sliding mode observer for sensorless.rar

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2016--New variable gain super-twisting sliding mode observer for sensorless
sliding mode observer for sensorless.rar
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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/624fe37a6caf596192f79c91/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/624fe37a6caf596192f79c91/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Ne<span class="_ _0"></span>w<span class="_ _1"> </span>variable<span class="_ _1"> </span>gain<span class="_ _1"> </span>super<span class="_ _2"></span>-twisting<span class="_ _1"> </span>sliding<span class="_ _1"> </span>mode<span class="_ _1"> </span>observer<span class="_ _1"> </span>for<span class="_ _1"> </span>sensorless</div><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">vector<span class="_ _1"> </span>control<span class="_ _3"> </span>of<span class="_ _3"> </span>nonsinusoidal<span class="_ _3"> </span>back<span class="_ _2"></span>-EMF<span class="_ _3"> </span>PMSM</div><div class="t m1 x2 h3 y3 ff2 fs1 fc0 sc0 ls0 ws0">$</div><div class="t m2 x1 h4 y4 ff1 fs2 fc0 sc0 ls0 ws0">Cassio<span class="_ _4"> </span>Luciano<span class="_ _4"> </span>Baratieri</div><div class="t m3 x3 h5 y5 ff3 fs3 fc1 sc0 ls0 ws0">n</div><div class="t m2 x4 h4 y4 ff1 fs2 fc0 sc0 ls0 ws0">,<span class="_ _4"> </span>Humberto<span class="_ _4"> </span>Pinheiro</div><div class="t m4 x1 h6 y6 ff4 fs4 fc0 sc0 ls0 ws0">T<span class="_ _0"></span>echnology<span class="_ _5"> </span>Center<span class="_ _0"></span>,<span class="_ _5"> </span>Federal<span class="_ _5"> </span>University<span class="_ _5"> </span>of<span class="_ _5"> </span>Santa<span class="_ _5"> </span>Maria,<span class="_ _5"> </span>Santa<span class="_ _5"> </span>Maria,<span class="_ _6"> </span>1<span class="_ _0"></span>000<span class="_ _5"> </span>Roraima<span class="_ _5"> </span>Street,<span class="_ _6"> </span>97105-900<span class="_ _6"> </span>RS,<span class="_ _7"> </span>Brazil</div><div class="t m5 x1 h7 y7 ff5 fs5 fc0 sc0 ls1 ws0">article<span class="_ _8"> </span>info</div><div class="t m4 x1 h6 y8 ff4 fs4 fc0 sc0 ls0 ws0">Article<span class="_ _5"> </span>history:</div><div class="t m4 x1 h8 y9 ff1 fs4 fc0 sc0 ls0 ws0">Received<span class="_ _6"> </span>1<span class="_ _0"></span>7<span class="_ _6"> </span>August<span class="_ _5"> </span>201<span class="_ _0"></span>5</div><div class="t m4 x1 h8 ya ff1 fs4 fc0 sc0 ls0 ws0">Received<span class="_ _6"> </span>in<span class="_ _5"> </span>revised<span class="_ _5"> </span>form</div><div class="t m4 x1 h8 yb ff1 fs4 fc0 sc0 ls0 ws0">3<span class="_ _0"></span>1<span class="_ _5"> </span>December<span class="_ _5"> </span>201<span class="_ _0"></span>5</div><div class="t m4 x1 h8 yc ff1 fs4 fc0 sc0 ls0 ws0">Accepted<span class="_ _6"> </span>3<span class="_ _5"> </span>April<span class="_ _7"> </span>201<span class="_ _9"></span>6</div><div class="t m4 x1 h6 yd ff4 fs4 fc0 sc0 ls0 ws0">Keywords:</div><div class="t m4 x1 h8 ye ff1 fs4 fc0 sc0 ls0 ws0">Discrete-time<span class="_ _6"> </span>sliding<span class="_ _7"> </span>mode</div><div class="t m4 x1 h8 yf ff1 fs4 fc0 sc0 ls0 ws0">Nonsinusoidal<span class="_ _5"> </span>back<span class="_ _9"></span>-EMF</div><div class="t m4 x1 h8 y10 ff1 fs4 fc0 sc0 ls0 ws0">Permanent<span class="_ _5"> </span>magnet<span