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matlab模糊PID控制,包括文献及实例仿真程序
fuzzy-pid for matlab simulink.rar
  • example2.slx
    23.1KB
  • example3.slx
    23.3KB
  • fuzzy_pid.fis
    2.1KB
  • example1.slx
    23.9KB
  • Fuzzy Gain Scheduling of PID Controllers.pdf
    112.7KB
  • license.txt
    1.3KB
内容介绍
<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/625178426caf59619240f863/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="" src="https://static.pudn.com/prod/directory_preview_static/625178426caf59619240f863/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">1392 </div><div class="t m1 x2 h3 y1 ff2 fs1 fc0 sc0 ls1 ws0">IEEE <span class="_"> </span><span class="ls2">TRANSACTIONS </span></div><div class="t m2 x3 h4 y1 ff1 fs2 fc0 sc0 ls3 ws0">ON </div><div class="t m1 x4 h3 y1 ff2 fs1 fc0 sc0 ls4 ws0">SYSTEMS, <span class="_ _0"> </span><span class="ls5">MAN, <span class="_ _0"> </span><span class="ls6">AND <span class="_ _1"></span><span class="ls7">CYBERNETICS. </span></span></span></div><div class="t m3 x5 h5 y1 ff2 fs2 fc0 sc0 ls8 ws0">VOL. </div><div class="t m0 x6 h2 y1 ff1 fs0 fc0 sc0 ls9 ws0">23, </div><div class="t m1 x7 h3 y1 ff2 fs1 fc0 sc0 ls6 ws0">NO. </div><div class="t m4 x8 h6 y1 ff1 fs3 fc0 sc0 lsa ws0">5. </div><div class="t m1 x9 h3 y1 ff2 fs1 fc0 sc0 lsb ws0">SEPTEMBERIOCTOBER </div><div class="t m0 xa h2 y1 ff1 fs0 fc0 sc0 lsc ws0">1993 </div><div class="t m5 xb h7 y2 ff1 fs4 fc0 sc0 lsd ws0">Fuzzy <span class="_ _2"></span>Gain <span class="_ _3"></span>Scheduling </div><div class="t m6 xc h8 y2 ff1 fs5 fc0 sc0 lse ws0">of </div><div class="t m7 xd h9 y2 ff1 fs6 fc0 sc0 lsf ws0">PID </div><div class="t m5 xe h7 y2 ff1 fs4 fc0 sc0 lsd ws0">Controllers </div><div class="t m8 xf ha y3 ff1 fs7 fc0 sc0 ls10 ws0">Zhen-Yu <span class="_ _0"></span><span class="ls11">Zhao, </span></div><div class="t m9 x10 hb y3 ff3 fs8 fc0 sc0 ls12 ws0">Member, </div><div class="t ma x11 hc y3 ff3 fs9 fc0 sc0 ls13 ws0">IEEE, </div><div class="t m8 x12 ha y3 ff1 fs7 fc0 sc0 ls14 ws0">Masayoshi <span class="_ _4"></span><span class="ls11">Tomizuka, </span></div><div class="t m9 x13 hb y3 ff3 fs8 fc0 sc0 ls15 ws0">Member, </div><div class="t mb x14 hc y3 ff4 fs9 fc0 sc0 ls16 ws0">IEEE, </div><div class="t m8 x15 ha y3 ff1 fs7 fc0 sc0 ls10 ws0">and <span class="_ _1"></span>Satoru <span class="_ _5"></span><span class="ls14">Isaka, </span></div><div class="t m9 x16 hb y3 ff3 fs8 fc0 sc0 ls15 ws0">Member, </div><div class="t mc x17 hb y3 ff3 fs8 fc0 sc0 ls17 ws0">IEEE </div><div class="t md x18 hd y4 ff2 fsa fc0 sc0 ls18 ws0">Abstract-This <span class="_ _6"> </span><span class="ls19">paper <span class="_ _7"> </span>describes <span class="_ _7"> </span>the <span class="_ _7"> </span>development <span class="_"> </span><span class="ls1a">of <span class="_ _0"> </span></span>a <span class="_"> </span>fuzzy </span></div><div class="t md x19 hd y5 ff2 fsa fc0 sc0 ls19 ws0">gain scheduling <span class="_ _1"></span>scheme <span class="_ _1"></span><span class="ls1a">of <span class="_ _5"></span></span>PID <span class="_ _5"></span><span class="ls1a">controllers <span class="_ _4"></span>for <span class="ls19">process <span class="_ _1"></span></span>control. </span></div><div class="t md x19 hd y6 ff2 fsa fc0 sc0 ls19 ws0">Fuzzy rules <span class="_ _1"></span><span class="ls1a">and <span class="_ _4"></span><span class="ls19">reasoning <span class="_ _1"></span>are <span class="ls1a">utilized <span class="_ _4"></span>on-line <span class="_ _4"></span><span class="ls1b">to <span class="_ _4"></span><span class="ls19">determine <span class="_ _8"></span>the </span></span></span></span></span></div><div class="t md x19 hd y7 ff2 fsa fc0 sc0 ls19 ws0">controller <span class="_"> </span>parameters <span class="_ _7"> </span>based <span class="_ _7"> </span><span class="ls1b">on <span class="_ _8"></span></span>the <span class="_"> </span>error <span class="_"> </span>signal <span class="_ _7"> </span><span class="ls1a">and <span class="_ _0"></span>its <span class="_ _1"></span></span>first </div><div class="t md x19 hd y8 ff2 fsa fc0 sc0 ls19 ws0">difference. <span class="_ _0"></span>Simulation <span class="_ _7"> </span>results <span class="_ _0"> </span>demonstrate <span class="_ _7"> </span>that <span class="_ _3"> </span>better <span class="_ _0"> </span>control </div><div class="t md x19 hd y9 ff2 fsa fc0 sc0 ls19 ws0">performance <span class="_ _9"> </span><span class="ls1a">can <span class="_"> </span>be <span class="_"> </span></span>achieved <span class="_ _a"> </span>in <span class="_ _9"> </span>comparison <span class="_ _9"> </span>with <span class="_ _a"> </span>Ziegler- </div><div class="t md x19 hd ya ff2 fsa fc0 sc0 ls19 ws0">Nichols <span class="_ _5"></span>controllers <span class="_ _0"></span><span class="ls1a">and </span>Kitamori&#8217;s <span class="_ _0"></span>PID <span class="_ _5"></span>controllers. </div><div class="t m8 x1a ha yb ff1 fs7 fc0 sc0 ls1c ws0">I. <span class="_ _0"></span><span class="ls10">INTRODUCTION </span></div><div class="t m8 x1b ha yc ff1 fs7 fc0 sc0 ls11 ws0">HE <span class="_ _b"> </span><span class="ls1d">BEST-KNOWN <span class="_ _a"> </span>controllers <span class="_ _9"> </span><span class="ls19">used <span class="_ _c"> </span>in <span class="_ _d"> </span><span class="ls1e">industrial </span></span></span></div><div class="t me x19 he yd ff1 fsb fc0 sc0 ls19 ws0">T </div><div class="t m8 x1b ha yd ff1 fs7 fc0 sc0 ls1d ws0">control processes <span class="_ _5"></span>are proportional-integral-derivative </div><div class="t m8 x19 ha ye ff1 fs7 fc0 sc0 ls1d ws0">(PID) <span class="_ _4"></span>controllers <span class="_ _e"></span>because <span class="_ _4"></span><span class="ls1e">of <span class="_ _5"></span><span class="ls1d">their simple <span class="_ _4"></span>structure <span class="_ _e"></span><span class="ls10">and </span></span></span></div><div class="t mf x1c hf yf ff1 fs8 fc0 sc0 ls1f ws0">ro- </div><div class="t m8 x19 ha y10 ff1 fs7 fc0 sc0 ls1e ws0">bust <span class="_ _5"></span><span class="ls1d">performance </span>in a <span class="ls1d">wide range <span class="_ _4"></span><span class="ls1e">of <span class="ls1d">operating conditions. </span></span></span></div><div class="t m8 x19 ha y11 ff1 fs7 fc0 sc0 ls10 ws0">The <span class="_ _5"></span><span class="ls1d">design <span class="_ _8"></span><span class="ls1e">of <span class="_ _3"> </span></span>such <span class="_ _8"></span><span class="ls1e">a <span class="_ _3"> </span></span>controller <span class="_ _5"></span>requires <span class="_ _0"></span><span class="ls1e">specification <span class="_"> </span>of </span></span></div><div class="t m8 x19 ha y12 ff1 fs7 fc0 sc0 ls1e ws0">three <span class="_ _f"> </span><span class="ls1d">parameters: <span class="_ _2"> </span></span>proportional <span class="_ _d"> </span><span class="ls1d">gain, <span class="_"> </span></span>integral <span class="_ _a"> </span><span class="ls1d">time <span class="_ _2"> </span>con- </span></div><div class="t m8 x19 ha y13 ff1 fs7 fc0 sc0 ls1d ws0">stant, <span class="_ _4"></span>and <span class="_ _4"></span>derivative <span class="_ _e"></span>time constant. </div><div class="t m10 x1d ha y14 ff1 fs7 fc0 sc0 ls20 ws0">So </div><div class="t m8 x12 ha y14 ff1 fs7 fc0 sc0 ls10 ws0">far, <span class="_ _4"></span><span class="ls1d">great <span class="_ _4"></span><span class="ls19">effort <span class="_ _8"></span><span class="ls1e">has </span></span></span></div><div class="t m8 x19 ha y15 ff1 fs7 fc0 sc0 ls1e ws0">been <span class="_ _5"></span><span class="ls1d">devoted <span class="ls10">to <span class="_ _4"></span><span class="ls1d">develop <span class="_ _4"></span>methods <span class="ls1e">to <span class="_ _5"></span></span>reduce <span class="_ _4"></span>the <span class="_ _4"></span>time <span class="_ _5"></span>spent </span></span></span></div><div class="t m8 x19 ha y16 ff1 fs7 fc0 sc0 ls14 ws0">on <span class="_ _0"></span><span class="ls1d">optimizing <span class="_ _3"> </span>the <span class="_ _2"> </span>choice <span class="_ _7"> </span><span class="ls1e">of <span class="_ _f"> </span></span>controller <span class="_ _7"> </span>parameters <span class="_"> </span><span class="ls1e">[8], </span></span></div><div class="t m8 x19 ha y17 ff1 fs7 fc0 sc0 ls1e ws0">[15]. <span class="_ _0"></span><span class="ls10">The <span class="_ _5"></span><span class="ls1d">PID <span class="_ _5"></span>controllers <span class="_ _5"></span></span></span>in <span class="_ _8"></span><span class="ls1d">the <span class="_ _5"></span>literature <span class="_ _5"></span></span>can <span class="_ _8"></span><span class="ls14">be <span class="_ _4"></span><span class="ls1d">divided </span></span></div><div class="t m8 x19 ha y18 ff1 fs7 fc0 sc0 ls1e ws0">into <span class="_ _0"></span><span class="ls1d">two <span class="_ _0"></span></span>main <span class="_ _3"> </span><span class="ls1d">categories. <span class="_ _3"> </span>In <span class="_ _1"></span>the <span class="_ _0"></span><span class="ls19">first <span class="_ _3"> </span></span>category, <span class="_ _3"> </span></span>the <span class="_ _7"> </span><span class="ls10">con- </span></div><div class="t m8 x19 ha y19 ff1 fs7 fc0 sc0 ls1d ws0">troller <span class="_ _4"></span>parameters <span class="_ _4"></span><span class="ls14">are <span class="_ _e"></span><span class="ls19">fixed <span class="_ _1"></span><span class="ls1d">during <span class="ls1e">control <span class="_ _3"> </span></span>after <span class="_ _4"></span><span class="ls1e">they <span class="_ _0"></span><span class="ls1d">have </span></span></span></span></span></div><div class="t m8 x19 ha y1a ff1 fs7 fc0 sc0 ls1e ws0">been <span class="_ _10"> </span>tuned </div><div class="t mf x1e hf y1b ff1 fs8 fc0 sc0 ls21 ws0">or </div><div class="t m8 x1f ha y1b ff1 fs7 fc0 sc0 ls1d ws0">chosen <span class="_ _f"> </span><span class="ls19">in <span class="_ _a"> </span><span class="ls1e">a <span class="_ _a"> </span></span></span>certain <span class="_"> </span>optimal <span class="_"> </span><span class="ls10">way. </span></div><div class="t m8 x20 ha y1c ff1 fs7 fc0 sc0 ls14 ws0">The </div><div class="t m8 x19 ha