de transfer a circuitului cu reac tie este:" }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "Hr(s) = K*A(s)/(1+K*A(s) *B(s));" "6#/-%#HrG6#%\"sG*(%\"KG\"\"\"-%\"AG6#F'F*,&F*F**(F)F*-F,6#F' F*-%\"BG6#F'F*F*!\"\"" }{TEXT -1 1 "." }}{PARA 258 "" 0 "" {TEXT -1 5 "Cele " }{XPPEDIT 18 0 "P-Z;" "6#,&%\"PG\"\"\"%\"ZG!\"\"" }{TEXT -1 81 " asimptote are ramurilor care tind spre infinit se intalnesc intr- un punct numit " }{TEXT 262 19 "centru de greutate," }{TEXT -1 2 " (" }{XPPEDIT 18 0 "Cg;" "6#%#CgG" }{TEXT -1 25 "), care are coordonatele: " }}{PARA 257 "" 0 "" {XPPEDIT 18 0 "xCg = (Sum(Real(p[k]),k = 1 .. P) -Sum(Real(z[l]),l = 1 .. Z))/(P-Z);" "6#/%$xCgG*&,&-%$SumG6$-%%RealG6# &%\"pG6#%\"kG/F0;\"\"\"%\"PGF3-F(6$-F+6#&%\"zG6#%\"lG/F<;F3%\"ZG!\"\"F 3,&F4F3F?F@F@" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "yCg = 0;" "6#/%$yCgG\" \"!" }{TEXT -1 1 "." }}{PARA 259 "" 0 "" {TEXT -1 5 "Cele " }{XPPEDIT 18 0 "P-Z;" "6#,&%\"PG\"\"\"%\"ZG!\"\"" }{TEXT -1 81 " asimptote are r amurilor care tind spre infinit formeaza cu axa reala unghiurile:" }} {PARA 257 "" 0 "" {XPPEDIT 18 0 "theta[i] = (2*i+1)*Pi/(P-Z),i = 1 .. \+ P-Z;" "6$/&%&thetaG6#%\"iG*(,&*&\"\"#\"\"\"F'F,F,F,F,F,%#PiGF,,&%\"PGF ,%\"ZG!\"\"F1/F';F,,&F/F,F0F1" }{TEXT -1 1 " " }}{PARA 260 "" 0 "" {TEXT -1 29 "Ramurile de pe axa reala ale " }{TEXT 258 4 "L.R." } {TEXT 259 0 "" }{TEXT -1 35 " sunt situate la stanga unui numar " } {TEXT 264 5 "impar" }{TEXT -1 36 " de singularitati (poli si zerouri). " }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 16 "Reactie pozitiva" }}{PARA 0 "" 0 "" {TEXT -1 50 "Functia de transfer a circuitului cu reactie este :" }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "Hr(s) = K*A(s)/(1-K*A(s)*B(s)); " "6#/-%#HrG6#%\"sG*(%\"KG\"\"\"-%\"AG6#F'F*,&F*F**(F)F*-F,6#F'F*-%\"B G6#F'F*!\"\"F5" }{TEXT -1 1 "." }}{PARA 261 "" 0 "" {TEXT -1 5 "Cele \+ " }{XPPEDIT 18 0 "P-Z;" "6#,&%\"PG\"\"\"%\"ZG!\"\"" }{TEXT -1 81 " asi mptote are ramurilor care tind spre infinit se intalnesc intr-un punct numit " }{TEXT 263 18 "centru de greutate" }{TEXT -1 4 " , (" } {XPPEDIT 18 0 "Cg;" "6#%#CgG" }{TEXT -1 23 "),care are coordonatele" } }{PARA 257 "" 0 "" {XPPEDIT 18 0 "xCg = (Sum(Real(p[k]),k = 1 .. P)-Su m(Real(z[l]),l = 1 .. Z))/(P-Z);" "6#/%$xCgG*&,&-%$SumG6$-%%RealG6#&% \"pG6#%\"kG/F0;\"\"\"%\"PGF3-F(6$-F+6#&%\"zG6#%\"lG/F<;F3%\"ZG!\"\"F3, &F4F3F?F@F@" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "yCg = 0;" "6#/%$yCgG\"\" !" }{TEXT -1 0 "" }}{PARA 262 "" 0 "" {TEXT -1 18 "in planul complex. " }}{PARA 263 "" 0 "" {TEXT -1 5 "Cele " }{XPPEDIT 18 0 "P-Z;" "6#,&% \"PG\"\"\"%\"ZG!\"\"" }{TEXT -1 78 " asimptote are ramurilor care tind la infinit formeaza cu axa reala unghiurile" }}{PARA 257 "" 0 "" {XPPEDIT 18 0 "theta[i] = 2*i*Pi/(P-Z),i = 1 .. P-Z;" "6$/&%&thetaG6#% \"iG**\"\"#\"\"\"F'F*%#PiGF*,&%\"PGF*%\"ZG!\"\"F//F';F*,&F-F*F.F/" } {TEXT -1 1 " " }}{PARA 264 "" 0 "" {TEXT -1 29 "Ramurile de pe axa rea la ale " }{TEXT 260 4 "L.R." }{TEXT 261 0 "" }{TEXT -1 35 " sunt situa te la stanga unui numar " }{TEXT 265 3 "par" }{TEXT -1 36 " de singula ritati.