Index: /applications/dual/vahala/pcrb/pcrb3.lyx
===================================================================
--- /applications/dual/vahala/pcrb/pcrb3.lyx (revision 1418)
+++ /applications/dual/vahala/pcrb/pcrb3.lyx (revision 1418)
@@ -0,0 +1,1791 @@
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass article
+\use_default_options true
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding auto
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\use_hyperref false
+\papersize default
+\use_geometry false
+\use_amsmath 1
+\use_esint 1
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 1
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Title
+Výpočet PCRB
+\end_layout
+
+\begin_layout Subsection*
+PCRB obecně
+\end_layout
+
+\begin_layout Standard
+Výpočet PCRB (Posterior Cramer-Rao Bound) dle [Posterior Cramer-Rao Bounds
+ for Discrete-Time Nonlinear Filtering, 1998, Tichavský P.
+ et al.] jako:
+\begin_inset Formula 
+\[
+P\triangleq\mathtt{E}\left\{ \left[g(x)-\theta\right]\left[g(x)-\theta\right]^{T}\right\} \geq J^{-1}
+\]
+
+\end_inset
+
+kde 
+\begin_inset Formula $x$
+\end_inset
+
+ reprezentuje vektor měřených dat, 
+\begin_inset Formula $\theta$
+\end_inset
+
+ je vektorový estimovaný náhodný parametr a 
+\begin_inset Formula $g(x)$
+\end_inset
+
+ je funkce 
+\begin_inset Formula $x$
+\end_inset
+
+, která je odhadem 
+\begin_inset Formula $\theta$
+\end_inset
+
+.
+ 
+\begin_inset Formula $J$
+\end_inset
+
+ je (Fisherova) informační matice
+\begin_inset Formula 
+\[
+J_{ij}=\mathtt{E}\left[-\frac{\partial^{2}\log p_{x,\theta}(X,\Theta)}{\partial\Theta_{i}\partial\Theta_{j}}\right]
+\]
+
+\end_inset
+
+kde 
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
+\begin_inset Formula $p_{x,\theta}(X,\Theta)$
+\end_inset
+
+ je sdružená hustota pravděpodobnosti dvojice 
+\begin_inset Formula $(x,\theta)$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection*
+PCRB nelineární filtrace
+\end_layout
+
+\begin_layout Standard
+Spodní mez pro nelineární filtrační problém systému
+\begin_inset Formula 
+\begin{eqnarray*}
+x_{n+1} & = & f_{n}(x_{n},w_{n})\\
+z_{n} & = & h_{n}(x_{n},v_{n})
+\end{eqnarray*}
+
+\end_inset
+
+kde 
+\begin_inset Formula $x_{n}$
+\end_inset
+
+ je stav systému v čase 
+\begin_inset Formula $n$
+\end_inset
+
+, 
+\begin_inset Formula $z_{n}$
+\end_inset
+
+ je pozorování v čase 
+\begin_inset Formula $n$
+\end_inset
+
+, 
+\begin_inset Formula $w$
+\end_inset
+
+ a 
+\begin_inset Formula $v$
+\end_inset
+
+ jsou vzájemně nezávislé bílé procesy a 
+\begin_inset Formula $f_{n}$
+\end_inset
+
+ a 
+\begin_inset Formula $h_{n}$
+\end_inset
+
+ jsou obecně nelineární funkce.
+ Pak je možné počítat rekurzivně posloupnost matic 
+\begin_inset Formula $J_{n}$
+\end_inset
+
+ jako:
+\begin_inset Formula 
+\begin{equation}
+J_{n+1}=D_{n}^{22}-D_{n}^{21}\left(J_{n}+D_{n}^{11}\right)^{-1}D_{n}^{12}\label{eq: rekurze J}
+\end{equation}
+
+\end_inset
+
+kde se matice 
+\begin_inset Formula $D_{n}$
+\end_inset
+
+ počítají jako
+\begin_inset Formula 
+\begin{eqnarray}
+D_{n}^{11} & = & \mathtt{E}\left\{ -\triangle_{x_{n}}^{x_{n}}\log p(x_{n+1}\mid x_{n})\right\} \nonumber \\
+D_{n}^{12} & = & \mathtt{E}\left\{ -\triangle_{x_{n}}^{x_{n+1}}\log p(x_{n+1}\mid x_{n})\right\} \label{eq:matice Dn}\\
+D_{n}^{21} & = & \mathtt{E}\left\{ -\triangle_{x_{n+1}}^{x_{n}}\log p(x_{n+1}\mid x_{n})\right\} =\left(D_{n}^{12}\right)^{T}\nonumber \\