class="_ _5"> </span>synchronous<span class="_ _5"> </span>motor</div><div class="t m4 x1 h8 y11 ff1 fs4 fc0 sc0 ls0 ws0">Sliding<span class="_ _5"> </span>mode<span class="_ _5"> </span>observer</div><div class="t m4 x1 h8 y12 ff1 fs4 fc0 sc0 ls0 ws0">Sensorless<span class="_ _5"> </span>vector<span class="_ _6"> </span>control</div><div class="t m4 x1 h8 y13 ff1 fs4 fc0 sc0 ls0 ws0">Super<span class="_ _9"></span>-twisting<span class="_ _7"> </span>algorithm</div><div class="t m5 x5 h7 y7 ff5 fs5 fc0 sc0 ls2 ws0">abstract</div><div class="t m5 x5 h9 y14 ff1 fs6 fc0 sc0 ls0 ws0">This<span class="_ _8"> </span>paper<span class="_ _8"> </span>presents<span class="_ _8"> </span>a<span class="_ _7"> </span>new<span class="_ _8"> </span>discrete-time<span class="_ _8"> </span>super<span class="_ _9"></span>-twisting<span class="_ _8"> </span>sliding<span class="_ _8"> </span>mode<span class="_ _8"> </span>observer<span class="_ _8"> </span>with<span class="_ _7"> </span>variable<span class="_ _8"> </span>gains<span class="_ _8"> </span>for</div><div class="t m5 x5 h9 y15 ff1 fs6 fc0 sc0 ls0 ws0">sensorless<span class="_ _4"> </span>nonsinusoidal<span class="_ _a"> </span>vector<span class="_ _a"> </span>control<span class="_ _a"> </span>of<span class="_ _4"> </span>permanent<span class="_ _a"> </span>magnet<span class="_ _4"> </span>synchronous<span class="_ _4"> </span>motors.<span class="_ _a"> </span>This<span class="_ _a"> </span>observer<span class="_ _4"> </span>is</div><div class="t m5 x5 h9 y16 ff1 fs6 fc0 sc0 ls0 ws0">adopted<span class="_ _5"> </span>to<span class="_ _8"> </span>estimate<span class="_ _5"> </span>the<span class="_ _7"> </span>back<span class="_ _7"> </span>electromotive<span class="_ _7"> </span>forces<span class="_ _7"> </span>(back<span class="_ _9"></span>-EMF)<span class="_ _8"> </span>that<span class="_ _7"> </span>are<span class="_ _7"> </span>required<span class="_ _5"> </span>for<span class="_ _7"> </span>the<span class="_ _8"> </span>ro<span class="_ _9"></span>tor<span class="_ _8"> </span>speed<span class="_ _5"> </span>es-</div><div class="t m5 x5 h9 y17 ff1 fs6 fc0 sc0 ls0 ws0">timation<span class="_ _5"> </span>and<span class="_ _7"> </span>for<span class="_ _7"> </span>the<span class="_ _7"> </span>nonsinusoidal<span class="_ _5"> </span>vector<span class="_ _5"> </span>control.<span class="_ _7"> </span>In<span class="_ _7"> </span>addition,<span class="_ _7"> </span>their<span class="_ _7"> </span>gains<span class="_ _5"> </span>are<span class="_ _7"> </span>time-varying<span class="_ _5"> </span>to<span class="_ _7"> </span>minimize</div><div class="t m5 x5 h9 y18 ff1 fs6 fc0 sc0 ls0 ws0">the<span class="_ _8"> </span>chattering.<span class="_ _5"> </span>So,<span class="_ _8"> </span>they<span class="_ _7"> </span>are<span class="_ _7"> </span>adjusted<span class="_ _8"> </span>based<span class="_ _8"> </span>on<span class="_ _7"> </span>internal<span class="_ _7"> </span>states<span class="_ _8"> </span>of<span class="_ _8"> </span>the<span class="_ _7"> </span>super<span class="_ _9"></span>-twisting<span class="_ _8"> </span>algorithm.