(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. The line below identifies what version of Mathematica created this file, but it can be opened using any other version as well."; FrontEndVersion = "NeXT Mathematica Notebook Front End Version 2.2"; NeXTStandardFontEncoding; fontset = title, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L1, e8, 24, "Times"; ; fontset = subtitle, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L1, e6, 18, "Times"; ; fontset = subsubtitle, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, L1, e6, 14, "Times"; ; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, L1, a20, 18, "Times"; ; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, L1, a15, 14, "Times"; ; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, L1, a12, 12, "Times"; ; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 10, "Times"; ; fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L1, 12, "Courier"; ; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; ; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, L1, 12, "Courier"; ; fontset = name, inactive, noPageBreakInGroup, nohscroll, preserveAspect, M7, italic, B65535, L1, 10, "Times"; ; fontset = header, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, L1, 12, "Times"; ; fontset = leftheader, 12; fontset = footer, inactive, nohscroll, noKeepOnOnePage, preserveAspect, center, M7, italic, L1, 12, "Times"; ; fontset = leftfooter, 12; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Courier"; ; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; paletteColors = 128; automaticGrouping; currentKernel; ] :[font = title; inactive; preserveAspect; startGroup] The Control Package :[font = subsubtitle; inactive; preserveAspect] (Author: Wilhelm Haager) :[font = section; inactive; Cclosed; preserveAspect; startGroup] Reading the Package "Control" :[font = input; preserveAspect; endGroup] <0.1)+(Fs/.a->1))/(Fs/.a->2) :[font = output; output; inactive; preserveAspect; endGroup; endGroup] (1 + 2*s + s^2)*((1 + 0.1*s + s^2)^(-1) + (1 + s + s^2)^(-1)) ;[o] 2 1 1 (1 + 2 s + s ) (-------------- + ----------) 2 2 1 + 0.1 s + s 1 + s + s :[font = section; inactive; Cclosed; preserveAspect; startGroup] Poles and Zeros :[font = input; preserveAspect; startGroup] Poles[F1] :[font = output; output; inactive; preserveAspect; endGroup] {-0.5 - 0.866025403784439*I, -0.5 + 0.866025403784439*I, -0.0500000000000001 - 0.998749217771909*I, -0.0500000000000001 + 0.998749217771909*I} ;[o] {-0.5 - 0.866025 I, -0.5 + 0.866025 I, -0.05 - 0.998749 I, -0.05 + 0.998749 I} :[font = input; preserveAspect; startGroup] Zeros[F1] :[font = output; output; inactive; preserveAspect; endGroup; endGroup] {-1.000000000000003, -0.999999999999997, -0.275 - 0.961444226151471*I, -0.275 + 0.961444226151471*I} ;[o] {-1., -1., -0.275 - 0.961444 I, -0.275 + 0.961444 I} :[font = section; inactive; Cclosed; preserveAspect; startGroup] (Inverse) Laplace Transform :[font = text; inactive; preserveAspect] LT is a convenient form of the Laplace Transform with t assumed to be the time variable and s assumed to be the Laplace Variable. ILT and NILT calculate the inverse Laplace Transform. ;[s] 10:0,0;2,1;54,2;55,3;92,4;93,5;131,6;134,7;139,8;143,9;184,-1; 10:1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = input; preserveAspect; startGroup] F1t = ILT[F1] :[font = output; output; inactive; preserveAspect; endGroup] (1.9*Cos[0.998749217771909*t])/E^(0.05*t) + Cos[(3^(1/2)*t)/2]/E^(0.5*t) + 2*DiracDelta[t] - (0.0951189731211342*Sin[0.998749217771909*t])/ E^(0.05*t) - Sin[(3^(1/2)*t)/2]/(3^(1/2)*E^(0.5*t)) ;[o] Sqrt[3] t Cos[---------] 1.9 Cos[0.998749 t] 2 ------------------- + -------------- + 0.05 t 0.5 t E E 0.095119 Sin[0.998749 t] 2 DiracDelta[t] - ------------------------ - 0.05 t E Sqrt[3] t Sin[---------] 2 -------------- 0.5 t Sqrt[3] E :[font = input; preserveAspect; startGroup] Chop[LT[F1t] - F1 // Simplify] :[font = output; output; inactive; preserveAspect; endGroup; endGroup] 0 ;[o] 0 :[font = section; inactive; Cclosed; preserveAspect; startGroup] Step Responses :[font = text; inactive; preserveAspect] The first argument is a transfer function or a list of transfer functions, the second argument is the displayed time interval. Additional options are passed to the function Plot. ;[s] 3:0,0;174,1;178,2;179,-1; 3:1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = input; preserveAspect; startGroup] StepResponse[Table[Fs, {a, 0.1, 1, 0.1}], 10] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.02381 0.095238 0.014715 0.3174 [ [(0)] .02381 0 0 2 Msboxa [(2)] .21429 0 0 2 Msboxa [(4)] .40476 0 0 2 Msboxa [(6)] .59524 0 0 2 Msboxa [(8)] .78571 0 0 2 Msboxa [(10)] .97619 0 0 2 Msboxa [(0)] -0.0125 .01472 1 0 Msboxa [(0.25)] -0.0125 .09407 1 0 Msboxa [(0.5)] -0.0125 .17342 1 0 Msboxa [(0.75)] -0.0125 .25277 1 0 Msboxa [(1)] -0.0125 .33211 1 0 Msboxa [(1.25)] -0.0125 .41146 1 0 Msboxa [(1.5)] -0.0125 .49081 1 0 Msboxa [(1.75)] -0.0125 .57016 1 0 Msboxa [ 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.08333 .07004 L .10317 .10817 L .14286 .2008 L .18254 .29992 L .22222 .38889 L .24206 .42547 L .2619 .45525 L .27183 .46737 L .28175 .47755 L .29167 .48577 L .29663 .48914 L .30159 .49202 L .30655 .49442 L .31151 .49632 L .31399 .4971 L .31647 .49775 L .31895 .49829 L .32143 .49871 L .32267 .49887 L .32391 .49901 L .32515 .49911 L .32639 .49919 L .32763 .49924 L .32887 .49926 L .33011 .49926 L .33135 .49922 L .33259 .49916 L .33383 .49907 L .33631 .4988 L .33879 .49843 L .34127 .49794 L .34623 .49666 L .35119 .49495 L .36111 .49036 L .37103 .48427 L .38095 .47682 L .42063 .43613 L .46032 .38529 L .5 .33387 L Mistroke .51984 .3106 L .53968 .29008 L .55952 .27294 L .56944 .26579 L .57937 .25963 L .58929 .25449 L .59921 .25039 L .60417 .24873 L .60913 .24732 L .61409 .24617 L .61905 .24528 L .62153 .24493 L .62401 .24464 L .62649 .24441 L .62773 .24432 L .62897 .24424 L .63021 .24418 L .63145 .24414 L .63269 .24411 L .63393 .24409 L .63517 .24409 L .63641 .24411 L .63765 .24414 L .63889 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.28175 .45146 L .29167 .4592 L .30159 .46521 L .30655 .46756 L .31151 .4695 L .31647 .47102 L .32143 .47212 L .32391 .47252 L .32515 .47269 L .32639 .47282 L .32763 .47294 L .32887 .47303 L .33011 .47309 L .33135 .47313 L .33259 .47315 L .33383 .47314 L .33507 .47311 L .33631 .47306 L .33755 .47298 L .33879 .47288 L .34127 .4726 L .34375 .47224 L .34623 .47179 L .35119 .47062 L .35615 .46911 L .36111 .46727 L .38095 .45691 L .40079 .44245 L .42063 .42489 L .46032 .38456 L .5 .34372 L Mistroke .53968 .30876 L .55952 .29493 L .57937 .28399 L .58929 .27966 L .59921 .27611 L .60913 .27332 L .61905 .27131 L .62401 .27058 L .62649 .27028 L .62897 .27003 L .63145 .26983 L .63393 .26967 L .63517 .2696 L .63641 .26955 L .63765 .26951 L .63889 .26948 L .64013 .26946 L .64137 .26945 L .64261 .26945 L .64385 .26946 L .64509 .26948 L .64633 .26952 L .64881 .26961 L .65005 .26968 L .65129 .26975 L .65377 .26993 L .65873 .2704 L .66369 .27103 L .66865 .2718 L .67857 .27377 L .69841 .2792 L .7381 .29452 L .77778 .31276 L .81746 .33057 L .85714 .34526 L .87698 .35087 L .8869 .35319 L .89683 .35516 L .90675 .35679 L .91667 .35808 L .92163 .35859 L .92659 .35902 L .93155 .35937 L .93403 .35952 L .93651 .35964 L .93899 .35974 L .94147 .35982 L .94271 .35986 L .94395 .35989 L .94519 .35991 L Mistroke .94643 .35993 L .94767 .35995 L .94891 .35996 L .95015 .35996 L .95139 .35996 L .95263 .35996 L .95387 .35995 L .95511 .35993 L .95635 .35992 L .95883 .35986 L .96131 .3598 L .96379 .35971 L .96627 .35961 L .97619 .35902 L Mfstroke P P p 1 0 0 r p .004 w .02381 .01472 m .02505 .01474 L .02629 .01482 L .02753 .01496 L .02877 .01514 L .03125 .01567 L .03373 .0164 L .03869 .01846 L .04365 .0213 L .05357 .02917 L .06349 .03975 L .08333 .06791 L .10317 .10351 L .14286 .18778 L .18254 .27526 L .22222 .352 L .24206 .38325 L .2619 .40875 L .27183 .41922 L .28175 .42814 L .29167 .43551 L .30159 .44135 L .30655 .4437 L .31151 .44569 L .31647 .4473 L .32143 .44856 L .32391 .44906 L .32639 .44948 L .32887 .4498 L .33011 .44993 L .33135 .45005 L .33259 .45014 L .33383 .4502 L .33507 .45025 L .33631 .45028 L .33755 .45029 L .33879 .45028 L .34003 .45025 L .34127 .4502 L .34375 .45004 L .34499 .44993 L .34623 .4498 L .35119 .4491 L .35615 .44811 L .36111 .44684 L .37103 .44351 L .38095 .43921 L .40079 .42812 L .42063 .41444 L .46032 .38268 L Mistroke .5 .35029 L .53968 .32232 L .55952 .31108 L .57937 .30201 L .58929 .29834 L .59921 .29524 L .60913 .29271 L .61905 .29076 L .62401 .28999 L .62897 .28935 L .63393 .28885 L .63641 .28865 L .63889 .28849 L .64137 .28835 L .64261 .28829 L .64385 .28824 L .64509 .2882 L .64633 .28817 L .64757 .28815 L .64881 .28813 L .65005 .28812 L .65129 .28811 L .65253 .28812 L .65377 .28813 L .65501 .28815 L .65625 .28818 L .65749 .28821 L .65873 .28825 L .66369 .28849 L .66617 .28865 L .66865 .28883 L .67857 .28983 L .68849 .29122 L .69841 .29294 L .7381 .30253 L .77778 .31447 L .81746 .32644 L .85714 .33663 L .87698 .34066 L .89683 .34387 L .91667 .34623 L .92659 .34709 L .93155 .34744 L .93651 .34774 L .94147 .34799 L .94643 .34818 L .94891 .34826 L .95139 .34833 L .95387 .34839 L .95635 .34843 L Mistroke .95759 .34845 L .95883 .34847 L .96007 .34848 L .96131 .34849 L .96255 .34849 L .96379 .3485 L .96503 .3485 L .96627 .3485 L .96751 .34849 L .96875 .34848 L .96999 .34847 L .97123 .34846 L .97371 .34843 L .97619 .34838 L Mfstroke P P p 1 0 0 r p .004 w .02381 .01472 m .02505 .01474 L .02629 .01482 L .02753 .01496 L .02877 .01514 L .03125 .01567 L .03373 .01639 L .03869 .01844 L .04365 .02126 L .05357 .02903 L .06349 .03942 L .08333 .0669 L .10317 .10132 L .14286 .18181 L .18254 .26425 L .22222 .33591 L .24206 .36503 L .2619 .38887 L .27183 .39873 L .28175 .4072 L .29167 .41428 L .30159 .42001 L .31151 .42442 L .32143 .42755 L .32639 .42866 L .32887 .4291 L .33135 .42947 L .33383 .42976 L .33631 .42999 L .33755 .43008 L .33879 .43014 L .34003 .4302 L .34127 .43023 L .34251 .43025 L .34375 .43025 L .34499 .43023 L .34623 .4302 L .34747 .43015 L .34871 .43009 L .35119 .42991 L .35367 .42968 L .35615 .42938 L .36111 .4286 L .36607 .42759 L .37103 .42636 L .38095 .4233 L .40079 .41506 L .42063 .40459 L .46032 .37986 L .5 .35429 L Mistroke .53968 .33191 L .55952 .32275 L .57937 .31521 L .59921 .30938 L .60913 .3071 L .61905 .30525 L .62897 .30381 L .63393 .30324 L .63889 .30277 L .64385 .30239 L .64881 .3021 L .65129 .30199 L .65377 .30191 L .65625 .30184 L .65749 .30182 L .65873 .3018 L .65997 .30178 L .66121 .30178 L .66245 .30177 L .66369 .30177 L .66493 .30178 L .66617 .30179 L .66741 .30181 L .66865 .30183 L .67113 .30189 L .67361 .30197 L .67857 .30218 L .68353 .30247 L .68849 .30282 L .69841 .30372 L .71825 .30619 L .7381 .30937 L .77778 .31696 L .81746 .32489 L .85714 .33188 L .87698 .33475 L .89683 .33714 L .91667 .33899 L .92659 .33972 L .93651 .34032 L .94643 .34079 L .95139 .34098 L .95635 .34114 L .96131 .34126 L .96627 .34136 L .96875 .3414 L .97123 .34143 L .97371 .34146 L .97619 .34148 L Mfstroke P P p 1 0 0 r p .004 w .02381 .01472 m .02505 .01474 L .02629 .01482 L .02753 .01495 L .02877 .01514 L .03125 .01566 L .03373 .01639 L .03869 .01843 L .04365 .02121 L .05357 .02888 L .06349 .0391 L .08333 .06591 L .10317 .09921 L .14286 .17617 L .18254 .25401 L .22222 .32115 L .24206 .34842 L .2619 .37086 L .28175 .3883 L .29167 .39517 L .30159 .40083 L .31151 .40533 L .32143 .4087 L .32639 .40998 L .33135 .41101 L .33631 .41178 L .33879 .41208 L .34127 .41231 L .34375 .41249 L .34499 .41255 L .34623 .41261 L .34747 .41264 L .34871 .41267 L .34995 .41268 L .35119 .41268 L .35243 .41266 L .35367 .41263 L .35491 .41258 L .35615 .41253 L .35863 .41238 L .36111 .41217 L .36607 .41162 L .37103 .41088 L .38095 .40887 L .39087 .40622 L .40079 .40301 L .42063 .39523 L .46032 .37627 L .5 .35627 L .53968 .33841 L Mistroke .55952 .33097 L .57937 .32471 L .59921 .3197 L .61905 .31596 L .62897 .31455 L .63889 .31344 L .64881 .31261 L .65377 .3123 L .65873 .31205 L .66369 .31186 L .66617 .31179 L .66865 .31174 L .67113 .3117 L .67237 .31169 L .67361 .31168 L .67485 .31167 L .67609 .31167 L .67733 .31167 L .67857 .31167 L .67981 .31168 L .68105 .31169 L .68229 .3117 L .68353 .31172 L .68601 .31176 L .68849 .31182 L .69345 .31197 L .69841 .31216 L .70833 .31269 L .71825 .31338 L .7381 .31515 L .77778 .31976 L .81746 .32486 L .85714 .32957 L .87698 .33159 L .89683 .33331 L .91667 .33473 L .93651 .33582 L .94643 .33625 L .95635 .3366 L .96627 .33688 L .97619 .33708 L Mfstroke P P p 1 0 0 r p .004 w .02381 .01472 m .02505 .01474 L .02629 .01482 L .02753 .01495 L .02877 .01514 L .03125 .01566 L .03373 .01638 L .03869 .01841 L .04365 .02117 L .05357 .02874 L .06349 .03878 L .08333 .06495 L .10317 .09718 L .14286 .17084 L .18254 .24448 L .22222 .3076 L .2619 .35447 L .28175 .37119 L .29167 .37788 L .30159 .3835 L .31151 .38809 L .32143 .39169 L .32639 .39313 L .33135 .39434 L .33631 .39534 L .34127 .39612 L .34375 .39643 L .34623 .3967 L .34871 .39691 L .35119 .39708 L .35243 .39714 L .35367 .39719 L .35491 .39724 L .35615 .39727 L .35739 .39728 L .35863 .39729 L .35987 .39729 L .36111 .39727 L .36235 .39725 L .36359 .39721 L .36607 .39711 L .36855 .39696 L .37103 .39678 L .37599 .39629 L .38095 .39566 L .39087 .39398 L .40079 .39182 L .42063 .38628 L .46032 .3721 L .5 .35665 L Mistroke .53968 .34253 L .55952 .3365 L .57937 .33134 L .59921 .32709 L .61905 .32376 L .62897 .32243 L .63889 .32133 L .64881 .32043 L .65873 .31974 L .66369 .31947 L .66865 .31924 L .67361 .31905 L .67857 .31891 L .68105 .31886 L .68353 .31881 L .68601 .31878 L .68725 .31876 L .68849 .31875 L .68973 .31874 L .69097 .31874 L .69221 .31873 L .69345 .31873 L .69469 .31873 L .69593 .31873 L .69717 .31874 L .69841 .31875 L .70089 .31877 L .70337 .3188 L .70585 .31883 L .70833 .31888 L .71329 .31899 L .71825 .31914 L .72817 .3195 L .7381 .31997 L .77778 .32254 L .81746 .32568 L .85714 .32875 L .89683 .33134 L .91667 .33238 L .93651 .33324 L .95635 .3339 L .97619 .33438 L Mfstroke P P p 1 0 0 r p .004 w .02381 .01472 m .02505 .01474 L .02629 .01482 L .02753 .01495 L .02877 .01514 L .03125 .01566 L .03373 .01638 L .03869 .01839 L .04365 .02113 L .05357 .02861 L .06349 .03847 L .08333 .06402 L .10317 .09523 L .14286 .16579 L .18254 .23559 L .22222 .29511 L .2619 .33953 L .28175 .35562 L .29167 .36218 L .30159 .36777 L .31151 .37245 L .32143 .37625 L .33135 .37921 L .33631 .3804 L .34127 .3814 L .34623 .38222 L .35119 .38287 L .35367 .38313 L .35615 .38335 L .35863 .38353 L .36111 .38367 L .36235 .38372 L .36359 .38377 L .36483 .3838 L .36607 .38383 L .36731 .38385 L .36855 .38386 L .36979 .38386 L .37103 .38385 L .37227 .38384 L .37351 .38381 L .37475 .38378 L .37599 .38374 L .38095 .38349 L .38343 .38332 L .38591 .38312 L .39087 .38263 L .40079 .38134 L .42063 .37768 L .46032 .36747 L Mistroke .5 .35579 L .53968 .34478 L .57937 .33575 L .59921 .33218 L .61905 .32928 L .63889 .32704 L .64881 .32616 L .65873 .32542 L .66865 .32483 L .67857 .32436 L .68353 .32418 L .68849 .32403 L .69345 .32391 L .69841 .32381 L .70089 .32377 L .70337 .32374 L .70585 .32372 L .70833 .3237 L .70957 .32369 L .71081 .32369 L .71205 .32368 L .71329 .32368 L .71453 .32368 L .71577 .32368 L .71701 .32368 L .71825 .32368 L .71949 .32369 L .72073 .32369 L .72321 .32371 L .72569 .32373 L .72817 .32376 L .73313 .32383 L .7381 .32391 L .74802 .32413 L .75794 .32442 L .77778 .32513 L .81746 .3269 L .85714 .32881 L .89683 .33052 L .91667 .33125 L .93651 .33188 L .97619 .3328 L Mfstroke P P P % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect; endGroup; endGroup] Graphics["<<>>"] ;[o] -Graphics- :[font = section; inactive; Cclosed; preserveAspect; startGroup] Bode Diagrams :[font = text; inactive; preserveAspect] The first argument is a transfer function or a list of transfer functions, of which the frequency response is to be plotted. The option LogRange defines the logarithmic limits for the angular frequency. Further options are passed to the function Plot. ;[s] 5:0,0;137,1;145,2;248,3;252,4;253,-1; 5:1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = subsection; inactive; preserveAspect; startGroup] Magnitude Plot: :[font = input; preserveAspect; startGroup] BodePlot[Table[Fs, {a, 0.1, 1, 0.1}], PlotRange->{-2,1}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.47619 0.412023 0.206011 [ [(-1)] .02381 0 0 2 Msboxa [(-0.5)] .2619 0 0 2 Msboxa [(0)] .5 0 0 2 Msboxa [(0.5)] .7381 0 0 2 Msboxa [(1)] .97619 0 0 2 Msboxa [(-2)] -0.0125 0 1 0 Msboxa [(-1.5)] -0.0125 .10301 1 0 Msboxa [(-1)] -0.0125 .20601 1 0 Msboxa [(-0.5)] -0.0125 .30902 1 0 Msboxa [(0)] -0.0125 .41202 1 0 Msboxa [(0.5)] -0.0125 .51503 1 0 Msboxa [(1)] -0.0125 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(-1)] .02381 0 0 2 Mshowa p .002 w .2619 0 m .2619 .00625 L s P [(-0.5)] .2619 0 0 2 Mshowa p .002 w .5 0 m .5 .00625 L s P [(0)] .5 0 0 2 Mshowa p .002 w .7381 0 m .7381 .00625 L s P [(0.5)] .7381 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(1)] .97619 0 0 2 Mshowa p .001 w .07143 0 m .07143 .00375 L s P p .001 w .11905 0 m .11905 .00375 L s P p .001 w .16667 0 m .16667 .00375 L s P p .001 w .21429 0 m .21429 .00375 L s P p .001 w .30952 0 m .30952 .00375 L s P p .001 w .35714 0 m .35714 .00375 L s P p .001 w .40476 0 m .40476 .00375 L s P p .001 w .45238 0 m .45238 .00375 L s P p .001 w .54762 0 m .54762 .00375 L s P p .001 w .59524 0 m .59524 .00375 L s P p .001 w .64286 0 m .64286 .00375 L s P p .001 w .69048 0 m .69048 .00375 L s P 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.0515 m 1 .0515 L s P p .001 w .99625 .06867 m 1 .06867 L s P p .001 w .99625 .08584 m 1 .08584 L s P p .001 w .99625 .12017 m 1 .12017 L s P p .001 w .99625 .13734 m 1 .13734 L s P p .001 w .99625 .15451 m 1 .15451 L s P p .001 w .99625 .17168 m 1 .17168 L s P p .001 w .99625 .20601 m 1 .20601 L s P p .001 w .99625 .22318 m 1 .22318 L s P p .001 w .99625 .24035 m 1 .24035 L s P p .001 w .99625 .25751 m 1 .25751 L s P p .001 w .99625 .29185 m 1 .29185 L s P p .001 w .99625 .30902 m 1 .30902 L s P p .001 w .99625 .32618 m 1 .32618 L s P p .001 w .99625 .34335 m 1 .34335 L s P p .001 w .99625 .37769 m 1 .37769 L s P p .001 w .99625 .39486 m 1 .39486 L s P p .001 w .99625 .41202 m 1 .41202 L s P p .001 w .99625 .42919 m 1 .42919 L s P p .001 w .99625 .46353 m 1 .46353 L s P p .001 w .99625 .48069 m 1 .48069 L s P p .001 w .99625 .49786 m 1 .49786 L s P p .001 w .99625 .51503 m 1 .51503 L s P p .001 w .99625 .54936 m 1 .54936 L s P p .001 w .99625 .56653 m 1 .56653 L s P p .001 w .99625 .5837 m 1 .5837 L s P p .001 w .99625 .60087 m 1 .60087 L s P p .002 w 1 0 m 1 .61803 L s P P p P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p 1 0 0 r p .004 w .02381 .61605 m .06349 .61562 L .10317 .61508 L .14286 .61442 L .18254 .61359 L .22222 .61253 L .2619 .61112 L .28175 .61025 L .30159 .60921 L .32143 .60795 L .34127 .60641 L .36111 .60445 L .38095 .60189 L .39087 .60028 L .40079 .59836 L .41071 .59604 L .42063 .59315 L .43056 .58949 L .44048 .58465 L .44544 .5816 L .4504 .57798 L .45536 .57359 L .46032 .56818 L .46528 .56135 L .47024 .55246 L .4752 .54049 L .47768 .53284 L .48016 .52364 L .48512 .49865 L .4876 .48136 L .49008 .45949 L .49256 .43174 L .49504 .39702 L .5 .30902 L .50496 .22102 L .50744 .18629 L .50992 .15855 L .5124 .13667 L .51488 .11939 L .51736 .10558 L .51984 .09439 L .5248 .07754 L .52976 .06557 L .53472 .05669 L .53968 .04985 L .5496 .04006 L .55456 .03643 L .55952 .03338 L .56944 .02855 L .57937 .02488 L Mistroke .59921 .01967 L .60913 .01775 L .61905 .01614 L .63889 .01358 L .65873 .01163 L .67857 .01008 L .69841 .00883 L .7381 .00691 L .77778 .00551 L .81746 .00444 L .85714 .00361 L .89683 .00295 L .93651 .00242 L .97619 .00199 L Mfstroke P P p 1 0 0 r p .004 w .02381 .61406 m .06349 .6132 L .10317 .61213 L .14286 .61081 L .18254 .60915 L .22222 .60702 L .2619 .60423 L .28175 .60248 L .30159 .60041 L .32143 .59792 L .34127 .59486 L .36111 .591 L .38095 .58596 L .39087 .58281 L .40079 .57907 L .41071 .57457 L .42063 .56905 L .43056 .56209 L .44048 .55309 L .4504 .54099 L .45536 .53327 L .46032 .52401 L .47024 .49888 L .4752 .48153 L .48016 .4596 L .48512 .4318 L .49008 .39704 L .5 .30902 L .50992 .221 L .51488 .18623 L .51984 .15843 L .5248 .1365 L .52976 .11915 L .53472 .10527 L .53968 .09402 L .5496 .07704 L .55952 .06495 L .56944 .05594 L .57937 .04899 L .59921 .03896 L .60913 .03522 L .61905 .03207 L .63889 .02703 L .65873 .02317 L .67857 .02011 L .69841 .01762 L .7381 .0138 L .77778 .01101 L .81746 .00888 L .85714 .00722 L Mistroke .89683 .0059 L .93651 .00484 L .97619 .00397 L Mfstroke P P p 1 0 0 r p .004 w .02381 .61207 m .06349 .61078 L .10317 .60919 L .14286 .60721 L .18254 .60472 L .22222 .60154 L .2619 .59737 L .28175 .59477 L .30159 .59169 L .32143 .588 L .34127 .58348 L .36111 .5778 L .38095 .57045 L .39087 .56588 L .40079 .56051 L .41071 .55411 L .42063 .54635 L .43056 .53675 L .44048 .52463 L .4504 .50893 L .46032 .48809 L .47024 .45979 L .48016 .4211 L .49008 .36993 L .5 .30902 L .50992 .2481 L .51984 .19694 L .52976 .15824 L .53968 .12994 L .5496 .1091 L .55952 .09341 L .56944 .08128 L .57937 .07169 L .59921 .05752 L .60913 .05215 L .61905 .04759 L .63889 .04023 L .65873 .03456 L .67857 .03004 L .69841 .02634 L .7381 .02066 L .77778 .01649 L .81746 .01331 L .85714 .01083 L .89683 .00885 L .93651 .00725 L .97619 .00596 L s P P p 1 0 0 r p .004 w .02381 .61009 m .06349 .60837 L .10317 .60624 L .14286 .60361 L .18254 .6003 L .22222 .59608 L .2619 .59056 L .28175 .58713 L .30159 .58307 L .32143 .57823 L .34127 .57232 L .36111 .56496 L .38095 .55551 L .40079 .54295 L .41071 .53498 L .42063 .52548 L .44048 .49983 L .4504 .48223 L .46032 .46005 L .48016 .39713 L .5 .30902 L .51984 .22091 L .53968 .15798 L .5496 .13581 L .55952 .1182 L .56944 .10407 L .57937 .09256 L .59921 .07508 L .61905 .06252 L .63889 .05308 L .65873 .04571 L .67857 .03981 L .69841 .03496 L .7381 .02747 L .77778 .02195 L .81746 .01773 L .85714 .01442 L .89683 .01179 L .93651 .00967 L .97619 .00794 L s P P p 1 0 0 r p .004 w .02381 .60811 m .06349 .60595 L .10317 .60331 L .14286 .60002 L .18254 .5959 L .22222 .59066 L .2619 .58382 L .28175 .57957 L .30159 .57459 L .32143 .56865 L .34127 .56145 L .36111 .55256 L .38095 .54129 L .40079 .52656 L .42063 .50663 L .44048 .47868 L .4504 .46039 L .46032 .43838 L .48016 .3812 L .5 .30902 L .51984 .23683 L .53968 .17965 L .5496 .15764 L .55952 .13936 L .57937 .1114 L .59921 .09148 L .61905 .07675 L .63889 .06547 L .65873 .05658 L .67857 .04939 L .69841 .04345 L .7381 .03421 L .77778 .02737 L .81746 .02213 L .85714 .01801 L .89683 .01473 L .93651 .01208 L .97619 .00993 L s P P p 1 0 0 r p .004 w .02381 .60613 m .06349 .60355 L .10317 .60037 L .14286 .59645 L .18254 .59153 L .22222 .58528 L .2619 .57716 L .30159 .56626 L .32143 .5593 L .34127 .55093 L .36111 .54068 L .38095 .52786 L .40079 .51143 L .42063 .48983 L .44048 .4608 L .46032 .42151 L .48016 .37 L .5 .30902 L .51984 .24804 L .53968 .19652 L .55952 .15723 L .57937 .1282 L .59921 .10661 L .61905 .09018 L .63889 .07735 L .65873 .0671 L .69841 .05177 L .7381 .04088 L .77778 .03276 L .81746 .02651 L .85714 .02159 L .89683 .01766 L .93651 .01449 L .97619 .01191 L s P P p 1 0 0 r p .004 w .02381 .60415 m .06349 .60114 L .10317 .59745 L .14286 .59288 L .18254 .58718 L .22222 .57995 L .2619 .57059 L .30159 .55812 L .32143 .55022 L .34127 .54079 L .38095 .51527 L .40079 .49758 L .42063 .47496 L .44048 .44574 L .46032 .40818 L .5 .30902 L .51984 .25631 L .53968 .20985 L .55952 .17229 L .57937 .14307 L .59921 .12046 L .61905 .10276 L .63889 .08867 L .65873 .07724 L .69841 .05991 L .7381 .04744 L .77778 .03809 L .81746 .03086 L .85714 .02515 L .89683 .02058 L .93651 .01689 L .97619 .01389 L s P P p 1 0 0 r p .004 w .02381 .60217 m .06349 .59874 L .10317 .59454 L .14286 .58934 L .18254 .58286 L .22222 .57467 L .2619 .56413 L .30159 .55019 L .32143 .54143 L .34127 .53107 L .38095 .50355 L .40079 .48497 L .42063 .46185 L .46032 .39748 L .5 .30902 L .53968 .22055 L .57937 .15618 L .59921 .13306 L .61905 .11448 L .63889 .09939 L .65873 .08696 L .69841 .06784 L .7381 .05391 L .77778 .04337 L .81746 .03518 L .85714 .0287 L .89683 .0235 L .93651 .01929 L .97619 .01586 L s P P p 1 0 0 r p .004 w .02381 .6002 m .06349 .59635 L .10317 .59163 L .14286 .58581 L .18254 .57857 L .22222 .56945 L .2619 .55778 L .30159 .54248 L .34127 .52178 L .38095 .49268 L .40079 .47354 L .42063 .45031 L .46032 .38875 L .5 .30902 L .53968 .22929 L .57937 .16773 L .59921 .14449 L .61905 .12535 L .65873 .09625 L .69841 .07555 L .7381 .06025 L .77778 .04858 L .81746 .03946 L .85714 .03222 L .89683 .0264 L .93651 .02168 L .97619 .01784 L s P P p 1 0 0 r p .004 w .02381 .59823 m .06349 .59397 L .10317 .58874 L .14286 .58231 L .18254 .57432 L .22222 .56431 L .2619 .55156 L .30159 .53501 L .34127 .51294 L .38095 .48264 L .42063 .44013 L .46032 .38151 L .5 .30902 L .53968 .23653 L .57937 .17791 L .61905 .1354 L .65873 .1051 L .69841 .08303 L .7381 .06647 L .77778 .05373 L .81746 .04371 L .85714 .03573 L .89683 .02929 L .93651 .02407 L .97619 .0198 L s P P P % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect; endGroup; endGroup; endGroup] Graphics["<<>>"] ;[o] -Graphics- :[font = section; inactive; Cclosed; preserveAspect; startGroup] Nyquist Diagrams :[font = text; inactive; preserveAspect] The argument is a transfer function or a list of transfer functions, of which the frequency response is to be plotted. The logarithmic range for the angular frequency can be given with the option LogRange. Further options are passed to the function ParametricPlot. ;[s] 5:0,0;197,1;205,2;251,3;265,4;266,-1; 5:1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = input; preserveAspect; startGroup] NyquistPlot[Table[Fs, {a, 0.1, 1, 0.1}], AspectRatio->Automatic, Axes->True, GridLines->Automatic] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 383; pictureHeight = 207] %! %%Creator: Mathematica %%AspectRatio: .54136 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.432342 0.181777 0.528467 0.181777 [ [(-2)] .06879 0 0 2 Msboxa [(-1)] .25057 0 0 2 Msboxa [(0)] .43234 0 0 2 Msboxa [(1)] .61412 0 0 2 Msboxa [(2)] .7959 0 0 2 Msboxa [(3)] .97767 0 0 2 Msboxa [(-2.5)] -0.0125 .07402 1 0 Msboxa [(-2)] -0.0125 .16491 1 0 Msboxa [(-1.5)] -0.0125 .2558 1 0 Msboxa [(-1)] -0.0125 .34669 1 0 Msboxa [(-0.5)] 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1 .18309 L s P p .001 w .99625 .20127 m 1 .20127 L s P p .001 w .99625 .21945 m 1 .21945 L s P p .001 w .99625 .23762 m 1 .23762 L s P p .001 w .99625 .27398 m 1 .27398 L s P p .001 w .99625 .29216 m 1 .29216 L s P p .001 w .99625 .31033 m 1 .31033 L s P p .001 w .99625 .32851 m 1 .32851 L s P p .001 w .99625 .36487 m 1 .36487 L s P p .001 w .99625 .38305 m 1 .38305 L s P p .001 w .99625 .40122 m 1 .40122 L s P p .001 w .99625 .4194 m 1 .4194 L s P p .001 w .99625 .45576 m 1 .45576 L s P p .001 w .99625 .47393 m 1 .47393 L s P p .001 w .99625 .49211 m 1 .49211 L s P p .001 w .99625 .51029 m 1 .51029 L s P p .001 w .99625 .05585 m 1 .05585 L s P p .001 w .99625 .03767 m 1 .03767 L s P p .001 w .99625 .01949 m 1 .01949 L s P p .001 w .99625 .00131 m 1 .00131 L s P p .002 w 1 0 m 1 .54136 L s P P p p .002 w 0 .52847 m 1 .52847 L s P p .002 w .43234 0 m .43234 .54136 L s P P 0 0 m 1 0 L 1 .54136 L 0 .54136 L closepath clip newpath p p 1 0 0 r p .004 w .61412 .52845 m .61412 .52844 L .61412 .52843 L .61412 .52842 L .61412 .52841 L .61412 .52839 L .61412 .52836 L .61413 .52833 L .61414 .52828 L .61415 .52822 L .61418 .52814 L .61422 .52804 L .6143 .52789 L .61444 .5277 L .61469 .52744 L .61514 .52709 L .61594 .52661 L .61738 .52595 L .61999 .52502 L .63407 .52138 L .65286 .51716 L .66966 .51332 L .6964 .50675 L .74276 .49361 L .78022 .48115 L .83584 .45933 L .87465 .44157 L .92478 .41529 L .9912 .37397 L s 1 .36711 m .9912 .37397 L s s s s s s s s s s s s s s s s 0 .39407 m .04235 .42065 L s .04235 .42065 m .11256 .45497 L .20544 .48959 L .26293 .50542 L .30144 .51377 L .34884 .5216 L .37607 .52487 L .39313 .52646 L .40442 .52729 L .41217 .52776 L .42152 .52819 L .42641 .52836 L .42905 .52842 L .43051 .52845 L .43131 .52846 L .43177 .52846 L .43202 .52847 L .43216 .52847 L .43224 .52847 L .43228 .52847 L .43231 .52847 L .43232 .52847 L .43233 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L s P P p 1 0 0 r p .004 w .61412 .52843 m .61412 .52842 L .61412 .5284 L .61412 .52838 L .61412 .52835 L .61412 .52831 L .61412 .52826 L .61413 .52819 L .61414 .5281 L .61415 .52798 L .61417 .52782 L .61422 .5276 L .61429 .52731 L .61443 .52693 L .61467 .52641 L .61511 .52571 L .61588 .52476 L .61727 .52345 L .6198 .52158 L .63332 .51434 L .65113 .50602 L .6668 .49853 L .69118 .48589 L .73158 .46126 L .76225 .43872 L .80403 .40109 L .83029 .37211 L .86035 .33172 L .87655 .30544 L .89307 .27373 L .90918 .23523 L .92358 .18829 L .93407 .13108 L .93703 .06178 L s .92939 0 m .93703 .06178 L s s s s s s s s s s .02778 0 m .01925 .06982 L s .01925 .06982 m .02564 .15239 L .04232 .21955 L .06397 .27337 L .0874 .31634 L .11083 .3507 L .1544 .40071 L .22332 .45684 L .27169 .48476 L .30616 .50013 L .35049 .515 L .37674 .52137 L .39343 .52448 L .40457 .52613 L .41224 .52705 L .42154 .52792 L .42641 .52825 L .42905 .52838 L .43051 .52843 L .43131 .52845 L .43177 .52846 L .43202 .52846 L .43216 .52847 L .43224 .52847 L .43228 .52847 L .43231 .52847 L .43232 .52847 L .43233 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L s P P p 1 0 0 r p .004 w .61412 .52841 m .61412 .52839 L .61412 .52837 L .61412 .52834 L .61412 .52829 L .61412 .52824 L .61412 .52816 L .61413 .52806 L .61414 .52792 L .61415 .52774 L .61417 .5275 L .61421 .52717 L .61428 .52674 L .61441 .52616 L .61464 .52538 L .61505 .52433 L .61579 .52291 L .6171 .52094 L .61949 .51816 L .6321 .50741 L .64832 .49523 L .6622 .48445 L .68293 .46664 L .69709 .45286 L .71463 .43337 L .73608 .40452 L .7482 .38467 L .76088 .35959 L .7672 .34456 L .77329 .32753 L .77892 .30818 L .78373 .28618 L .78723 .26119 L .78876 .23287 L .78739 .20095 L .78194 .16533 L .77092 .12621 L .75254 .08433 L .72492 .04119 L s .68703 0 m .72492 .04119 L s s s s s s s .2723 0 m .2494 .02023 L s .2494 .02023 m .21234 .07024 L .18793 .12142 L .17431 .17057 L .16914 .21577 L .17018 .25615 L .1755 .29154 L .18363 .32219 L .19344 .34854 L .20416 .37113 L .22631 .40704 L .24759 .4335 L .28443 .46811 L .3133 .48836 L .3531 .50892 L .37784 .51803 L .39393 .52256 L .40481 .52499 L .41237 .52636 L .42157 .52765 L .42642 .52814 L .42906 .52833 L .43051 .52841 L .43131 .52844 L .43177 .52846 L .43202 .52846 L .43216 .52846 L .43224 .52847 L .43228 .52847 L .43231 .52847 L .43232 .52847 L .43233 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L s P P p 1 0 0 r p .004 w .61412 .52839 m .61412 .52837 L .61412 .52834 L .61412 .52829 L .61412 .52824 L .61412 .52816 L .61412 .52806 L .61413 .52792 L .61413 .52774 L .61415 .5275 L .61417 .52717 L .6142 .52674 L .61427 .52616 L .61439 .52539 L .6146 .52435 L .61498 .52296 L .61566 .52106 L .61687 .51845 L .61905 .51475 L .6304 .50063 L .64451 .48494 L .65604 .47135 L .67223 .44955 L .68243 .43324 L .6939 .41098 L .69988 .39673 L .70573 .37972 L .70847 .36999 L .711 .35932 L .71319 .34762 L .71494 .33478 L .71606 .32071 L .71635 .30529 L .71554 .28846 L .71332 .27016 L .70928 .25038 L .70297 .2292 L .69387 .2068 L .68141 .18352 L .665 .15991 L .64415 .13676 L .6185 .11509 L .58801 .09617 L .55303 .08141 L .51445 .07215 L .47363 .06949 L .43234 .07402 L .39252 .08571 L .35594 .10383 L .324 .12715 L Mistroke .29754 .15412 L .27683 .18314 L .26166 .21281 L .25148 .24197 L .24557 .26979 L .24315 .29577 L .24349 .31963 L .24592 .34127 L .24988 .36073 L .25494 .37812 L .26072 .3936 L .27343 .41955 L .28652 .43995 L .29921 .45603 L .32204 .47892 L .34102 .49369 L .35648 .50351 L .37929 .51492 L .39461 .52073 L .40514 .52388 L .41254 .52568 L .42162 .52739 L .42644 .52803 L .42906 .52829 L .43051 .52839 L .43132 .52844 L .43177 .52845 L .43202 .52846 L .43216 .52846 L .43224 .52847 L .43228 .52847 L .43231 .52847 L .43232 .52847 L .43233 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L Mfstroke P P p 1 0 0 r p .004 w .61412 .52838 m .61412 .52835 L .61412 .5283 L .61412 .52825 L .61412 .52818 L .61412 .52808 L .61412 .52796 L .61413 .52778 L .61413 .52756 L .61414 .52725 L .61416 .52685 L .6142 .52631 L .61426 .52559 L .61436 .52462 L .61455 .52333 L .61489 .52158 L .61549 .51922 L .61656 .51596 L .61849 .51138 L .62827 .49405 L .63979 .47527 L .64859 .45944 L .6539 .44863 L .65974 .43496 L .66277 .42673 L .6658 .41735 L .66871 .40662 L .67007 .40067 L .67133 .39428 L .67246 .38743 L .67342 .38008 L .67416 .37218 L .6746 .3637 L .6747 .3546 L .67434 .34485 L .67344 .33441 L .67188 .32326 L .6695 .31139 L .66614 .29882 L .66163 .28557 L .65575 .27173 L .64829 .25741 L .63902 .24278 L .62771 .2281 L .61418 .21368 L .59827 .19992 L .57992 .18731 L .55918 .17639 L .53626 .16773 L .51152 .16185 L Mistroke .48549 .15924 L .45884 .16022 L .43234 .16491 L .40678 .17323 L .38289 .18488 L .36126 .19936 L .34235 .21608 L .32639 .23436 L .31342 .25355 L .30336 .27307 L .29599 .29241 L .29101 .31118 L .28812 .32911 L .28697 .346 L .28726 .36175 L .28871 .37631 L .29106 .38969 L .2941 .40192 L .29764 .41307 L .3057 .43238 L .31437 .44823 L .33156 .47188 L .34709 .48789 L .36043 .4989 L .38106 .5121 L .39545 .51901 L .40556 .52282 L .41275 .52502 L .42168 .52713 L .42646 .52793 L .42907 .52824 L .43051 .52837 L .43132 .52843 L .43177 .52845 L .43202 .52846 L .43216 .52846 L .43224 .52847 L .43228 .52847 L .43231 .52847 L .43232 .52847 L .43233 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L Mfstroke P P p 1 0 0 r p .004 w .61412 .52836 m .61412 .52832 L .61412 .52827 L .61412 .52821 L .61412 .52812 L .61412 .52801 L .61412 .52785 L .61413 .52765 L .61413 .52738 L .61414 .52701 L .61416 .52653 L .61418 .52588 L .61424 .52501 L .61433 .52385 L .61449 .5223 L .61477 .52021 L .61528 .51738 L .61619 .51349 L .6178 .50803 L .62572 .4877 L .62949 .47862 L .63431 .46631 L .63712 .4584 L .64014 .44888 L .64324 .43728 L .64474 .43051 L .64613 .42297 L .64676 .41888 L .64734 .41456 L .64784 .40999 L .64825 .40515 L .64855 .40003 L .64872 .39461 L .64872 .38888 L .64853 .38281 L .64811 .37639 L .64742 .36961 L .6464 .36245 L .64501 .3549 L .64318 .34697 L .64083 .33864 L .63427 .32088 L .6246 .30185 L .61101 .28208 L .5927 .26247 L .58157 .25315 L .56907 .24443 L .55519 .23655 L .54001 .22979 L .52363 .2244 L Mistroke .50624 .22064 L .48809 .21874 L .46948 .21886 L .45077 .22111 L .43234 .22551 L .41456 .23197 L .39778 .24036 L .3823 .25043 L .36835 .2619 L .35608 .27446 L .34558 .28778 L .33684 .30154 L .32981 .31547 L .32439 .3293 L .32044 .34285 L .3178 .35594 L .31632 .36847 L .31582 .38034 L .31616 .39152 L .31719 .40199 L .31879 .41173 L .32084 .42077 L .32324 .42913 L .32878 .44395 L .33488 .45648 L .34117 .46704 L .3535 .48343 L .36474 .49511 L .38306 .50959 L .39643 .51741 L .40605 .52182 L .413 .52439 L .42175 .52687 L .42648 .52782 L .42907 .5282 L .43051 .52836 L .43132 .52842 L .43177 .52845 L .43202 .52846 L .43216 .52846 L .43224 .52847 L .43228 .52847 L .43231 .52847 L .43232 .52847 L .43233 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L Mistroke .43234 .52847 L .43234 .52847 L Mfstroke P P p 1 0 0 r p .004 w .61412 .52834 m .61412 .5283 L .61412 .52824 L .61412 .52816 L .61412 .52806 L .61412 .52793 L .61412 .52775 L .61412 .52751 L .61413 .52719 L .61414 .52677 L .61415 .5262 L .61417 .52545 L .61421 .52444 L .61428 .52309 L .61441 .52128 L .61464 .51884 L .61504 .51555 L .61575 .51104 L .617 .50473 L .61917 .49561 L .6228 .48162 L .6253 .47155 L .62671 .46536 L .62819 .45815 L .62965 .4497 L .63034 .44492 L .63097 .43971 L .63125 .43693 L .6315 .43403 L .63171 .43099 L .63189 .4278 L .63202 .42448 L .63209 .42099 L .63209 .41734 L .63201 .41352 L .63184 .40952 L .63157 .40532 L .63118 .40093 L .63064 .39633 L .62906 .38649 L .62663 .37575 L .6231 .36408 L .61818 .35152 L .6115 .33815 L .60266 .32418 L .59124 .30996 L .57682 .29602 L .55912 .28312 L .54901 .27735 L .53807 .27221 L Mistroke .52635 .26785 L .51393 .2644 L .50091 .26199 L .48743 .26075 L .47364 .26076 L .45973 .26209 L .4459 .26477 L .43234 .26879 L .41927 .27409 L .40686 .28058 L .39527 .28815 L .38464 .29663 L .37506 .30586 L .36659 .31567 L .35926 .32587 L .35306 .3363 L .34795 .34681 L .34387 .35726 L .34076 .36752 L .33852 .37752 L .33707 .38717 L .33632 .39642 L .33618 .40524 L .33656 .41359 L .33739 .42147 L .33859 .42888 L .34009 .43581 L .34184 .4423 L .3459 .45398 L .35041 .46407 L .35993 .48022 L .3692 .49212 L .38524 .50742 L .39751 .51596 L .40661 .52088 L .4133 .52378 L .42184 .52662 L .4265 .52772 L .42908 .52816 L .43052 .52834 L .43132 .52841 L .43177 .52844 L .43202 .52846 L .43216 .52846 L .43224 .52846 L .43228 .52847 L .43231 .52847 L .43232 .52847 L .43233 .52847 L .43234 .52847 L Mistroke .