+D_{n}^{22} & = & \mathtt{E}\left\{ -\triangle_{x_{n+1}}^{x_{n+1}}\log p(x_{n+1}\mid x_{n})\right\} +\mathtt{E}\left\{ -\triangle_{x_{n+1}}^{x_{n+1}}\log p(z_{n+1}\mid x_{n+1})\right\} \nonumber 
+\end{eqnarray}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection*
+PCRB Gaussovské
+\end_layout
+
+\begin_layout Standard
+Pro aditivní Gaussovský šum s nulovou střední hodnotou a invertovatelnými
+ kovariančními maticemi 
+\begin_inset Formula $Q_{n}$
+\end_inset
+
+ a 
+\begin_inset Formula $R_{n}$
+\end_inset
+
+ platí následující vztahy pro výpočet matic 
+\begin_inset Formula $D_{n}$
+\end_inset
+
+ jako speciální případ (
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:matice Dn"
+
+\end_inset
+
+):
+\begin_inset Formula 
+\begin{eqnarray}
+D_{n}^{11} & = & \mathtt{E}\left\{ \left[\nabla_{x_{n}}f_{n}^{T}(x_{n})\right]Q_{n}^{-1}\left[\nabla_{x_{n}}f_{n}^{T}(x_{n})\right]^{T}\right\} \nonumber \\
+D_{n}^{12} & = & -\mathtt{E}\left\{ \nabla_{x_{n}}f_{n}^{T}(x_{n})\right\} Q_{n}^{-1}\label{eq:matice Dn gauss}\\
+D_{n}^{22} & = & Q_{n}^{-1}+\mathtt{E}\left\{ \left[\nabla_{x_{n+1}}h_{n+1}^{T}(x_{n+1})\right]R_{n+1}^{-1}\left[\nabla_{x_{n+1}}h_{n+1}^{T}(x_{n+1})\right]^{T}\right\} \nonumber 
+\end{eqnarray}
+
+\end_inset
+
+V případě linearity funkcí 
+\begin_inset Formula $f_{n}$
+\end_inset
+
+ a 
+\begin_inset Formula $h_{n}$
+\end_inset
+
+ pak rekurzivní výpočet matice 
+\begin_inset Formula $J_{n}$
+\end_inset
+
+ (
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq: rekurze J"
+
+\end_inset
+
+) spolu s dosazením výše uvedených matic 
+\begin_inset Formula $D_{n}$
+\end_inset
+
+ (
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:matice Dn gauss"
+
+\end_inset
+
+) odpovídá výpočtu aposteriorní kovarianční matice 
+\begin_inset Formula $P_{n}$
+\end_inset
+
+ Kalmanova filtru při označení 
+\begin_inset Formula $\left(P_{n}\right)^{-1}=J_{n}$
+\end_inset
+
+.
+ Uvažovaný systém (PMSM) je však nelineární, je tedy užíváno rozšířeného
+ Kalmanova filtru (EKF), ve kterém se do napočtených matic derivací dosazují
+ odhady stavu.
+ 
+\end_layout
+
+\begin_layout Subsection*
+Užité modely
+\end_layout
+
+\begin_layout Standard
+Obecně byly použity čtyři typy modelů v souřadném systému 
+\begin_inset Formula $\alpha\beta$
+\end_inset
+
+.
+ Souřadný systém 
+\begin_inset Formula $dq$
+\end_inset
+
+ totiž nemá smysl používat, jelikož mez stále roste, což lze jednak usuzovat
+ na základě tvaru ronvic, ale bylo ověřeno i experimentálně.
+ Tyto modely se liší tím, jestli je uvažován 
+\emph on
+plný 
+\emph default
+nebo 
+\emph on
+redukovaný
+\emph default
+ stav systému.
+ Dále pak jestli byl uvažován model motoru (PMSM) se stejnými (
+\series bold
+Ls
+\series default
+) nebo různými (
+\series bold
+Ldq
+\series default
+) indukčnostmi v osách 
+\begin_inset Formula $d$
+\end_inset
+
+ a 
+\begin_inset Formula $q$
+\end_inset
+
+.
+ Budou následovat matice derivací 
+\begin_inset Formula $A_{n}=\left[\nabla_{x_{n}}f_{n}^{T}(x_{n})\right]^{T}$
+\end_inset
+
+ zobrazení 
+\begin_inset Formula $f_{n}$
+\end_inset
+
+ a matice 
+\begin_inset Formula $C_{n+1}=\left[\nabla_{x_{n+1}}h_{n+1}^{T}(x_{n+1})\right]^{T}$
+\end_inset
+
+ zobrazení 
+\begin_inset Formula $h_{n+1}$
+\end_inset
+
+ dle jednotlivých stavových veličin.
+ Tyto matice však budou uvedeny pouze pro případ stejných indukčností.