(poli si zerouri)." }}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 12 "M od de lucru" }}{PARA 0 "" 0 "" {TEXT -1 133 "In afara de functiile inc luse in libraria standard Maple, in aceasta lucrare vor fi utilizate c ateva functii din libraria aditionala " }{TEXT 271 7 "SCSlib." }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 57 "Pentru calcularea functiei de t ransfer in bucla deschisa:" }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " } {TEXT 274 67 "PZ[numeric] \+ " }{HYPERLNK 17 "help" 1 "..\\Help\\Helpfile.mws" "Functia \+ PZ[numeric]" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 100 "Pentru re prezentarea locului radacinilor, in plan si in spatiu, corespunzator s istemului cu reactie:" }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " } {TEXT 272 12 "LocRad[plan]" }{TEXT -1 54 " \+ " }{HYPERLNK 17 "help" 1 "..\\Help\\Helpfile .mws" "Functia LocRad[plan]" }{TEXT -1 1 " " }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " }{TEXT 273 14 "LocRad[spatiu]" }{TEXT -1 51 " \+ " }{HYPERLNK 17 "help" 1 ".. \\Help\\Helpfile.mws" "Functia LocRad[spatiu]" }{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:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with (LinearAlgebra):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "rp := ' reactie = pozitiva':rn := 'reactie = negativa':" }}}}{SECT 0 {PARA 3 " " 0 "" {TEXT -1 7 "Exemple" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 11 "Exe mplul IV" }}{PARA 0 "" 0 "" {TEXT -1 137 "Ne propunem sa studiem stabi litatea unui sistem cu reactie pentru care functia de transfer in bucl a deschisa la amplificare unitara este:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Hd:=1/((s+1)*(s^2+s+1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#HdG*&\"\"\"F&*&,&%\"sGF&F&F&F&,(*$)F)\"\"#F&F&F)F&F& F&F&!\"\"" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 62 "Poli si zerourile f unctiei de transfer in bucla deschisa Hd(s)" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 60 "p:=PZ[numeric](Hd,s,singularitati=poli):P:= RowDime nsion(p);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG\"\" $" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "z:=PZ[numeric](Hd,s,si ngularitati=zerouri):Z:= RowDimension(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "PZ[numeric](Hd,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$ \")o4q\")-%'MATRIXG6#7%7$%#p1G^$$!%+]!\"%$\"%g')F07$%#p2G$!\"\"\"\"!7$ %#p3G^$F.$!%g')F0" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 16 "Reactie ne gativa" }}{SECT 0 {PARA 20 "" 0 "" {TEXT -1 22 "Trasarea rapida a L.R. " }}{PARA 0 "" 0 "" {TEXT -1 94 "Asimptota ramurii care tind spre infi nitse intersecteaza in centrul de greutate de coordonate:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "xCg:=(sum('Re(p[k,2])','k'=1..P)-su m('Re(z[l,2])','l'=1..Z))/(P-Z);yCg:=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xCgG$!+nmmmm!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$yCgG\" \"!" }}}{PARA 265 "" 0 "" {TEXT -1 73 "Asimptota ramurii care tinde la infinit formeaza cu axa reala unghiurile:" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 42 "theta:=[seq((2*i+1)*Pi/(P-Z),i=0..P-Z-1)];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&thetaG7%,$%#PiG#\"\"\"\"\"$F',$F'# \"\"&F*" }}}}{PARA 0 "" 0 "" {TEXT -1 25 "Locul radacinilor pentru " } {TEXT 266 17 "reactiei negativa" }{TEXT -1 6 " este:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "LocRad[plan](Hd,rn,interval=0..20);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6e^l-%'POINTSG6%7$ $!+++++]!