<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><meta name="Microsoft Theme 2.00" content="strtedge 111"><meta http-equiv=Content-Type content="text/html; charset=iso-8859-1"><meta name=Generator content="Microsoft Word 15 (filtered medium)"><style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Arial",sans-serif;
color:black;
mso-fareast-language:EN-US;}
h1
{mso-style-priority:9;
mso-style-link:"Titre 1 Car";
margin-top:12.0pt;
margin-right:0cm;
margin-bottom:0cm;
margin-left:0cm;
margin-bottom:.0001pt;
page-break-after:avoid;
font-size:16.0pt;
font-family:"Arial",sans-serif;
color:black;
mso-fareast-language:EN-US;}
h2
{mso-style-priority:9;
mso-style-link:"Titre 2 Car";
margin-top:2.0pt;
margin-right:0cm;
margin-bottom:0cm;
margin-left:0cm;
margin-bottom:.0001pt;
page-break-after:avoid;
font-size:14.0pt;
font-family:"Arial",sans-serif;
color:black;
mso-fareast-language:EN-US;
font-weight:normal;}
h3
{mso-style-priority:9;
mso-style-link:"Titre 3 Car";
margin-top:2.0pt;
margin-right:0cm;
margin-bottom:0cm;
margin-left:0cm;
margin-bottom:.0001pt;
page-break-after:avoid;
font-size:13.0pt;
font-family:"Arial",sans-serif;
color:black;
mso-fareast-language:EN-US;
font-weight:normal;}
h4
{mso-style-priority:9;
mso-style-link:"Titre 4 Car";
margin-top:2.0pt;
margin-right:0cm;
margin-bottom:0cm;
margin-left:0cm;
margin-bottom:.0001pt;
page-break-after:avoid;
font-size:14.0pt;
font-family:"Arial",sans-serif;
color:black;
mso-fareast-language:EN-US;
font-weight:normal;}
h5
{mso-style-priority:9;
mso-style-link:"Titre 5 Car";
margin-top:2.0pt;
margin-right:0cm;
margin-bottom:0cm;
margin-left:0cm;
margin-bottom:.0001pt;
page-break-after:avoid;
font-size:13.0pt;
font-family:"Arial",sans-serif;
color:black;
mso-fareast-language:EN-US;
font-weight:normal;}
h6
{mso-style-priority:9;
mso-style-link:"Titre 6 Car";
margin-top:2.0pt;
margin-right:0cm;
margin-bottom:0cm;
margin-left:0cm;
margin-bottom:.0001pt;
page-break-after:avoid;
font-size:11.0pt;
font-family:"Arial",sans-serif;
color:black;
mso-fareast-language:EN-US;
font-weight:normal;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:#003399;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:#660000;
text-decoration:underline;}
span.Titre1Car
{mso-style-name:"Titre 1 Car";
mso-style-priority:9;
mso-style-link:"Titre 1";
font-family:"Arial",sans-serif;
color:black;
font-weight:bold;}
span.Titre2Car
{mso-style-name:"Titre 2 Car";
mso-style-priority:9;
mso-style-link:"Titre 2";
font-family:"Arial",sans-serif;
color:black;}
span.Titre3Car
{mso-style-name:"Titre 3 Car";
mso-style-priority:9;
mso-style-link:"Titre 3";
font-family:"Arial",sans-serif;
color:black;}
span.Titre4Car
{mso-style-name:"Titre 4 Car";
mso-style-priority:9;
mso-style-link:"Titre 4";
font-family:"Arial",sans-serif;
color:black;}
span.Titre5Car
{mso-style-name:"Titre 5 Car";
mso-style-priority:9;
mso-style-link:"Titre 5";
font-family:"Arial",sans-serif;
color:black;}
span.Titre6Car
{mso-style-name:"Titre 6 Car";
mso-style-priority:9;
mso-style-link:"Titre 6";
font-family:"Arial",sans-serif;
color:black;}
p.msonormal0, li.msonormal0, div.msonormal0
{mso-style-name:msonormal;
mso-margin-top-alt:auto;
margin-right:0cm;
mso-margin-bottom-alt:auto;
margin-left:0cm;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
span.EmailStyle24
{mso-style-type:personal;
font-family:"Calibri",sans-serif;
color:windowtext;}
span.EmailStyle25
{mso-style-type:personal-reply;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:612.0pt 792.0pt;
margin:70.85pt 70.85pt 70.85pt 70.85pt;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]--></head><body bgcolor=white background="cid:image001.gif@01D44F41.E2BFB4B0" lang=FR link="#003399" vlink="#660000"><img src="cid:image001.gif@01D44F41.E2BFB4B0" v:src="cid:image001.gif@01D44F41.E2BFB4B0" v:shapes="_x0000_Mail" width=0 height=0 class=shape style='display:none;width:0;height:0'><!--[if gte mso 9]><xml>
<v:background id="_x0000_s1025" o:bwmode="white" o:targetscreensize="1024,768">
<v:fill src="cid:image001.gif@01D44F41.E2BFB4B0" o:title="strbkgde" type="frame" />
</v:background></xml><![endif]--><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>Dears,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>We here simulate on xcos and matlab/simulink platform, an oscillator to get the behavior of a hydraulic water <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>harmmer in a penstock, following a transmittance of 2 order : b*s/(1+a*s^2). <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>Our main reference is based on a canonic method using only two integrators and we also do some tests with a <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>state space representation, with xcos and simulink <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>The tfss2 function to go from transmittance state-space representation, in xcos, gives results : <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>XCOS STATE-SPACE MATRIX <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> A =[ 0. - 1.3782485 ; 1. 0. ] <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> B=[ 5.2800843 ; 0.] <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> C=[- 5.2800843 0. ] <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> D=[ 0. ] <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> X0[ 0. ; 0.] <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> MATLAB STATE-SPACE MATRIX <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>A =[ 0. - 0.7256 ; 1. 0.] <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> B =[ 1. ; 0. ] <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> C=[ - 20.2281 0. ] <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> D = [ 0. ] <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> X0 = [ 0. ; 0.] <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> TRANSFER FUNCTIONS <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> TRANSMITTANCE H <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> - 20.228058s <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> -------------- <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> 1 + 0.7255586s ^2 <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> TRANSMITTANCE MATLAB SYSMATLAB <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> - 27.877756s <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> -------------- <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> 1 + 1.3781698s ^2 <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>Entering in a numerical scop XY, X=canonic method, Y=State-Space method, we cleary see a correct behavior <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>X=Y with Matlab/Simulink coefficients, and a a very strong dispersion with Scilab/Xcos computing parameters. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>On another way, and because we need a stable state at t=0 (no oscillation), apparently, only the canonic <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>method runs in all modes (sequence=1 ou 2 in the script). The initial vector X0 is only able to controll the first <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>point, but not the stability in this case, so it works only with a zero initial condition. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>Program Xcos/Scilab, ou Matlab/Simulink, schemes, results are available in buggzilla n°15771 <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>Tests have been done with Scilab 5.5.2 under windows W10. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>To read you. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>Sincerely <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>Pierre Perrichon<o:p></o:p></span></p></div></body></html>