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Simulation and Modelling Dynamic Performances of the Servo-Solenoid Directional Valve using Matlab
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<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/626097a2090cbf2c4ed8faa2/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" 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sc0">ah</span><span class="fc3 sc0">r</span><span class="fc3 sc0">ain</span><span class="_ _1"></span><span class="fc3 sc0"> </span></div><div class="t m0 x6 h4 y6 ff1 fs2 fc0 sc0 ls0 ws0"><span class="fc3 sc0">C</span><span class="fc3 sc0">o</span><span class="fc3 sc0">r</span><span class="fc3 sc0">r</span><span class="fc3 sc0">esp</span><span class="fc3 sc0">o</span><span class="fc3 sc0">n</span><span class="fc3 sc0">d</span><span class="fc3 sc0">in</span><span class="fc3 sc0">g</span><span class="fc3 sc0"> </span><span class="fc3 sc0">Au</span><span class="fc3 sc0">t</span><span class="_ _1"></span><span class="fc3 sc0">h</span><span class="fc3 sc0">o</span><span class="fc3 sc0">r</span><span class="ff2"><span class="fc3 sc0">&#8217;</span></span><span class="fc3 sc0">s</span><span class="fc3 sc0"> </span><span class="fc3 sc0">E</span><span class="fc3 sc0">m</span><span class="fc3 sc0">ai</span><span class="fc3 sc0">l:</span><span class="fc3 sc0"> </span></div><div class="t m0 x7 h4 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class="fc3 sc0">D</span><span class="fc3 sc0">U</span><span class="fc3 sc0">C</span><span class="fc3 sc0">T</span><span class="fc3 sc0">I</span><span class="_ _0"></span><span class="fc3 sc0">O</span><span class="fc3 sc0">N</span><span class="fs3"><span class="fc3 sc0"> </span></span></span></div><div class="t m0 x9 h2 ya ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">The</span><span class="fc3 sc0"> </span><span class="_ _2"> </span><span class="fc3 sc0">propo</span><span class="fc3 sc0">rtiona</span><span class="fc3 sc0">l</span><span class="fc3 sc0"> </span><span class="fc3 sc0">e</span><span class="fc3 sc0">l</span><span class="fc3 sc0">e</span><span class="fc3 sc0">c</span><span class="fc3 sc0">tro</span><span class="fc3 sc0">h</span><span class="fc3 sc0">y</span><span class="fc3 sc0">dr</span><span class="fc3 sc0">a</span><span class="fc3 sc0">uli</span><span class="fc3 sc0">c</span><span class="fc3 sc0"> </span><span class="_ _2"> </span><span class="fc3 sc0">se</span><span class="fc3 sc0">rvo</span><span class="fc3 sc0">-</span><span class="fc3 sc0">solenoid</span><span class="fc3 sc0"> </span><span class="_ _3"> </span><span class="fc3 sc0">dire</span><span class="fc3 sc0">c</span><span class="fc3 sc0">ti</span><span class="fc3 sc0">ona</span><span class="fc3 sc0">l </span><span class="_ _2"> </span><span class="fc3 sc0">va</span><span class="fc3 sc0">lv</span><span class="fc3 sc0">e</span><span class="fc3 sc0"> </span><span class="_ _2"> </span><span class="fc3 sc0">c</span><span class="fc3 sc0">a</span><span class="fc3 sc0">n</span><span class="fc3 sc0"> </span><span class="_ _3"> </span><span class="fc3 sc0">b</span><span class="fc3 sc0">e</span><span class="fc3 sc0"> </span><span class="_ _2"> </span><span class="fc3 sc0">a</span><span class="fc3 sc0">ppli</span><span class="fc3 sc0">e</span><span class="fc3 sc0">d</span><span class="fc3 sc0"> </span><span class="_ _2"> </span><span class="fc3 sc0">with </span></div><div class="t m0 xa h2 yb ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">de</span><span class="fc3 sc0">fe</span><span class="fc3 sc0">r</span><span class="fc3 sc0">e</span><span class="fc3 sc0">nt </span><span class="_ _4"></span><span class="fc3 sc0">a</span><span class="fc3 sc0">ppli</span><span class="fc3 sc0">c</span><span class="fc3 sc0">a</span><span class="fc3 sc0">ti</span><span class="fc3 sc0">ons</span><span class="fc3 sc0">, </span><span class="_ _4"></span><span class="ff2"><span class="fc3 sc0">&#8220;</span><span class="fc3 sc0">I</span><span class="fc3 sc0">t</span></span><span class="fc3 sc0"> </span><span class="_ _4"></span><span class="fc3 sc0">is </span><span class="_ _4"></span><span class="fc3 sc0">found</span><span class="fc3 sc0"> that </span><span class="_ _4"></span><span class="fc3 sc0">in</span><span class="fc3 sc0"> the </span><span class="_ _4"></span><span class="fc3 