<span class="_ _8"> </span>The<span class="_ _7"> </span>sta-</div><div class="t m5 x5 h9 y19 ff1 fs6 fc0 sc0 ls0 ws0">bility<span class="_ _6"> </span>analysis<span class="_ _6"> </span>is<span class="_ _6"> </span>investigated<span class="_ _6"> </span>from<span class="_ _6"> </span>the<span class="_ _6"> </span>L<span class="_ _0"></span>yapunov<span class="_ _6"> </span>theory<span class="_ _6"> </span>for<span class="_ _6"> </span>discrete-time<span class="_ _6"> </span>syst<span class="_ _0"></span>ems.<span class="_ _6"> </span>Finally,<span class="_ _6"> </span>simulation<span class="_ _6"> </span>and</div><div class="t m5 x5 h9 y1a ff1 fs6 fc0 sc0 ls0 ws0">experimental<span class="_ _8"> </span>resul<span class="_ _9"></span>ts<span class="_ _8"> </span>are<span class="_ _8"> </span>present<span class="_ _0"></span>ed<span class="_ _8"> </span>to<span class="_ _7"> </span>demonstrate<span class="_ _8"> </span>the<span class="_ _7"> </span>good<span class="_ _8"> </span>performance<span class="_ _8"> </span>and<span class="_ _7"> </span>the<span class="_ _8"> </span>effectiveness<span class="_ _7"> </span>of<span class="_ _8"> </span>the</div><div class="t m5 x5 h9 y1b ff1 fs6 fc0 sc0 ls0 ws0">proposed<span class="_ _7"> </span>observer<span class="_ _9"></span>.</div><div class="t m5 x6 h9 y1c ff3 fs6 fc0 sc0 ls0 ws0">&amp;<span class="_ _7"> </span><span class="ff1">201<span class="_ _2"></span>6<span class="_ _8"> </span>Elsevier<span class="_ _5"> </span>Ltd.<span class="_ _7"> </span>All<span class="_ _8"> </span>rights<span class="_ _5"> </span>reserved.</span></div><div class="t m6 x1 ha y1d ff6 fs7 fc0 sc0 ls0 ws0">1.<span class="_ _b"> </span>Introduction</div><div class="t m6 x7 ha y1e ff1 fs7 fc0 sc0 ls0 ws0">Sensorless<span class="_ _a"> </span>control<span class="_ _8"> </span>of<span class="_ _a"> </span>permanent<span class="_ _a"> </span>magnet<span class="_ _a"> </span>synchronous<span class="_ _a"> </span>motors</div><div class="t m6 x1 ha y1f ff1 fs7 fc0 sc0 ls0 ws0">(PMSMs)<span class="_ _4"> </span>has<span class="_ _4"> </span>been<span class="_ _4"> </span>a<span class="_ _4"> </span>focus<span class="_ _4"> </span>of<span class="_ _4"> </span>intensive<span class="_ _a"> </span>research<span class="_ _4"> </span>during<span class="_ _4"> </span>the<span class="_ _4"> </span>last</div><div class="t m6 x1 ha y20 ff1 fs7 fc0 sc0 ls0 ws0">decades<span class="_ _5"> </span>(<span class="fc1">Betin<span class="_ _5"> </span>et<span class="_ _5"> </span>al.,<span class="_ _7"> </span>201<span class="_ _2"></span>4<span class="fc0">).<span class="_ _5"> </span>The<span class="_ _7"> </span>main<span class="_ _5"> </span>reason<span class="_ _5"> </span>for<span class="_ _5"> </span>this<span class="_ _5"> </span>interest<span class="_ _5"> </span>is<span class="_ _7"> </span>the</span></span></div><div class="t m6 x1 ha y21 ff1 fs7 fc0 sc0 ls0 ws0">elimination<span class="_ _8"> </span>of<span class="_ _8"> </span>rotor<span class="_ _8"> </span>position<span class="_ _8"> </span>or/and<span class="_ _8"> </span>speed<span class="_ _8"> </span>sensors<span class="_ _a"> </span>that<span class="_ _8"> </span>results<span class="_ _8"> </span>in</div><div class="t m6 x1 ha y22 ff1 fs7 fc0 sc0 ls0 ws0">cost<span class="_ _a"> </span>reduction,<span class="_ _4"> </span>increased<span class="_ _4"> </span>robustness<span class="_ _4"> </span>and<span class="_ _a"> </span>compactness<span class="_ _4"> </span>(<span class="fc1">Briz<span class="_ _4"> </span>and</span></div><div class="t m6 x1 ha y23 ff1 fs7 fc1 sc0 ls0 ws0">Degner<span class="_ _9"></span>,<span class="_ _a"> </span>201<span class="_ _2"></span>1<span class="fc0">).