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<TITLE>Vector XY Graph for Phase Portraits</TITLE>
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<I><A HREF="index.html">NelinSys - a program tool for analysis and synthesis of nonlinear control systems</A></I><HR>
<H2>Vector XY Graph for Phase Portraits</H2>
<H3>Block description</H3>
<P ALIGN="JUSTIFY">This block is a more general equivalent of the <I>XY Graph</I> block from the <I>Simulink/Sinks</I> library - unlike <I>XY Graph</I>, it is not restricted to scalar inputs, it can handle vector <I>X</I> and <I>Y</I> as well (of course, the two vectors need to have the same number of elements). In every time instant <I>t</I> during the simulation, for a couple of vectors <I>X = (x1,x2,...,xN)</I>, <I>Y = (y1,y2,...,yN)</I>, <I>N</I> points <I>(x1,y1)</I>, <I>(x2,y2)</I>, ..., <I>(xN,yN)</I> are drawn simultaneously. In order to be able to distinguish individual curves, they are drawn in colours - 8 different colours are used in this order: <FONT COLOR="Blue">blue</FONT>, <FONT COLOR="Red">red</FONT>, <FONT COLOR="#00FF00">green</FONT>, <FONT COLOR="#FF00FF">violet</FONT>, <FONT COLOR="#00FFFF">cyan</FONT>, <FONT COLOR="Black">black</FONT>, <FONT COLOR="Yellow">yellow</FONT>, <FONT COLOR="#CCCCCC">gray</FONT> - if <I>N > 8</I>, these colours are repeated in given order.</P>
<P ALIGN="JUSTIFY">The block is typically used to display a phase-plane portrait of a system - if this is the case, then each phase-plane trajectory corresponds to one pair of elements of the vectors <I>X</I> and <I>Y</I>.</P>
<H3>Block parameters</H3>
<CENTER><IMG SRC="sfunvxy_dialog.jpg" ALT="Block parameters setup"></CENTER>
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<DT><I>x-min, x-max, y-min, y-max</I></DT><DD><P ALIGN="JUSTIFY">Real numbers determining the display range i.e. the <I>x</I> and <I>y</I> margins. As the block is most typically used to display phase-plane portraits, the axes are denoted as <I>x1</I> and <I>x2</I> in the graphic plot.</DD></P>
<DT><I>Sample time</I></DT><DD><P ALIGN="JUSTIFY">Sampling period - the meaning of this field is the same as the meaning of corresponding field of the <I>XY Graph</I> block. If the sampling period does not need to be specified explicitly, set this field to <I>-1</I>.</DD></P>
<DT><I>Show grid</I></DT><DD><P ALIGN="JUSTIFY">Checking this box will display the grid (similarly as MATLAB command <I>grid on</I> does).</DD></P>
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<H3>Usage examples</H3>
<P ALIGN="JUSTIFY">The block is used in following Simulink schemes:</P>
<UL>
<LI><A HREF="fazrov_auton1.html#priklad"><I>Phase-plane portraits of 1st-order autonomous systems</I></A></LI>
<LI><A HREF="fazrov_auton2.html#priklad"><I>Phase-plane portraits of 2nd-order autonomous systems</I></A></LI>
<LI><A HREF="fazrov_typ1.html#priklad"><I>Phase-plane portraits of 1st-order loops with hard nonlinearities</I></A></LI>
<LI><A HREF="fazrov_typnl.html#priklad"><I>Phase-plane portraits of 2nd-order loops with hard nonlinearities</I></A></LI>
</UL>
<H3>See also</H3>
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<LI><I>XY Graph (from Simulink/Sinks library)</I>
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