y1d ff1 fs7 fc0 sc0 ls1e ws0">Ziegler-Nichols <span class="_ _d"> </span><span class="ls1d">tuning formula is perhaps the </span>most <span class="_ _8"></span>well- </div><div class="t m8 x19 ha y1e ff1 fs7 fc0 sc0 ls1e ws0">known <span class="_ _5"></span>tuning <span class="_ _1"></span>method <span class="_ _0"></span>[5], </div><div class="t m11 x21 h10 y1f ff5 fsa fc0 sc0 ls19 ws0">[ </div><div class="t m8 x22 ha y1f ff1 fs7 fc0 sc0 ls20 ws0">191. <span class="ls1d">Some <span class="_ _e"></span>other <span class="_ _4"></span>methods <span class="_ _4"></span>exist </span></div><div class="t m12 x19 h11 y20 ff1 fs9 fc0 sc0 ls22 ws0">for </div><div class="t m8 x23 ha y20 ff1 fs7 fc0 sc0 ls1e ws0">the <span class="_ _8"></span><span class="ls10">PID <span class="ls1d">tuning <span class="_ _5"></span>(see <span class="ls1c">e.g., [l], </span></span></span></div><div class="t m13 x24 h12 y20 ff2 fs8 fc0 sc0 ls19 ws0">[6], </div><div class="t m8 x12 ha y20 ff1 fs7 fc0 sc0 ls1e ws0">[7]). <span class="_ _3"> </span><span class="ls1d">The <span class="_ _5"></span><span class="ls10">PID <span class="_ _5"></span></span>con- </span></div><div class="t m8 x19 ha y21 ff1 fs7 fc0 sc0 ls1e ws0">trollers <span class="_ _0"></span>of <span class="_ _8"></span>this <span class="_ _1"></span>category <span class="_ _3"> </span><span class="ls1d">are <span class="ls10">simple, </span></span>but <span class="_ _0"></span><span class="ls1d">cannot always ef- </span></div><div class="t m8 x19 ha y22 ff1 fs7 fc0 sc0 ls1e ws0">fectively <span class="_ _7"> </span><span class="ls1d">control <span class="_ _8"></span>systems <span class="_ _5"></span></span>with <span class="_ _7"> </span><span class="ls1d">changing <span class="_ _8"></span>parameters, <span class="_ _3"></span></span>and </div><div class="t m8 x19 ha y23 ff1 fs7 fc0 sc0 ls19 ws0">may <span class="_ _8"></span><span class="ls1e">need <span class="_ _5"></span><span class="ls1d">frequent <span class="_ _4"></span>on-line <span class="_ _e"></span>retuning. <span class="ls14">The <span class="_ _11"></span><span class="ls1d">controllers <span class="_ _e"></span><span class="ls19">of <span class="_ _5"></span><span class="ls1d">the </span></span></span></span></span></span></div><div class="t m8 x19 ha y24 ff1 fs7 fc0 sc0 ls1e ws0">second <span class="_ _3"></span>category <span class="_ _7"> </span><span class="ls1d">have <span class="_ _1"></span></span>a <span class="_ _0"></span><span class="ls1d">structure <span class="_ _8"></span>similar <span class="_ _5"></span></span>to <span class="_ _3"> </span><span class="ls1d">PID <span class="_ _1"></span>control- </span></div><div class="t m8 x19 ha y25 ff1 fs7 fc0 sc0 ls10 ws0">lers, <span class="_ _0"></span><span class="ls1e">but <span class="_"> </span><span class="ls1d">their <span class="_ _0"></span>parameters <span class="_ _3"> </span></span></span>are <span class="_ _1"></span><span class="ls1d">adapted <span class="_ _7"> </span>on-line <span class="_ _0"></span><span class="ls1e">based <span class="_ _f"> </span></span>on </span></div><div class="t m8 x19 ha y26 ff1 fs7 fc0 sc0 ls1d ws0">parameter <span class="_ _5"></span>estimation, <span class="_ _3"> </span><span class="ls1e">which <span class="_"> </span></span>requires <span class="_ _1"></span>certain <span class="_ _1"></span>knowledge </div><div class="t m8 x19 ha y27 ff1 fs7 fc0 sc0 ls19 ws0">of <span class="_ _1"></span><span class="ls1d">the process, <span class="_ _1"></span><span class="ls1c">e.g., </span>the <span class="_ _5"></span>structure <span class="ls1e">of <span class="_ _8"></span></span>the <span class="_ _8"></span><span class="ls1e">plant <span class="_ _0"></span></span>model <span class="_ _8"></span>[2], </span></div><div class="t m14 x19 h13 y28 ff5 fsc fc0 sc0 ls19 ws0">[ </div><div class="t m8 x25 ha y28 ff1 fs7 fc0 sc0 ls20 ws0">171. <span class="ls1e">Such <span class="_ _8"></span><span class="ls1d">controllers <span class="ls10">are <span class="_ _4"></span><span class="ls1d">called adaptive PID <span class="_ _5"></span>controllers </span></span></span></span></div><div class="t m8 x19 ha y29 ff1 fs7 fc0 sc0 ls19 ws0">in <span class="_ _8"></span><span class="ls1d">order <span class="ls1e">to <span class="_ _1"></span>differentiate <span class="_ _3"> </span></span>them <span class="_ _8"></span>from <span class="_ _5"></span>those <span class="_ _5"></span><span class="ls1e">of <span class="_ _1"></span></span>the <span class="_ _5"></span></span>first <span class="_ _0"></span><span class="ls1d">cate- </span></div><div class="t m15 x19 h14 y2a ff5 fsd fc0 sc0 ls23 ws0">wry. </div><div class="t m8 x26 ha y2b ff1 fs7 fc0 sc0 ls14 ws0">The <span class="_ _12"></span><span class="ls1d">application </span></div><div class="t m16 x27 h15 y2b ff1 fse fc0 sc0 ls24 ws0">of </div><div class="t m8 x28 ha y2b ff1 fs7 fc0 sc0 ls1e ws0">knowledge-based <span class="_"> </span><span class="ls1d">systems <span class="_ _4"></span><span class="ls19">in <span class="_ _5"></span><span class="ls1d">process </span></span></span></div><div class="t m8 x19 