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<Startup-Code startupcode="#####################\012# Loading Libraries #\012#####################\012interface(warnlevel=0):\012interface(displayprecision=4):\012with(inttrans):\012with(LinearAlgebra):\012with(plots):\012\012#############################\012# Defining Custom Functions #\012#############################\012get_parameter := proc (text_id)\012 parse (DocumentTools:-GetProperty (text_id, 'value'));\012end proc:\012\012##########################################################\012# getTF\012#\012# This procedure extracts the transfer functions from the set\012# of transformed differential equations, given a list of\012# desired output and the given input. It returns the transfer\012# function as a list in the same order as the output variables.\012#\012getTF := proc( TEqnSet, TInput, TOutputList::list )\012\012   local sol, outputList;\012\012   sol := solve( TEqnSet, convert(TOutputList, set) );\012\012   outputList := [ seq(\012                      simplify(\012                         simplify( eval( TOutputList[i], sol ) )\012                         /\012                         ( TInput )\012                         ), i=1..nops(TOutputList)\012                      ) ];\012   # Sort the output\012   [ seq( simplify( sort(expand(numer(outputList[i]))) /\012                    sort(expand(denom(outputList[i]))) ),\012          i=1..nops(outputList)\012        ) ];\012\012end proc:\012##########################################################\012#\012# DETransferFn\012#\012# This function creates a transfer function from the\012# specified differential equation(s).\012#\012DETransferFn := proc(ineqns, input::{function, list},\012                             output::{function, list},\012                             t, s)\012\012  local eq_set,\012        numInput, numOutput,\012        inputList_t, outputList_t,\012        inputList_s, outputList_s,\012        VarSet_t, VarSet_s, VarSet,\012        VarList_t,          VarList,\012        VarSet_eqn_s,\012        lt, zc,\012        l_outputSet,    l_outputSet_t,\012        l_outputList_s, l_outputList_t, l_outputList_i,\012        S_output, S_input,\012        TFList, outIndex,\012        xin_t, i, tempIndex;\012\012  #\012  # Checking for the number of input and output\012  #\012  if( type( input, function ) ) then\012     numInput := 1;\012     inputList_t := [input];\012  else\012     numInput := nops( input );\012     inputList_t := input;\012  end if;\012\012  if( type( output, function ) ) then\012     numOutput := 1;\012     outputList_t := [output];\012  else\012     numOutput := nops( output );\012     outputList_t := output;\012  end if;\012  outputList_s := [seq(S_||i, i=map2(op,0,outputList_t))];\012\012  #\012  # Check if the input system is a set of equations\012  #\012  if( not type( ineqns, set ) ) then\012     eq_set := {ineqns};\012  else\012     eq_set := ineqns;\012  end if:\012\012  #\012  # Now select from the list, a list of terms that are dependent on t\012  #\012  VarSet_t := indets( eq_set, anyfunc( identical( (t) ) ) );\012  VarList_t := convert( VarSet_t, list );\012  #\012  # Finally, we obtain a list of variables names (by isolating the\012  # &quot;function of t&quot;, (t) part )\012  #\012  VarSet := map2 (op, 0, VarSet_t);     # Variable set in name\012  VarList := map2( op, 0, VarList_t);   # Variable list in name\012  VarSet_s := {seq( S_ || i, i=VarSet )};       # Transformed Variable Set\012  # Replace time representation by s representation\012  VarSet_eqn_s := {seq( laplace( i(t), t, s ) = S_ || i, i=VarSet )};\012\012  # Check to see if the input and output variables are actually in\012  # the input DE... and to check if the number of equations matched\012  # the number of unknown (requirement for a solution to exist)\012  # i.e. trapping any possible user error\012  if( not( andmap( member, outputList_t, VarList_t  ) ) or\012      not( andmap( member, inputList_t, VarList_t ) ) or\012      not( nops(eq_set) = (nops(VarList_t)-1) )\012    ) then\012     error &quot;Unknown variable(s) or number of equations does not match&quot;;\012  end if;\012  #\012  # Performing the Laplace transform of the set of differential equations\012  #\012  lt := inttrans[laplace] (eq_set, t, s);\012  #\012  # Next, replace the variables with their generic names for further\012  # manipulations.\012  # The only terms in functional form are the initial conditions for the\012  # time dependent variables.\012  #\012  lt := eval (lt, VarSet_eqn_s);\012  #\012  # Generating a set initial conditions. All initial states set to zero.\012  #\012  zc := map (x-&gt; x = 0, indets(lt, function));\012  #\012  # Applying the initial conditions.