+\begin_inset Formula 
+\[
+A_{full}^{Ls}=\left[\begin{array}{cccc}
+a & 0 & b\sin\vartheta & b\omega\cos\vartheta\\
+0 & a & -b\cos\vartheta & b\omega\sin\vartheta\\
+-e\sin\vartheta & e\cos\vartheta & d & -e\left(i_{\alpha}\cos\vartheta+i_{\beta}\sin\vartheta\right)\\
+0 & 0 & \Delta t & 1
+\end{array}\right]
+\]
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+C_{full}^{Ls}=\left[\begin{array}{cccc}
+1 & 0 & 0 & 0\\
+0 & 1 & 0 & 0
+\end{array}\right]
+\]
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+A_{red}^{Ls}=\left[\begin{array}{cc}
+d & -e\left(i_{\alpha}\cos\vartheta+i_{\beta}\sin\vartheta\right)\\
+\Delta t & 1
+\end{array}\right]
+\]
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+C_{red}^{Ls}=\left[\begin{array}{cc}
+b\sin\vartheta & b\omega\cos\vartheta\\
+-b\cos\vartheta & b\omega\sin\vartheta
+\end{array}\right]
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pro přehlednost je souhrn použitých modelů uveden v následující tabulce:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="3">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\alpha-\beta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $L_{s}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $L_{dq}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+full
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+red
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+4
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dále pak budou jednotlivé modely oznáčovány jejich číslem z tabulky.
+\end_layout
+
+\begin_layout Subsection*
+Užitá řízení
+\end_layout
+
+\begin_layout Standard
+Použitá řízení shrnuje následující seznam, dále budou označována svým číslem
+ položky:
+\end_layout
+
+\begin_layout Enumerate
+\begin_inset Formula $\omega=\overline{\omega}$
+\end_inset
+
+, 
+\begin_inset Formula $\vartheta=\int\omega$
+\end_inset
+
+, 
+\begin_inset Formula $i_{\alpha}=i_{\beta}=0$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+PI
+\end_layout
+
+\begin_layout Enumerate
+PI + injektáž sin do 
+\begin_inset Formula $d-q$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+PI + injektáž obdélníků do 
+\begin_inset Formula $d-q$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+PI + injektáž konstanty do 
+\begin_inset Formula $d$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+PI + náhodná chyba na 
+\begin_inset Formula $\overline{\omega}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+PI + injektáž sin do 
+\begin_inset Formula $\alpha-\beta$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+PI + injektáž obdélníků do 
+\begin_inset Formula $\alpha-\beta$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+PI + bikriteriální metoda se 
+\begin_inset Formula $\mathrm{sign}\omega$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+PI + bikriteriální metoda náhodný výběr 5 možností
+\end_layout
+
+\begin_layout Subsection*
+Kovarianční matice
+\end_layout
+
+\begin_layout Standard
+Testování proběhlo s následujícími kovariančními maticemi: 
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\begin{eqnarray*}
+Q & = & \mathrm{diag}\left[\begin{array}{cccc}
+0.01 & 0.01 & 0.001 & 0.00001\end{array}\right]\\
+R & = & \mathrm{diag}\left[\begin{array}{cc}
+0.005 & 0.005\end{array}\right]
+\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Labeling
+\labelwidthstring 00.00.0000
+V
+\begin_inset space ~
+\end_inset
+
+případě redukovaných modelů mají odpovídající kovarianční matice tvar:
+\begin_inset Formula 
+\[
+Q_{red}=\mathrm{diag}\left(\left[\begin{array}{cc}
+Q_{33} & Q_{44}\end{array}\right]\right)
+\]
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+R_{red}=R+\mathrm{diag}\left(\left[\begin{array}{cc}
+Q_{11} & Q_{22}\end{array}\right]\right)
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection*
+Omezování hodnot meze
+\end_layout
+
+\begin_layout Standard
+Vzhledem k tomu, že poloha 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ je vyjádřena jako úhel (v radiánech), má smysl ji uvažovat pouze v intervalu
+ 
+\begin_inset Formula $\left\langle -\pi,\pi\right\rangle $
+\end_inset
+
+ (případně s vyloučením jedné z krajních hodnot).
+ V modelu pro výpočet PCRB je však 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ uvažována jako náhodná veličina s normálním rozdělením, které může nabývat
+ hodnot z celé reálné osy a následně může PCRB nabývat velmi vysokých hodnot.
+ Tyto hodnoty však pro interpretaci ve vztahu k PMSM nemají smysl, protože
+ nejhorší případ (ve smyslu největší neznalosti parametru 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+) nastává, když je hodnota 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ rovnoměrně rozdělena v intervalu 
+\begin_inset Formula $\left\langle -\pi,\pi\right\rangle $
+\end_inset
+
+, tj.
+ o hodnotě úhlu natočení 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ není žádná informace.
+ Proto má smysl uvažovat hodnoty PCRB 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ jen do velikosti variance rovnoměrného rozdělení na intervalu 
+\begin_inset Formula $\left\langle -\pi,\pi\right\rangle $
+\end_inset
+
+, tato hodnota je 
+\begin_inset Formula $\frac{\pi^{2}}{3}$
+\end_inset
+
+.