sc0">indu</span><span class="fc3 sc0">strial </span><span class="_ _4"></span><span class="fc3 sc0">fie</span><span class="fc3 sc0">ld </span><span class="_ _4"></span><span class="fc3 sc0">a</span><span class="fc3 sc0">nd </span><span class="_ _4"></span><span class="fc3 sc0">that </span><span class="_ _5"></span><span class="fc3 sc0">e</span><span class="fc3 sc0">qui</span><span class="fc3 sc0">pment </span><span class="_ _4"></span><span class="fc3 sc0">must</span><span class="fc3 sc0"> sa</span><span class="fc3 sc0">ti</span><span class="fc3 sc0">sf</span><span class="fc3 sc0">y</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">the</span><span class="_ _1"></span><span class="fc3 sc0"> </span></div><div class="t m0 xa h2 yc ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">spe</span><span class="fc3 sc0">c</span><span class="fc3 sc0">ial</span><span class="fc3 sc0"> </span><span class="fc3 sc0">re</span><span class="fc3 sc0">quir</span><span class="fc3 sc0">e</span><span class="fc3 sc0">ments </span><span class="fc3 sc0">of </span><span class="fc3 sc0">t</span><span class="_ _1"></span><span class="fc3 sc0">he</span><span class="fc3 sc0"> </span><span class="fc3 sc0">indus</span><span class="fc3 sc0">tria</span><span class="fc3 sc0">l </span><span class="fc3 sc0">a</span><span class="fc3 sc0">nd </span><span class="fc3 sc0">mobi</span><span class="fc3 sc0">le </span><span class="_ _1"></span><span class="fc3 sc0">inst</span><span class="fc3 sc0">a</span><span class="fc3 sc0">ll</span><span class="fc3 sc0">a</span><span class="fc3 sc0">ti</span><span class="fc3 sc0">ons. </span><span class="fc3 sc0">The</span><span class="fc3 sc0">y</span><span class="fc3 sc0"> </span><span class="fc3 sc0">ha</span><span class="fc3 sc0">ve</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">known </span><span class="fc3 sc0">a</span><span class="fc3 sc0">n </span><span class="fc3 sc0">incr</span><span class="fc3 sc0">e</span><span class="fc3 sc0">a</span><span class="fc3 sc0">sing</span><span class="fc3 sc0"> </span><span class="fc3 sc0">in</span><span class="fc3 sc0"> </span></div><div class="t m0 xa h2 yd ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">de</span><span class="fc3 sc0">ve</span><span class="fc3 sc0">lopi</span><span class="fc3 sc0">ng</span><span class="fc3 sc0"> </span><span class="_ _6"> </span><span class="fc3 sc0">a</span><span class="fc3 sc0">nd </span><span class="_"> </span><span class="fc3 sc0">use</span><span class="fc3 sc0"> </span><span class="_ _6"> </span><span class="fc3 sc0">of </span><span class="_"> </span><span class="fc3 sc0">e</span><span class="fc3 sc0">lec</span><span class="fc3 sc0">tronic</span><span class="fc3 sc0">s </span><span class="_ _6"> </span><span class="fc3 sc0">a</span><span class="fc3 sc0">nd </span><span class="_"> </span><span class="fc3 sc0">mi</span><span class="fc3 sc0">c</span><span class="fc3 sc0">ropr</span><span class="fc3 sc0">oc</span><span class="_ _0"></span><span class="fc3 sc0">e</span><span class="fc3 sc0">ssors </span><span class="_"> </span><span class="fc3 sc0">c</span><span class="fc3 sc0">ontroll</span><span class="fc3 sc0">e</span><span class="fc3 sc0">rs </span><span class="_ _6"> </span><span class="fc3 sc0">whi</span><span class="fc3 sc0">c</span><span class="fc3 sc0">h </span><span class="_"> </span><span class="fc3 sc0">c</span><span class="fc3 sc0">ontribut</span><span class="fc3 sc0">e</span><span class="fc3 sc0">d </span><span class="_ _6"> </span><span class="fc3 sc0">to </span><span class="_"> </span><span class="fc3 sc0">the</span><span class="_ _0"></span><span class="fc3 sc0"> </span></div><div class="t m0 xa h2 ye ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">im</span><span class="fc3 sc0">prove</span><span class="fc3 sc0">ment </span><span class="_ _1"></span><span class="fc3 sc0">of </span><span class="_ _1"></span><span class="fc3 sc0">th</span><span class="_ _1"></span><span class="fc3 sc0">e</span><span class="fc3 sc0">ir </span><span class="_ _1"></span><span class="fc3 sc0">d</span><span class="_ _1"></span><span class="fc3 sc0">y</span><span class="_ _0"></span><span class="fc3 sc0">na</span><span class="fc3 sc0">mi</span><span class="fc3 sc0">c</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">pe</span><span class="fc3 sc0">r</span><span