ha y2c ff1 fs7 fc0 sc0 ls1e ws0">control <span class="_ _0"></span>is <span class="ls1d">growing, <span class="_ _5"></span></span>especially <span class="_"> </span>in <span class="_ _4"></span><span class="ls1d">the <span class="_ _5"></span><span class="ls19">field </span></span></div><div class="t m16 x29 h15 y2d ff1 fse fc0 sc0 ls24 ws0">of </div><div class="t m8 x2a ha y2d ff1 fs7 fc0 sc0 ls1e ws0">fuzzy <span class="_ _8"></span><span class="ls1d">control </span></div><div class="t m8 x19 ha y2e ff1 fs7 fc0 sc0 ls1d ws0">[9], <span class="_ _1"></span><span class="ls11">[lo], </span></div><div class="t m17 x2b h13 y2f ff5 fsc fc0 sc0 ls19 ws0">[ </div><div class="t m8 x2c ha y2f ff1 fs7 fc0 sc0 ls25 ws0">121-[ <span class="_ _1"></span><span class="ls20">141. <span class="_ _8"></span><span class="ls1d">In <span class="_ _8"></span><span class="ls1e">fuzzy <span class="_ _3"> </span></span>control, <span class="_ _0"></span><span class="ls1e">linguistic <span class="_"> </span></span>descrip- </span></span></div><div class="t m8 x19 ha y30 ff1 fs7 fc0 sc0 ls1e ws0">tions <span class="_ _1"></span>of <span class="_ _8"></span><span class="ls1d">human <span class="_ _5"></span>expertise </span>in <span class="_ _8"></span><span class="ls1d">controlling </span></div><div class="t m5 x2d h16 y31 ff2 fsd fc0 sc0 ls19 ws0">a </div><div class="t m8 x29 ha y31 ff1 fs7 fc0 sc0 ls1d ws0">process are <span class="_ _5"></span><span class="ls1e">rep- </span></div><div class="t m8 x19 ha y32 ff1 fs7 fc0 sc0 ls1e ws0">resented <span class="_ _0"></span><span class="ls14">as <span class="_ _4"></span><span class="ls1e">fuzzy <span class="_ _1"></span>rules </span></span></div><div class="t m18 x2e h17 y33 ff1 fsf fc0 sc0 ls26 ws0">or </div><div class="t m8 x2f ha y33 ff1 fs7 fc0 sc0 ls1d ws0">relations. <span class="_ _5"></span>This <span class="_ _8"></span>knowledge <span class="ls1e">base </span></div><div class="t m8 x19 ha y34 ff1 fs7 fc0 sc0 ls1e ws0">is <span class="_ _1"></span>used <span class="_ _3"> </span><span class="ls20">by <span class="_"> </span><span class="ls10">an <span class="_ _5"></span><span class="ls1d">inference <span class="_ _8"></span>mechanism, <span class="_ _7"> </span></span></span></span>in <span class="_ _0"></span><span class="ls1d">conjunction <span class="_ _8"></span></span>with </div><div class="t m8 x19 ha y35 ff1 fs7 fc0 sc0 ls1d ws0">some <span class="_ _3"> </span>knowledge </div><div class="t m13 x27 hf y36 ff1 fs8 fc0 sc0 ls27 ws0">of </div><div class="t m8 x30 ha y36 ff1 fs7 fc0 sc0 ls1d ws0">the <span class="_"> </span>states <span class="_ _3"> </span><span class="ls1e">of <span class="_ _f"> </span></span>the <span class="_"> </span><span class="ls1e">process <span class="_ _d"> </span></span>(say, <span class="_"> </span><span class="ls1e">of </span></div><div class="t m8 x19 ha y37 ff1 fs7 fc0 sc0 ls1e ws0">measured <span class="_ _7"> </span><span class="ls1d">response <span class="_ _8"></span>variables) <span class="_ _1"></span><span class="ls19">in <span class="_ _0"></span></span>order </span></div><div class="t m19 x31 h11 y38 ff1 fs9 fc0 sc0 ls28 ws0">to </div><div class="t m8 x32 ha y38 ff1 fs7 fc0 sc0 ls1d ws0">determine <span class="_ _1"></span>con- </div><div class="t m0 x18 h2 y39 ff1 fs0 fc0 sc0 ls29 ws0">Manuscript <span class="ls2a">received <span class="_ _0"> </span>April </span></div><div class="t m1a x33 h18 y39 ff5 fs10 fc0 sc0 ls2b ws0">10, </div><div class="t m0 x2f h2 y39 ff1 fs0 fc0 sc0 ls29 ws0">1992; <span class="ls2a">revised <span class="_ _1"> </span><span class="ls2c">October </span></span></div><div class="t m1b x34 h19 y39 ff2 fs11 fc0 sc0 ls2d ws0">3, </div><div class="t m0 x35 h2 y39 ff1 fs0 fc0 sc0 ls29 ws0">1992. </div><div class="t m1c x18 h1a y3a ff1 fs11 fc0 sc0 ls2e ws0">Z.-Y. </div><div class="t m0 x36 h2 y3a ff1 fs0 fc0 sc0 ls29 ws0">Zhao <span class="_ _5"></span>was <span class="_ _8"></span><span class="ls2a">with <span class="_ _1"></span></span>the <span class="_ _8"></span>Department </div><div class="t m5 x11 h1b y3a ff1 fs1 fc0 sc0 ls19 ws0">of </div><div class="t m0 x24 h2 y3a ff1 fs0 fc0 sc0 ls29 ws0">Mechanical <span class="_ _5"></span>Engineering, <span class="_ _0"> </span>Uni- </div><div class="t m0 x37 h2 y3b ff1 fs0 fc0 sc0 ls2a ws0">versity </div><div class="t m1d x38 h19 y3c ff2 fs11 fc0 sc0 ls2f ws0">of </div><div class="t m0 x39 h2 y3c ff1 fs0 fc0 sc0 ls29 ws0">California <span class="_ _1"></span>at <span class="_ _1"></span>Berkeley, <span class="_ _0"> </span>Berkeley, <span class="_ _0"> </span><span class="ls30">CA <span class="_ _8"></span><span class="ls2c">94720, <span class="_ _8"></span></span></span>and <span class="_ _3"> </span><span class="ls2a">is <span class="_ _1"></span></span>currently </div><div class="t m0 x37 h2 y3d ff1 fs0 fc0 sc0 ls2a ws0">with <span class="_ _5"></span><span class="ls29">Omron <span class="_ _5"></span>Advanced <span class="_ _5"></span>Systems, <span class="_ _8"></span><span class="ls31">Inc., <span class="ls9">in <span class="_ _1"></span></span></span>Santa <span class="ls2c">Clara, <span