+ Nad touto hranicí nemá smysl PCRB 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ uvažovat a vyšší hodnoty je buď možno oříznout pevnou mezí nebo pomocí
+ výpočtu oříznutého normálního rozdělení, který bude užit dále.
+ Srovnání obou možností je zachyceno na grafech (Figure 1).
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\noindent
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/amp5cutpi23ex.eps
+	scale 40
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/amp5cutex.eps
+	scale 40
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+a) oříznutí pevnou mezí 
+\begin_inset Formula $\frac{\pi^{2}}{3}$
+\end_inset
+
+ (čárkovaně)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+b) oříznutí pomocí oříznutého normálního rozdělení
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Hodnoty PCRB polohy 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ v závislosti na amplitudě injektovaného konstantního signálu (viz legenda).
+ 
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Paragraph*
+Oříznuté normální rozdělení
+\end_layout
+
+\begin_layout Standard
+[The Variational Bayes Method in Signal Processing, 2006, Šmídl V., Quinn
+ A.]
+\end_layout
+
+\begin_layout Standard
+Oříznuté normální rozdělení pro skalární váhodnou veličinu 
+\begin_inset Formula $x$
+\end_inset
+
+ je definováno jako normální rozdělení 
+\begin_inset Formula $\mathrm{N}\left(\mu,r\right)$
+\end_inset
+
+ na omezeném supportu 
+\begin_inset Formula $a<x\leq b$
+\end_inset
+
+.
+ Momenty tohoto rozdělení jsou:
+\begin_inset Formula 
+\begin{eqnarray*}
+\hat{x} & = & \mu-\sqrt{r}\varphi(\mu,r)\\
+\hat{x^{2}} & = & r+\mu\hat{x}-\sqrt{r}\kappa(\mu,r)
+\end{eqnarray*}
+
+\end_inset
+
+kde
+\begin_inset Formula 
+\begin{eqnarray*}
+\varphi(\mu,r) & = & \frac{\sqrt{2}\left(\exp(-\beta^{2})-\exp(-\alpha^{2})\right)}{\sqrt{\pi}\left(\mathrm{erf}(\beta)-\mathrm{erf}(\alpha)\right)}\\
+\kappa(\mu,r) & = & \frac{\sqrt{2}\left(b\exp(-\beta^{2})-a\exp(-\alpha^{2})\right)}{\sqrt{\pi}\left(\mathrm{erf}(\beta)-\mathrm{erf}(\alpha)\right)}
+\end{eqnarray*}
+
+\end_inset
+
+a
+\begin_inset Formula 
+\begin{eqnarray*}
+\alpha & = & \frac{a-\mu}{\sqrt{2r}}\\
+\beta & = & \frac{b-\mu}{\sqrt{2r}}
+\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Nyní pro speciální případ 
+\begin_inset Formula $a=-\pi$
+\end_inset
+
+, 
+\begin_inset Formula $b=\pi$
+\end_inset
+
+ a 
+\begin_inset Formula $\mu=0$
+\end_inset
+
+ je 
+\begin_inset Formula $\alpha=-\frac{\pi}{\sqrt{2r}}=-\beta$
+\end_inset
+
+.
+ Zřejmě tedy 
+\begin_inset Formula $\alpha^{2}=\beta^{2}$
+\end_inset
+
+ a čitatel 
+\begin_inset Formula $\varphi$
+\end_inset
+
+ je nulový, tedy 
+\begin_inset Formula $\varphi=0$
+\end_inset
+
+.
+ Z tohoto pak hned vyplývá, že 
+\begin_inset Formula $\hat{x}=0$
+\end_inset
+
+ a 
+\begin_inset Formula $\mathrm{Var}(x)=\hat{x^{2}}-\hat{x}^{2}=\hat{x^{2}}$
+\end_inset
+
+.