class="fc3 sc0">for</span><span class="fc3 sc0">man</span><span class="fc3 sc0">c</span><span class="fc3 sc0">e</span><span class="fc3 sc0">s </span><span class="_ _4"></span><span class="fc3 sc0">o</span><span class="fc3 sc0">f </span><span class="_ _1"></span><span class="fc3 sc0">t</span><span class="_ _1"></span><span class="fc3 sc0">he</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">propo</span><span class="fc3 sc0">rtiona</span><span class="fc3 sc0">l</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">e</span><span class="fc3 sc0">le</span><span class="_ _1"></span><span class="fc3 sc0">c</span><span class="fc3 sc0">troh</span><span class="fc3 sc0">y</span><span class="fc3 sc0">dra</span><span class="fc3 sc0">uli</span><span class="fc3 sc0">c</span><span class="fc3 sc0"> </span><span class="_ _4"></span><span class="fc3 sc0">se</span><span class="fc3 sc0">rvo</span><span class="fc3 sc0">-</span><span class="fc3 sc0">solenoid </span></div><div class="t m0 xa h2 yf ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">dire</span><span class="fc3 sc0">c</span><span class="fc3 sc0">ti</span><span class="fc3 sc0">ona</span><span class="fc3 sc0">l </span><span class="fc3 sc0">va</span><span class="fc3 sc0">lve</span><span class="fc3 sc0">. Th</span><span class="fc3 sc0">e</span><span class="fc3 sc0"> pr</span><span class="fc3 sc0">og</span><span class="fc3 sc0">r</span><span class="fc3 sc0">e</span><span class="fc3 sc0">ss re</span><span class="fc3 sc0">g</span><span class="fc3 sc0">ist</span><span class="fc3 sc0">e</span><span class="fc3 sc0">r</span><span class="fc3 sc0">e</span><span class="fc3 sc0">d in t</span><span class="fc3 sc0">he</span><span class="fc3 sc0"> d</span><span class="fc3 sc0">omain of</span><span class="fc3 sc0"> prop</span><span class="fc3 sc0">ortiona</span><span class="fc3 sc0">l.</span><span class="fc3 sc0"> </span></div><div class="t m0 x9 h2 y10 ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">Ele</span><span class="fc3 sc0">c</span><span class="fc3 sc0">troh</span><span class="fc3 sc0">y</span><span class="fc3 sc0">dra</span><span class="fc3 sc0">uli</span><span class="fc3 sc0">c</span><span class="fc3 sc0"> </span><span class="_ _7"> </span><span class="fc3 sc0">dir</span><span class="fc3 sc0">e</span><span class="fc3 sc0">c</span><span class="fc3 sc0">ti</span><span class="fc3 sc0">ona</span><span class="fc3 sc0">l </span><span class="_ _8"> </span><span class="fc3 sc0">va</span><span class="fc3 sc0">lves </span><span class="_ _7"> </span><span class="fc3 sc0">e</span><span class="fc3 sc0">nha</span><span class="fc3 sc0">nc</span><span class="fc3 sc0">e</span><span class="fc3 sc0">d </span><span class="_ _8"> </span><span class="fc3 sc0">their</span><span class="fc3 sc0"> </span><span class="_ _7"> </span><span class="fc3 sc0">pe</span><span class="fc3 sc0">rf</span><span class="fc3 sc0">o</span><span class="fc3 sc0">rma</span><span class="fc3 sc0">nc</span><span class="fc3 sc0">e</span><span class="fc3 sc0">s </span><span class="_ _7"> </span><span class="fc3 sc0">whi</span><span class="_ _1"></span><span class="fc3 sc0">c</span><span class="fc3 sc0">h </span><span class="_ _7"> </span><span class="fc3 sc0">im</span><span class="fc3 sc0">prove</span><span class="fc3 sc0"> </span><span class="_ _8"> </span><span class="fc3 sc0">the</span><span class="fc3 sc0"> </span></div><div class="t m0 xa h2 y11 ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">a</span><span class="fc3 sc0">c</span><span class="fc3 sc0">c</span><span class="fc3 sc0">ur</span><span class="fc3 sc0">a</span><span class="fc3 sc0">c</span><span class="fc3 sc0">y</span><span class="fc3 sc0"> o</span><span class="fc3 sc0">f the</span><span class="fc3 sc0"> h</span><span class="fc3 sc0">y</span><span class="fc3 sc0">dra</span><span class="fc3 sc0">uli</span><span class="fc3 sc0">c</span><span class="fc3 sc0"> c</span><span class="fc3 sc0">irc</span><span class="fc3 sc0">uit</span><span class="fc3 sc0"> a</span><span class="_ _0"></span><span class="fc3 sc0">s will</span><span class="fc3 sc0"> re</span><span class="fc3 sc0">duc</span><span class="fc3 sc0">e</span><span class="fc3 sc0"> the</span><span class="fc3 sc0"> noise a</span><span class="fc3 sc0">nd ove</span><span class="fc3 sc0">rshoot of</span><span class="fc3 sc0"> t</span><span class="fc3 sc0">he</span><span class="fc3 sc0"> o</span><span class="_ _1"></span><span class="fc3 sc0">utput</span><span class="fc3 sc0">.