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Text File | 1992-06-09 | 84.1 KB | 4,900 lines
(*^ ::[paletteColors = 128; showRuler; currentKernel; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, L1, e8, 28, "Times"; ; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, L1, e6, 22, "Times"; ; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, L1, e6, 16, "Times"; ; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, L1, a20, 22, "Times"; ; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, L1, a15, 16, "Times"; ; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, L1, a12, 14, "Times"; ; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 14, "Times"; ; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = input, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeInput, M42, N23, L1, 14, "Courier"; ; fontset = output, output, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 14, "Courier"; ; fontset = message, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 14, "Courier"; ; fontset = print, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 14, "Courier"; ; fontset = info, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 14, "Courier"; ; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, L1, 14, "Courier"; ; fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = header, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 14, "Times"; ; fontset = Left Header, nohscroll, cellOutline, 14, "Times"; ; fontset = footer, inactive, nohscroll, noKeepOnOnePage, preserveAspect, center, M7, L1, 14, "Times"; ; fontset = Left Footer, cellOutline, blackBox, 14, "Times"; ; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 14, "Times"; ; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 14, "Courier"; ; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 14, "Times"; ; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 14, "Times"; ; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 14, "Times"; ; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 14, "Times"; ; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 14, "Times"; ;] :[font = title; inactive; preserveAspect; rightWrapOffset = 522; fontColorBlue = 65535; ] COSY_PAK Control Systems Analysis Package for Mathematica ;[s] 3:0,0;49,1;60,2;62,-1; 3:1,25,19,Times,1,28,0,0,0;1,26,20,Times,3,28,0,0,0;1,25,19,Times,1,28,0,0,0; :[font = subtitle; inactive; preserveAspect; rightWrapOffset = 522; ] By C.K. Chen N. Sreenath 1992 :[font = message; inactive; preserveAspect; center; rightWrapOffset = 522; fontName = "Courier"; ] Systems Engineering Department Case School of Engineering Case Western Reserve University Cleveland, OH, 44106-7070 :[font = message; inactive; dontPreserveAspect; center; rightWrapOffset = 522; ] Support from CWRU Information and Network Services - Dr. Ray Neff Case Alumni Association The Lilly Foundation :[font = subtitle; inactive; preserveAspect; leftWrapOffset = 23; rightWrapOffset = 522; ] Chapter 5 Root-Locus Analysis :[font = section; inactive; Cclosed; preserveAspect; rightWrapOffset = 522; startGroup; ] Initialization :[font = input; initialization; preserveAspect; rightWrapOffset = 522; fontName = "Courier"; ] *) (* Initialization of Path *) (* Example For UNIX machine (Default) *) $Path=Join[$Path, {"~/Library/Mathematica/Packages"}]; (* Example For IBM PC *) (* $Path=Join[$Path, {"c:\winmath\packages"}]; *) (* Example For MAC *) (* $Path=Join[$Path, {"My_Harddisk:Mathematica:Package"}]; *) (* :[font = input; initialization; preserveAspect; rightWrapOffset = 522; fontName = "Courier"; endGroup; ] *) Needs["COSYPAK`chap5`"] (* :[font = section; inactive; Cclosed; preserveAspect; rightWrapOffset = 522; startGroup; ] Root Locus :[font = text; inactive; preserveAspect; rightWrapOffset = 522; ] The root locus plot allows the designer of a control system to graph the locations of a system's closed loop poles for varying gains. The characteristic equation of the system is satisfied by the values of s that cause the closed loop transfer funtion to be -1. This principle is utilized by the root-locus method. The root locus plot shows the loci of the locations of the system's closed loop poles for all gains. The root locus method is extremely useful in the design of control systems. It allows the designer to take an interactive approach to finding a controller by allowing