+ 
+\begin_inset Formula $\kappa$
+\end_inset
+
+ má po dosazení tvar
+\begin_inset Formula 
+\[
+\kappa=\frac{2\sqrt{2}\pi\exp\left(-\frac{\pi^{2}}{2r}\right)}{2\sqrt{\pi}\mathrm{erf}\left(\frac{\pi}{\sqrt{2r}}\right)}
+\]
+
+\end_inset
+
+Hodnota variance 
+\begin_inset Formula $x$
+\end_inset
+
+ je tedy
+\begin_inset Formula 
+\[
+\mathrm{Var}(x)=r-\sqrt{2\pi r}\frac{\exp\left(-\frac{\pi^{2}}{2r}\right)}{\mathrm{erf}\left(\frac{\pi}{\sqrt{2r}}\right)}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection*
+Experimenty
+\end_layout
+
+\begin_layout Standard
+Následující experimenty byly prováděny s ohledem na následující poznatky:
+\end_layout
+
+\begin_layout Itemize
+variance na proudech se ve všech případech ukazovaly jako malé (stále kolem
+ 
+\begin_inset Formula $0.0367$
+\end_inset
+
+) a dále již pak nebyly testovány
+\end_layout
+
+\begin_layout Itemize
+modely pro stejné (Ls) a různé (Ldq) indukčnosti a při uvažování plného
+ a redukovaného modelu lze relativně dobře porovnat při různých řízeních
+ na grafech (Figure 6 a 7)
+\end_layout
+
+\begin_layout Itemize
+nastavení kovariančních matic 
+\begin_inset Formula $Q$
+\end_inset
+
+ a 
+\begin_inset Formula $R$
+\end_inset
+
+ nemá vliv na tvar křivek znázorňujících PCRB (neuvažujeme-li ořez), ovlivňuje
+ však značně jejich hodnoty v absolutním měřítku, proto je třeba nastavit
+ dostatečně malé
+\end_layout
+
+\begin_layout Itemize
+hodnoty počáteční kovariance 
+\begin_inset Formula $P_{0}$
+\end_inset
+
+ se projevují pouze na počátku a jejich vliv s rostoucím časem asymptoticky
+ vymizí
+\end_layout
+
+\begin_layout Itemize
+dále je třeba zkoumat především vliv jednotlivých řízení, a tedy i amplitud
+ a případně frekvencí injektovaných signálů
+\end_layout
+
+\begin_layout Subsubsection*
+Závislost PCRB 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ na použité amplitudě přídavného budícího signálu pro PI řízení s konstantní
+ injektáží do osy 
+\emph on
+d
+\end_layout
+
+\begin_layout Itemize
+Testované řízení: 
+\begin_inset Quotes eld
+\end_inset
+
+5 -- PI + injection (const.
+ -> ud)
+\begin_inset Quotes erd
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Použitý model: 
+\begin_inset Quotes eld
+\end_inset
+
+alpha-beta Ls
+\begin_inset Quotes erd
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Injektovaný signál:
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+amplituda: různá, konstantní -- 
+\emph on
+předmět experimentu
+\end_layout
+
+\begin_layout Itemize
+frekvence: 
+\begin_inset Formula $\omega_{inj}\equiv0$
+\end_inset
+
+, tj.
+ neperiodický konstantní signál
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+Kovarianční matice systému: 
+\begin_inset Formula 
+\begin{eqnarray*}
+Q & = & \mathrm{diag}\left[\begin{array}{cccc}
+0.01 & 0.01 & 0.001 & 0.00001\end{array}\right]\\
+R & = & \mathrm{diag}\left[\begin{array}{cc}
+0.005 & 0.005\end{array}\right]
+\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Časový horizont: standartní 120000 vzorků, tj.
+ 15s
+\end_layout
+
+\begin_layout Itemize
+Referenční signál: nulový 
+\begin_inset Formula $\overline{\omega}=0$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Počáteční kovariance: 
+\begin_inset Formula $1\mathrm{Eye}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Výsledné hodnoty PCRB polohy 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ v závislosti na amplitudě injektáže zachycuje graf (Figure 2).
+ 
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+	filename grafy/amp5cut.eps
+	scale 60
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Hodnoty PCRB polohy 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ v závislosti na amplitudě injektovaného konstantního signálu (viz legenda).
+ 
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection*
+Porovnání PCRB 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ pro jednotlivá řízení a užité modely
+\end_layout
+
+\begin_layout Itemize
+Testovaná řízení: 1 -- 10
+\end_layout
+
+\begin_layout Itemize
+Použitý model: plný i redukovaný alpha-beta se stejnými (Ls) i různými (Ldq)
+ indukčnostimi
+\end_layout
+
+\begin_layout Itemize
+Injektovaný signál:
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+amplituda: 
+\begin_inset Formula $amp=10.0$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+frekvence: 
+\begin_inset Formula $\omega_{inj}=1000$
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+Kovarianční matice systému: 
+\begin_inset Formula 
+\begin{eqnarray*}
+Q & = & \mathrm{diag}\left[\begin{array}{cccc}
+0.01 & 0.01 & 0.001 & 0.00001\end{array}\right]\\
+R & = & \mathrm{diag}\left[\begin{array}{cc}
+0.005 & 0.005\end{array}\right]
+\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Časový horizont: standartní 120000 vzorků, tj.
+ 15s
+\end_layout
+
+\begin_layout Itemize
+Referenční signál: 
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+nulový 
+\begin_inset Formula $\overline{\omega}\equiv0$
+\end_inset
+
+ 
+\end_layout
+
+\begin_layout Itemize
+profil 
+\begin_inset Formula $\overline{\omega}_{profile}=\left[\begin{array}{cccccccccccccccc}
+0 & -1 & 3 & 6 & 9 & 6 & 3 & 0 & 0 & 0 & 0 & 0 & 0 & -3 & -6 & -3\end{array}\right]$
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+Počáteční kovariance: 
+\begin_inset Formula $1\mathrm{Eye}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Výsledné hodnoty PCRB polohy 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ v závislosti na užitém referenčním signálu a použitém řízení zachycují
+ grafy (Figure 3 a 4).