\012  #\012  lt := eval (lt, zc);\012\012  #\012  # Now, perform the conversion based on the number of input-output\012  # pair requested\012  #\012  # For each input, generate transfer function with all possible output\012  #\012  for xin_t in inputList_t do\012     # local output set is the total variable set minus the current input\012     l_outputSet_t := VarSet_t minus {xin_t};\012     # name only set\012     l_outputSet := map2( op, 0, l_outputSet_t );\012     # transformed list\012     l_outputList_t[xin_t] := convert( l_outputSet_t, list );\012     l_outputList_s[xin_t] := [ seq( S_ || i,\012                                i=map2( op, 0, l_outputList_t[xin_t] ) ) ];\012\012     # Extract the input variable name and generate its generic name\012     # assign it to the variable S_input\012     S_input := op(0, xin_t);\012     S_input := S_ || S_input;\012\012     # Solving for all possible transfer function given the input\012     TFList[ xin_t ] := getTF( lt, (S_input),\012                               l_outputList_s[xin_t] );\012     # Generating the local index list for the output\012     for i from 1 to nops( outputList_t ) do\012        member( outputList_t[i], l_outputList_t[ xin_t ], 'tempIndex' );\012        outIndex[ i ] := eval(tempIndex);\012     end do;\012     l_outputList_i[ xin_t ] := [ seq( outIndex[ i ],\012                                  i=1..nops(outputList_t) ) ];\012  end do;\012\012  # Formulating the output\012  if( (numInput = 1) and (numOutput = 1) ) then\012     # SISO system: output is a single transfer function\012     return ((TFList)[ inputList_t[1] ])[ l_outputList_i[ inputList_t[1] ][1] ];\012  else\012     # MIMO system: output is a matrix\012     return LinearAlgebra:-Transpose(\012               Matrix( [ seq(\012                         [ seq( (TFList[i])[\012                              l_outputList_i[i][j]\012                              ],\012                         j=1..nops(l_outputList_i[i]) ) ],\012                         i=inputList_t ) ] )\012                    );\012  end if;\012end proc:\012\012TFStepResponse := proc(TF, s, range, newcolor, newlegend)\012\012 local td, t;\012\012 td := inttrans[invlaplace](TF/s,s,t);\012 if (nargs = 5) then\012  plt:=plot(td, t = range, numpoints = 500, \012   color=newcolor, legend=newlegend, gridlines=true, thickness=2);\012 elif (nargs = 4) then\012  plt:=plot(td, t = range, numpoints = 500, \012   color=newcolor, gridlines=true, thickness=2);\012 else\012  plt:=plot(td, t = range, numpoints = 500, \012   gridlines=true, thickness=2);\012 end if;\012\012 return plt;\012\012end proc:\012\012"/>
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<Text-field style="Text" layout="Normal">The model corresponds to a second order system with <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> as the input and <Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EwJkFwcGx5RnVuY3Rpb247RicvJSdmYW1pbHlHUSZTZXJpZkYnLyUnb3BhcXVlR0Y2L0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRy8lKXN0cmV0Y2h5R0ZHLyUqc3ltbWV0cmljR0ZHLyUobGFyZ2VvcEdGRy8lLm1vdmFibGVsaW1pdHNHRkcvJSdhY2NlbnRHRkcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZWLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEidEYnRjRGN0ZDRkNGK0ZDRitGQw==</Equation> as the output. The system is defined by the angular frequency <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEnJiM5Njk7RicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjU=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEnJiM5Njk7RicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjU=</Equation>, the attenuation <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjU=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjU=</Equation>, and the gain <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation><Font size="12">.</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">Input variable</Font> <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">Output variable </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEiKEYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSV0cnVlRicvJSpzZXBhcmF0b3JHUSZmYWxzZUYnLyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYmUSJ5RidGLy8lJ2l0YWxpY0dGNy9GM1EnaXRhbGljRidGMg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEiKEYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSV0cnVlRicvJSpzZXBhcmF0b3JHUSZmYWxzZUYnLyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYmUSJ5RidGLy8lJ2l0YWxpY0dGNy9GM1EnaXRhbGljRidGMg==</Equation><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y7USdub3JtYWxGJ0Y9LUkjbW9HRiQ2LVEiKUYnRj0vJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGRy8lKGxhcmdlb3BHRkcvJS5tb3ZhYmxlbGltaXRzR0ZHLyUnYWNjZW50R0ZHLyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGVEY9">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y7USdub3JtYWxGJ0Y9LUkjbW9HRiQ2LVEiKUYnRj0vJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGRy8lKGxhcmdlb3BHRkcvJS5tb3ZhYmxlbGltaXRzR0ZHLyUnYWNjZW50R0ZHLyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGVEY9</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">Parameters:</Font></Text-field></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal">Angular