him or her to compare the effects of different open loop pole locations. COSY_PAK Function RootLocus[Transf, s, {k,kmin,kmax}, gopts]: Plots the root-locus plot of the transfer function Transf(s) with the Parameter k varying from k=kmin to k=kmax. Returns graphics. ;[s] 13:0,0;661,1;678,2;679,3;721,4;774,5;783,6;802,7;804,8;818,9;824,10;828,11;835,12;853,-1; 13:1,13,10,Times,0,14,0,0,0;1,12,9,Times,1,14,0,0,0;1,13,10,Times,2,14,0,0,0;1,12,9,Times,1,14,0,0,0;1,13,10,Times,0,14,0,0,0;1,12,9,Times,1,14,0,0,0;1,13,10,Times,0,14,0,0,0;1,12,9,Times,1,14,0,0,0;1,13,10,Times,0,14,0,0,0;1,12,9,Times,1,14,0,0,0;1,13,10,Times,0,14,0,0,0;1,12,9,Times,1,14,0,0,0;1,13,10,Times,0,14,0,0,0; :[font = subsection; inactive; Cclosed; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; startGroup; ] Example 1 :[font = input; Cclosed; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; startGroup; ] g1 = (s+1)/s^2/(s+3.6); SequenceForm["The transfer function: ", g1] RootLocus[g1,s,{k,0,10}] :[font = output; output; inactive; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; fontLeading = 0; ] "The transfer function: "(1 + s)/(s^2*(3.6 + s)) ;[o] 1 + s The transfer function: ------------ 2 s (3.6 + s) :[font = postscript; 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Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = subsection; inactive; Cclosed; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; startGroup; ] Example 2 :[font = input; Cclosed; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; startGroup; ] g1 = 1/s/(s+1)/(s^2 + 4s +13); SequenceForm["The transfer function: ", g1] RootLocus[g1,s,{k,0,300}] :[font = output; output; inactive; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; ] "The transfer function: "1/(s*(1 + s)*(13 + 4*s + s^2)) ;[o] 1 The transfer function: ------------------------- 2 s (1 + s) (13 + 4 s + s ) :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; pictureLeft = 22; pictureWidth = 462; pictureHeight = 286; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.72789 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Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = subsection; inactive; Cclosed; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; startGroup; ] Example 3 :[font = input; Cclosed; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; startGroup; animationSpeed = 2; infiniteLoop; loopDistance = 1; ] g1 = (s+0.4)/s^2/(s+3.6); SequenceForm["The transfer function: ", g1] RootLocus[g1,s,{k,0,10}] :[font = output; output; inactive; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; fontLeading = 0; ] "The transfer function: "(0.4 + s)/(s^2*(3.6 + s)) ;[o] 0.4 + s The transfer function: ------------ 2 s (3.6 + s) :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; pictureLeft = 22; pictureWidth = 462; pictureHeight = 286; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont 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lineto 0.76097 0.35593 lineto 0.65873 0.30902 lineto 0.65873 0.30902 lineto 0.73988 0.30902 lineto 0.79247 0.30902 lineto 0.81099 0.30902 lineto 0.82215 0.30902 lineto 0.82992 0.30902 lineto 0.83575 0.30902 lineto 0.84033 0.30902 lineto 0.84403 0.30902 lineto 0.8471 0.30902 lineto 0.84968 0.30902 lineto 0.85188 0.30902 lineto 0.85216 0.30902 lineto stroke grestore grestore grestore 0 0 moveto 1 0 lineto 1 0.61803 lineto 0 0.61803 lineto closepath clip newpath % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; fontLeading = 0; endGroup; endGroup; ] The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = subsection; inactive; Cclosed; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; startGroup; ] Example 4 :[font = input; Cclosed; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; startGroup; ] g1 = (s+2)(s+3)/s/(s+1); SequenceForm["The transfer function: ", g1] RootLocus[g1,s,{k,0,20}] :[font = output; output; inactive; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; fontLeading = 0; ] "The transfer function: "((2 + s)*(3 + s))/(s*(1 + s)) ;[o] (2 + s) (3 + s) The transfer function: --------------- s (1 + s) :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; leftWrapOffset = 30; rightWrapOffset = 522; pictureLeft = 22; pictureWidth = 462; pictureHeight = 286; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.97619 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