+ Některé výsledky jsou prakticky totožné, proto z podobných řízení bude
+ zobrazen pouze vybraný zástupce.
+ Hodnota PCRB 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ je omezována pomocí oříznutého normálního rozdělení na interval 
+\begin_inset Formula $\left\langle -\pi,\pi\right\rangle $
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc2z.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc2n.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+a) Řízení č.
+ 1 a 2, ref.
+ 
+\begin_inset Formula $\overline{\omega}\equiv0$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+b) Řízení č.
+ 1 a 2, ref.
+ 
+\begin_inset Formula $\overline{\omega}_{profile}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc7z.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc7n.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+c) Řízení č.
+ 3 a 7, ref.
+ 
+\begin_inset Formula $\overline{\omega}\equiv0$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+d) Řízení č.
+ 3 a 7, ref.
+ 
+\begin_inset Formula $\overline{\omega}_{profile}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc8z.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc8n.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+e) Řízení č.
+ 4 a 8, ref.
+ 
+\begin_inset Formula $\overline{\omega}\equiv0$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+f) Řízení č.
+ 4 a 8, ref.
+ 
+\begin_inset Formula $\overline{\omega}_{profile}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc5z.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc5n.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+g) Řízení č.
+ 5, ref.
+ 
+\begin_inset Formula $\overline{\omega}\equiv0$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+h) Řízení č.
+ 5, ref.
+ 
+\begin_inset Formula $\overline{\omega}_{profile}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Hodnoty PCRB 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ dle volby řízení, referenčního signálu a použitého modelu.
+ Ve grafech a) a b) splývají křivky 1 s 2 a 3 s 4, pro g) a h) pak splývá
+ vše (1-4).
+ Čárkovaná přímka představuje limitní hodnotu -- varianci rovnoměrného rozdělení
+ na 
+\begin_inset Formula $\left\langle -\pi,\pi\right\rangle $
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc6z.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc6n.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+i) Řízení č.
+ 6, ref.
+ 
+\begin_inset Formula $\overline{\omega}\equiv0$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+j) Řízení č.
+ 6, ref.
+ 
+\begin_inset Formula $\overline{\omega}_{profile}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc9z.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc9n.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+k) Řízení č.
+ 9, ref.
+ 
+\begin_inset Formula $\overline{\omega}\equiv0$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+l) Řízení č.
+ 9, ref.
+ 
+\begin_inset Formula $\overline{\omega}_{profile}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc10z.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename grafy/ntc10n.eps
+	scale 30
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+m) Řízení č.
+ 10, ref.
+ 
+\begin_inset Formula $\overline{\omega}\equiv0$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+n) Řízení č.
+ 10, ref.
+ 
+\begin_inset Formula $\overline{\omega}_{profile}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Hodnoty PCRB 
+\begin_inset Formula $\vartheta$
+\end_inset
+
+ dle volby řízení, referenčního signálu a použitého modelu.
+ V grafech i) až l) splývají křivky pro téměř všechny modely.
+ Čárkovaná přímka představuje limitní hodnotu -- varianci rovnoměrného rozdělení
+ na 
+\begin_inset Formula $\left\langle -\pi,\pi\right\rangle $
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
Index: /applications/dual/vahala/pcrb/grafy/ntc7n.eps
===================================================================
--- /applications/dual/vahala/pcrb/grafy/ntc7n.eps (revision 1418)
+++ /applications/dual/vahala/pcrb/grafy/ntc7n.eps (revision 1418)
@@ -0,0 +1,2638 @@
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+%%CreationDate: 01/04/2012  21:08:36
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+/xstore {exch store} bdef
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Index: /applications/dual/vahala/pcrb/grafy/ntc9n.eps
===================================================================
--- /applications/dual/vahala/pcrb/grafy/ntc9n.eps (revision 1418)
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Index: /applications/dual/vahala/pcrb/grafy/ntc1z.eps
===================================================================
--- /applications/dual/vahala/pcrb/grafy/ntc1z.eps (revision 1418)
+++ /applications/dual/vahala/pcrb/grafy/ntc1z.eps (revision 1418)
@@ -0,0 +1,2519 @@
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Index: /applications/dual/vahala/pcrb/grafy/ntc3z.eps
===================================================================
--- /applications/dual/vahala/pcrb/grafy/ntc3z.eps (revision 1418)
+++ /applications/dual/vahala/pcrb/grafy/ntc3z.eps (revision 1418)
@@ -0,0 +1,2701 @@
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Index: /applications/dual/vahala/pcrb/grafy/ntc5z.eps
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+end %%Color Dict
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+eplot
+%%EndObject
