WebSVN – svnkaklik – Path Comparison – / – /dokumenty Rev 1061 and /dokumenty/ Rev 1062

Ignore whitespace Rev 1061 → Rev 1062

/dokumenty/skolni/TDS/12uloha/kakonjak_reseni12.aux
0,0 → 1,7
\relax
\catcode`"\active
\catcode`-\active
\select@language{czech}
\@writefile{toc}{\select@language{czech}}
\@writefile{lof}{\select@language{czech}}
\@writefile{lot}{\select@language{czech}}

 /dokumenty/skolni/TDS/12uloha/kakonjak_reseni12.log
 ,0 → 1,552
+This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/Debian) (format=pdflatex 2012.12.8)  10 DEC 2012 01:08
+entering extended mode
+ restricted \write18 enabled.
+ %&-line parsing enabled.
+**kakonjak_reseni12.tex
+(./kakonjak_reseni12.tex
+LaTeX2e <2011/06/27>
+Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, lo
+aded.
+(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
+Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
+(/usr/share/texlive/texmf-dist/tex/latex/base/fleqn.clo
+File: fleqn.clo 1998/08/17 v1.1c Standard LaTeX option (flush left equations)
+\mathindent=\dimen102
+)
+(/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo
+File: size12.clo 2007/10/19 v1.4h Standard LaTeX file (size option)
+)
+\c@part=\count79
+\c@section=\count80
+\c@subsection=\count81
+\c@subsubsection=\count82
+\c@paragraph=\count83
+\c@subparagraph=\count84
+\c@figure=\count85
+\c@table=\count86
+\abovecaptionskip=\skip41
+\belowcaptionskip=\skip42
+\bibindent=\dimen103
+)
+(/usr/share/texlive/texmf-dist/tex/generic/babel/babel.sty
+Package: babel 2008/07/08 v3.8m The Babel package
+(/usr/share/texlive/texmf-dist/tex/generic/babel/czech.ldf
+Language: czech 2008/07/06 v3.1a Czech support from the babel system
+(/usr/share/texlive/texmf-dist/tex/generic/babel/babel.def
+File: babel.def 2008/07/08 v3.8m Babel common definitions
+\babel@savecnt=\count87
+\U@D=\dimen104
+)
+Package babel Warning: No hyphenation patterns were loaded for
+(babel)                the language `Czech'
+(babel)                I will use the patterns loaded for \language=0 instead.
+\l@czech = a dialect from \language0
+Package babel Info: Making " an active character on input line 172.
+\cs@wordlen=\count88
+Package babel Info: Making - an active character on input line 226.
+)) (/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
+Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)
+(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty
+Package: keyval 1999/03/16 v1.13 key=value parser (DPC)
+\KV@toks@=\toks14
+)
+(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty
+Package: graphics 2009/02/05 v1.0o Standard LaTeX Graphics (DPC,SPQR)
+(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty
+Package: trig 1999/03/16 v1.09 sin cos tan (DPC)
+)
+(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/graphics.cfg
+File: graphics.cfg 2010/04/23 v1.9 graphics configuration of TeX Live
+)
+Package graphics Info: Driver file: pdftex.def on input line 91.
+(/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def
+File: pdftex.def 2011/05/27 v0.06d Graphics/color for pdfTeX
+(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty
+Package: infwarerr 2010/04/08 v1.3 Providing info/warning/error messages (HO)
+)
+(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty
+Package: ltxcmds 2011/11/09 v1.22 LaTeX kernel commands for general use (HO)
+)
+\Gread@gobject=\count89
+))
+\Gin@req@height=\dimen105
+\Gin@req@width=\dimen106
+)
+(/usr/share/texlive/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty
+\fancy@headwidth=\skip43
+\f@ncyO@elh=\skip44
+\f@ncyO@erh=\skip45
+\f@ncyO@olh=\skip46
+\f@ncyO@orh=\skip47
+\f@ncyO@elf=\skip48
+\f@ncyO@erf=\skip49
+\f@ncyO@olf=\skip50
+\f@ncyO@orf=\skip51
+)
+(/usr/share/texlive/texmf-dist/tex/latex/tools/multicol.sty
+Package: multicol 2011/06/27 v1.7a multicolumn formatting (FMi)
+\c@tracingmulticols=\count90
+\mult@box=\box26
+\multicol@leftmargin=\dimen107
+\c@unbalance=\count91
+\c@collectmore=\count92
+\doublecol@number=\count93
+\multicoltolerance=\count94
+\multicolpretolerance=\count95
+\full@width=\dimen108
+\page@free=\dimen109
+\premulticols=\dimen110
+\postmulticols=\dimen111
+\multicolsep=\skip52
+\multicolbaselineskip=\skip53
+\partial@page=\box27
+\last@line=\box28
+\mult@rightbox=\box29
+\mult@grightbox=\box30
+\mult@gfirstbox=\box31
+\mult@firstbox=\box32
+\@tempa=\box33
+\@tempa=\box34
+\@tempa=\box35
+\@tempa=\box36
+\@tempa=\box37
+\@tempa=\box38
+\@tempa=\box39
+\@tempa=\box40
+\@tempa=\box41
+\@tempa=\box42
+\@tempa=\box43
+\@tempa=\box44
+\@tempa=\box45
+\@tempa=\box46
+\@tempa=\box47
+\@tempa=\box48
+\@tempa=\box49
+\c@columnbadness=\count96
+\c@finalcolumnbadness=\count97
+\last@try=\dimen112
+\multicolovershoot=\dimen113
+\multicolundershoot=\dimen114
+\mult@nat@firstbox=\box50
+\colbreak@box=\box51
+\multicol@sort@counter=\count98
+)
+(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty
+Package: inputenc 2008/03/30 v1.1d Input encoding file
+\inpenc@prehook=\toks15
+\inpenc@posthook=\toks16
+(/usr/share/texlive/texmf-dist/tex/latex/base/utf8.def
+File: utf8.def 2008/04/05 v1.1m UTF-8 support for inputenc
+Now handling font encoding OML ...
