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Asachi\", Iasi, Facultatea de Electronica si Telecomunicatii" }}{PARA 19 "" 0 "" {TEXT -1 43 "Labor atorul de Semnale, Circuite si Sisteme" }}{PARA 19 "" 0 "" {URLLINK 17 "http://scs4.etc.tuiasi.ro" 4 "http://scs4.etc.tuiasi.ro/scslabs/Si mbolice/simbolice.htm" "" }{TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 16 "Breviar teoretic" }}{PARA 0 "" 0 "" {TEXT -1 62 "Chestiun i teoretice sunt descrise in Partea I a laboratorului." }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 46 "Reguli de trasare rapida a locului radaci nilor" }}{PARA 0 "" 0 "" {TEXT -1 49 "Consideram functia de transfer i n 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 scur t formulele importante de calcul." }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 16 "Reactie negativa" }}{PARA 0 "" 0 "" {TEXT -1 50 "Functia de transf er 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*-%\"BG6#F'F*F*!\"\"" }{TEXT -1 1 "." }} {PARA 260 "" 0 "" {TEXT -1 5 "Cele " }{XPPEDIT 18 0 "P-Z;" "6#,&%\"PG \"\"\"%\"ZG!\"\"" }{TEXT -1 81 " asimptote are ramurilor care tind spr e 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!\"\"F3,&F4F3F?F@F@" }{TEXT -1 2 ", " } {XPPEDIT 18 0 "yCg = 0;" "6#/%$yCgG\"\"!" }{TEXT -1 1 "." }}{PARA 261 "" 0 "" {TEXT -1 5 "Cele " }{XPPEDIT 18 0 "P-Z;" "6#,&%\"PG\"\"\"%\"ZG !\"\"" }{TEXT -1 81 " asimptote are ramurilor care tind spre infinit f ormeaza cu axa reala unghiurile:" }}{PARA 257 "" 0 "" {XPPEDIT 18 0 "t heta[i] = (2*i+1)*Pi/(P-Z),i = 1 .. P-Z;" "6$/&%&thetaG6#%\"iG*(,&*&\" \"#\"\"\"F'F,F,F,F,F,%#PiGF,,&%\"PGF,%\"ZG!\"\"F1/F';F,,&F/F,F0F1" } {TEXT -1 1 " " }}{PARA 262 "" 0 "" {TEXT -1 29 "Ramurile de pe axa rea la ale " }{TEXT 258 4 "L.R." }{TEXT 259 0 "" }{TEXT -1 35 " sunt situa te la stanga unui numar " }{TEXT 264 5 "impar" }{TEXT -1 36 " de singu laritati (poli si zerouri)." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 16 "R eactie 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*-%\"BG6#F'F*!\"\"F5" }{TEXT -1 1 "." }}{PARA 263 "" 0 "" {TEXT -1 5 "Cele " }{XPPEDIT 18 0 "P-Z;" "6#,&%\"PG\"\"\"%\"ZG !\"\"" }{TEXT -1 81 " asimptote are ramurilor care tind spre infinit s e 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)-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!\"\"F3,&F4F3F?F@F@" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "yCg = \+ 0;" "6#/%$yCgG\"\"!" }{TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT -1 18 "i n planul complex." }}{PARA 265 "" 0 "" {TEXT -1 5 "Cele " }{XPPEDIT 18 0 "P-Z;" "6#,&%\"PG\"\"\"%\"ZG!\"\"" }{TEXT -1 78 " asimptote are r amurilor care tind la infinit formeaza cu axa reala unghiurile" }} {PARA 257 "" 0 "" {XPPEDIT 18 0 "theta[i] = 2*i*Pi/(P-Z),i = 1 .. P-Z; " "6$/&%&thetaG6#%\"iG**\"\"#\"\"\"F'F*%#PiGF*,&%\"PGF*%\"ZG!\"\"F//F' ;F*,&F-F*F.F/" }{TEXT -1 1 " " }}{PARA 266 "" 0 "" {TEXT -1 29 "Ramuri le de pe axa reala ale " }{TEXT 260 4 "L.R." }{TEXT 261 0 "" }{TEXT -1 35 " sunt situate la stanga unui numar " }{TEXT 265 3 "par" }{TEXT -1 36 " de singularitati.(poli si zerouri)." }}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 12 "Mod de lucru" }}{PARA 0 "" 0 "" {TEXT -1 133 "In afa ra de functiile incluse in libraria standard Maple, in aceasta lucrare vor fi utilizate cateva functii din libraria aditionala " }{TEXT 272 7 "SCSlib." }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 57 "Pentru calcu larea functiei de transfer in bucla deschisa:" }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " }{TEXT 275 67 "PZ[numeric] \+ " }{HYPERLNK 17 "help" 1 "..\\Help\\ Helpfile.mws" "Functia PZ[numeric]" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 100 "Pentru reprezentarea locului radacinilor, in plan si in \+ spatiu, corespunzator sistemului cu reactie:" }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " }{TEXT 273 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 274 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 12 "Exemplul III" }}{PARA 0 "" 0 "" {TEXT -1 137 "Ne \+ propunem sa studiem stabilitatea unui sistem cu reactie pentru care fu nctia de transfer in bucla deschisa la amplificare unitara este:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Hd:=s*(s+10)/((s+1)*(s^2+s+1 00)*(s+100));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#HdG*&*&%\"sG\"\"\" ,&F'F(\"#5F(F(F(*(,&F'F(F(F(F(,(*$)F'\"\"#F(F(F'F(\"$+\"F(F(,&F'F(F1F( F(!