class="ls32">CA. </span></span></span></div><div class="t m0 x18 h2 y3e ff1 fs0 fc0 sc0 ls33 ws0">M. <span class="_ _e"></span><span class="ls29">Tomizuka <span class="_ _1"></span><span class="ls2a">is <span class="_ _8"></span>with <span class="_ _0"> </span></span>the <span class="_ _5"></span>Department </span></div><div class="t m1e x11 h1a y3f ff1 fs11 fc0 sc0 ls2f ws0">of </div><div class="t m0 x24 h2 y3f ff1 fs0 fc0 sc0 ls29 ws0">Mechanical <span class="_ _5"></span>Engineering, <span class="_ _0"> </span>Uni- </div><div class="t m0 x37 h2 y40 ff1 fs0 fc0 sc0 ls2a ws0">versity </div><div class="t m1d x38 h19 y41 ff2 fs11 fc0 sc0 ls2f ws0">of </div><div class="t m0 x3a h2 y41 ff1 fs0 fc0 sc0 ls29 ws0">California at Berkeley, <span class="_ _8"></span>Berkeley, <span class="_ _8"></span><span class="ls30">CA <span class="_ _4"></span><span class="ls2c">94720. </span></span></div><div class="t m1b x3b h19 y42 ff2 fs11 fc0 sc0 ls34 ws0">S. </div><div class="t m0 x3c h2 y42 ff1 fs0 fc0 sc0 ls2a ws0">Isaka </div><div class="t m1d x39 h19 y42 ff2 fs11 fc0 sc0 ls2f ws0">is </div><div class="t m0 x2b h2 y42 ff1 fs0 fc0 sc0 ls9 ws0">with <span class="_ _8"></span><span class="ls29">Omron Advanced <span class="_ _4"></span>Systems, <span class="ls2c">Inc., <span class="ls2a">Santa <span class="_ _5"></span></span>Clara, </span></span></div><div class="t m1f x3d h1c y42 ff2 fs0 fc0 sc0 ls32 ws0">CA </div><div class="t m0 x3e h2 y42 ff1 fs0 fc0 sc0 ls29 ws0">95054. </div><div class="t m0 x3b h2 y43 ff1 fs0 fc0 sc0 ls2c ws0">IEEE </div><div class="t m20 x3f h1d y44 ff1 fs12 fc0 sc0 ls19 ws0">Log </div><div class="t m0 x2b h2 y44 ff1 fs0 fc0 sc0 ls29 ws0">Number <span class="ls2c">920968 </span></div><div class="t m21 x33 h18 y44 ff5 fs10 fc0 sc0 ls35 ws0">1. </div><div class="t m8 x40 ha y45 ff1 fs7 fc0 sc0 ls1e ws0">trol <span class="_ _8"></span><span class="ls1d">actions. <span class="_ _5"></span></span>Although <span class="_ _1"></span>they <span class="_ _1"></span><span class="ls14">do <span class="_ _e"></span><span class="ls19">not <span class="_ _1"></span><span class="ls1d">have <span class="ls10">an <span class="_ _4"></span>apparent <span class="_ _12"></span><span class="ls1e">struc- </span></span></span></span></span></div><div class="t m8 x40 ha y46 ff1 fs7 fc0 sc0 ls1e ws0">ture <span class="_ _7"> </span>of <span class="_"> </span><span class="ls1d">PID <span class="_ _3"> </span>controllers, <span class="_ _7"> </span></span>fuzzy <span class="_"> </span>logic <span class="_"> </span><span class="ls1d">controllers <span class="_ _0"></span><span class="ls19">may <span class="_ _f"> </span></span>be </span></div><div class="t m8 x40 ha y47 ff1 fs7 fc0 sc0 ls1e ws0">considered <span class="_ _a"> </span><span class="ls1d">nonlinear <span class="_ _0"></span><span class="ls10">PID <span class="_ _7"> </span></span>controllers <span class="_ _0"></span>whose <span class="_ _3"> </span>parameters </span></div><div class="t m8 x40 ha y48 ff1 fs7 fc0 sc0 ls1e ws0">can <span class="_ _0"></span><span class="ls1d">be <span class="_ _1"></span>determined <span class="_ _8"></span>on-line <span class="_ _8"></span></span>based <span class="_ _7"> </span><span class="ls14">on <span class="ls1d">the <span class="_ _1"></span>error <span class="_ _0"></span></span></span>signal <span class="_ _7"> </span><span class="ls1d">and </span></div><div class="t m8 x40 ha y49 ff1 fs7 fc0 sc0 ls1e ws0">their <span class="_ _1"></span><span class="ls1d">time derivative </span></div><div class="t mf x5 hf y4a ff1 fs8 fc0 sc0 ls21 ws0">or </div><div class="t m8 x41 ha y4a ff1 fs7 fc0 sc0 ls1d ws0">difference. </div><div class="t m8 x42 ha y4b ff1 fs7 fc0 sc0 ls19 ws0">In <span class="_ _1"></span><span class="ls1e">this <span class="_ _0"></span><span class="ls1d">paper, <span class="_ _1"></span></span>a <span class="_ _0"></span>rule-based <span class="_"> </span><span class="ls10">scheme </span></span></div><div class="t m13 x43 hf y4c ff1 fs8 fc0 sc0 ls19 ws0">for </div><div class="t m8 x44 ha y4c ff1 fs7 fc0 sc0 ls1d ws0">gain <span class="_ _8"></span>scheduling </div><div class="t m8 x40 ha y4d ff1 fs7 fc0 sc0 ls19 ws0">of <span class="_"> </span><span class="ls1d">PID <span class="_ _1"></span>controllers <span class="_ _1"></span>is <span class="_ _0"></span><span class="ls1e">proposed </span></span></div><div class="t m22 x45 hf y4e ff1 fs8 fc0 sc0 ls21 ws0">for </div><div class="t m8 x46 ha y4e ff1 fs7 fc0 sc0 ls1d ws0">process <span class="_ _1"></span>control. <span class="_ _7"> </span><span class="ls10">The </span></div><div class="t m8 x40 ha y4f ff1 fs7 fc0 sc0 ls19 ws0">new <span class="_"> </span><span class="ls1d">scheme <span class="_ _5"></span><span class="ls1e">utilizes <span class="_"> </span>fuzzy <span class="_"> </span>rules <span class="_ _3"> </span><span class="ls10">and <span class="_ _0"></span></span>reasoning <span class="_"> </span>to <span class="_ _3"> </span></span>deter- </span></div><div class="t m8 x40 ha y50 ff1 fs7 fc0 sc0 ls1e ws0">mine <span class="_ _7"> </span><span class="ls1d">the <span class="_ _7"> </span>controller <span class="_ _0"></span>parameters, <span class="_"> </span>and <span class="_ _3"> </span>the <span class="_ _7"> </span><span class="ls10">PID <span class="_ _3"> </span></span>controller </span></div><div class="t m8 x40 ha y51 ff1 fs7 fc0 sc0 ls1e ws0">generates <span class="_ _0"></span>the <span class="_ _8"></span>control <span class="_ _0"></span><span class="ls1d">signal. <span class="_ _8"></span><span class="ls19">It <span class="_ _1"></span></span></span>is <span class="ls1d">demonstrated <span class="_ _5"></span><span class="ls19">in <span class="_ _8"></span></span></span>this <span class="_ _8"></span>pa- </div><div class="t m8 x40 ha y52 ff1 fs7 fc0 sc0 ls1e ws0">per <span class="_ _1"></span>that <span class="_ _3"> </span>human <span class="_ _7"> </span><span class="ls1d">expertise <span class="_ _5"></span><span class="ls19">on <span class="_ _3"> </span><span class="ls10">PID <span class="_ _1"></span></span></span>gain <span class="_ _8"></span>scheduling <span class="_ _5"></span></span>can <span class="_ _0"></span><span class="ls14">be </span></div><div class="t m8 x40 ha y53 ff1 fs7 fc0 sc0 ls1e ws0">represented <span class="_ _10"> </span><span class="ls19">in <span class="_"> </span></span>fuzzy <span class="_ _9"> </span><span class="ls1d">rules. <span class="_"> </span>Furthermore, <span class="_"> </span>better <span class="_ _7"> </span></span>control </div><div class="t m8 x40 ha y54 ff1 fs7 fc0 sc0 ls1e ws0">performance <span class="_ _0"></span>can <span class="ls14">be <span class="_ _e"></span><span class="ls1d">expected <span class="ls19">in </span>the <span class="_ _4"></span><span class="ls1e">proposed <span class="_ _0"></span>method <span class="_ _1"></span>than </span></span></span></div><div class="t m8 x40 ha y55 ff1 fs7 fc0 sc0 ls1e ws0">that <span class="_ _8"></span><span class="ls19">of <span class="_ _0"></span></span>the <span class="_ _1"></span><span class="ls10">PID <span class="ls1d">controllers </span></span>with <span class="_ _0"></span><span class="ls19">fixed <span class="_ _1"></span><span class="ls1d">parameters. </span></span></div><div class="t m8 x15 ha y56 ff1 fs7 fc0 sc0 ls36 ws0">11. <span class="_ _9"> </span><span class="ls10">PID <span class="_ _2"> </span>CONTROLLER </span></div><div class="t m8 x42 ha y57 ff1 fs7 fc0 sc0 ls1e ws0">The <span class="_ _3"> </span><span class="ls1d">transfer <span class="_ _1"></span></span>function <span class="_ _7"> </span><span class="ls10">of <span class="_ _0"></span></span>a <span class="_ _3"> </span><span class="ls10">PID <span class="_ _1"></span><span class="ls1d">controller <span class="_ _1"></span>has <span class="_ _1"></span>the <span class="_ _0"></span>fol- </span></span></div><div class="t m8 x47 ha y58 ff1 fs7 fc0 sc0 ls1e ws0">lowing <span class="_ _1"></span><span class="ls1d">form: </span></div><div class="t m8 x48 ha y59 ff1 fs7 fc0 sc0 ls1e ws0">(1) </div><div class="t m8 x40 ha y5a ff1 fs7 fc0 sc0 ls1e ws0">where </div><div class="t m9 x49 hb y5b ff3 fs8 fc0 sc0 ls12 ws0">K,, </div><div class="t m23 x4a hb y5b ff4 fs8 fc0 sc0 ls12 ws0">Ki, </div><div class="t m8 x4b ha y5b ff1 fs7 fc0 sc0 ls1d ws0">and </div><div class="t m23 x4c hb y5b ff3 fs8 fc0 sc0 ls37 ws0">Kd </div><div class="t m8 x4d ha y5b ff1 fs7 fc0 sc0 ls10 ws0">are <span class="_ _5"></span><span class="ls1e">the <span class="_ _3"> </span><span class="ls1d">proportional, <span class="_ _0"></span>integral, <span class="_ _0"></span>and </span></span></div><div class="t m8 x40 ha y5c ff1 fs7 fc0 sc0 ls1d ws0">derivative <span class="_ _4"></span>gains, <span class="_ _0"></span>respectively. <span class="_ _0"></span>Another <span class="_ _8"></span><span class="ls1e">useful <span class="_ _3"> </span></span>equivalent </div><div class="t m8 x40 ha y5d ff1 fs7 fc0 sc0 ls1e ws0">form <span class="_ _8"></span>of <span class="_ _8"></span><span class="ls1d">the <span class="_ _5"></span><span class="ls10">PID </span>controller <span class="_ _5"></span></span>is </div><div class="t m24 x4e h1e y5e ff6 fs13 fc0 sc0 ls38 ws0">G,(s) </div><div class="t m25 x5 h1f y5e ff5 fs11 fc0 sc0 ls19 ws0">= </div><div class="t m9 x41 hb y5e ff3 fs8 fc0 sc0 ls39 ws0">Kp </div><div class="t m26 x4f h20 y5e ff5 fs14 fc0 sc0 ls19 ws0">+ </div><div class="t m9 x50 hb y5e ff3 fs8 fc0 sc0 ls3a ws0">Ki/s </div><div class="t m27 x51 h21 y5e ff5 fs15 fc0 sc0 ls19 ws0">+ </div><div class="t m28 x52 h22 y5e ff4 fsf fc0 sc0 ls3b ws0">Kds </div><div class="t m24 x53 h1e y5f ff6 fs13 fc0 sc0 ls3c ws0">G,(s) </div><div class="t m29 x54 h23 y5f ff5 fs16 fc0 sc0 ls19 ws0">= </div><div class="t m2a x5 h24 y5f ff4 fs7 fc0 sc0 ls3d ws0">Kp(l </div><div class="t m2b x55 h25 y5f ff5 fs17 fc0 sc0 ls19 ws0">+ </div><div class="t m2c x56 h11 y5f ff1 fs9 fc0 sc0 ls13 ws0">l/(T,s) </div><div class="t m2d x43 h21 y5f ff5 fs15 fc0 sc0 ls19 ws0">+ </div><div class="t m2e x57 h22 y5f ff4 fsf fc0 sc0 ls3e ws0">Tds) </div><div class="t m8 x48 ha y60 ff1 fs7 fc0 sc0 ls19 ws0">(2) </div><div class="t m8 x40 ha y61 ff1 fs7 fc0 sc0 ls1e ws0">where </div><div class="t