+... no UTF-8 mapping file for font encoding OML
+Now handling font encoding T1 ...
+... processing UTF-8 mapping file for font encoding T1
+(/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.dfu
+File: t1enc.dfu 2008/04/05 v1.1m UTF-8 support for inputenc
+   defining Unicode char U+00A1 (decimal 161)
+   defining Unicode char U+00A3 (decimal 163)
+   defining Unicode char U+00AB (decimal 171)
+   defining Unicode char U+00BB (decimal 187)
+   defining Unicode char U+00BF (decimal 191)
+   defining Unicode char U+00C0 (decimal 192)
+   defining Unicode char U+00C1 (decimal 193)
+   defining Unicode char U+00C2 (decimal 194)
+   defining Unicode char U+00C3 (decimal 195)
+   defining Unicode char U+00C4 (decimal 196)
+   defining Unicode char U+00C5 (decimal 197)
+   defining Unicode char U+00C6 (decimal 198)
+   defining Unicode char U+00C7 (decimal 199)
+   defining Unicode char U+00C8 (decimal 200)
+   defining Unicode char U+00C9 (decimal 201)
+   defining Unicode char U+00CA (decimal 202)
+   defining Unicode char U+00CB (decimal 203)
+   defining Unicode char U+00CC (decimal 204)
+   defining Unicode char U+00CD (decimal 205)
+   defining Unicode char U+00CE (decimal 206)
+   defining Unicode char U+00CF (decimal 207)
+   defining Unicode char U+00D0 (decimal 208)
+   defining Unicode char U+00D1 (decimal 209)
+   defining Unicode char U+00D2 (decimal 210)
+   defining Unicode char U+00D3 (decimal 211)
+   defining Unicode char U+00D4 (decimal 212)
+   defining Unicode char U+00D5 (decimal 213)
+   defining Unicode char U+00D6 (decimal 214)
+   defining Unicode char U+00D8 (decimal 216)
+   defining Unicode char U+00D9 (decimal 217)
+   defining Unicode char U+00DA (decimal 218)
+   defining Unicode char U+00DB (decimal 219)
+   defining Unicode char U+00DC (decimal 220)
+   defining Unicode char U+00DD (decimal 221)
+   defining Unicode char U+00DE (decimal 222)
+   defining Unicode char U+00DF (decimal 223)
+   defining Unicode char U+00E0 (decimal 224)
+   defining Unicode char U+00E1 (decimal 225)
+   defining Unicode char U+00E2 (decimal 226)
+   defining Unicode char U+00E3 (decimal 227)
+   defining Unicode char U+00E4 (decimal 228)
+   defining Unicode char U+00E5 (decimal 229)
+   defining Unicode char U+00E6 (decimal 230)
+   defining Unicode char U+00E7 (decimal 231)
+   defining Unicode char U+00E8 (decimal 232)
+   defining Unicode char U+00E9 (decimal 233)
+   defining Unicode char U+00EA (decimal 234)
+   defining Unicode char U+00EB (decimal 235)
+   defining Unicode char U+00EC (decimal 236)
+   defining Unicode char U+00ED (decimal 237)
+   defining Unicode char U+00EE (decimal 238)
+   defining Unicode char U+00EF (decimal 239)
+   defining Unicode char U+00F0 (decimal 240)
+   defining Unicode char U+00F1 (decimal 241)
+   defining Unicode char U+00F2 (decimal 242)
+   defining Unicode char U+00F3 (decimal 243)
+   defining Unicode char U+00F4 (decimal 244)
+   defining Unicode char U+00F5 (decimal 245)
+   defining Unicode char U+00F6 (decimal 246)
+   defining Unicode char U+00F8 (decimal 248)
+   defining Unicode char U+00F9 (decimal 249)
+   defining Unicode char U+00FA (decimal 250)
+   defining Unicode char U+00FB (decimal 251)
+   defining Unicode char U+00FC (decimal 252)
+   defining Unicode char U+00FD (decimal 253)
+   defining Unicode char U+00FE (decimal 254)
+   defining Unicode char U+00FF (decimal 255)
+   defining Unicode char U+0102 (decimal 258)
+   defining Unicode char U+0103 (decimal 259)
+   defining Unicode char U+0104 (decimal 260)