</span><span class="fc3 sc0"> </span></div><div class="t m0 xa h2 y12 ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">The</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">propo</span><span class="_ _1"></span><span class="fc3 sc0">rtiona</span><span class="fc3 sc0">l </span><span class="_ _1"></span><span class="fc3 sc0">solenoi</span><span class="_ _1"></span><span class="fc3 sc0">d </span><span class="_ _1"></span><span class="fc3 sc0">va</span><span class="fc3 sc0">lves </span><span class="_ _4"></span><span class="fc3 sc0">a</span><span class="fc3 sc0">r</span><span class="_ _1"></span><span class="fc3 sc0">e</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">use</span><span class="fc3 sc0">d</span><span class="fc3 sc0"> </span><span class="_ _4"></span><span class="fc3 sc0">in </span><span class="_ _4"></span><span class="fc3 sc0">the</span><span class="fc3 sc0"> </span><span class="fc3 sc0">a</span><span class="fc3 sc0">ppli</span><span class="fc3 sc0">c</span><span class="fc3 sc0">a</span><span class="fc3 sc0">ti</span><span class="fc3 sc0">on </span><span class="_ _4"></span><span class="fc3 sc0">of</span><span class="fc3 sc0"> </span><span class="_ _4"></span><span class="fc3 sc0">c</span><span class="fc3 sc0">ontrol </span><span class="_ _4"></span><span class="fc3 sc0">in</span><span class="fc3 sc0"> </span><span class="_ _4"></span><span class="fc3 sc0">the</span><span class="_ _1"></span><span class="fc3 sc0"> c</span><span class="fc3 sc0">losed</span><span class="fc3 sc0"> loop </span><span class="_ _1"></span><span class="fc3 sc0">with </span><span class="_ _4"></span><span class="fc3 sc0">a</span><span class="fc3 sc0"> </span></div><div class="t m0 xa h2 y13 ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">low </span><span class="_ _1"></span><span class="fc3 sc0">pric</span><span class="fc3 sc0">e</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">a</span><span class="fc3 sc0">nd </span><span class="_ _1"></span><span class="fc3 sc0">low </span><span class="_ _1"></span><span class="fc3 sc0">c</span><span class="fc3 sc0">ost </span><span class="_ _1"></span><span class="fc3 sc0">of </span><span class="_ _1"></span><span class="fc3 sc0">maintena</span><span class="fc3 sc0">nc</span><span class="fc3 sc0">e</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">ne</span><span class="fc3 sc0">e</span><span class="fc3 sc0">ds. </span><span class="_ _1"></span><span class="fc3 sc0">At </span><span class="_ _1"></span><span class="fc3 sc0">the </span><span class="_ _1"></span><span class="fc3 sc0">propo</span><span class="fc3 sc0">rtiona</span><span class="fc3 sc0">l </span><span class="_ _1"></span><span class="fc3 sc0">solenoid </span><span class="_ _1"></span><span class="fc3 sc0">va</span><span class="fc3 sc0">lves, </span><span class="_ _1"></span><span class="fc3 sc0">the </span><span class="_ _1"></span><span class="fc3 sc0">c</span><span class="fc3 sc0">omm</span><span class="fc3 sc0">a</span><span class="fc3 sc0">nd</span><span class="fc3 sc0"> </span></div><div class="t m0 xa h2 y14 ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">for</span><span class="fc3 sc0">c</span><span class="fc3 sc0">e</span><span class="fc3 sc0"> </span><span class="_ _2"> </span><span class="fc3 sc0">g</span><span class="fc3 sc0">e</span><span class="_ _0"></span><span class="fc3 sc0">n</span><span class="fc3 sc0">e</span><span class="fc3 sc0">ra</span><span class="fc3 sc0">t</span><span class="fc3 sc0">e</span><span class="fc3 sc0">s </span><span class="_ _2"> </span><span class="fc3 sc0">the </span><span class="_ _2"> </span><span class="fc3 sc0">displ</span><span class="fc3 sc0">a</span><span class="fc3 sc0">c</span><span class="fc3 sc0">e</span><span class="_ _0"></span><span class="fc3 sc0">ment </span><span class="_ _2"> </span><span class="fc3 sc0">of </span><span class="_ _2"> </span><span class="fc3 sc0">a</span><span class="fc3 sc0"> </span><span class="_ _2"> </span><span class="fc3 sc0">spool</span><span class="fc3 sc0"> </span><span class="_ _9"> </span><span class="fc3 sc0">whic</span><span class="fc3 sc0">h </span><span class="_ _9"> </span><span class="fc3 sc0">modi</span><span