frequency <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtaUdGJDYmUScmIzk2OTtGJy8lJXNpemVHUSMxMEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGOkY0RjpGOg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtaUdGJDYmUScmIzk2OTtGJy8lJXNpemVHUSMxMEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGOkY0RjpGOg==</Equation></Text-field></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal">Attenuation <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtaUdGJDYmUScmIzk1MjtGJy8lJXNpemVHUSMxMEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGOkY0RjpGOg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtaUdGJDYmUScmIzk1MjtGJy8lJXNpemVHUSMxMEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGOkY0RjpGOg==</Equation></Text-field></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal">Gain <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtaUdGJDYmUSJBRicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjtRJ25vcm1hbEYnRjRGPUY9">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYlLUYjNiQtSSNtaUdGJDYmUSJBRicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjtRJ25vcm1hbEYnRjRGPUY9</Equation></Text-field></Table-Cell></Table-Row></Table>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Model Description</Text-field></Title><Presentation-Block>
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<Text-field bookmark="ModelDescription" style="Text" layout="Normal">The system is defined with the following differential equation (DE):</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="`+`(diff(y(t), t, t), `*`(2, `*`(omega, `*`(theta, `*`(diff(y(t), t))))), `*`(`^`(omega, 2), `*`(y(t)))) = `*`(`^`(omega, 2), `*`(A, `*`(u(t))))" display="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">LywoLUklZGlmZkclKnByb3RlY3RlZEc2JS1JInlHNiI2I0kidEdGKkYsRiwiIiIqKiIiI0YtSSZvbWVnYUdGKkYtSSZ0aGV0YUdGKkYtLUYlNiRGKEYsRi1GLSomKUYwRi9GLUYoRi1GLSooRjVGLUkiQUdGKkYtLUkidUdGKkYrRi0=</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L127" drawlabel="true" redirect-source="L126">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L126" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LywoLUklZGlmZkclKnByb3RlY3RlZEc2JC1GJTYkLUkieUc2IjYjSSJ0R0YsRi5GLiIiIiooSSZvbWVnYUdGLEYvSSZ0aGV0YUdGLEYvRihGLyIiIyomRjFGM0YqRi9GLyooRjFGM0kiQUdGLEYvLUkidUdGLEYtRi8=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L144" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="``" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L128" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font style="Text">The transfer function that results from this DE is:</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L183" drawlabel="true" redirect-target="L184">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="`:=`(Gs, DETransferFn(`+`(diff(diff(y(t), t), t), `*`(2, `*`(omega, `*`(theta, `*`(diff(y(t), t))))), `*`(`^`(omega, 2), `*`(y(t)))) = `*`(`^`(omega, 2), `*`(A, `*`(u(t)))), u(t), y(t), t, s))" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEjR3NGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUS1ERVRyYW5zZmVyRm5GJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2MC1GLDYjUSFGJy1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUWVyLywoLUklZGlmZkclKnByb3RlY3RlZEc2JC1GJTYkLUkieUc2IjYjSSJ0R0YsRi5GLiIiIiooSSZvbWVnYUdGLEYvSSZ0aGV0YUdGLEYvRihGLyIiIyomRjFGM0YqRi9GLyooRjFGM0kiQUdGLEYvLUkidUdGLEYtRi9GJy8lK2FjdGlvbnR5cGVHUTptYXBsZXNvZnQuY29tOmxhYmVsKEwxMjcpRicvJSV2aWV3R1EmbGFiZWxGJy1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUYsNiVRInVGJ0YvRjItRlM2JC1GIzYlLUYsNiVRInRGJ0YvRjIvJStleGVjdXRhYmxlR0Y9RjlGOUZhby1GLDYlUSJ5RidGL0YyRlxwRmFvRmBwRmFvLUYsNiVRInNGJ0YvRjJGY3BGOUY5RmNwRjk=">PkkjR3NHNiItSS1ERVRyYW5zZmVyRm5HRiQ2Jy8sKC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRis2JC1JInlHRiQ2I0kidEdGJEYzRjMiIiIqKEkmb21lZ2FHRiRGNEkmdGhldGFHRiRGNEYuRjQiIiMqJkY2RjhGMEY0RjQqKEY2RjhJIkFHRiRGNC1JInVHRiRGMkY0RjxGMEYzSSJzR0Yk</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L184" drawlabel="true" redirect-source="L183">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L183" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KihJJm9tZWdhRzYiIiIjSSJBR0YkIiIiLCgqKEkic0dGJEYnRiNGJ0kmdGhldGFHRiRGJ0YlKiRGKkYlRicqJEYjRiVGJyEiIg==</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L180" drawlabel="true" redirect-target="L181">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L224" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="``" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><CodeEditor-ExecGroup autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L113" display="button"><EC-CodeEditor id="CodeEditRegion0" pixel-width="500" pixel-height="200"># Uncontrolled Step Response
draw_now:=proc()