+   defining Unicode char U+0105 (decimal 261)
+   defining Unicode char U+0106 (decimal 262)
+   defining Unicode char U+0107 (decimal 263)
+   defining Unicode char U+010C (decimal 268)
+   defining Unicode char U+010D (decimal 269)
+   defining Unicode char U+010E (decimal 270)
+   defining Unicode char U+010F (decimal 271)
+   defining Unicode char U+0110 (decimal 272)
+   defining Unicode char U+0111 (decimal 273)
+   defining Unicode char U+0118 (decimal 280)
+   defining Unicode char U+0119 (decimal 281)
+   defining Unicode char U+011A (decimal 282)
+   defining Unicode char U+011B (decimal 283)
+   defining Unicode char U+011E (decimal 286)
+   defining Unicode char U+011F (decimal 287)
+   defining Unicode char U+0130 (decimal 304)
+   defining Unicode char U+0131 (decimal 305)
+   defining Unicode char U+0132 (decimal 306)
+   defining Unicode char U+0133 (decimal 307)
+   defining Unicode char U+0139 (decimal 313)
+   defining Unicode char U+013A (decimal 314)
+   defining Unicode char U+013D (decimal 317)
+   defining Unicode char U+013E (decimal 318)
+   defining Unicode char U+0141 (decimal 321)
+   defining Unicode char U+0142 (decimal 322)
+   defining Unicode char U+0143 (decimal 323)
+   defining Unicode char U+0144 (decimal 324)
+   defining Unicode char U+0147 (decimal 327)
+   defining Unicode char U+0148 (decimal 328)
+   defining Unicode char U+014A (decimal 330)
+   defining Unicode char U+014B (decimal 331)
+   defining Unicode char U+0150 (decimal 336)
+   defining Unicode char U+0151 (decimal 337)
+   defining Unicode char U+0152 (decimal 338)
+   defining Unicode char U+0153 (decimal 339)
+   defining Unicode char U+0154 (decimal 340)
+   defining Unicode char U+0155 (decimal 341)
+   defining Unicode char U+0158 (decimal 344)
+   defining Unicode char U+0159 (decimal 345)
+   defining Unicode char U+015A (decimal 346)
+   defining Unicode char U+015B (decimal 347)
+   defining Unicode char U+015E (decimal 350)
+   defining Unicode char U+015F (decimal 351)
+   defining Unicode char U+0160 (decimal 352)
+   defining Unicode char U+0161 (decimal 353)
+   defining Unicode char U+0162 (decimal 354)
+   defining Unicode char U+0163 (decimal 355)
+   defining Unicode char U+0164 (decimal 356)
+   defining Unicode char U+0165 (decimal 357)
+   defining Unicode char U+016E (decimal 366)
+   defining Unicode char U+016F (decimal 367)
+   defining Unicode char U+0170 (decimal 368)
+   defining Unicode char U+0171 (decimal 369)
+   defining Unicode char U+0178 (decimal 376)
+   defining Unicode char U+0179 (decimal 377)
+   defining Unicode char U+017A (decimal 378)
+   defining Unicode char U+017B (decimal 379)
+   defining Unicode char U+017C (decimal 380)
+   defining Unicode char U+017D (decimal 381)
+   defining Unicode char U+017E (decimal 382)
+   defining Unicode char U+200C (decimal 8204)
+   defining Unicode char U+2013 (decimal 8211)
+   defining Unicode char U+2014 (decimal 8212)
+   defining Unicode char U+2018 (decimal 8216)
+   defining Unicode char U+2019 (decimal 8217)
+   defining Unicode char U+201A (decimal 8218)
+   defining Unicode char U+201C (decimal 8220)
+   defining Unicode char U+201D (decimal 8221)
+   defining Unicode char U+201E (decimal 8222)
+   defining Unicode char U+2030 (decimal 8240)
+   defining Unicode char U+2031 (decimal 8241)
+   defining Unicode char U+2039 (decimal 8249)
+   defining Unicode char U+203A (decimal 8250)
+   defining Unicode char U+2423 (decimal 9251)
+)
+Now handling font encoding OT1 ...