class="fc3 sc0">fi</span><span class="_ _1"></span><span class="fc3 sc0">e</span><span class="fc3 sc0">s </span><span class="_ _9"> </span><span class="fc3 sc0">the </span><span class="_ _2"> </span><span class="fc3 sc0">a</span><span class="fc3 sc0">re</span><span class="fc3 sc0">a</span><span class="fc3 sc0"> </span><span class="_ _9"> </span><span class="fc3 sc0">of </span><span class="_ _9"> </span><span class="fc3 sc0">c</span><span class="fc3 sc0">e</span><span class="fc3 sc0">rta</span><span class="fc3 sc0">in </span><span class="_ _9"> </span><span class="fc3 sc0">a</span><span class="fc3 sc0">pe</span><span class="fc3 sc0">rtur</span><span class="fc3 sc0">e</span><span class="fc3 sc0">s </span><span class="_ _2"> </span><span class="fc3 sc0">that</span><span class="fc3 sc0"> </span></div><div class="t m0 xa h2 y15 ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">c</span><span class="fc3 sc0">ontrol </span><span class="_ _1"></span><span class="fc3 sc0">flow</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">a</span><span class="fc3 sc0">nd </span><span class="_ _1"></span><span class="fc3 sc0">p</span><span class="fc3 sc0">re</span><span class="fc3 sc0">ssur</span><span class="_ _1"></span><span class="fc3 sc0">e</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">in </span><span class="_ _1"></span><span class="fc3 sc0">the</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">s</span><span class="_ _1"></span><span class="fc3 sc0">y</span><span class="_ _0"></span><span class="fc3 sc0">st</span><span class="fc3 sc0">e</span><span class="fc3 sc0">m. </span><span class="_ _1"></span><span class="fc3 sc0">The</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">c</span><span class="fc3 sc0">h</span><span class="fc3 sc0">a</span><span class="fc3 sc0">ng</span><span class="fc3 sc0">e</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">of</span><span class="fc3 sc0"> </span><span class="_ _4"></span><span class="fc3 sc0">the </span><span class="_ _1"></span><span class="fc3 sc0">a</span><span class="fc3 sc0">re</span><span class="fc3 sc0">a</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">is </span><span class="_ _1"></span><span class="fc3 sc0">d</span><span class="fc3 sc0">e</span><span class="fc3 sc0">sig</span><span class="fc3 sc0">n</span><span class="fc3 sc0">e</span><span class="fc3 sc0">d </span><span class="_ _1"></span><span class="fc3 sc0">to </span><span class="_ _4"></span><span class="fc3 sc0">be</span><span class="fc3 sc0"> </span><span class="_ _1"></span><span class="fc3 sc0">a</span><span class="fc3 sc0">pp</span><span class="fc3 sc0">rox</span><span class="fc3 sc0">im</span><span class="fc3 sc0">a</span><span class="fc3 sc0">tel</span><span class="_ _1"></span><span class="fc3 sc0">y</span><span class="_ _0"></span><span class="fc3 sc0"> </span></div><div class="t m0 xa h2 y16 ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">li</span><span class="fc3 sc0">ne</span><span class="fc3 sc0">a</span><span class="fc3 sc0">r </span><span class="_ _3"> </span><span class="fc3 sc0">with </span><span class="_ _6"> </span><span class="fc3 sc0">the </span><span class="_ _3"> </span><span class="fc3 sc0">displ</span><span class="_ _1"></span><span class="fc3 sc0">a</span><span class="fc3 sc0">c</span><span class="fc3 sc0">e</span><span class="fc3 sc0">ment </span><span class="_ _3"> </span><span class="fc3 sc0">of </span><span class="_ _6"> </span><span class="fc3 sc0">the </span><span class="_ _3"> </span><span class="fc3 sc0">spool</span><span class="fc3 sc0">. </span><span class="_ _6"> </span><span class="fc3 sc0">The</span><span class="fc3 sc0"> </span><span class="_ _3"> </span><span class="fc3 sc0">pe</span><span class="fc3 sc0">rtur</span><span class="fc3 sc0">ba</span><span class="fc3 sc0">ti</span><span class="fc3 sc0">ons </span><span class="_ _6"> </span><span class="fc3 sc0">in </span><span class="_ _3"> </span><span class="fc3 sc0">the </span><span class="_ _6"> </span><span class="fc3 sc0">mot</span><span class="fc3 sc0">ion </span><span class="_ _6"> </span><span class="fc3 sc0">of </span><span class="_ _3"> </span><span class="fc3 sc0">the </span><span class="_ _6"> </span><span class="fc3 sc0">spool</span><span class="fc3 sc0"> </span><span class="_ _3"> </span><span class="fc3 