\"\"" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 62 "Poli si zerourile fun ctiei de transfer in bucla deschisa Hd(s)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "p:=PZ[numeric](Hd,s,singularitati=poli):P:= RowDimens ion(p);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG\"\"% " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "z:=PZ[numeric](Hd,s,sin gularitati=zerouri):Z:= RowDimension(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "PZ[num eric](Hd,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\")'*3q\") -%'MATRIXG6#7(7$%#z1G$\"\"!F.7$%#z2G$!#5F.7$%#p1G^$$!%+]!\"%$\"%()**! \"$7$%#p2G$!\"\"F.7$%#p3G$!$+\"F.7$%#p4G^$F6$!%()**F;" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 16 "Reactie negativa" }}{SECT 0 {PARA 20 "" 0 "" {TEXT -1 22 "Trasarea rapida a L.R." }}{PARA 0 "" 0 "" {TEXT -1 94 "Asimptota ramurii care tind spre infinitse intersecteaza in centru l de greutate de coordonate:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "xCg:=(sum('Re(p[k,2])','k'=1..P)-sum('Re(z[l,2])','l'=1..Z))/(P-Z) ;yCg:=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xCgG$!+++++Y!\")" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$yCgG\"\"!" }}}{PARA 267 "" 0 "" {TEXT -1 73 "Asimptota ramurii care tinde la infinit formeaza cu axa r eala unghiurile:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "theta:=[ seq((2*i+1)*Pi/(P-Z),i=0..P-Z-1)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%&thetaG7$,$%#PiG#\"\"\"\"\"#,$F'#\"\"$F*" }}}}{PARA 0 "" 0 "" {TEXT -1 25 "Locul radacinilor pentru " }{TEXT 266 17 "reactiei negativa" } {TEXT -1 6 " este:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "LocRad [plan](Hd,rn,interval=0..5000);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6^el-%'POINTSG6%7$$!+++++]!#5$\"+y@\\()**!\"*-%'SYMBO LG6$%&CROSSG\"\")-%'COLOURG6&%$RGBG\"\"!F6F6-F$6%7$$!\"\"F6$F6F6F-F2-F 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ctie~negativaFO" 1 2 0 1 10 0 2 1 1 4 2 1.000000 48.000000 3.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7 " "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Cur ve 14" "Curve 15" "Curve 16" "Curve 17" "Curve 18" "Curve 19" "Curve 2 0" "Curve 21" "Curve 22" "Curve 23" "Curve 24" }}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 23 "Discutia de stabilitate" }{TEXT -1 0 "" } }{PARA 258 "" 0 "" {TEXT -1 58 "Pe baza graficelor anterioare, observa m ca toate ramurile " }{TEXT 267 5 "L.R. " }{TEXT -1 90 "sunt situate \+ in totalitate in semiplanul complex sting. Putem spune asadar ca siste mul cu " }{TEXT 269 16 "reactie negativa" }{TEXT -1 6 " este " }{TEXT 268 20 "neconditionat stabil" }{TEXT -1 1 "." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 16 "Reactie pozitiva" }}{SECT 0 {PARA 20 "" 0 "" {TEXT -1 22 "Trasarea rapida a L.R." }}{PARA 268 "" 0 "" {TEXT -1 93 "Asimptota ramurii care tinde spre infinit, 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)-sum('Re(z[l,2])','l'=1..Z))/(P-Z);yCg:=0;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xCgG$!+++++Y!\")" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%$yCgG\"\"!" }}}{PARA 269 "" 0 "" {TEXT -1 73 "Asimp tota 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 " }}}}{PARA 0 "" 0 "" {TEXT -1 25 "Locul radacinilor pentru " }{TEXT 270 17 "reactiei pozitiva" }{TEXT -1 6 " este:" }}{EXCHG 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"Curve 20" "Curve 21" "Curve 22" "Curve 23" "Curve 24" }}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 23 "Discutia de stabilitate" } {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 367 "Pe baza graficelor ant erior, observam ca exista o valoare limita K=K1 cind la cresterea lui \+ K, doua ramuri trec din semiplanul sting in semiplanul drept. Pentru v alori mici ale lui K (KK1) 2 ramuri sunt in semiplanu l drept. Putem spune asadar ca sistemul cu reactie pozitiva este " } {TEXT 271 31 "neconditionat instabil (stabil)" }{TEXT -1 1 "." }}} {PARA 0 "" 0 "" {TEXT -1 252 "Specificul exemplului este perechea de p oli complex conjugati din semiplanul sting. La reactie pozitiva, ramur ile care pleaca din acesti poli ajung pe axa reala in semiplanul drept . La reactie negativa, ramurile diverg la infinit prin semiplanul stin g." }}}}}{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 81700896 }{RTABLE M6R0 I5RTABLE_SAVE/81700896X,%)anythingG6"6"][[[[[p-"'"#%#z1G%#z2G%#p1G%#p2G%#p3G%#p 4G$""!F.$!#5F.^$$!%+]!"%$"%()**!"$$!""F.$!$+"F.^$F2$!%()**F76" }