+... processing UTF-8 mapping file for font encoding OT1
+(/usr/share/texlive/texmf-dist/tex/latex/base/ot1enc.dfu
+File: ot1enc.dfu 2008/04/05 v1.1m UTF-8 support for inputenc
+   defining Unicode char U+00A1 (decimal 161)
+   defining Unicode char U+00A3 (decimal 163)
+   defining Unicode char U+00B8 (decimal 184)
+   defining Unicode char U+00BF (decimal 191)
+   defining Unicode char U+00C5 (decimal 197)
+   defining Unicode char U+00C6 (decimal 198)
+   defining Unicode char U+00D8 (decimal 216)
+   defining Unicode char U+00DF (decimal 223)
+   defining Unicode char U+00E6 (decimal 230)
+   defining Unicode char U+00EC (decimal 236)
+   defining Unicode char U+00ED (decimal 237)
+   defining Unicode char U+00EE (decimal 238)
+   defining Unicode char U+00EF (decimal 239)
+   defining Unicode char U+00F8 (decimal 248)
+   defining Unicode char U+0131 (decimal 305)
+   defining Unicode char U+0141 (decimal 321)
+   defining Unicode char U+0142 (decimal 322)
+   defining Unicode char U+0152 (decimal 338)
+   defining Unicode char U+0153 (decimal 339)
+   defining Unicode char U+2013 (decimal 8211)
+   defining Unicode char U+2014 (decimal 8212)
+   defining Unicode char U+2018 (decimal 8216)
+   defining Unicode char U+2019 (decimal 8217)
+   defining Unicode char U+201C (decimal 8220)
+   defining Unicode char U+201D (decimal 8221)
+)
+Now handling font encoding OMS ...
+... processing UTF-8 mapping file for font encoding OMS
+(/usr/share/texlive/texmf-dist/tex/latex/base/omsenc.dfu
+File: omsenc.dfu 2008/04/05 v1.1m UTF-8 support for inputenc
+   defining Unicode char U+00A7 (decimal 167)
+   defining Unicode char U+00B6 (decimal 182)
+   defining Unicode char U+00B7 (decimal 183)
+   defining Unicode char U+2020 (decimal 8224)
+   defining Unicode char U+2021 (decimal 8225)
+   defining Unicode char U+2022 (decimal 8226)
+)
+Now handling font encoding OMX ...
+... no UTF-8 mapping file for font encoding OMX
+Now handling font encoding U ...
+... no UTF-8 mapping file for font encoding U
+   defining Unicode char U+00A9 (decimal 169)
+   defining Unicode char U+00AA (decimal 170)
+   defining Unicode char U+00AE (decimal 174)
+   defining Unicode char U+00BA (decimal 186)
+   defining Unicode char U+02C6 (decimal 710)
+   defining Unicode char U+02DC (decimal 732)
+   defining Unicode char U+200C (decimal 8204)
+   defining Unicode char U+2026 (decimal 8230)
+   defining Unicode char U+2122 (decimal 8482)
+   defining Unicode char U+2423 (decimal 9251)
+))
+(/usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty
+Package: geometry 2010/09/12 v5.6 Page Geometry
+(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifpdf.sty
+Package: ifpdf 2011/01/30 v2.3 Provides the ifpdf switch (HO)
+Package ifpdf Info: pdfTeX in PDF mode is detected.
+)
+(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifvtex.sty
+Package: ifvtex 2010/03/01 v1.5 Detect VTeX and its facilities (HO)
+Package ifvtex Info: VTeX not detected.
+)
+(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty
+Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional
+)
+\Gm@cnth=\count99
+\Gm@cntv=\count100
+\c@Gm@tempcnt=\count101
+\Gm@bindingoffset=\dimen115
+\Gm@wd@mp=\dimen116
+\Gm@odd@mp=\dimen117
+\Gm@even@mp=\dimen118
+\Gm@layoutwidth=\dimen119
+\Gm@layoutheight=\dimen120
+\Gm@layouthoffset=\dimen121
+\Gm@layoutvoffset=\dimen122
+\Gm@dimlist=\toks17
+)
+(/usr/share/texlive/texmf-dist/tex/latex/rotating/rotating.sty
+Package: rotating 2009/03/28 v2.16a rotated objects in LaTeX
+(/usr/share/texlive/texmf-dist/tex/latex/base/ifthen.sty
+Package: ifthen 2001/05/26 v1.1c Standard LaTeX ifthen package (DPC)
+)
+\c@r@tfl@t=\count102
+\rotFPtop=\skip54
+\rotFPbot=\skip55
+\rot@float@box=\box52
+\rot@mess@toks=\toks18
+)
+(./kakonjak_reseni12.aux)
+\openout1 = `kakonjak_reseni12.aux'.
+LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 10.
+LaTeX Font Info:    ... okay on input line 10.
+LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 10.
+LaTeX Font Info:    ... okay on input line 10.
+LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 10.
+LaTeX Font Info:    ... okay on input line 10.
+LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 10.
+LaTeX Font Info:    ... okay on input line 10.
+LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 10.
+LaTeX Font Info:    ... okay on input line 10.
+LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 10.
+LaTeX Font Info:    ... okay on input line 10.
+(/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii
+[Loading MPS to PDF converter (version 2006.09.02).]