sc0">a</span><span class="fc3 sc0">re</span><span class="fc3 sc0"> </span></div><div class="t m0 xa h2 y17 ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">unde</span><span class="fc3 sc0">sira</span><span class="fc3 sc0">ble </span><span class="_ _4"></span><span class="fc3 sc0">whic</span><span class="fc3 sc0">h </span><span class="_ _5"></span><span class="fc3 sc0">is </span><span class="_ _5"></span><span class="fc3 sc0">c</span><span class="fc3 sc0">a</span><span class="fc3 sc0">u</span><span class="fc3 sc0">se</span><span class="fc3 sc0">d</span><span class="fc3 sc0"> </span><span class="ls3"><span class="fc3 sc0">by</span></span><span class="fc3 sc0"> </span><span class="_ _4"></span><span class="fc3 sc0">the </span><span class="_ _5"></span><span class="fc3 sc0">fr</span><span class="fc3 sc0">iction </span><span class="_ _5"></span><span class="fc3 sc0">fo</span><span class="fc3 sc0">rc</span><span class="fc3 sc0">e</span><span class="fc3 sc0">s</span><span class="fc3 sc0"> </span><span class="_ _5"></span><span class="fc3 sc0">be</span><span class="fc3 sc0">twe</span><span class="fc3 sc0">e</span><span class="fc3 sc0">n </span><span class="_ _4"></span><span class="fc3 sc0">a</span><span class="fc3 sc0"> </span><span class="_ _5"></span><span class="fc3 sc0">spool</span><span class="fc3 sc0"> </span><span class="_ _5"></span><span class="fc3 sc0">a</span><span class="fc3 sc0">nd</span><span class="fc3 sc0"> </span><span class="_ _5"></span><span class="fc3 sc0">th</span><span class="fc3 sc0">e</span><span class="fc3 sc0"> </span><span class="_ _5"></span><span class="fc3 sc0">va</span><span class="fc3 sc0">lve</span><span class="fc3 sc0"> </span><span class="_ _5"></span><span class="fc3 sc0">bod</span><span class="_ _1"></span><span class="fc3 sc0">y</span><span class="_ _0"></span><span class="fc3 sc0">, </span><span class="_ _4"></span><span class="fc3 sc0">a</span><span class="fc3 sc0">nd </span><span class="_ _5"></span><span class="fc3 sc0">the</span><span class="fc3 sc0"> </span></div><div class="t m0 xa h2 y18 ff1 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">static </span><span class="_ _4"></span><span class="fc3 sc0">pre</span><span class="fc3 sc0">ssure</span><span class="fc3 sc0"> </span><span class="_ _4"></span><span class="fc3 sc0">for</span><span class="fc3 sc0">c</span><span class="fc3 sc0">e</span><span class="fc3 sc0">s </span><span class="_ _5"></span><span class="fc3 sc0">c</span><span class="fc3 sc0">a</span><span class="fc3 sc0">use</span><span class="fc3 sc0">d </span><span class="_ _5"></span><span class="fc3 sc0">b</span><span class="fc3 sc0">y</span><span class="fc3 sc0"> </span><span class="_ _4"></span><span class="fc3 sc0">the </span><span class="_ _5"></span><span class="fc3 sc0">g</span><span class="fc3 sc0">e</span><span class="fc3 sc0">ometr</span><span class="fc3 sc0">y</span><span class="fc3 sc0"> </span><span class="_ _4"></span><span class="fc3 sc0">of</span><span class="fc3 sc0"> </span><span class="_ _5"></span><span class="fc3 sc0">the </span><span class="_ _5"></span><span class="fc3 sc0">spool</span><span class="fc3 sc0"> </span><span class="_ _4"></span><span class="fc3 sc0">or </span><span class="_ _5"></span><span class="fc3 sc0">b</span><span class="fc3 sc0">y</span><span class="fc3 sc0"> </span><span class="_ _4"></span><span class="fc3 sc0">the </span><span class="_ _4"></span><span class="fc3 sc0">iner</span><span class="_ _1"></span><span class="fc3 sc0">ti</span><span class="fc3 sc0">a</span><span class="fc3 sc0"> </span><span class="_ _4"></span><span class="fc3 sc0">for</span><span class="fc3 sc0">c</span><span class="fc3 sc0">e</span><span class="fc3 sc0">s </span><span class="_ _4"></span><span class="fc3 sc0">g</span><span class="fc3 sc0">e</span><span class="fc3 sc0">n</span><span class="fc3 sc0">e</span><span class="fc3 sc0">ra</span><span class="fc3 sc0">ted </span><span class="_ _4"></span><span class="fc3 sc0">b</span><span class="_ _1"></span><span class="fc3 sc0">y</span><span class="fc3 sc0"> </span></div><div class="t m0 xa h2 y19 ff2 fs0 fc2 sc0 ls0 ws0"><span class="fc3 sc0">the </span><span class="fc3 sc0">f</span><span class="fc3 sc0">low&#8221;</span><span class="fc3 sc0">.