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L Mfstroke P P p 1 0 0 r p .004 w .61412 .52832 m .61412 .52827 L .61412 .52821 L .61412 .52812 L .61412 .52801 L .61412 .52785 L .61412 .52765 L .61412 .52738 L .61413 .52701 L .61413 .52653 L .61414 .52588 L .61416 .52502 L .61418 .52386 L .61424 .52232 L .61432 .52025 L .61448 .51748 L .61476 .51373 L .61525 .5086 L .61609 .50147 L .61747 .49125 L .61842 .4844 L .61953 .47585 L .62011 .47076 L .62069 .46498 L .62096 .46179 L .6212 .45839 L .62141 .45474 L .6215 .45281 L .62158 .45082 L .62163 .44875 L .62167 .44661 L .62169 .44439 L .62169 .44209 L .62165 .43969 L .62158 .43721 L .62148 .43463 L .62134 .43195 L .62115 .42917 L .6209 .42628 L .62022 .42015 L .61924 .41354 L .61787 .4064 L .61603 .39871 L .61358 .39045 L .61039 .38161 L .60629 .3722 L .60109 .36228 L .59457 .35194 L .58649 .34133 L .57661 .33071 L Mistroke .56473 .32041 L .55069 .31086 L .54284 .30655 L .53445 .30263 L .52554 .2992 L .51615 .29633 L .50632 .2941 L .49611 .29259 L .48562 .29186 L .47492 .29196 L .46413 .29294 L .45336 .29481 L .44273 .29759 L .43234 .30125 L .42233 .30575 L .41278 .31103 L .39547 .32366 L .38095 .33839 L .3695 .35439 L .36492 .36262 L .36109 .37087 L .35796 .37908 L .35549 .38716 L .35364 .39506 L .35234 .40274 L .35155 .41015 L .35121 .41726 L .35127 .42406 L .35168 .43054 L .35238 .43669 L .35334 .4425 L .35587 .45316 L .35899 .46257 L .36616 .47807 L .37367 .48987 L .38752 .50558 L .39869 .51466 L .40723 .52 L .41362 .5232 L .42193 .52637 L .42653 .52761 L .42909 .52811 L .43052 .52832 L .43132 .5284 L .43177 .52844 L .43202 .52846 L .43216 .52846 L .43224 .52846 L .43228 .52847 L .43231 .52847 L Mistroke .43232 .52847 L .43233 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L Mfstroke P P p 1 0 0 r p .004 w .61412 .5283 m .61412 .52825 L .61412 .52818 L .61412 .52808 L .61412 .52795 L .61412 .52778 L .61412 .52755 L .61412 .52724 L .61412 .52683 L .61413 .52628 L .61413 .52556 L .61414 .52458 L .61415 .52329 L .61418 .52155 L .61423 .51923 L .61431 .51612 L .61445 .51191 L .61506 .49827 L .61531 .49316 L .61558 .48703 L .61571 .48349 L .61577 .48158 L .61583 .47958 L .61588 .47747 L .6159 .47637 L .61592 .47524 L .61593 .47408 L .61595 .47289 L .61595 .47166 L .61596 .4704 L .61595 .46911 L .61594 .46778 L .61593 .46641 L .6159 .465 L .61587 .46355 L .61583 .46205 L .61572 .45893 L .61555 .45561 L .61532 .45208 L .61501 .44833 L .6146 .44433 L .6134 .43554 L .61149 .42554 L .60855 .41418 L .60409 .40134 L .59748 .38699 L .58785 .37131 L .57415 .35487 L .56543 .34671 L .5553 .33886 L Mistroke .54368 .33162 L .53056 .32531 L .52345 .32262 L .516 .32031 L .50824 .31842 L .5002 .31701 L .49192 .31611 L .48346 .31576 L .47487 .31599 L .46621 .31684 L .45756 .31832 L .44898 .32042 L .44055 .32315 L .43234 .32649 L .41686 .33487 L .40301 .34521 L .39115 .35706 L .38145 .36989 L .37396 .38321 L .37101 .3899 L .36856 .39654 L .36659 .40309 L .36506 .40951 L .36394 .41577 L .3632 .42184 L .3628 .42771 L .3627 .43335 L .36287 .43876 L .36329 .44393 L .36391 .44886 L .36472 .45354 L .36677 .46219 L .36926 .46993 L .37204 .4768 L .37803 .48827 L .38409 .49717 L .38986 .50406 L .39993 .51351 L .40789 .51919 L .41398 .52266 L .42204 .52614 L .42656 .52751 L .4291 .52807 L .43052 .5283 L .43132 .5284 L .43177 .52844 L .43202 .52845 L .43216 .52846 L .43224 .52846 L .43228 .52847 L Mistroke .43231 .52847 L .43232 .52847 L .43233 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L Mfstroke P P p 1 0 0 r p .004 w .61412 .52828 m .61412 .52827 L .61412 .52826 L .61412 .52824 L .61412 .52822 L .61412 .52821 L .61412 .52819 L .61412 .52817 L .61412 .52814 L .61412 .52812 L .61412 .52809 L .61412 .52807 L .61412 .52804 L .61412 .528 L .61412 .52797 L .61412 .52793 L .61412 .52789 L .61412 .52785 L .61412 .5278 L .61412 .52775 L .61412 .5277 L .61412 .52764 L .61412 .52758 L .61412 .52752 L .61412 .52744 L .61412 .52737 L .61412 .52729 L .61412 .5272 L .61412 .5271 L .61412 .527 L .61412 .52689 L .61412 .52677 L .61412 .52665 L .61412 .52651 L .61412 .52637 L .61412 .52621 L .61412 .52604 L .61412 .52586 L .61412 .52567 L .61412 .52546 L .61412 .52523 L .61412 .52499 L .61412 .52473 L .61412 .52445 L .61412 .52415 L .61412 .52383 L .61412 .52349 L .61412 .52311 L .61412 .52271 L .61412 .52228 L Mistroke .61412 .52182 L .61412 .52132 L .61412 .52079 L .61412 .52021 L .61412 .51959 L .61412 .51893 L .61412 .51821 L .61412 .51744 L .61412 .51661 L .61411 .51572 L .61411 .51476 L .61411 .51372 L .61411 .51261 L .61411 .5114 L .6141 .51011 L .61409 .50871 L .61409 .5072 L .61408 .50556 L .61406 .5038 L .61404 .50188 L .61401 .49981 L .61398 .49756 L .61393 .49512 L .61387 .49246 L .61378 .48957 L .61367 .4864 L .61351 .48294 L .6133 .47915 L .61302 .47498 L .61264 .47038 L .61212 .4653 L .61142 .45967 L .61046 .45341 L .60916 .44645 L .60739 .43869 L .60496 .43003 L .60164 .4204 L .5971 .40973 L .59093 .39805 L .58256 .38547 L .57137 .37235 L .55666 .35937 L .5478 .35326 L .53787 .34765 L .52688 .34275 L .52099 .34064 L .51487 .3388 L .50851 .33726 L .50195 .33604 L .4952 .33519 L Mistroke .4883 .33472 L .48128 .33465 L .47418 .33502 L .46704 .33583 L .45991 .3371 L .45282 .33882 L .44583 .341 L .43234 .34669 L .41979 .35402 L .40847 .36275 L .39863 .37258 L .39038 .38317 L .38377 .39419 L .37875 .4053 L .37681 .41081 L .37521 .41624 L .37395 .42157 L .373 .42679 L .37233 .43186 L .37193 .43678 L .37176 .44154 L .3718 .44612 L .37204 .45053 L .37246 .45475 L .37302 .45878 L .37372 .46263 L .37543 .46979 L .37749 .47625 L .38219 .48722 L .38722 .49595 L .3922 .50284 L .40121 .5125 L .40859 .51846 L .41436 .52215 L .41879 .52446 L .42215 .52591 L .4266 .52741 L .42911 .52803 L .43052 .52828 L .43132 .52839 L .43177 .52843 L .43202 .52845 L .43216 .52846 L .43224 .52846 L .43228 .52847 L .43231 .52847 L .43232 .52847 L .43233 .52847 L .43234 .52847 L .43234 .52847 L Mistroke .