﻿<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio" version="0.85"?>
<regions>
  <settings>
    <editable>true</editable>
    <calculation>
      <functions>1</functions>
      <precision>4</precision>
      <angle>radians</angle>
      <fractions>decimal</fractions>
      <recalculation>false</recalculation>
    </calculation>
  </settings>
  <region id="0" left="27" top="18" width="306" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="cze">
      <p bold="false" href="">// Nyquist plot, second order system</p>
    </text>
  </region>
  <region id="1" left="27" top="54" width="61" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="cze">
      <p bold="false" href="">//gain</p>
    </text>
  </region>
  <region id="2" left="342" top="54" width="43" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <math evaluate="true">
      <e type="operand">K</e>
      <e type="operand">2</e>
      <e type="operator" args="2">←</e>
    </math>
  </region>
  <region id="3" left="27" top="81" width="143" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="cze">
      <p bold="false" href="">// time constant</p>
    </text>
  </region>
  <region id="4" left="342" top="81" width="43" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <math evaluate="true">
      <e type="operand">T</e>
      <e type="operand">1</e>
      <e type="operator" args="2">←</e>
    </math>
  </region>
  <region id="5" left="27" top="108" width="282" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="cze">
      <p bold="false" href="">// system with damped oscillation</p>
    </text>
  </region>
  <region id="6" left="342" top="108" width="68" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <math evaluate="true">
      <e type="operand">ξ1</e>
      <e type="operand">0,5</e>
      <e type="operator" args="2">←</e>
    </math>
  </region>
  <region id="7" left="27" top="144" width="175" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="cze">
      <p bold="false" href="">// overdamped system</p>
    </text>
  </region>
  <region id="8" left="342" top="144" width="51" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <math evaluate="true">
      <e type="operand">ξ2</e>
      <e type="operand">2</e>
      <e type="operator" args="2">←</e>
    </math>
  </region>
  <region id="9" left="27" top="180" width="543" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="cze">
      <p bold="false" href="">// transfer function of second order system in frequency response</p>
    </text>
  </region>
  <region id="10" left="27" top="207" width="260" height="52" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <math evaluate="true">
      <e type="operand">ω</e>
      <e type="operand">ξ</e>
      <e type="function" args="2">Gjω</e>
      <e type="operand">K</e>
      <e type="operand">1</e>
      <e type="operand">2</e>
      <e type="operand">ξ</e>
      <e type="operator" args="2">*</e>
      <e type="operand">i</e>
      <e type="operator" args="2">*</e>
      <e type="operand">ω</e>
      <e type="operator" args="2">*</e>
      <e type="operand">T</e>
      <e type="operator" args="2">*</e>
      <e type="operator" args="2">+</e>
      <e type="operand">i</e>
      <e type="operand">ω</e>
      <e type="operator" args="2">*</e>
      <e type="operand">T</e>
      <e type="operator" args="2">*</e>
      <e type="bracket">(</e>
      <e type="operand">2</e>
      <e type="operator" args="2">^</e>
      <e type="operator" args="2">+</e>
      <e type="operator" args="2">/</e>
      <e type="operator" args="2">←</e>
    </math>
  </region>
  <region id="11" left="27" top="261" width="127" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="cze">
      <p bold="false" href="">// calculation</p>
    </text>
  </region>
  <region id="12" left="18" top="297" width="153" height="26" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <math evaluate="true">
      <e type="operand">G1</e>
      <e type="operand">100</e>
      <e type="operand">2</e>
      <e type="function" args="2">matrix</e>
      <e type="operator" args="2">←</e>
    </math>
  </region>
  <region id="13" left="171" top="297" width="153" height="26" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <math evaluate="true">
      <e type="operand">G2</e>
      <e type="operand">100</e>
      <e type="operand">2</e>
      <e type="function" args="2">matrix</e>
      <e type="operator" args="2">←</e>
    </math>
  </region>
  <region id="14" left="18" top="333" width="235" height="163" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <math evaluate="true">
      <e type="operand">k</e>
      <e type="operand">1</e>