</span><span class="ff1"><span class="fc3 sc0"> </span></span></div><div class="t m0 xa h2 y1a ff1 fs0 fc0 sc0 ls0 ws0"><span class="fc3 sc0"> </span></div><div class="t m0 xa h6 y1b ff3 fs0 fc0 sc0 ls0 ws0"><span class="fc3 sc0">1.1</span><span class="ff4"><span class="fc3 sc0"> </span><span class="_ _0"></span><span class="ff3"><span class="fc3 sc0"> </span><span class="_ _a"> </span><span class="fc3 sc0">Stat</span><span class="fc3 sc0">e</span><span class="fc3 sc0">me</span><span class="fc3 sc0">nt of</span><span class="fc3 sc0"> the P</span><span class="fc3 sc0">robl</span><span class="fc3 sc0">e</span><span class="fc3 sc0">m</span><span class="fc3 sc0"> </span></span></span></div><div class="t m0 x9 h2 y1c ff1 fs0 fc0 sc0 ls0 ws0"><span class="fc3 sc0">I</span><span class="fc3 sc0">n</span><span class="fc3 sc0"> </span><span class="_ _7"> </span><span class="fc3 sc0">the </span><span class="_ _7"> </span><span class="fc3 sc0">fie</span><span class="fc3 sc0">ld </span><span class="_ _8"> </span><span class="fc3 sc0">of</span><span class="fc3 sc0"> </span><span class="_ _7"> </span><span class="fc3 sc0">the </span><span class="_ _8"> </span><span class="fc3 sc0">e</span><span class="fc3 sc0">le</span><span class="fc3 sc0">c</span><span class="fc3 sc0">tro-</span><span class="fc3 sc0">h</span><span class="fc3 sc0">y</span><span class="fc3 sc0">dra</span><span class="fc3 sc0">uli</span><span class="fc3 sc0">c</span><span class="fc3 sc0"> </span><span class="_ _7"> </span><span class="fc3 sc0">c</span><span class="fc3 sc0">ontrol</span><span class="fc3 sc0"> </span><span class="_ _8"> </span><span class="fc3 sc0">sy</span><span class="_ _0"></span><span class="fc3 sc0">s</span><span class="fc3 sc0">tem </span><span class="_ _7"> </span><span class="fc3 sc0">the</span><span class="_ _1"></span><span class="fc3 sc0"> </span><span class="_ _7"> </span><span class="fc3 sc0">pe</span><span class="fc3 sc0">rf</span><span class="fc3 sc0">orma</span><span class="fc3 sc0">n</span><span class="fc3 sc0">c</span><span class="fc3 sc0">e</span><span class="fc3 sc0">,</span><span class="fc3 sc0"> </span><span class="_ _7"> </span><span class="fc3 sc0">including </span><span class="_ _8"> </span><span class="fc3 sc0">the</span><span class="fc3 sc0"> </span></div><div class="t m0 xb h2 y1d ff1 fs0 fc0 sc0 ls0 ws0"><span class="fc3 sc0">stabili</span><span class="fc3 sc0">t</span><span class="fc3 sc0">y</span><span class="fc3 sc0"> </span><span class="_ _6"> </span><span class="fc3 sc0">o</span><span class="fc3 sc0">f </span><span class="_ _6"> </span><span class="fc3 sc0">the </span><span class="_ _6"> </span><span class="fc3 sc0">s</span><span class="_ _1"></span><span class="fc3 sc0">y</span><span class="_ _0"></span><span class="fc3 sc0">stem </span><span class="_"> </span><span class="fc3 sc0">a</span><span class="fc3 sc0">re</span><span class="_ _0"></span><span class="fc3 sc0"> </span><span class="_"> </span><span class="fc3 sc0">im</span><span class="fc3 sc0">porta</span><span class="fc3 sc0">nt</span><span class="fc3 sc0"> </span><span class="_ _6"> </span><span class="fc3 sc0">p</span><span class="fc3 sc0">a</span><span class="fc3 sc0">rts </span><span class="_ _6"> </span><span class="fc3 sc0">of </span><span class="_"> </span><span class="fc3 sc0">t</span><span class="fc3 sc0">he</span><span class="fc3 sc0"> </span><span class="_ _6"> </span><span class="fc3 sc0">h</span><span class="fc3 sc0">y</span><span class="fc3 sc0">dra</span><span class="fc3 sc0">uli</span><span class="fc3 sc0">c</span><span class="fc3 sc0"> </span><span class="_ _6"> </span><span class="fc3 sc0">s</span><span class="fc3 sc0">y</span><span class="fc3 sc0">stem </span><span class="_"> </span><span class="fc3 sc0">wo</span><span class="fc3 sc0">rking</span><span class="fc3 sc0">. </span><span class="_"> </span><span class="fc3 sc0">I</span><span class="_ _0"></span><span class="fc3 sc0">n </span><span class="_ _6"> </span><span class="fc3 sc0">thi</span><span class="fc3 sc0">s </span><span class="_"> </span><span class="fc3 sc0">wor</span><span class="fc3 sc0">k, </span></div><div class="t m0 xb h2 y1e ff1 fs0 fc0 sc0 ls0 ws0"><span class="fc3 sc0">e</span><span class="fc3 sc0">lec</span><span class="fc3 sc0">tro</span><span class="fc3 sc0">-</span><span class="fc3 sc0">h</span><span class="fc3 sc0">y</span><span class="fc3 sc0">d</span><span class="fc3 sc0">ra</span><span class="fc3 