+\scratchcounter=\count103
+\scratchdimen=\dimen123
+\scratchbox=\box53
+\nofMPsegments=\count104
+\nofMParguments=\count105
+\everyMPshowfont=\toks19
+\MPscratchCnt=\count106
+\MPscratchDim=\dimen124
+\MPnumerator=\count107
+\makeMPintoPDFobject=\count108
+\everyMPtoPDFconversion=\toks20
+) (/usr/share/texlive/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty
+Package: pdftexcmds 2011/11/29 v0.20 Utility functions of pdfTeX for LuaTeX (HO
+)
+(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifluatex.sty
+Package: ifluatex 2010/03/01 v1.3 Provides the ifluatex switch (HO)
+Package ifluatex Info: LuaTeX not detected.
+)
+Package pdftexcmds Info: LuaTeX not detected.
+Package pdftexcmds Info: \pdf@primitive is available.
+Package pdftexcmds Info: \pdf@ifprimitive is available.
+Package pdftexcmds Info: \pdfdraftmode found.
+)
+(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty
+Package: epstopdf-base 2010/02/09 v2.5 Base part for package epstopdf
+(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty
+Package: grfext 2010/08/19 v1.1 Manage graphics extensions (HO)
+(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/kvdefinekeys.sty
+Package: kvdefinekeys 2011/04/07 v1.3 Define keys (HO)
+))
+(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty
+Package: kvoptions 2011/06/30 v3.11 Key value format for package options (HO)
+(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty
+Package: kvsetkeys 2012/04/25 v1.16 Key value parser (HO)
+(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/etexcmds.sty
+Package: etexcmds 2011/02/16 v1.5 Avoid name clashes with e-TeX commands (HO)
+Package etexcmds Info: Could not find \expanded.
+(etexcmds)             That can mean that you are not using pdfTeX 1.50 or
+(etexcmds)             that some package has redefined \expanded.
+(etexcmds)             In the latter case, load this package earlier.
+)))
+Package grfext Info: Graphics extension search list:
+(grfext)             [.png,.pdf,.jpg,.mps,.jpeg,.jbig2,.jb2,.PNG,.PDF,.JPG,.JPE
+G,.JBIG2,.JB2,.eps]
+(grfext)             \AppendGraphicsExtensions on input line 452.
+(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg
+File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv
+e
+))
+*geometry* driver: auto-detecting
+*geometry* detected driver: pdftex
+*geometry* verbose mode - [ preamble ] result:
+* driver: pdftex
+* paper: a4paper
+* layout: <same size as paper>
+* layoutoffset:(h,v)=(0.0pt,0.0pt)
+* hratio: 1:1
+* vratio: 1:1
+* modes:
+* h-part:(L,W,R)=(56.90552pt, 483.69684pt, 56.90552pt)
+* v-part:(T,H,B)=(66.86397pt, 711.3189pt, 66.86398pt)
+* \paperwidth=597.50787pt
+* \paperheight=845.04684pt
+* \textwidth=483.69684pt
+* \textheight=711.3189pt
+* \oddsidemargin=-15.36447pt
+* \evensidemargin=-15.36447pt
+* \topmargin=-42.40602pt
+* \headheight=12.0pt
+* \headsep=25.0pt
+* \topskip=12.0pt
+* \footskip=30.0pt
+* \marginparwidth=44.0pt
+* \marginparsep=10.0pt
+* \columnsep=10.0pt
+* \skip\footins=10.8pt plus 4.0pt minus 2.0pt
+* \hoffset=0.0pt
+* \voffset=0.0pt
+* \mag=1000
+* \@twocolumnfalse
+* \@twosidefalse
+* \@mparswitchfalse
+* \@reversemarginfalse
+* (1in=72.27pt=25.4mm, 1cm=28.453pt)
+LaTeX Font Info:    External font `cmex10' loaded for size
+(Font)              <12> on input line 19.
+LaTeX Font Info:    External font `cmex10' loaded for size
+(Font)              <8> on input line 19.
+LaTeX Font Info:    External font `cmex10' loaded for size
+(Font)              <6> on input line 19.
+[1
+{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}]
+Overfull \hbox (83.25053pt too wide) detected at line 314
+$ \OML/cmm/m/it/12 H\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 s\OT1/cmr/m/n/12 ) = \OML
+/cmm/m/it/12 C\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 sI \OMS/cmsy/m/n/12 ^^@ \OML/cm
+m/m/it/12 A\OT1/cmr/m/n/12 )[]\OML/cmm/m/it/12 B \OT1/cmr/m/n/12 + \OML/cmm/m/i
+t/12 D \OT1/cmr/m/n/12 = [] [] [] = []$ []
+ []
+[2]
+Overfull \hbox (3.59666pt too wide) in paragraph at lines 422--423
+[]\OT1/cmr/m/n/12 Stavov^^Sy syst^^Sem s po-zorovatelem a stavovou zp^^Tetnou v
+azbou vyu^^Tz^^S^^Pvaj^^S^^Pc^^S^^P po-zorovatelem
+ []
+[3] [4] (./kakonjak_reseni12.aux) )
+Here is how much of TeX's memory you used:
+strings out of 495059
+string characters out of 3182030
+words of memory out of 3000000
+multiletter control sequences out of 15000+200000
+words of font info for 25 fonts, out of 3000000 for 9000
+hyphenation exceptions out of 8191
+i,13n,43p,306b,344s stack positions out of 5000i,500n,10000p,200000b,50000s
+</usr/share/texlive/texmf-dist/fonts/type1/p
+ublic/amsfonts/cm/cmbx12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/
+amsfonts/cm/cmex10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfon
+ts/cm/cmmi12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/
+cmmi8.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.p
+fb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr
+/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share
+/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy8.pfb>
+Output written on kakonjak_reseni12.pdf (4 pages, 88060 bytes).