m2f x49 hb y62 ff4 fs8 fc0 sc0 ls3f ws0">Ti </div><div class="t m29 x58 h23 y62 ff5 fs16 fc0 sc0 ls19 ws0">= </div><div class="t m9 x53 hb y62 ff3 fs8 fc0 sc0 ls40 ws0">K,/Ki </div><div class="t m8 x59 ha y62 ff1 fs7 fc0 sc0 ls1d ws0">and </div><div class="t m2f x5a hb y62 ff4 fs8 fc0 sc0 ls19 ws0">Td </div><div class="t m30 x5b h1f y62 ff5 fs11 fc0 sc0 ls19 ws0">= </div><div class="t m9 x7 hb y62 ff3 fs8 fc0 sc0 ls41 ws0">Kd/Kp. </div><div class="t m31 x5c h26 y62 ff7 fsc fc0 sc0 ls42 ws0">T, </div><div class="t m8 x5d ha y62 ff1 fs7 fc0 sc0 ls1d ws0">and </div><div class="t m5 x5e hb y62 ff4 fs8 fc0 sc0 ls1f ws0">Td </div><div class="t m8 x5f ha y62 ff1 fs7 fc0 sc0 ls10 ws0">are <span class="ls1e">known </span></div><div class="t m8 x40 ha y63 ff1 fs7 fc0 sc0 ls10 ws0">as <span class="_ _11"></span><span class="ls1e">the <span class="_ _5"></span>integral <span class="_ _1"></span>and <span class="_ _5"></span><span class="ls1d">derivative <span class="_ _e"></span>time <span class="_ _4"></span>constants, respectively. </span></span></div><div class="t m8 x42 ha y64 ff1 fs7 fc0 sc0 ls1d ws0">The <span class="_ _4"></span>discrete-time <span class="_ _12"></span>equivalent <span class="_ _e"></span>expression <span class="_ _4"></span><span class="ls10">for <span class="_ _e"></span><span class="ls1d">PID control </span></span></div><div class="t m8 x40 ha y65 ff1 fs7 fc0 sc0 ls19 ws0">used <span class="_ _3"> </span><span class="ls1e">in <span class="_ _5"></span>this <span class="_ _1"></span><span class="ls1d">paper <span class="_ _8"></span></span></span>is <span class="_ _8"></span><span class="ls1d">given <span class="_ _5"></span><span class="ls14">as </span></span></div><div class="t m32 x60 h27 y66 ff8 fs18 fc0 sc0 ls19 ws0">n </div><div class="t m33 x61 h28 y67 ff3 fse fc0 sc0 ls43 ws0">u(k) </div><div class="t m30 x14 h1f y67 ff5 fs11 fc0 sc0 ls19 ws0">= </div><div class="t m9 x62 hb y67 ff3 fs8 fc0 sc0 ls44 ws0">K,e(k) </div><div class="t m34 x63 h29 y67 ff5 fs19 fc0 sc0 ls19 ws0">+ </div><div class="t m35 x64 h26 y67 ff7 fsc fc0 sc0 ls45 ws0">KIT, </div><div class="t m36 x50 h2a y67 ff4 fs1a fc0 sc0 ls19 ws0">c </div><div class="t m9 x65 hb y67 ff3 fs8 fc0 sc0 ls41 ws0">e(i) </div><div class="t m26 x52 h20 y67 ff5 fs14 fc0 sc0 ls19 ws0">+ </div><div class="t m37 x66 h2b y67 ff5 fs1b fc0 sc0 ls19 ws0">- </div><div class="t m38 x66 h2c y67 ff4 fs1c fc0 sc0 ls46 ws0">Kd </div><div class="t m9 x67 hb y67 ff3 fs8 fc0 sc0 ls40 ws0">Ae(k). </div><div class="t m39 x68 h2d y68 ff1 fs1d fc0 sc0 ls47 ws0">r=l </div><div class="t m3a x44 hc y68 ff3 fs9 fc0 sc0 ls48 ws0">TS </div><div class="t m8 x40 ha y69 ff1 fs7 fc0 sc0 ls1d ws0">Here, </div><div class="t m3b x69 h28 y69 ff3 fse fc0 sc0 ls49 ws0">u(k) </div><div class="t m8 x14 ha y69 ff1 fs7 fc0 sc0 ls1e ws0">is <span class="_ _5"></span>the <span class="_ _1"></span><span class="ls1d">control signal, </span></div><div class="t m9 x45 hb y69 ff3 fs8 fc0 sc0 ls4a ws0">e(k) </div><div class="t m8 x6a ha y69 ff1 fs7 fc0 sc0 ls1d ws0">is the error between </div><div class="t m8 x40 ha y6a ff1 fs7 fc0 sc0 ls1e ws0">the <span class="_ _3"> </span><span class="ls1d">reference <span class="_ _5"></span>and <span class="_ _8"></span>the <span class="_ _1"></span>process <span class="_ _1"></span>output, </span></div><div class="t m3c x6b h2e y6b ff3 fs1e fc0 sc0 ls19 ws0">Ts </div><div class="t m8 x44 ha y6b ff1 fs7 fc0 sc0 ls1e ws0">is <span class="_ _1"></span><span class="ls1d">the <span class="_ _0"></span>sampling </span></div><div class="t m8 x40 ha y6c ff1 fs7 fc0 sc0 ls1e ws0">period <span class="_ _0"></span><span class="ls1d">for </span>the <span class="_ _1"></span><span class="ls1d">controller, <span class="_ _8"></span><span class="ls10">and </span></span></div><div class="t m9 x56 hb y6d ff3 fs8 fc0 sc0 ls4a ws0">Ae(k) </div><div class="t m3d x5d h28 y6d ff3 fse fc0 sc0 ls49 ws0">e(k) </div><div class="t m3e x6c h2b y6d ff5 fs1b fc0 sc0 ls19 ws0">- </div><div class="t m3f x6d h22 y6d ff3 fsf fc0 sc0 ls4b ws0">e(k </div><div class="t m3e x6e h2b y6d ff5 fs1b fc0 sc0 ls19 ws0">- </div><div class="t m40 x48 h2f y6d ff2 fs7 fc0 sc0 ls4c ws0">1). </div><div class="t m8 x42 ha y6e ff1 fs7 fc0 sc0 ls10 ws0">The <span class="ls1e">parameters <span class="_ _3"> </span>of <span class="_ _8"></span><span class="ls1d">the <span class="_ _5"></span></span></span>PID <span class="_ _5"></span><span class="ls1d">controller </span></div><div class="t m41 x6f hb y6e ff3 fs8 fc0 sc0 ls4d ws0">Kp, </div><div class="t m23 x5e hb y6e ff3 fs8 fc0 sc0 ls44 ws0">Ki, </div><div class="t m8 x70 ha y6e ff1 fs7 fc0 sc0 ls1d ws0">and </div><div class="t m9 x71 hb y6e ff3 fs8 fc0 sc0 ls21 ws0">Kd </div><div class="t mf x72 hf y6e ff1 fs8 fc0 sc0 ls21 ws0">or </div><div class="t m9 x40 hb y6f ff3 fs8 fc0 sc0 ls12 ws0">K,, </div><div class="t m2f xc hb y6f ff4 fs8 fc0 sc0 ls17 ws0">Ti, </div><div class="t m8 x73 ha y6f ff1 fs7 fc0 sc0 ls1e ws0">and </div><div class="t m5 x74 hb y6f ff4 fs8 fc0 sc0 ls19 ws0">Td </div><div class="t m8 x4b ha y6f ff1 fs7 fc0 sc0 ls1e ws0">can <span class="_ _8"></span><span