sc0">uli</span><span class="fc3 sc0">c</span><span class="fc3 sc0"> </span><span class="_ _b"></span><span class="fc3 sc0">c</span><span class="fc3 sc0">ont</span><span class="fc3 sc0">rol </span><span class="_ _b"></span><span class="fc3 sc0">c</span><span class="fc3 sc0">irc</span><span class="fc3 sc0">uit</span><span class="fc3 sc0">s </span><span class="_ _9"> </span><span class="fc3 sc0">including</span><span class="fc3 sc0"> </span><span class="_ _b"></span><span class="fc3 sc0">a</span><span class="fc3 sc0"> </span><span class="_ _9"> </span><span class="fc3 sc0">pro</span><span class="fc3 sc0">portiona</span><span class="fc3 sc0">l </span><span class="_ _b"></span><span class="fc3 sc0">dire</span><span class="fc3 sc0">c</span><span class="fc3 sc0">ti</span><span class="fc3 sc0">ona</span><span class="fc3 sc0">l </span><span class="_ _9"> </span><span class="fc3 sc0">c</span><span class="fc3 sc0">on</span><span class="fc3 sc0">trol </span><span class="_ _b"></span><span class="fc3 sc0">va</span><span class="fc3 sc0">lve </span><span class="_ _9"> </span><span class="fc3 sc0">ha</span><span class="fc3 sc0">ve</span><span class="fc3 sc0"> </span><span class="_ _b"></span><span class="fc3 sc0">b</span><span class="fc3 sc0">e</span><span class="fc3 sc0">e</span><span class="fc3 sc0">n</span><span class="fc3 sc0"> </span></div><div class="t m0 xb h2 y1f ff1 fs0 fc0 sc0 ls0 ws0"><span class="fc3 sc0">de</span><span class="fc3 sc0">sig</span><span class="fc3 sc0">ne</span><span class="fc3 sc0">d.</span><span class="fc3 sc0"> </span><span class="_ _9"> </span><span class="fc3 sc0">A </span><span class="_ _9"> </span><span class="fc3 sc0">mathe</span><span class="fc3 sc0">matic</span><span class="fc3 sc0">a</span><span class="fc3 sc0">l </span><span class="_ _9"> </span><span class="fc3 sc0">model </span><span class="_ _2"> </span><span class="fc3 sc0">de</span><span class="fc3 sc0">ve</span><span class="fc3 sc0">loped </span><span class="_ _9"> </span><span class="fc3 sc0">to </span><span class="_ _9"> </span><span class="fc3 sc0">de</span><span class="fc3 sc0">ter</span><span class="fc3 sc0">mi</span><span class="fc3 sc0">ne</span><span class="fc3 sc0"> </span><span class="_ _9"> </span><span class="fc3 sc0">the </span><span class="_ _9"> </span><span class="fc3 sc0">na</span><span class="fc3 sc0">tur</span><span class="fc3 sc0">a</span><span class="fc3 sc0">l </span><span class="_ _9"> </span><span class="fc3 sc0">fr</span><span class="fc3 sc0">e</span><span class="fc3 sc0">que</span><span class="fc3 sc0">nc</span><span class="_ _1"></span><span class="fc3 sc0">y</span><span class="_ _0"></span><span class="fc3 sc0"> </span><span class="_ _9"> </span><span class="fc3 sc0">a</span><span class="fc3 sc0">nd </span><span class="_ _9"> </span><span class="fc3 sc0">da</span><span class="fc3 sc0">mpi</span><span class="fc3 sc0">n</span><span class="fc3 sc0">g </span></div><div class="t m0 xb h2 y20 ff1 fs0 fc0 sc0 ls0 ws0"><span class="fc3 sc0">ra</span><span class="fc3 sc0">ti</span><span class="fc3 sc0">o of the</span><span class="fc3 sc0"> P</span><span class="fc3 sc0">EH</span><span class="fc3 sc0">S</span><span class="fc3 sc0">V using</span><span class="fc3 sc0"> Ma</span><span class="fc3 sc0">tl</span><span class="fc3 sc0">a</span><span class="fc3 sc0">b so</span><span class="fc3 sc0">ftw</span><span class="fc3 sc0">a</span><span class="fc3 sc0">r</span><span class="fc3 sc0">e</span><span class="fc3 sc0">.</span><span class="ff5"><span class="fc3 sc0"> </span><span class="fc3 sc0"> </span></span></div><div class="t m0 xc h7 y21 ff6 fs5 fc0 sc0 ls0 ws0"><span class="fc3 sc0">International Journal of Advanced Research in Basic Engineering Sciences and Technology (IJARBEST)</span></div><div class="t m0 xd h7 y22 ff6 fs5 fc0 sc0 ls0 ws0"><span class="fc3 sc0">ISSN (ONLINE):2456-5717</span><span class="_ _c"> </span><span class="fc3 sc0">Vol.4, Issue.11, November 2018</span></div><div class="t m0 xc h8 y23 ff7 fs6 fc0 sc0 ls0 ws0">International Journal of Advanced Research in Basic Engineering Sciences and Technology (IJARBEST)</div><div class="t m0 xd h8 y24 ff7 fs6 fc0 sc0 ls0 ws0">ISSN (ONLINE):2456-5717<span class="_ _d"> </span>41<span class="_ _e"> </span>Vol.4, Issue.11, November 2018</div><a class="l" 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