#5$\"+QSDg')F)-%'SYMBOLG6$%&CROSSG\"\")-%'COLOURG6&%$RGBG\"\" !F5F5-F$6%7$$!\"\"F5$F5F5F,F1-F$6%7$F'$!+QSDg')F)F,F1-%%TEXTG6(F&Q$p1~ 6\"%+ALIGNBELOWG%*ALIGNLEFTG-%%FONTG6$%*HELVETICAG\"#5F1-FB6(F8Q$p2~FE FFFGFHF1-FB6(F>Q$p3~FEFFFGFHF1-F$6%7$$!+nmmmmF)F;-F-6$%(DIAMONDG\"\"#- F26&F4F5F5\"\"\"-FB6&FUQ$~Cg6\"-FI6%FK%%BOLDGFL-%&COLORGFgn-%'CURVESG6 &7`qFU7$$!+dEV`7!\"*$\"+PhqgM!#>7$$!+*[XfS\"Fio$\"+4l@gVF\\p7$$!+k'HH^ \"Fio$\"+R>?\"*\\F\\p7$$!+<'*4)f\"Fio$\"+i&GN\\&F\\p7$$!+(RA+n\"Fio$\" +aUsS=Fio$\"+wAT@pF\\p7$$!+6\"*=()=Fio$\"+\\)e&)>(F\\p7$$!+sc\"3 $>Fio$\"+c`'eX(F\\p7$$!+ZDir>Fio$\"+Y:a'p(F\\p7$$!+Ra-5?Fio$\"+1#RI#zF \\p7$$!+%*)\\j/#Fio$\"+'Qys8)F\\p7$$!+!=c33#Fio$\"+FTzS$)F\\p7$$!+Pgv8 @Fio$\"+f_$[`)F\\p7$$!+7VAX@Fio$\"+=IV?()F\\p7$$!+csSv@Fio$\"+!)*\\%)* ))F\\p7$$!+(eGW?#Fio$\"+Gehp!*F\\p7$$!+.SRKAFio$\"+hRbM#*F\\p7$$!+3YRf AFio$\"+/fBFio$\"+yQS#)**F\\p7$$!+J3Q#Q #Fio$\"+8m\">,\"!#=7$$!+1'e\\S#Fio$\"+KGBD5Few7$$!+QY'pU#Fio$\"+T=@Q5F ew7$$!+-QV[CFio$\"+4U(30\"Few7$$!+#p(RpCFio$\"+p&QK1\"Few7$$!+E]))*[#F io$\"+g=Kv5Few7$$!+(*>#*4DFio$\"+I&Rr3\"Few7$$!+oD`HDFio$\"+8dq)4\"Few 7$$!+D(Q([DFio$\"+uL.56Few7$$!+%pgvc#Fio$\"+WW8@6Few7$$!+Ir,'e#Fio$\"+ D*>?8\"Few7$$!+z_7/EFio$\"+*)**pU6Few7$$!+A6!>i#Fio$\"+hS=`6Few7$$!+' \\f$REFio$\"+#*3[j6Few7$$!+3U^cEFio$\"+D')ft6Few7$$!+F\"yLn#Fio$\"+^[a $=\"Few7$$!+rK'**o#Fio$\"+dmK$>\"Few7$$!+%)3G1FFio$\"+u1&H?\"Few7$$!+* \\TBs#Fio$\"+;JU77Few7$$!+/]:QFFio$\"+:)\\9Few7$$!+:n*[3$Fio$\"+JdDE9Few7$$! 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de poli complex conjugati din semiplanul complex sting la K=0, pentru valori mici ale amplificarii K (KK1) sunt in semiplanul d rept. Putem spune asadar ca sistemul cu " }{TEXT 268 16 "reactie negat iva" }{TEXT -1 6 " este " }{TEXT 267 29 "conditionat stabil (instabil) " }{TEXT -1 1 "." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 16 "Reactie pozi tiva" }}{SECT 0 {PARA 20 "" 0 "" {TEXT -1 22 "Trasarea rapida a L.R." }}{PARA 267 "" 0 "" {TEXT -1 93 "Asimptota ramurii care tinde spre inf init, are originea in centrul de greutate de coordonate:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "xCg:=(sum('Re(p[k,2])','k'=1..P)-su m('Re(z[l,2])','l'=1..Z))/(P-Z);yCg:=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xCgG$!+nmmmm!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$yCgG\" \"!" }}}{PARA 268 "" 0 "" {TEXT -1 73 "Asimptota ramurii care tinde la infinit formeaza cu axa reala unghiurile:" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 38 "theta:=[seq(2*i*Pi/(P-Z),i=0..P-Z-1)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&thetaG7%\"\"!,$%#PiG#\"\"#\"\"$,$F(#\"\"%F+ " }}}}{PARA 0 "" 0 "" {TEXT -1 25 "Locul radacinilor pentru " }{TEXT 269 17 "reactiei pozitiva" 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Putem spune asadar ca sis temul cu reactie pozitiva este " }{TEXT 270 22 "neconditionat instabil " }{TEXT -1 1 "." }}}{PARA 0 "" 0 "" {TEXT -1 221 "Specificul exemplul ui este perechea de poli complex conjugati din semiplanul sting. La re actie pozitiva, sistemul este instabil. La reactie negativa, sistemul \+ poate fi stabil sau instabil. Asimptotele sunt in numar de 3 ." }}}}} {MARK "6 10 0 0" 20 }{VIEWOPTS 1 1 1 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 81700968 }{RTABLE M6R0 I5RTABLE_SAVE/81700968X,%)anythingG6"6"][[[[[p'"$"#%#p1G%#p2G%#p3G^$$!%+]!"%$"% g')F-$!""""!^$F+$!%g')F-6" }