<span class="_ _a"> </span>Other<span class="_ _a"> </span>moti<span class="_ _0"></span>vations<span class="_ _8"> </span>result<span class="_ _a"> </span>from<span class="_ _a"> </span>advances<span class="_ _a"> </span>in<span class="_ _8"> </span>power</span></div><div class="t m6 x1 ha y24 ff1 fs7 fc0 sc0 ls0 ws0">electronic<span class="_ _4"> </span>devices<span class="_ _1"> </span>and<span class="_ _4"> </span>in<span class="_ _4"> </span>digital<span class="_ _1"> </span>signal<span class="_ _4"> </span>processors<span class="_ _1"> </span>that<span class="_ _a"> </span>have<span class="_ _4"> </span>al-</div><div class="t m6 x1 ha y25 ff1 fs7 fc0 sc0 ls0 ws0">lowed<span class="_ _a"> </span>product<span class="_ _a"> </span>developers<span class="_ _a"> </span>to<span class="_ _a"> </span>apply<span class="_ _a"> </span>high-performance<span class="_ _4"> </span>sensorless</div><div class="t m6 x1 ha y26 ff1 fs7 fc0 sc0 ls0 ws0">methods<span class="_ _8"> </span>to<span class="_ _5"> </span>low-cost<span class="_ _8"> </span>PMSM<span class="_ _7"> </span>drives<span class="_ _8"> </span>(<span class="fc1">Bose,<span class="_ _7"> </span>20<span class="_ _c"></span>09</span>;<span class="_ _8"> </span><span class="fc1">Pacas,<span class="_ _7"> </span>20<span class="_ _0"></span>1<span class="_ _2"></span>1<span class="fc0">).<span class="_ _8"> </span>As<span class="_ _7"> </span>a</span></span></div><div class="t m6 x1 ha y27 ff1 fs7 fc0 sc0 ls0 ws0">result,<span class="_ _1"> </span>these<span class="_ _4"> </span>motor<span class="_ _4"> </span>drives<span class="_ _1"> </span>hav<span class="_ _0"></span>e<span class="_ _1"> </span>been<span class="_ _4"> </span>widely<span class="_ _4"> </span>adopted<span class="_ _1"> </span>in<span class="_ _4"> </span>manu-</div><div class="t m6 x1 ha y28 ff1 fs7 fc0 sc0 ls0 ws0">facturing<span class="_ _a"> </span>processes<span class="_ _8"> </span>as<span class="_ _a"> </span>well<span class="_ _a"> </span>as<span class="_ _8"> </span>in<span class="_ _a"> </span>large-scale<span class="_ _a"> </span>applications<span class="_ _a"> </span>such<span class="_ _8"> </span>as</div><div class="t m6 x1 ha y29 ff1 fs7 fc0 sc0 ls0 ws0">compressors,<span class="_ _8"> </span>pumps<span class="_ _7"> </span>and<span class="_ _8"> </span>fans<span class="_ _8"> </span>(<span class="fc1">Rahman,<span class="_ _7"> </span>201<span class="_ _2"></span>3<span class="fc0">).</span></span></div><div class="t m6 x7 ha y2a ff1 fs7 fc0 sc0 ls0 ws0">Now<span class="_ _0"></span>adays,<span class="_ _a"> </span>the<span class="_ _4"> </span>sensorless<span class="_ _4"> </span>control<span class="_ _4"> </span>methods<span class="_ _1"> </span>for<span class="_ _a"> </span>PMSM<span class="_ _4"> </span>can<span class="_ _4"> </span>be</div><div class="t m6 x1 ha y2b ff1 fs7 fc0 sc0 ls0 ws0">summarized<span class="_ _4"> </span>in<span class="_ _1"> </span>two<span class="_ _4"> </span>categories<span class="_ _4"> </span>(<span class="fc1">Betin<span class="_ _1"> </span>et<span class="_ _4"> </span>al.,<span class="_ _4"> </span>201<span class="_ _9"></span>4<span class="fc0">;<span class="_ _4"> </span></span>Acarnley<span class="_ _4"> </span>and</span></div><div class="t m6 x1 ha y2c ff1 fs7 fc1 sc0 ls0 ws0">W<span class="_ _9"></span>atson,<span class="_ _8"> </span>20<span class="_ _c"></span>06<span class="fc0">):<span class="_ _8"> </span>fundamental<span class="_ _8"> </span>ex<span class="_ _9"></span>citation<span class="_ _8"> </span>signal<span class="_ _8"> </span>(FES)<span class="_ _8"> </span>and<span class="_ _8"> </span>high-fre-</span></div><div class="t m6 x1 ha y2d ff1 fs7 fc0 sc0 ls0 ws0">quency<span class="_ _8"> </span>signal<span class="_ _a"> </span>injection<span class="_ _8"> </span>(HFSI).