local range;

	range:=0..0.3;

	omega_in:=DocumentTools:-GetProperty('w_dial',value);
	theta_in:=DocumentTools:-GetProperty('z_dial',value)/100;

	params := {omega = omega_in, theta = theta_in, A = 1}:
	tf_p := eval(Gs, params);
	plt[2]:=TFStepResponse(tf_p,s,0..0.3, red, &quot;System output&quot;);
	plt[1]:=plot(Heaviside(t),t=range, color=blue,thickness=2, legend=&quot;Step input&quot;);
	DocumentTools:-SetProperty ('plt_step', value, display([plt[1], plt[2]], axis=[gridlines=[10,linestyle=dot]]));				

end proc:

draw_now();

</EC-CodeEditor></CodeEditor-ExecGroup><Table alignment="left" showinput="true" interior="group" order="row" exterior="all" width="98.63013698630137%" randomized="false" showlabel="true" postexecute="insert" pagebreak="row" showgroup="true"><Table-Column weight="720" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]"><Table alignment="left" showinput="true" interior="all" order="row" exterior="all" width="99.24924924924925%" randomized="false" showlabel="true" postexecute="insert" pagebreak="row" showgroup="true"><Table-Column weight="241" separator="true"></Table-Column><Table-Column weight="420" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Dial id="z_dial" tooltip="theta" lower-bound="0" upper-bound="200" control-position="33" major-tick-spacing="50" minor-ticks="10" inputenabled="true" visible="true" show-labels="true" show-ticks="true" continuous-update="true" pixel-width="128" pixel-height="128"><MapleCode action="position-event-handler">use DocumentTools in 
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use: 
#    Do( %component_name );
# and
#    Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
#    Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.

draw_now();
end use; 
</MapleCode></EC-Dial><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRitGK0YrLUkjbWlHRiQ2KFEnJiM5NTI7RicvJSVzaXplR1EjMjJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHRjQvRjBRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRlNGLw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRitGK0YrLUkjbWlHRiQ2KFEnJiM5NTI7RicvJSVzaXplR1EjMjJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHRjQvRjBRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRlNGLw==</Equation></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Dial id="w_dial" tooltip="omega" lower-bound="50" upper-bound="200" control-position="63" major-tick-spacing="25" minor-ticks="5" inputenabled="true" visible="true" show-labels="true" show-ticks="true" continuous-update="true" pixel-width="128" pixel-height="128"><MapleCode action="position-event-handler">use DocumentTools in 
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use: 
#    Do( %component_name );
# and
#    Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
#    Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.