+PDF statistics:
+PDF objects out of 1000 (max. 8388607)
+compressed objects within 1 object stream
+named destinations out of 1000 (max. 500000)
+words of extra memory for PDF output out of 10000 (max. 10000000)

/dokumenty/skolni/TDS/12uloha/kakonjak_reseni12.pdf
Cannot display: file marked as a binary type.
svn:mime-type = application/octet-stream
Property changes:
Added: svn:mime-type
+application/octet-stream
\ No newline at end of property

/dokumenty/skolni/TDS/12uloha/kakonjak_reseni12.synctex.gz
Cannot display: file marked as a binary type.
svn:mime-type = application/octet-stream
Property changes:
Added: svn:mime-type
+application/octet-stream
\ No newline at end of property

 /dokumenty/skolni/TDS/12uloha/kakonjak_reseni12.tex
 ,0 → 1,518
+\documentclass[12pt,notitlepage,fleqn]{article}
+\usepackage[czech]{babel}
+\usepackage[pdftex]{graphicx}
+\usepackage{fancyhdr,multicol} %nastavení češtiny, fancy, grafiky, sloupce
+\usepackage[utf8]{inputenc} %vstupni soubory v kodovani UTF-8
+\usepackage[a4paper,text={17cm,25cm},centering]{geometry} %nastavení okrajů
+\usepackage{rotating}
+\begin{document}
+\section*{Řešení 12. zadané úlohy          -        Jakub Kákona}
+\begin{enumerate}
+\item
+Sestavíme minimální realizaci sytému v řiditelné formě
+\begin{equation}
+D_c = \lim _{ s \to \infty} H_1(s) = 0
+\end{equation}
+\begin{equation}
+C_c=[b_0, b_1, \cdots , b_{n-1} ] = \left[\begin{array}{cc}
+& 0 \\
+\end{array}\right]
+\end{equation}
+\begin{equation}
+A_c = \left[ \begin{array}{cccc}
+& 1 & \cdots & 0 \\
+\vdots & \vdots & \ddots & \vdots  \\
+& 0 & \cdots & 1 \\
+-a_0 & -a_1 & \cdots & -a_{n-1} \\
+\end{array}
+\right] =
+ \left[ \begin{array}{cc}
+& 1 \\
+& 0 \\
+\end{array}
+\right]
+\end{equation}
+\begin{equation}
+B_c = \left[\begin{array}{c}
+\\
+\\
+\end{array}\right]
+\end{equation}
+Potřebujeme vybrat takové matice
+$F =  \left[\begin{array}{cc}
+a & b \\
+\end{array}\right]$,
+$K =  \left[\begin{array}{c}
+c \\
+d \\
+\end{array}\right]$, že vlastní čísla matic $A + BF$ a $A -KC$ budou mít zápornou reálnou část.
+\begin{equation}
+\det(sI - (A + BF)) = s^2 - sb - a \\
+F = \left[\begin{array}{cc}
+-1 & -2 \\
+\end{array}\right]
+\end{equation}
+\begin{equation}
+\det(sI - (A + KC)) = s^2 + sc + d \\
+K = \left[\begin{array}{c}
+\\
+\\
+\end{array}\right]
+\end{equation}
+Stabilizující regulátory $H_2$ mají tuto stavovou reprezentaci:
+\begin{eqnarray}
+\dot{x} =& Ax + Bu +K(y-(Cx + Du))\\
+u =& Fx +K'(q)(y-(Cx + Du))
+\end{eqnarray}
+Kde $K'(q)$ je stabilní ryzí matice.
+Po dosazení známých hodnot dostaneme všechny ryzí regulátory $H_2$ stabilizující systém $H_1$
+\begin{eqnarray}
+\dot{x} =&
+\left[ \begin{array}{cc}
+& 1 \\
+& 0 \\
+\end{array}
+\right]x
++
+\left[ \begin{array}{c}
+\\
+\\
+\end{array}
+\right]u
++
+\left[ \begin{array}{c}
+\\
+\\
+\end{array}
+\right](y-
+\left[ \begin{array}{cc}
+& 0 \\
+\end{array}
+\right]x)\\
+u =&
+\left[ \begin{array}{cc}
+& 2 \\
+\end{array}
+\right] + K'(q)(y-
+\left[ \begin{array}{cc} 1 & 0 \\ \end{array} \right]
+x)
+\end{eqnarray}
+\item
+\item
+\item
+\begin{enumerate}
+\item
+Stavová reprezentace systému pro případ  $\theta = x_1, \dot{\theta}=x_2$ stejná jako v případě úkolu 10.