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L .43234 .52847 L Mfstroke P P P % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect; endGroup; endGroup] Graphics["<<>>"] ;[o] -Graphics- :[font = section; inactive; Cclosed; preserveAspect; startGroup] Root Locus Plots :[font = text; inactive; preserveAspect] Let Fo be an open-loop transfer function with the amplification k: ;[s] 5:0,0;4,1;6,2;64,3;65,4;66,-1; 5:1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = input; preserveAspect; startGroup] Fo = k Fs/s /. a->3 :[font = output; output; inactive; preserveAspect; endGroup] k/(s*(1 + 3*s + s^2)) ;[o] k ---------------- 2 s (1 + 3 s + s ) :[font = text; inactive; preserveAspect] The closed-loop transfer function Fw becomes: ;[s] 3:0,0;34,1;36,2;45,-1; 3:1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = input; preserveAspect; startGroup] Fw = Fo/(1 + Fo) // Simplify :[font = output; output; inactive; preserveAspect; endGroup] k/(k + s + 3*s^2 + s^3) ;[o] k ----------------- 2 3 k + s + 3 s + s :[font = text; inactive; preserveAspect] The first argument of RootLocus is the transfer function, the second argument is the varying parameter. The option of LinRange or LogRange gives the linear or logarithmic range for the parameter, the option Points gives the number of calculated points, the option EndMarks determines whether the beginning and ends of the curves shall be marked. Additional options are passed to the function Graphics. ;[s] 13:0,0;22,1;31,2;119,3;127,4;131,5;139,6;208,7;214,8;265,9;273,10;394,11;402,12;404,-1; 13:1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = input; preserveAspect; startGroup] RootLocus[Fw, k, PlotRange->{{-4,2},{-3,3}}, GridLines->Automatic] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 282] %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.666667 0.166667 0.5 0.166667 [ [(-3)] .16667 0 0 2 Msboxa [(-2)] .33333 0 0 2 Msboxa [(-1)] .5 0 0 2 Msboxa [(0)] .66667 0 0 2 Msboxa [(1)] .83333 0 0 2 Msboxa [(2)] 1 0 0 2 Msboxa [(-3)] -0.0125 0 1 0 Msboxa [(-2)] -0.0125 .16667 1 0 Msboxa [(-1)] -0.0125 .33333 1 0 Msboxa [(0)] -0.0125 .5 1 0 Msboxa [(1)] -0.0125 .66667 1 0 Msboxa [(2)] -0.0125 .83333 1 0 Msboxa [(3)] -0.0125 1 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 1.001 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p 0 0 .5 r .001 w .16667 0 m .16667 1 L s P p 0 0 .5 r .001 w .33333 0 m .33333 1 L s P p 0 0 .5 r .001 w .5 0 m .5 1 L s P p 0 0 .5 r .001 w .66667 0 m .66667 1 L s P p 0 0 .5 r .001 w .83333 0 m .83333 1 L s P p 0 0 .5 r .001 w 0 .16667 m 1 .16667 L s P p 0 0 .5 r .001 w 0 .33333 m 1 .33333 L s P p 0 0 .5 r .001 w 0 .5 m 1 .5 L s P p 0 0 .5 r .001 w 0 .66667 m 1 .66667 L s P p 0 0 .5 r .001 w 0 .83333 m 1 .83333 L s P p .002 w .16667 0 m .16667 .00625 L s P [(-3)] .16667 0 0 2 Mshowa p .002 w .33333 0 m .33333 .00625 L s P [(-2)] .33333 0 0 2 Mshowa p .002 w .5 0 m .5 .00625 L s P [(-1)] .5 0 0 2 Mshowa p .002 w .66667 0 m .66667 .00625 L s P [(0)] .66667 0 0 2 Mshowa p .002 w .83333 0 m .83333 .00625 L s P [(1)] .83333 0 0 2 Mshowa p .002 w 1 0 m 1 .00625 L s P [(2)] 1 0 0 2 Mshowa p .001 w .03333 0 m .03333 .00375 L s P p .001 w .06667 0 m .06667 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .13333 0 m .13333 .00375 L s P p .001 w .2 0 m .2 .00375 L s P p .001 w .23333 0 m .23333 .00375 L s P p .001 w .26667 0 m .26667 .00375 L s P p .001 w .3 0 m .3 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .4 0 m .4 .00375 L s P p .001 w .43333 0 m .43333 .00375 L s P p .001 w .46667 0 m .46667 .00375 L s P p .001 w .53333 0 m .53333 .00375 L s P p .001 w .56667 0 m .56667 .00375 L s P p .001 w .6 0 m .6 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .7 0 m .7 .00375 L s P p .001 w .73333 0 m .73333 .00375 L s P p .001 w .76667 0 m .76667 .00375 L s P p .001 w .8 0 m .8 .00375 L s P p .001 w .86667 0 m .86667 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .93333 0 m .93333 .00375 L s P p .001 w .96667 0 m .96667 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w 0 0 m .00625 0 L s P [(-3)] -0.0125 0 1 0 Mshowa p .002 w 0 .16667 m .00625 .16667 L s P [(-2)] -0.0125 .16667 1 0 Mshowa p .002 w 0 .33333 m .00625 .33333 L s P [(-1)] -0.0125 .33333 1 0 Mshowa p .002 w 0 .5 m .00625 .5 L s P [(0)] -0.0125 .5 1 0 Mshowa p .002 w 0 .66667 m .00625 .66667 L s P [(1)] -0.0125 .66667 1 0 Mshowa p .002 w 0 .83333 m .00625 .83333 L s P [(2)] -0.0125 .83333 1 0 Mshowa p .002 w 0 1 m .00625 1 L s P [(3)] -0.0125 1 1 0 Mshowa p .001 w 0 .03333 m .00375 .03333 L s P p .001 w 0 .06667 m .00375 .06667 L s P p .001 w 0 .1 m .00375 .1 L s P p .001 w 0 .13333 m .00375 .13333 L s P p .001 w 0 .2 m .00375 .2 L s P p .001 w 0 .23333 m .00375 .23333 L s P p .001 w 0 .26667 m .00375 .26667 L s P p .001 w 0 .3 m .00375 .3 L s P p .001 w 0 .36667 m .00375 .36667 L s P p .001 w 0 .4 m .00375 .4 L s P p .001 w 0 .43333 m .00375 .43333 L s P p .001 w 0 .46667 m .00375 .46667 L s P p .001 w 0 .53333 m .00375 .53333 L s P p .001 w 0 .56667 m .00375 .56667 L s P p .001 w 0 .6 m .00375 .6 L s P p .001 w 0 .63333 m .00375 .63333 L s P p .001 w 0 .7 m .00375 .7 L s P p .001 w 0 .73333 m .00375 .73333 L s P p .001 w 0 .76667 m .00375 .76667 L s P p .001 w 0 .8 m .00375 .8 L s P p .001 w 0 .86667 m .00375 .86667 L s P p .001 w 0 .9 m .00375 .9 L s P p .001 w 0 .93333 m .00375 .93333 L s P p .001 w 0 .96667 m .00375 .96667 L s P p .002 w 0 0 m 0 1 L s P P p p .002 w 0 .99375 m 0 1 L s P p .002 w .16667 .99375 m .16667 1 L s P p .002 w .33333 .99375 m .33333 1 L s P p .002 w .5 .99375 m .5 1 L s P p .002 w .66667 .99375 m .66667 1 L s P p .002 w .83333 .99375 m .83333 1 L s P p .001 w .03333 .99625 m .03333 1 L s P p .001 w .06667 .99625 m .06667 1 L s P p .001 w .1 .99625 m .1 1 L s P p .001 w .13333 .99625 m .13333 1 L s P p .001 w .2 .99625 m .2 1 L s P p .001 w .23333 .99625 m .23333 1 L s P p .001 w .26667 .99625 m .26667 1 L s P p .001 w .3 .99625 m .3 1 L s P p .001 w .36667 .99625 m .36667 1 L s P p .001 w .4 .99625 m .4 1 L s P p .001 w .43333 .99625 m .43333 1 L s P p .001 w .46667 .99625 m .46667 1 L s P p .001 w .53333 .99625 m .53333 1 L s P p .001 w .56667 .99625 m .56667 1 L s P p .001 w .6 .99625 m .6 1 L s P p .001 w .63333 .99625 m .63333 1 L s P p .001 w .7 .99625 m .7 1 L s P p .001 w .73333 .99625 m .73333 1 L s P p .001 w .76667 .99625 m .76667 1 L s P p .001 w .8 .99625 m .8 1 L s P p .001 w .86667 .99625 m .86667 1 L s P p .001 w .9 .99625 m .9 1 L s P p .001 w .93333 .99625 m .93333 1 L s P p .001 w .96667 .99625 m .96667 1 L s P p .002 w 0 1 m 1 1 L s P p .002 w .99375 0 m 1 0 L s P p .002 w .99375 .16667 m 1 .16667 L s P p .002 w .99375 .33333 m 1 .33333 L s P p .002 w .99375 .5 m 1 .5 L s P p .002 w .99375 .66667 m 1 .66667 L s P p .002 w .99375 .83333 m 1 .83333 L s P p .001 w .99625 .03333 m 1 .03333 L s P p .001 w .99625 .06667 m 1 .06667 L s P p .001 w .99625 .1 m 1 .1 L s P p .001 w .99625 .13333 m 1 .13333 L s P p .001 w .99625 .2 m 1 .2 L s P p .001 w .99625 .23333 m 1 .23333 L s P p .001 w .99625 .26667 m 1 .26667 L s P p .001 w .99625 .3 m 1 .3 L s P p .001 w .99625 .36667 m 1 .36667 L s P p .001 w .99625 .4 m 1 .4 L s P p .001 w .99625 .43333 m 1 .43333 L s P p .001 w .99625 .46667 m 1 .46667 L s P p .001 w .99625 .53333 m 1 .53333 L s P p .001 w .99625 .56667 m 1 .56667 L s P p .001 w .99625 .6 m 1 .6 L s P p .001 w .99625 .63333 m 1 .63333 L s P p .001 w .99625 .7 m 1 .7 L s P p .001 w .99625 .73333 m 1 .73333 L s P p .001 w .99625 .76667 m 1 .76667 L s P p .001 w .99625 .8 m 1 .8 L s P p .001 w .99625 .86667 m 1 .86667 L s P p .001 w .99625 .9 m 1 .9 L s P p .001 w .99625 .93333 m 1 .93333 L s P p .001 w .99625 .96667 m 1 .96667 L s P p .002 w 1 0 m 1 1 L s P P p p .002 w 0 .5 m 1 .5 L s P p .002 w .66667 0 m .66667 1 L s P P 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath p 1 0 0 r p .004 w .2303 .5 m .2303 .5 L .23029 .5 L .23029 .5 L .23029 .5 L .23029 .5 L .23028 .5 L .23028 .5 L .23028 .5 L .23027 .5 L .23027 .5 L .23027 .5 L .23026 .5 L .23026 .5 L .23025 .5 L .23025 .5 L .23024 .5 L .23024 .5 L .23023 .5 L .23022 .5 L .23021 .5 L .23021 .5 L .2302 .5 L .23019 .5 L .23018 .5 L .23017 .5 L .23015 .5 L .23014 .5 L .23013 .5 L .23011 .5 L .2301 .5 L .23008 .5 L .23007 .5 L .23005 .5 L .23003 .5 L .23 .5 L .22998 .5 L .22996 .5 L .22993 .5 L .2299 .5 L .22987 .5 L .22984 .5 L .2298 .5 L .22977 .5 L .22973 .5 L .22968 .5 L .22964 .5 L .22959 .5 L .22953 .5 L .22948 .5 L Mistroke .22942 .5 L .22935 .5 L .22928 .5 L .22921 .5 L .22913 .5 L .22904 .5 L .22895 .5 L .22885 .5 L .22874 .5 L .22863 .5 L .22851 .5 L .22838 .5 L .22824 .5 L .22809 .5 L .22794 .5 L .22777 .5 L .22758 .5 L .22739 .5 L .22718 .5 L .22696 .5 L .22672 .5 L .22647 .5 L .22619 .5 L .2259 .5 L .22559 .5 L .22526 .5 L .22491 .5 L .22453 .5 L .22412 .5 L .22369 .5 L .22323 .5 L .22274 .5 L .22221 .5 L .22165 .5 L .22105 .5 L .22042 .5 L .21974 .5 L .21902 .5 L .21825 .5 L .21743 .5 L .21656 .5 L .21564 .5 L .21466 .5 L .21362 .5 L .21251 .5 L .21133 .5 L .21009 .5 L .20877 .5 L .20737 .5 L .20589 .5 L Mistroke .20432 .5 L .20267 .5 L .20092 .5 L .19907 .5 L .19713 .5 L .19507 .5 L .19291 .5 L .19063 .5 L .18824 .5 L .18572 .5 L .18307 .5 L .18029 .5 L .17738 .5 L .17433 .5 L .17113 .5 L .16779 .5 L .16429 .5 L .16063 .5 L .15681 .5 L .15283 .5 L .14868 .5 L .14435 .5 L .13985 .5 L .13516 .5 L .13029 .5 L .12523 .5 L .11997 .5 L .11451 .5 L .10885 .5 L .10299 .5 L .09691 .5 L .09062 .5 L .0841 .5 L .07737 .5 L .07041 .5 L .06321 .5 L .05578 .5 L .04811 .5 L .04019 .5 L .03202 .5 L .0236 .5 L .01491 .5 L .00597 .5 L Mfstroke 0 .5 m .00597 .5 L s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s .6032 .5 m .60322 .5 L .60323 .5 L .60325 .5 L .60326 .5 L .60328 .5 L .6033 .5 L .60332 .5 L .60335 .5 L .60337 .5 L .6034 .5 L .60343 .5 L .60346 .5 L .60349 .5 L .60352 .5 L .60356 .5 L .6036 .5 L .60365 .5 L .60369 .5 L .60374 .5 L .6038 .5 L .60385 .5 L .60392 .5 L .60398 .5 L .60405 .5 L .60413 .5 L .60421 .5 L .6043 .5 L .60439 .5 L .6045 .5 L .60461 .5 L .60472 .5 L .60485 .5 L .60499 .5 L .60513 .5 L .60529 .5 L .60546 .5 L .60564 .5 L .60584 .5 L .60605 .5 L .60628 .5 L .60653 .5 L .6068 .5 L .60709 .5 L .6074 .5 L .60774 .5 L .60811 .5 L .6085 .5 L .60894 .5 L .60941 .5 L Mistroke .60992 .5 L .61048 .5 L .61109 .5 L .61177 .5 L .61251 .5 L .61332 .5 L .61423 .5 L .61524 .5 L .61638 .5 L .61767 .5 L .61915 .5 L .62089 .5 L .62298 .5 L .62567 .5 L .62963 .5 L .63612 .49468 L .63621 .48987 L .63631 .48651 L .63641 .48366 L .63652 .48107 L .63664 .47865 L .63677 .47633 L .6369 .47408 L .63705 .47187 L .6372 .46968 L .63737 .4675 L .63755 .46532 L .63774 .46314 L .63794 .46093 L .63816 .45871 L .63839 .45645 L .63863 .45416 L .63889 .45184 L .63917 .44947 L .63947 .44706 L .63979 .4446 L .64013 .44209 L .64049 .43953 L .64087 .4369 L .64128 .43422 L .64172 .43147 L .64218 .42866 L .64267 .42578 L .64319 .42282 L .64375 .41979 L .64433 .41669 L .64496 .41351 L .64562 .41024 L .64632 .40689 L .64706 .40346 L Mistroke .64784 .39994 L .64867 .39632 L .64954 .39262 L .65046 .38882 L .65144 .38492 L .65246 .38092 L .65355 .37682 L .65468 .37262 L .65588 .36831 L .65714 .36389 L .65846 .35937 L .65985 .35473 L .66131 .34998 L .66284 .34511 L .66443 .34012 L .66611 .33502 L .66786 .32979 L .66968 .32444 L .67159 .31896 L .67358 .31335 L .67566 .30761 L .67782 .30174 L .68008 .29573 L .68242 .28958 L .68486 .2833 L .68739 .27687 L .69002 .2703 L .69274 .26358 L .69557 .25671 L .69851 .24968 L .70155 .2425 L .70469 .23516 L .70795 .22766 L .71132 .21999 L .7148 .21215 L .7184 .20414 L .72211 .19595 L .72595 .18759 L .72991 .17904 L .73399 .1703 L .7382 .16138 L .74254 .15226 L .74702 .14293 L .75162 .13341 L .75637 .12368 L .76125 .11373 L .76628 .10356 L .77145 .09318 L .77677 .08256 L .78224 .07171 L Mistroke .78787 .06063 L .79365 .0493 L .79959 .03771 L .80569 .02588 L .81196 .01378 L .8184 .00142 L Mfstroke .81914 0 m .8184 .00142 L s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s .6665 .5 m .66649 .5 L .66647 .5 L .66646 .5 L .66645 .5 L .66643 .5 L .66641 .5 L .66639 .5 L .66637 .5 L .66635 .5 L .66633 .5 L .66631 .5 L .66628 .5 L .66625 .5 L .66622 .5 L .66619 .5 L .66616 .5 L .66612 .5 L .66608 .5 L .66604 .5 L .66599 .5 L .66594 .5 L .66589 .5 L .66583 .5 L .66577 .5 L .6657 .5 L .66563 .5 L .66556 .5 L .66548 .5 L .66539 .5 L .6653 .5 L .66519 .5 L .66508 .5 L .66497 .5 L .66484 .5 L .6647 .5 L .66456 .5 L .6644 .5 L .66423 .5 L .66404 .5 L .66385 .5 L .66363 .5 L .6634 .5 L .66315 .5 L .66287 .5 L .66258 .5 L .66226 .5 L .66191 .5 L .66153 .5 L .66111 .5 L Mistroke .66066 .5 L .66017 .5 L .65963 .5 L .65903 .5 L .65837 .5 L .65764 .5 L .65682 .5 L .65591 .5 L .65488 .5 L .6537 .5 L .65234 .5 L .65073 .5 L .64877 .5 L .64624 .5 L .64244 .5 L .63612 .50532 L .63621 .51013 L .63631 .51349 L .63641 .51634 L .63652 .51893 L .63664 .52135 L .63677 .52367 L .6369 .52592 L .63705 .52813 L .6372 .53032 L .63737 .5325 L .63755 .53468 L .63774 .53686 L .63794 .53907 L .63816 .54129 L .63839 .54355 L .63863 .54584 L .63889 .54816 L .63917 .55053 L .63947 .55294 L .63979 .5554 L .64013 .55791 L .64049 .56047 L .64087 .5631 L .64128 .56578 L .64172 .56853 L .64218 .57134 L .64267 .57422 L .64319 .57718 L .64375 .58021 L .64433 .58331 L .64496 .58649 L .64562 .58976 L .64632 .59311 L .64706 .59654 L Mistroke .64784 .60006 L .64867 .60368 L .64954 .60738 L .65046 .61118 L .65144 .61508 L .65246 .61908 L .65355 .62318 L .65468 .62738 L .65588 .63169 L .65714 .63611 L .65846 .64063 L .65985 .64527 L .66131 .65002 L .66284 .65489 L .66443 .65988 L .66611 .66498 L .66786 .67021 L .66968 .67556 L .67159 .68104 L .67358 .68665 L .67566 .69239 L .67782 .69826 L .68008 .70427 L .68242 .71042 L .68486 .7167 L .68739 .72313 L .69002 .7297 L .69274 .73642 L .69557 .74329 L .69851 .75032 L .70155 .7575 L .70469 .76484 L .70795 .77234 L .71132 .78001 L .7148 .78785 L .7184 .79586 L .72211 .80405 L .72595 .81241 L .72991 .82096 L .73399 .8297 L .7382 .83862 L .74254 .84774 L .74702 .85707 L .75162 .86659 L .75637 .87632 L .76125 .88627 L .76628 .89644 L .77145 .90682 L .77677 .91744 L .78224 .92829 L Mistroke .78787 .93937 L .79365 .9507 L .79959 .96229 L .80569 .97412 L .81196 .98622 L .8184 .99858 L Mfstroke .81914 1 m .8184 .99858 L s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s P p p p /Arial findfont 8 scalefont setfont [(X)] .2303 .5 0 0 Mshowa P p /Arial findfont 8 scalefont setfont [(X)] .6032 .5 0 0 Mshowa P p /Arial findfont 8 scalefont setfont [(X)] .6665 .5 0 0 Mshowa P P p p /Arial findfont 8 scalefont setfont [(O)] -1.17833 .5 0 0 Mshowa P p /Arial findfont 8 scalefont setfont [(O)] 1.33916 -0.93424 0 0 Mshowa P p /Arial findfont 8 scalefont setfont [(O)] 1.33916 1.93424 0 0 Mshowa P P P P % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect; endGroup] Graphics["<<>>"] ;[o] -Graphics- :[font = text; inactive; preserveAspect] Contrary to common root locus programs the varying parameter need not be the open-loop amplification, but can be any arbitrary parameter: :[font = input; preserveAspect; startGroup] RootLocus[Fs, a, LinRange->{0,3}, Points->100] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 215] %! %%Creator: Mathematica %%AspectRatio: .76393 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.97619 0.363777 0.381966 0.363777 [ [(-2.5)] .06675 0 0 2 Msboxa [(-2)] .24864 0 0 2 Msboxa [(-1.5)] .43052 0 0 2 Msboxa [(-1)] .61241 0 0 2 Msboxa [(-0.5)] .7943 0 0 2 Msboxa [(0)] .97619 0 0 2 Msboxa [(-1)] -0.0125 .01819 1 0 Msboxa [(-0.5)] -0.0125 .20008 1 0 Msboxa [(0)] -0.0125 .38197 1 0 Msboxa [(0.5)] -0.0125 .56385 1 0 Msboxa 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