draw_now();
end use; 
</MapleCode></EC-Dial>    <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2KFEnJiM5Njk7RicvJSVzaXplR1EjMjJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y6L0Y5USdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2KFEnJiM5Njk7RicvJSVzaXplR1EjMjJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y6L0Y5USdub3JtYWxGJw==</Equation></Text-field>
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<Text-field style="Text" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false">By changing the slider values for <Font style="2D Math" encoding="UTF-8">\316\270 </Font>and <Font style="2D Math" encoding="UTF-8">\317\211</Font>, the step response for the corresponding system is displayed.</Text-field>
<Text-field style="Text" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"></Text-field>
<Text-field style="Text" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false">In this example, <Font style="2D Math" encoding="UTF-8">\316\270 </Font>controls the damping, such that a system with<Font style="2D Math"> </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiw2JVEoJnRoZXRhO0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjxGJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkAvJSlzdHJldGNoeUdGQC8lKnN5bW1ldHJpY0dGQC8lKGxhcmdlb3BHRkAvJS5tb3ZhYmxlbGltaXRzR0ZALyUnYWNjZW50R0ZALyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTy1JI21uR0YkNiRRIjFGJ0Y8Rjw=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiw2JVEoJnRoZXRhO0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjxGJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkAvJSlzdHJldGNoeUdGQC8lKnN5bW1ldHJpY0dGQC8lKGxhcmdlb3BHRkAvJS5tb3ZhYmxlbGltaXRzR0ZALyUnYWNjZW50R0ZALyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTy1JI21uR0YkNiRRIjFGJ0Y8Rjw=</Equation> results in a system that is under damped and results in an overshoot.  For the cases with <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>the system is over damped and the response has no overshoot.  If <Equation executable="false" style="Text" input-equation="" display="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">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</Equation><Font encoding="UTF-8"> the system is critically damped, resulting in the fastest rise time of the system without overshooting the final value. The parameter \317\211 is the natural frequency of the system.</Font></Text-field>
<Text-field style="Text" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"></Text-field>
<Text-field style="Text" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false">The amplitude <Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEiQUYnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGL0YyL0Y8USdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEiQUYnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGL0YyL0Y8USdub3JtYWxGJw==</Equation> is set to 1 for this example.</Text-field></Table-Cell></Table-Row></Table>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">P Controller</Text-field></Title><Presentation-Block>
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<Text-field bookmark="PController" prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="`:=`(CsP, Kr):" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEkQ3NQRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEjS3JGJ0YvRjItRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0vJStleGVjdXRhYmxlR0Y9Rjk=">QyQ+SSRDc1BHNiJJI0tyR0YlISIi</Equation></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L136" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L164" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
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<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L162" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Open Loop Transfer Function</Text-field>
</Input>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="`:=`(GosP, `*`(CsP, `*`(Gs)))" display="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">PkklR29zUEc2IiomSSRDc1BHRiQiIiJJI0dzR0YkRic=</Equation></Text-field>
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<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L159" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KipJI0tyRzYiIiIiSSZvbWVnYUdGJCIiI0kiQUdGJEYlLCgqKEkic0dGJEYlRiZGJUkmdGhldGFHRiRGJUYnKiRGK0YnRiUqJEYmRidGJSEiIg==</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font style="Text">Closed Loop Transfer Function</Font></Text-field>
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<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L166" drawlabel="true" redirect-target="L175">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="`:=`(GcsP, simplify(`/`(`*`(GosP), `*`(`+`(1, GosP)))))" display="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">PkklR2NzUEc2Ii1JKXNpbXBsaWZ5R0YkNiMqJkklR29zUEdGJCIiIiwmRipGKkYpRiohIiI=</Equation></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L166" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L171" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="Text" input-equation="``" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">JSFH</Equation></Text-field>
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</Group></Presentation-Block><CodeEditor-ExecGroup autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L225" display="button"><EC-CodeEditor id="CodeEditRegion1" pixel-width="500" pixel-height="200"># P Controller Step Response

draw_now_closed_p:=proc()

local range;

	range:=0..0.3;

	kr_in:=DocumentTools:-GetProperty('kr_p_gauge',value);
	omega_in:=DocumentTools:-GetProperty('w_dial',value);
	theta_in:=DocumentTools:-GetProperty('z_dial',value)/100;

	params := {omega = omega_in, theta = theta_in, A = 1, Kr=kr_in}:
	tf_open := eval(Gs, params);
	tf_closed_p := eval(GcsP, params);
	plt[2]:=TFStepResponse(tf_open,s,0..0.3, green, &quot;Open loop response&quot;);
	plt[3]:=TFStepResponse(tf_closed_p,s,0..0.3, red, &quot;Closed loop response&quot;);
	plt[1]:=plot(Heaviside(t),t=range, color=blue,thickness=2, legend=&quot;Step input&quot;);
	DocumentTools:-SetProperty ('plt_closed_p', value, display([plt[1], plt[2], plt[3]], axis=[gridlines=[10,linestyle=dot]]));				

end proc:

draw_now_closed_p();

</EC-CodeEditor></CodeEditor-ExecGroup><Table alignment="left" showinput="true" interior="group" order="row" exterior="all" width="100.0%" randomized="false" showlabel="true" postexecute="insert" pagebreak="row" showgroup="true"><Table-Column weight="756" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]"><Table alignment="left" showinput="true" interior="all" order="row" exterior="all" width="100.0%" randomized="false" showlabel="true" postexecute="insert" pagebreak="row" showgroup="true"><Table-Column weight="206" separator="true"></Table-Column><Table-Column weight="408" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Meter id="kr_p_gauge" lower-bound="0" upper-bound="10" control-position="8" major-tick-spacing="2" minor-ticks="1" inputenabled="true" visible="true" show-labels="true" show-ticks="true" continuous-update="true" pixel-width="207" pixel-height="97"><MapleCode action="position-event-handler">use DocumentTools in 
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use: 
#    Do( %component_name );
# and
#    Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
#    Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.