      <e type="operator" args="2">←</e>
      <e type="operand">k</e>
      <e type="operand">G1</e>
      <e type="function" args="1">rows</e>
      <e type="operator" args="2">≤</e>
      <e type="operand">k</e>
      <e type="operand">k</e>
      <e type="operand">1</e>
      <e type="operator" args="2">+</e>
      <e type="operator" args="2">←</e>
      <e type="operand">ω</e>
      <e type="operand">e</e>
      <e type="operand">k</e>
      <e type="operand">1</e>
      <e type="operator" args="2">-</e>
      <e type="bracket">(</e>
      <e type="operand">0,03</e>
      <e type="operator" args="2">*</e>
      <e type="operator" args="2">^</e>
      <e type="operand">1</e>
      <e type="operator" args="2">-</e>
      <e type="operator" args="2">←</e>
      <e type="operand">G1</e>
      <e type="operand">k</e>
      <e type="operand">1</e>
      <e type="function" args="3">el</e>
      <e type="operand">ω</e>
      <e type="operand">ξ1</e>
      <e type="function" args="2">Gjω</e>
      <e type="function" args="1">Re</e>
      <e type="operator" args="2">←</e>
      <e type="operand">G1</e>
      <e type="operand">k</e>
      <e type="operand">2</e>
      <e type="function" args="3">el</e>
      <e type="operand">ω</e>
      <e type="operand">ξ1</e>
      <e type="function" args="2">Gjω</e>
      <e type="function" args="1">Im</e>
      <e type="operator" args="2">←</e>
      <e type="operand">G2</e>
      <e type="operand">k</e>
      <e type="operand">1</e>
      <e type="function" args="3">el</e>
      <e type="operand">ω</e>
      <e type="operand">ξ2</e>
      <e type="function" args="2">Gjω</e>
      <e type="function" args="1">Re</e>
      <e type="operator" args="2">←</e>
      <e type="operand">G2</e>
      <e type="operand">k</e>
      <e type="operand">2</e>
      <e type="function" args="3">el</e>
      <e type="operand">ω</e>
      <e type="operand">ξ2</e>
      <e type="function" args="2">Gjω</e>
      <e type="function" args="1">Im</e>
      <e type="operator" args="2">←</e>
      <e type="operand">5</e>
      <e type="operand">1</e>
      <e type="function" args="7">line</e>
      <e type="function" args="4">for</e>
    </math>
  </region>
  <region id="15" left="27" top="513" width="512" height="56" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="cze">
      <p bold="false" href="">Nyquist plot is represented by a graph in polar coordinates.Axis x matches real part and y axis matches imaginary part ofpolar coordinates </p>
    </text>
  </region>
  <region id="16" left="36" top="567" width="360" height="297" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <plot type="2d" render="lines" scale_x="12,8447884553825" scale_y="12,8447884553825" scale_z="12,8447884553825" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-67" transpose_y="100" transpose_z="0" evaluate="true">
      <e type="operand">G1</e>
      <e type="operand">G2</e>
      <e type="operand">2</e>
      <e type="operand">1</e>
      <e type="function" args="4">sys</e>
    </plot>
  </region>
  <region id="17" left="36" top="909" width="596" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="cze">
      <p bold="false" href="">// blue curve is Nyquist plot of system with damped oscillation, ξ1=0,5 </p>
    </text>
  </region>
  <region id="18" left="36" top="936" width="466" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="cze">
      <p bold="false" href="">// red curve is Nyquist plot of overdamped system, ξ2=2 </p>
    </text>
  </region>
  <region id="19" left="36" top="981" width="396" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <text lang="cze">
      <p bold="false" href="">// oscillation frequency of system with ξ1=0,1  </p>
    </text>
  </region>
  <region id="20" left="36" top="1008" width="142" height="44" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <math evaluate="true">
      <e type="operand">ωres</e>
      <e type="operand">1</e>
      <e type="operand">T</e>
      <e type="operator" args="2">/</e>
      <e type="operand">1</e>
      <e type="operand">ξ1</e>
      <e type="operand">2</e>
      <e type="operator" args="2">^</e>
      <e type="operator" args="2">-</e>
      <e type="function" args="1">sqrt</e>
      <e type="operator" args="2">*</e>
      <e type="operator" args="2">←</e>
    </math>
  </region>
  <region id="21" left="198" top="1017" width="99" height="24" border="false" color="#000000" background-color="#ffffff" font-size="10">
    <math evaluate="true">
      <e type="operand">ωres</e>
      <e type="operand">0,866</e>
      <e type="operator" args="2">=</e>
    </math>
  </region>
</regions>