+\begin{eqnarray}
+\left[ \begin{array}{c}
+\dot{x}_1 \\
+\dot{x}_2 \\
+\end{array}
+\right] =&
+\left[ \begin{array}{cc}
+& 1 \\
+& -1 \\
+\end{array}
+\right]
+\left[ \begin{array}{cc}
+x_1 \\
+x_2 \\
+\end{array}
+\right]
+\left[ \begin{array}{cc}
+\\
+\\
+\end{array}
+\right]u
+\\
+y =&
+\left[ \begin{array}{cc}
+& 1 \\
+\end{array}
+\right]
+\left[ \begin{array}{cc}
+x_1 \\
+x_2 \\
+\end{array}
+\right]
+\end{eqnarray}
+\item
+Podmínka požaduje charakteristický polynom systému se stavovou zpětnou vazbou ve tvaru
+\begin{equation}
+(s + 1) (s + 1) = s^2 + 2s + 1
+\end{equation}
+\begin{equation}
+\det(sI - (A + BF)) = s^2 - s(1 - b) - a
+\end{equation}
+Kde $ F = \left[\begin{array}{cc}
+a & b \\
+\end{array}\right]$
+Porovnáním koeficientů obou polynomů dostaneme matici stavové zpětné vazby
+\begin{equation}
+F = \left[\begin{array}{cc}
+-1 & -1 \\
+\end{array}\right]
+\end{equation}
+\item
+Podmínka požaduje charakteristický polynom pozorovatele ve tvaru
+\begin{equation}
+(s + 5) (s + 5) = s^2 + 10s + 25
+\end{equation}
+Obecný charakteristický polynom pozorovatele je
+\begin{equation}
+\det(sI - (A + KC)) = s^2 - s(1 - a) + a +b
+\end{equation}
+Kde $ K = \left[\begin{array}{c}
+a \\
+b \\
+\end{array}\right]$
+Porovnáním koeficientů obou polynomů dostaneme matici stavové zpětné vazby
+\begin{equation}
+K = \left[\begin{array}{cc}
+\\
+\\
+\end{array}\right]
+\end{equation}
+\item
+Stavový popis systému systému s pozorovatelem a stavovou zpětnou vazbou je
+\begin{eqnarray}
+\left[ \begin{array}{c}
+\dot{x} \\
+\dot{\hat{x}} \\
+\end{array}
+\right] =&
+\left[ \begin{array}{cc}
+A & BF\\
+KC & A- KC + BF \\
+\end{array}
+\right]
+\left[ \begin{array}{c}
+x_1 \\
+x_2 \\
+\end{array}
+\right]
++
+\left[ \begin{array}{c}
+B \\
+B \\
+\end{array}
+\right]r
+\\
+y =&
+\left[ \begin{array}{cc}
+C & DF \\
+\end{array}
+\right]
+\left[ \begin{array}{c}
+x \\
+x \\
+\end{array}
+\right]
++
+Dr
+\end{eqnarray}
+Po dosazení dostaneme:
+\begin{eqnarray}
+\left[ \begin{array}{c}
+\dot{x} \\
+\dot{\hat{x}} \\
+\end{array}
+\right] =&
+\left[ \begin{array}{cccc}
+& 1 & 0 & 0 \\
+& -1 & -1 & -1 \\
+& 0 & -9 & 1 \\
+& 0 & -17 & -2 \\
+\end{array}
+\right]
+\left[ \begin{array}{c}
+x \\
+\hat{x} \\
+\end{array}
+\right]
++
+\left[ \begin{array}{c}
+\\
+\\
+\\
+\\
+\end{array}
+\right]r\\
+y =&
+\left[ \begin{array}{cccc}
+& 0 & 0 & 0 \\
+\end{array}
+\right]
+\left[ \begin{array}{c}
+x \\
+\hat{x} \\
+\end{array}
+\right]
+\end{eqnarray}
+Přenos tohoto systému pak je:
+\begin{equation}
+H(s)= C (sI - A)^{-1} B + D =
+\left[ \begin{array}{cccc}
+& 0 & 0 & 0 \\
+\end{array}
+\right]
+\left[ \begin{array}{cccc}
+s & -1 & 0 & 0 \\
+& s + 1 & 1 & 1 \\
+-9 & 0 & s+9 & -1 \\
+-16 & 0 & 17 & s + 2 \\
+\end{array}
+\right]
+\left[ \begin{array}{c}
+\\
+\\
+\\
+\\
+\end{array}
+\right] = \frac{1}{(s+1)^2}
+\end{equation}
+Charakteristický polynom systému je
+\begin{equation}
+\det(sI - A ) = (s + 5)^2 (s + 1)^2
+\end{equation}
+Vlastní čísla leží na záporné ose a systém je stabilní.