draw_now_closed_p();

end use; 
</MapleCode></EC-Meter></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true" family="Arial" size="22">P</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]">
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L199" drawlabel="true" redirect-source="L203">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L203" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KipJI0tyRzYiIiIiLCZGJUYlKiZJInNHRiRGJUkjVG5HRiRGJUYlRiVGKCEiIkYpRio=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L206" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L208" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Open Loop Transfer Function</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L200" drawlabel="true" redirect-target="L205">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="`:=`(GosPI, `*`(CsPI, `*`(Gs)))" display="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">PkkmR29zUElHNiIqJkklQ3NQSUdGJCIiIkkjR3NHRiRGJw==</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L205" drawlabel="true" redirect-source="L200">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L200" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KjBJI0tyRzYiIiIiLCZGJUYlKiZJInNHRiRGJUkjVG5HRiRGJUYlRiVGKCEiIkYpRipJJm9tZWdhR0YkIiIjSSJBR0YkRiUsKCooRihGJUYrRiVJJnRoZXRhR0YkRiVGLCokRihGLEYlKiRGK0YsRiVGKg==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L207" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L209" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font style="Text">Closed Loop Transfer Function</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L210" drawlabel="true" redirect-target="L202">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="`:=`(GcsPI, simplify(`/`(`*`(GosPI), `*`(`+`(1, GosPI)))))" display="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">PkkmR2NzUElHNiItSSlzaW1wbGlmeUdGJDYjKiZJJkdvc1BJR0YkIiIiLCZGKkYqRilGKiEiIg==</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L202" drawlabel="true" redirect-source="L210">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L210" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KixJI0tyRzYiIiIiLCZGJUYlKiZJInNHRiRGJUkjVG5HRiRGJUYlRiVJJm9tZWdhR0YkIiIjSSJBR0YkRiUsLCoqRihGK0YpRiVGKkYlSSZ0aGV0YUdGJEYlRisqJkYoIiIkRilGJUYlKihGKEYlRilGJUYqRitGJSooRiNGJUYqRitGLEYlRiUqLEYjRiVGKkYrRixGJUYoRiVGKUYlRiUhIiI=</Equation></Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L201" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><CodeEditor-ExecGroup autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L204" display="button"><EC-CodeEditor id="CodeEditRegion2" pixel-width="500" pixel-height="200"># PI Controller Step Response

draw_now_closed_pi:=proc()

local range;

	range:=0..0.3;

	kr_in:=DocumentTools:-GetProperty('kr_pi_dial',value);
	tn_in:=DocumentTools:-GetProperty('tn_pi_slider',value);
	omega_in:=DocumentTools:-GetProperty('w_dial',value);
	theta_in:=DocumentTools:-GetProperty('z_dial',value)/100;

	params := evalf({omega = omega_in, theta = theta_in, A = 1, Kr=kr_in, Tn=tn_in}):
	tf_open := simplify(eval(Gs, params));
	tf_closed_pi := simplify(eval(GcsPI, params));
	plt[2]:=TFStepResponse(tf_open,s,0..0.3, green, &quot;Open loop response&quot;);
	if tn_in &gt; 0 then
		plt[3]:=TFStepResponse(tf_closed_pi, s,0..0.3, red, &quot;Closed loop response&quot;);
	else
		plt[3] := NULL;
	end if;
	plt[1]:=plot(Heaviside(t),t=range, color=blue,thickness=2, legend=&quot;Step input&quot;);
	DocumentTools:-SetProperty ('plt_closed_pi', value, display([plt[1], plt[2], plt[3]], axis=[gridlines=[10,linestyle=dot]]));				

end proc:

draw_now_closed_pi();

</EC-CodeEditor></CodeEditor-ExecGroup><Table alignment="left" showinput="true" interior="group" order="row" exterior="all" width="100.0%" randomized="false" showlabel="true" postexecute="insert" pagebreak="row" showgroup="true"><Table-Column weight="756" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]"><Table alignment="left" showinput="true" interior="all" order="row" exterior="all" width="100.0%" randomized="false" showlabel="true" postexecute="insert" pagebreak="row" showgroup="true"><Table-Column weight="206" separator="true"></Table-Column><Table-Column weight="408" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Dial id="kr_pi_dial" lower-bound="0" upper-bound="10" control-position="9" major-tick-spacing="2" minor-ticks="1" inputenabled="true" visible="true" show-labels="true" show-ticks="true" continuous-update="true" pixel-width="128" pixel-height="128"><MapleCode action="position-event-handler">use DocumentTools in 
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use: 
#    Do( %component_name );
# and
#    Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
#    Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.

draw_now_closed_pi();

end use; 
</MapleCode></EC-Dial>   <Font bold="true" family="Arial" size="22">P</Font></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true" family="Arial" size="22"> </Font>  <EC-Slider id="tn_pi_slider" lower-bound="0.05" upper-bound="0.25" control-position="0.23021978" major-tick-spacing="0.05" minor-ticks="0.01" inputenabled="true" visible="true" filled="true" orientation="true" show-labels="true" show-ticks="true" snap-to-ticks="false" continuous-update="true"><MapleCode action="position-event-handler">use DocumentTools in 
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use: 
#    Do( %component_name );
# and
#    Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
#    Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.