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+epage
+end
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+showpage
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+%%Trailer
+%%EOF
Index: /applications/dual/vahala/pcrb/grafy/ntc7z.eps
===================================================================
--- /applications/dual/vahala/pcrb/grafy/ntc7z.eps (revision 1418)
+++ /applications/dual/vahala/pcrb/grafy/ntc7z.eps (revision 1418)
@@ -0,0 +1,2703 @@
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+%%Title: /home/michal/source/DP/grafy/ntc7z.eps
+%%CreationDate: 01/04/2012  21:08:22
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+/epage {pgsv restore} bdef
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+% coordinate system mappings
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+end %%Color Dict
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+eplot
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Index: /applications/dual/vahala/pcrb/grafy/ntc9z.eps
===================================================================
--- /applications/dual/vahala/pcrb/grafy/ntc9z.eps (revision 1418)
+++ /applications/dual/vahala/pcrb/grafy/ntc9z.eps (revision 1418)
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Index: /applications/dual/vahala/pcrb/grafy/amp5cutpi23ex.eps
===================================================================
--- /applications/dual/vahala/pcrb/grafy/amp5cutpi23ex.eps (revision 1418)
+++ /applications/dual/vahala/pcrb/grafy/amp5cutpi23ex.eps (revision 1418)
@@ -0,0 +1,3588 @@
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Index: /applications/dual/vahala/pcrb/grafy/amp5cutpi23.eps
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Index: /applications/dual/vahala/pcrb/grafy/amp5cut.eps
===================================================================
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Index: /applications/dual/vahala/pcrb/grafy/ntc2n.eps
===================================================================
--- /applications/dual/vahala/pcrb/grafy/ntc2n.eps (revision 1418)
+++ /applications/dual/vahala/pcrb/grafy/ntc2n.eps (revision 1418)
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+end %%Color Dict
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+eplot
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+showpage
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+%%Trailer
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Index: /applications/dual/vahala/pcrb/grafy/ntc4n.eps
===================================================================
--- /applications/dual/vahala/pcrb/grafy/ntc4n.eps (revision 1418)
+++ /applications/dual/vahala/pcrb/grafy/ntc4n.eps (revision 1418)
@@ -0,0 +1,2648 @@
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+%%Title: /home/michal/source/DP/grafy/ntc4n.eps
+%%CreationDate: 01/04/2012  20:37:54
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+  rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad
+  sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix
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Index: /applications/dual/vahala/pcrb/grafy/ntc6n.eps
===================================================================
--- /applications/dual/vahala/pcrb/grafy/ntc6n.eps (revision 1418)
+++ /applications/dual/vahala/pcrb/grafy/ntc6n.eps (revision 1418)
@@ -0,0 +1,2650 @@
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Index: /applications/dual/vahala/pcrb/grafy/ntc8n.eps
===================================================================
--- /applications/dual/vahala/pcrb/grafy/ntc8n.eps (revision 1418)
+++ /applications/dual/vahala/pcrb/grafy/ntc8n.eps (revision 1418)
@@ -0,0 +1,2647 @@
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+  vradius add translate hradius vradius scale 0 0 1 180 270 arc 
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+  hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix
+  lrx hradius sub lry vradius sub translate hradius vradius scale
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+  rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad
+  sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix
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Index: /applications/dual/vahala/pcrb/grafy/ntc6z.eps
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Index: /applications/dual/vahala/pcrb/grafy/ntc8z.eps
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Index: /applications/dual/vahala/pcrb/grafy/ampdepctr5hsvpoklze100cut.eps
===================================================================
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Index: /applications/dual/vahala/pcrb/grafy/ntc10z.eps
===================================================================
--- /applications/dual/vahala/pcrb/grafy/ntc10z.eps (revision 1418)
+++ /applications/dual/vahala/pcrb/grafy/ntc10z.eps (revision 1418)
@@ -0,0 +1,2625 @@
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+end %%Color Dict
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+eplot
+%%EndObject
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+epage
+end
+
+showpage
+
+%%Trailer
+%%EOF
Index: /applications/dual/vahala/pcrb/grafy/ntc1n.eps
===================================================================
--- /applications/dual/vahala/pcrb/grafy/ntc1n.eps (revision 1418)
+++ /applications/dual/vahala/pcrb/grafy/ntc1n.eps (revision 1418)