+Pozorovatelnost celkového systému:
+\begin{equation}
+O = \left[ \begin{array}{c}
+C \\
+C A\\
+\end{array}
+\right]=
+\left[ \begin{array}{cccc}
+& 0 & 0 & 0 \\
+& 1 & 0 & 0 \\
+& -1 & -1 & -1 \\
+-25 & 1 & 27 & 2 \\
+\end{array}
+\right]
+\end{equation}
+Hodnost matice pozorovatelnosti je 4 a systém je  pozorovatelný.
+Ověříme řiditelnost systému
+\begin{equation}
+C = \left[ \begin{array}{cc}
+B & AB \\
+\end{array}
+\right]=
+\left[ \begin{array}{cccc}
+& 1 & -2 & 3 \\
+& -2 & 4 & -4 \\
+& 1 & -2 & 3 \\
+& -2 & 3 & -4 \\
+\end{array}
+\right]
+\end{equation}
+Hodnost matice řiditelnosti je 2 a není úplně řiditelný.
+\end{enumerate}
+\item
+\begin{enumerate}
+\item
+Podmínka požaduje charakteristický polynom systému se stavovou zpětnou vazbou ve tvaru
+\begin{equation}
+(s + 0,5 +0,5j) (s + 0,5 + 0,5j) = s^2 + s + 0,5
+\end{equation}
+Obecný charakteristický polynom je
+\begin{equation}
+\det(sI - (A + BF)) = s^2 + sb + a - 1
+\end{equation}
+Kde $ F = \left[\begin{array}{cc}
+a & b \\
+\end{array}\right]$
+Porovnáním koeficientů obou polynomů dostaneme matici stavové zpětné vazby
+\begin{equation}
+F = \left[\begin{array}{cc}
+\frac{3}{2} & 1 \\
+\end{array}\right]
+\end{equation}
+\item
+Podmínka požaduje charakteristický polynom systému se stavovou zpětnou vazbou ve tvaru
+\begin{equation}
+(s + \alpha +j) (s + \alpha - j) = s^2 + \alpha s + \alpha ^2 + 1
+\end{equation}
+Obecný charakteristický polynom  pozorovatele je
+\begin{equation}
+\det(sI - (A - KC)) = s^2 + sa + b - 1
+\end{equation}
+Kde $ K = \left[\begin{array}{c}
+a \\
+b \\
+\end{array}\right]$
+Porovnáním koeficientů obou polynomů dostaneme matici stavové injekce
+\begin{equation}
+K = \left[\begin{array}{c}
+\alpha \\
+\alpha ^2 + 2 \\
+\end{array}\right]
+\end{equation}
+\item
+Stavový systém s pozorovatelem a stavovou zpětnou vazbou využívající pozorovatelem odhadované stavy je
+\begin{eqnarray}
+\left[ \begin{array}{c}
+\dot{x} \\
+\dot{\hat{x}} \\
+\end{array}
+\right] =&
+\left[ \begin{array}{cc}
+A & BF\\
+KC & A- KC + BF \\
+\end{array}
+\right]
+\left[ \begin{array}{c}
+x \\
+\hat{x} \\
+\end{array}
+\right]
++
+\left[ \begin{array}{c}
+B \\
+B \\
+\end{array}
+\right]r
+\\
+y =&
+\left[ \begin{array}{cc}
+C & DF \\
+\end{array}
+\right]
+\left[ \begin{array}{c}
+x \\
+\hat{x} \\
+\end{array}
+\right]
++
+Dr
+\end{eqnarray}
+Po dosazení dostaneme:
+\begin{eqnarray}
+\left[ \begin{array}{c}
+\dot{x} \\
+\dot{\hat{x}} \\
+\end{array}
+\right] =&
+\left[ \begin{array}{cccc}
+& 1 & 0 & 0 \\
+& 0 & -\frac{3}{2} & -1 \\
+\alpha & 0 & 2 \alpha & 1 \\
+\alpha ^2 + 2 & 0 & - \alpha ^2 - \frac{5}{2}  & -1 \\
+\end{array}
+\right]
+\left[ \begin{array}{c}
+x \\
+\hat{x} \\
+\end{array}
+\right]
++
+\left[ \begin{array}{c}
+\\
+-1 \\
+\\
+-1 \\
+\end{array}
+\right]r\\
+y =&
+\left[ \begin{array}{cccc}
+& 0 & 0 & 0 \\
+\end{array}
+\right]
+\left[ \begin{array}{c}
+x \\
+\hat{x} \\
+\end{array}
+\right]
+\end{eqnarray}
+\end{enumerate}
+\end{enumerate}
+\end{document}

Subversion Repositories svnkaklik

Compare Revisions

Ignore whitespace Rev 1061 → Rev 1062