draw_now_closed_pi();

end use; 
</MapleCode></EC-Slider><Font bold="true" family="Arial" size="22">  Tn</Font></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="serif" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Font style="Text">Note that by adding the integral component to the proportional controller, the offset error can been eliminated.</Font></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="serif" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Font style="Text">However, if the value of</Font><Font superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="serif" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]"> </Font><Equation executable="false" input-equation="" display="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">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</Equation><Font superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="serif" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]"> </Font><Font style="Text">is too small and combined with a relatively high P gain, the system may become unstable and begin oscillating out of control.</Font></Text-field></Table-Cell></Table-Row></Table>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">PID Controller</Text-field></Title><Presentation-Block>
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<Text-field bookmark="PIDController" prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="`:=`(CsPID, `/`(`*`(Kr, `*`(`+`(1, `*`(s, `*`(Tn))), `*`(`+`(1, `*`(s, `*`(`+`(Tv, Tc))))))), `*`(s, `*`(Tn, `*`(`+`(1, `*`(s, `*`(Tc))))))))" display="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">PkkmQ3NQSURHNiIqLkkjS3JHRiQiIiIsJkYnRicqJkkic0dGJEYnSSNUbkdGJEYnRidGJywmRidGJyomRipGJywmSSNUdkdGJEYnSSNUY0dGJEYnRidGJ0YnRiohIiJGK0YxLCZGJ0YnKiZGKkYnRjBGJ0YnRjE=</Equation></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ki5JI0tyRzYiIiIiLCZGJUYlKiZJInNHRiRGJUkjVG5HRiRGJUYlRiUsJkYlRiUqJkYoRiUsJkkjVHZHRiRGJUkjVGNHRiRGJUYlRiVGJUYoISIiRilGLywmRiVGJSomRihGJUYuRiVGJUYv</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal"></Text-field>
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<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L218" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Open Loop Transfer Function</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="`:=`(GosPID, `*`(CsPID, `*`(Gs)))" display="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">PkknR29zUElERzYiKiZJJkNzUElER0YkIiIiSSNHc0dGJEYn</Equation></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L212" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KjRJI0tyRzYiIiIiLCZGJUYlKiZJInNHRiRGJUkjVG5HRiRGJUYlRiUsJkYlRiUqJkYoRiUsJkkjVHZHRiRGJUkjVGNHRiRGJUYlRiVGJUYoISIiRilGLywmRiVGJSomRihGJUYuRiVGJUYvSSZvbWVnYUdGJCIiI0kiQUdGJEYlLCgqKEYoRiVGMkYlSSZ0aGV0YUdGJEYlRjMqJEYoRjNGJSokRjJGM0YlRi8=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font style="Text">Closed Loop Transfer Function</Font></Text-field>
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<Group autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L215" drawlabel="true" redirect-target="L220">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="`:=`(GcsPID, simplify(`/`(`*`(GosPID), `*`(`+`(1, GosPID)))))" display="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">PkknR2NzUElERzYiLUkpc2ltcGxpZnlHRiQ2IyomSSdHb3NQSURHRiQiIiIsJkYqRipGKUYqISIi</Equation></Text-field>
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<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L220" drawlabel="true" redirect-source="L215">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L215" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ki5JI0tyRzYiIiIiLCZGJUYlKiZJInNHRiRGJUkjVG5HRiRGJUYlRiUsKEYlRiUqJkYoRiVJI1R2R0YkRiVGJSomRihGJUkjVGNHRiRGJUYlRiVJJm9tZWdhR0YkIiIjSSJBR0YkRiUsOioqRihGMEYpRiVGL0YlSSZ0aGV0YUdGJEYlRjAqJkYoIiIkRilGJUYlKihGKEYlRilGJUYvRjBGJSosRihGNkYpRiVGLkYlRi9GJUY0RiVGMCooRigiIiVGKUYlRi5GJUYlKipGKEYwRilGJUYuRiVGL0YwRiUqKEYjRiVGL0YwRjFGJUYlKixGI0YlRi9GMEYxRiVGKEYlRixGJUYlKixGI0YlRi9GMEYxRiVGKEYlRi5GJUYlKixGI0YlRi9GMEYxRiVGKEYlRilGJUYlKi5GI0YlRi9GMEYxRiVGKEYwRilGJUYsRiVGJSouRiNGJUYvRjBGMUYlRihGMEYpRiVGLkYlRiUhIiI=</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="Text" input-equation="``" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">JSFH</Equation></Text-field>
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</Group></Presentation-Block><CodeEditor-ExecGroup autoexecute="true" view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L222" display="button"><EC-CodeEditor id="CodeEditRegion3" pixel-width="500" pixel-height="200"># PID Controller Step Response

draw_now_closed_pid:=proc()

local range;

	range:=0..0.3;