@@ -0,0 +1,2630 @@
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+%%Title: /home/michal/source/DP/grafy/ntc1n.eps
+%%CreationDate: 01/04/2012  20:10:47
+%%DocumentNeededFonts: Helvetica
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+/epage {pgsv restore} bdef
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+% coordinate system mappings
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Index: /applications/dual/vahala/pcrb/grafy/ntc3n.eps
===================================================================
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+  exch dup 3 1 roll findfont dup length dict begin
+  { 1 index /FID ne {def}{pop pop} ifelse } forall
+  /Encoding exch def currentdict end definefont pop} bdef
+/isroman {findfont /CharStrings get /Agrave known} bdef
+/FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse
+  exch FMS} bdef
+/csm {1 dpi2point div -1 dpi2point div scale neg translate
+ dup landscapeMode eq {pop -90 rotate}
+  {rotateMode eq {90 rotate} if} ifelse} bdef
+% line types: solid, dotted, dashed, dotdash
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+/DA { [6 dpi2point mul] 0 setdash } bdef
+/DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4
+  dpi2point mul] 0 setdash } bdef
+% macros for lines and objects
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+/MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef
+/AP {{rlineto} repeat} bdef
+/PDlw -1 def
+/W {/PDlw currentlinewidth def setlinewidth} def
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+/DP {closepath stroke} bdef
+/MR {4 -2 roll moveto dup  0 exch rlineto exch 0 rlineto
+  neg 0 exch rlineto closepath} bdef
+/FR {MR stroke} bdef
+/PR {MR fill} bdef
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+/tMatrix matrix def
+/MakeOval {newpath tMatrix currentmatrix pop translate scale
+0 0 1 0 360 arc tMatrix setmatrix} bdef
+/FO {MakeOval stroke} bdef
+/PO {MakeOval fill} bdef
+/PD {currentlinewidth 2 div 0 360 arc fill
+   PDlw -1 eq not {PDlw w /PDlw -1 def} if} def
+/FA {newpath tMatrix currentmatrix pop translate scale
+  0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef
+/PA {newpath tMatrix currentmatrix pop	translate 0 0 moveto scale
+  0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef
+/FAn {newpath tMatrix currentmatrix pop translate scale
+  0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef
+/PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale
+  0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef
+/vradius 0 def /hradius 0 def /lry 0 def
+/lrx 0 def /uly 0 def /ulx 0 def /rad 0 def
+/MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef
+  /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly
+  vradius add translate hradius vradius scale 0 0 1 180 270 arc 
+  tMatrix setmatrix lrx hradius sub uly vradius add translate
+  hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix
+  lrx hradius sub lry vradius sub translate hradius vradius scale
+  0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub
+  translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix
+  closepath} bdef
+/FRR {MRR stroke } bdef
+/PRR {MRR fill } bdef
+/MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def
+  newpath tMatrix currentmatrix pop ulx rad add uly rad add translate
+  rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad
+  sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix
+  closepath} bdef
+/FlrRR {MlrRR stroke } bdef
+/PlrRR {MlrRR fill } bdef
+/MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def
+  newpath tMatrix currentmatrix pop ulx rad add uly rad add translate
+  rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad
+  sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix
+  closepath} bdef
+/FtbRR {MtbRR stroke } bdef
+/PtbRR {MtbRR fill } bdef
+/stri 6 array def /dtri 6 array def
+/smat 6 array def /dmat 6 array def
+/tmat1 6 array def /tmat2 6 array def /dif 3 array def
+/asub {/ind2 exch def /ind1 exch def dup dup
+  ind1 get exch ind2 get sub exch } bdef
+/tri_to_matrix {
+  2 0 asub 3 1 asub 4 0 asub 5 1 asub
+  dup 0 get exch 1 get 7 -1 roll astore } bdef
+/compute_transform {
+  dmat dtri tri_to_matrix tmat1 invertmatrix 
+  smat stri tri_to_matrix tmat2 concatmatrix } bdef
+/ds {stri astore pop} bdef
+/dt {dtri astore pop} bdef
+/db {2 copy /cols xdef /rows xdef mul dup 3 mul string
+  currentfile 
+  3 index 0 eq {/ASCIIHexDecode filter}
+  {/ASCII85Decode filter 3 index 2 eq {/RunLengthDecode filter} if }
+  ifelse exch readstring pop
+  dup 0 3 index getinterval /rbmap xdef
+  dup 2 index dup getinterval /gbmap xdef
+  1 index dup 2 mul exch getinterval /bbmap xdef pop pop}bdef
+/it {gs np dtri aload pop moveto lineto lineto cp c
+  cols rows 8 compute_transform 
+  rbmap gbmap bbmap true 3 colorimage gr}bdef
+/il {newpath moveto lineto stroke}bdef
+currentdict end def
+%%EndProlog
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+%%BeginSetup
+MathWorks begin
+
+0 cap
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+end
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+%%Page: 1 1
+%%BeginPageSetup
+%%PageBoundingBox:    73   252   521   589
+MathWorks begin
+bpage
+%%EndPageSetup
+
+%%BeginObject: obj1
+bplot
+
+/dpi2point 12 def
+portraitMode 0876 7068 csm
+
+    0     0  5376  4034 rc
+85 dict begin %Colortable dictionary
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