class="ls1d">be <span class="_ _8"></span></span>manipulated <span class="_"> </span><span class="ls10">to <span class="ls1d">produce <span class="_ _8"></span>various <span class="_ _8"></span></span></span>re- </div><div class="t m8 x40 ha y70 ff1 fs7 fc0 sc0 ls1d ws0">sponse <span class="_ _11"></span>curves from <span class="_ _e"></span><span class="ls1e">a <span class="ls1d">given <span class="_ _4"></span>process. <span class="_ _8"></span>Finding <span class="_ _4"></span>optimum <span class="_ _4"></span>ad- </span></span></div><div class="t m8 x75 ha y71 ff1 fs7 fc0 sc0 ls1d ws0">justments <span class="ls19">of <span class="_ _1"></span><span class="ls1e">a <span class="_ _5"></span></span></span>controller for <span class="_ _4"></span><span class="ls1e">a <span class="_ _5"></span><span class="ls1d">given process </span>is <span class="_ _5"></span><span class="ls19">not <span class="_ _8"></span><span class="ls1d">trivial. </span></span></span></div><div class="t m8 x40 ha y72 ff1 fs7 fc0 sc0 ls19 ws0">In <span class="_ _10"> </span><span class="ls1e">the <span class="_ _d"> </span>following <span class="_ _c"> </span><span class="ls1d">section, <span class="_ _d"> </span></span>an <span class="_ _10"> </span><span class="ls1d">on-line <span class="_ _9"> </span>gain <span class="_ _10"> </span>scheduling </span></span></div><div class="t m8 x40 ha y73 ff1 fs7 fc0 sc0 ls1d ws0">scheme <span class="_ _5"></span><span class="ls1e">of <span class="_ _1"></span></span>the <span class="_ _8"></span>PID <span class="_ _1"></span>controller <span class="_ _5"></span>based <span class="_ _8"></span><span class="ls14">on <span class="_ _5"></span><span class="ls1e">fuzzy <span class="_ _3"> </span>rules <span class="_ _7"> </span></span></span>is <span class="_ _5"></span><span class="ls1e">in- </span></div><div class="t m8 x40 ha y74 ff1 fs7 fc0 sc0 ls1d ws0">troduced. </div><div class="t m8 x76 ha y75 ff1 fs7 fc0 sc0 ls4e ws0">111. </div><div class="t m42 x77 h30 y39 ff2 fsf fc0 sc0 ls26 ws0">Fuzzy </div><div class="t m8 x78 ha y39 ff1 fs7 fc0 sc0 ls1c ws0">GAIN <span class="_ _13"></span><span class="ls14">SCHEDULING </span></div><div class="t m8 x42 ha y76 ff1 fs7 fc0 sc0 ls10 ws0">Fig. <span class="_ _3"> </span><span class="ls1e">1 <span class="_ _4"></span><span class="ls1d">shows <span class="ls1e">the <span class="_ _1"></span></span>PID <span class="_ _8"></span>control <span class="_ _5"></span><span class="ls1e">system <span class="_ _0"></span>with <span class="_ _1"></span>a <span class="_ _8"></span>fuzzy <span class="_ _0"></span></span>gain </span></span></div><div class="t m8 x40 ha y77 ff1 fs7 fc0 sc0 ls1d ws0">scheduler. <span class="_ _0"></span><span class="ls14">The <span class="_ _1"></span></span>approach <span class="_ _0"></span><span class="ls1e">taken <span class="_"> </span></span>here <span class="_ _7"> </span><span class="ls1e">is <span class="_ _7"> </span><span class="ls10">to <span class="_ _3"> </span></span></span>exploit <span class="_ _0"></span><span class="ls1e">fuzzy </span></div><div class="t m8 x40 ha y78 ff1 fs7 fc0 sc0 ls19 ws0">rules <span class="_ _0"></span><span class="ls1e">and <span class="_ _1"></span>reasoning <span class="_ _3"> </span><span class="ls10">to <span class="ls1d">generate <span class="_ _5"></span>controller parameters. </span></span></span></div><div class="t m8 x42 ha y79 ff1 fs7 fc0 sc0 ls19 ws0">It <span class="_ _a"> </span><span class="ls1e">is <span class="_ _9"> </span><span class="ls1d">assumed <span class="_"> </span></span>that </span></div><div class="t m9 x79 hb y7a ff3 fs8 fc0 sc0 ls12 ws0">K,, </div><div class="t m41 x7a hb y7a ff4 fs8 fc0 sc0 ls37 ws0">Kd </div><div class="t m8 x7b ha y7a ff1 fs7 fc0 sc0 ls1d ws0">are <span class="_"> </span><span class="ls19">in <span class="_ _9"> </span><span class="ls1e">prescribed <span class="_ _c"> </span></span></span>ranges </div><div class="t m43 x40 hb y7b ff3 fs8 fc0 sc0 ls39 ws0">[K,. </div><div class="t m44 xc h31 y7b ff1 fs18 fc0 sc0 ls16 ws0">min, </div><div class="t m45 x7c h2e y7b ff4 fs1e fc0 sc0 ls4f ws0">Kp, </div><div class="t m46 x14 h32 y7b ff1 fs1f fc0 sc0 ls50 ws0">,,,I </div><div class="t m8 x7d ha y7b ff1 fs7 fc0 sc0 ls1d ws0">and </div><div class="t m9 x7e hb y7b ff3 fs8 fc0 sc0 ls12 ws0">[Kd. </div><div class="t m47 x41 h33 y7b ff1 fs20 fc0 sc0 ls51 ws0">minr </div><div class="t m9 x7a hb y7b ff3 fs8 fc0 sc0 ls12 ws0">K,, </div><div class="t m48 x7f h34 y7b ff1 fs1c fc0 sc0 ls46 ws0">,ax1 </div><div class="t m8 x46 ha y7b ff1 fs7 fc0 sc0 ls1d ws0">respectively. <span class="ls14">The <span class="_ _12"></span><span class="ls19">aP- </span></span></div><div class="t m0 x80 h2 y7c ff1 fs0 fc0 sc0 ls2c ws0">0018-9472/93$03,00 </div><div class="t m49 x13 h35 y7c ff9 fsa fc0 sc0 ls19 ws0">0 </div><div class="t m0 xc h2 y7c ff1 fs0 fc0 sc0 ls29 ws0">1993 <span class="_ _4"></span>IEEE </div><div class="d m4a"></div></div><div class="pi" data-data='{"ctm":[1.550689,0.000000,0.000000,1.550689,0.000000,0.000000]}'></div></div> </body> </html>
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