	kr_in:=DocumentTools:-GetProperty('kr_pid_volgauge',value);
	tn_in:=DocumentTools:-GetProperty('tn_pid_slider',value);
	omega_in:=DocumentTools:-GetProperty('w_dial',value);
	theta_in:=DocumentTools:-GetProperty('z_dial',value)/100;

	params := evalf({omega = omega_in, theta = theta_in, A = 1, 
		Kr=kr_in, Tn=tn_in, Tv=tn_in, Tc=tn_in/10}):
	tf_open := simplify (eval(Gs, params));
	tf_closed_pid := simplify (eval(GcsPID, params));
	plt[2]:=TFStepResponse(tf_open,s,0..0.3, green, &quot;Open loop response&quot;);
	if tn_in &gt; 0 then
		plt[3]:=TFStepResponse( simplify(tf_closed_pid), s, 
		0..0.3, red, &quot;Closed loop response&quot;);
	else
		plt[3] := NULL;
	end if;
	plt[1]:=plot(Heaviside(t),t=range, color=blue,thickness=2, legend=&quot;Step input&quot;);
	DocumentTools:-SetProperty ('plt_closed_pid', value, display([plt[1], plt[2], plt[3]], axis=[gridlines=[10,linestyle=dot]]));				

end proc:

draw_now_closed_pid();

</EC-CodeEditor></CodeEditor-ExecGroup><Table alignment="left" showinput="true" interior="group" order="row" exterior="all" width="100.0%" randomized="false" showlabel="true" postexecute="insert" pagebreak="row" showgroup="true"><Table-Column weight="756" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]"><Table alignment="left" showinput="true" interior="all" order="row" exterior="all" width="100.0%" randomized="false" showlabel="true" postexecute="insert" pagebreak="row" showgroup="true"><Table-Column weight="202" separator="true"></Table-Column><Table-Column weight="412" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Volume-Gauge id="kr_pid_volgauge" lower-bound="0" upper-bound="10" control-position="7" major-tick-spacing="2" minor-ticks="1" inputenabled="true" visible="true" show-labels="true" show-ticks="true" continuous-update="true" pixel-width="110" pixel-height="150"><MapleCode action="position-event-handler">use DocumentTools in 
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use: 
#    Do( %component_name );
# and
#    Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
#    Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.

draw_now_closed_pid();
end use; 
</MapleCode></EC-Volume-Gauge>   <Font bold="true" family="Arial" size="22">P </Font> </Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"> <EC-Slider id="tn_pid_slider" lower-bound="0.0015" upper-bound="0.0165" control-position="0.0052912088" major-tick-spacing="0.0050" minor-ticks="0.0010" inputenabled="true" visible="true" filled="true" orientation="true" show-labels="true" show-ticks="true" snap-to-ticks="false" continuous-update="true"><MapleCode action="position-event-handler">use DocumentTools in 
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use: 
#    Do( %component_name );
# and
#    Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
#    Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.

draw_now_closed_pid();

end use; 
</MapleCode></EC-Slider><Font bold="true" family="Arial" size="22">   Tn</Font> </Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]">
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="serif" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Font style="Text">By changing the value of the P slider and the Tn slider, the proportional controller gain and the integral controller gains are adjusted and the response is displayed.</Font></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="serif" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Font style="Text">The values of</Font><Font superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]"> </Font><Equation executable="false" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY1LUkjbWlHRiQ2NVEjVHZGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlc2l6ZUdRIzEyRicvJSVib2xkR1EmZmFsc2VGJy8lJ2l0YWxpY0dRJXRydWVGJy8lKnVuZGVybGluZUdGNy8lKnN1YnNjcmlwdEdGNy8lLHN1cGVyc2NyaXB0R0Y3LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSdvcGFxdWVHRjcvJStleGVjdXRhYmxlR0Y3LyUpcmVhZG9ubHlHRjcvJSljb21wb3NlZEdGNy8lKmNvbnZlcnRlZEdGNy8lK2ltc2VsZWN0ZWRHRjcvJSxwbGFjZWhvbGRlckdGNy8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGNy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGL0YyRjUvRjlGN0Y7Rj1GP0ZBRkRGR0ZJRktGTUZPRlFGU0ZVL0ZYUSdub3JtYWxGJw==">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</Equation><Font superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="serif" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]"> </Font><Font style="Text">and</Font><Font superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="serif" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]"> </Font><Equation executable="false" input-equation="" display="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">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</Equation><Font superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="serif" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]"> </Font><Font style="Text">corresponding to the derivative controller are set as follows:</Font></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="serif" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" input-equation="" display="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">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</Equation></Text-field></Table-Cell></Table-Row></Table>
</Section>
</Worksheet>