<span class="_ _a"> </span>In<span class="_ _8"> </span>the<span class="_ _a"> </span><span class="ff7">&#64257;</span>rst<span class="_ _8"> </span>category<span class="_ _0"></span>,<span class="_ _a"> </span>the<span class="_ _8"> </span>methods</div><div class="t m6 x1 ha y2e ff1 fs7 fc0 sc0 ls0 ws0">are<span class="_ _8"> </span>based<span class="_ _8"> </span>on<span class="_ _8"> </span>the<span class="_ _8"> </span>motor<span class="_ _8"> </span>model,<span class="_ _8"> </span>and<span class="_ _8"> </span>they<span class="_ _8"> </span>can<span class="_ _8"> </span>use<span class="_ _8"> </span>either<span class="_ _8"> </span>reduced-</div><div class="t m6 x1 ha y2f ff1 fs7 fc0 sc0 ls0 ws0">order<span class="_ _5"> </span>or<span class="_ _5"> </span>full-order<span class="_ _7"> </span>observers<span class="_ _5"> </span>for<span class="_ _7"> </span>the<span class="_ _7"> </span>closed-loop<span class="_ _7"> </span>operation.<span class="_ _5"> </span>On<span class="_ _7"> </span>the</div><div class="t m6 x8 ha y30 ff1 fs7 fc0 sc0 ls0 ws0">other<span class="_ _7"> </span>hand,<span class="_ _7"> </span>in<span class="_ _8"> </span>the<span class="_ _7"> </span>second<span class="_ _7"> </span>category<span class="_ _0"></span>,<span class="_ _7"> </span>the<span class="_ _8"> </span>ro<span class="_ _0"></span>tor<span class="_ _7"> </span>position<span class="_ _7"> </span>detection<span class="_ _8"> </span>is</div><div class="t m6 x8 ha y31 ff1 fs7 fc0 sc0 ls0 ws0">achieved<span class="_ _1"> </span>by<span class="_ _4"> </span>exploiting<span class="_ _1"> </span>the<span class="_ _1"> </span>motor<span class="_ _1"> </span>saliences<span class="_ _1"> </span>(i.e.<span class="_ _1"> </span>magnetic<span class="_ _1"> </span>rotor</div><div class="t m6 x8 ha y32 ff1 fs7 fc0 sc0 ls0 ws0">anisotrop<span class="_ _9"></span>y<span class="_ _7"> </span>and/or<span class="_ _7"> </span>magnetic<span class="_ _7"> </span>saturation).<span class="_ _5"> </span>In<span class="_ _7"> </span>this<span class="_ _7"> </span>method,<span class="_ _7"> </span>the<span class="_ _7"> </span>motor</div><div class="t m6 x8 ha y33 ff1 fs7 fc0 sc0 ls0 ws0">control<span class="_ _4"> </span>signals<span class="_ _1"> </span>are<span class="_ _4"> </span>synthesized<span class="_ _1"> </span>superposing<span class="_ _4"> </span>high-frequency<span class="_ _4"> </span>sig-</div><div class="t m6 x8 ha y34 ff1 fs7 fc0 sc0 ls0 ws0">nals<span class="_ _1"> </span>with<span class="_ _3"> </span>the<span class="_ _1"> </span>fundamental<span class="_ _3"> </span>e<span class="_ _9"></span>xcitation<span class="_ _3"> </span>allowing<span class="_ _1"> </span>to<span class="_ _1"> </span>estimate<span class="_ _1"> </span>the</div><div class="t m6 x8 ha y35 ff1 fs7 fc0 sc0 ls0 ws0">rotor<span class="_ _5"> </span>position<span class="_ _7"> </span>even<span class="_ _7"> </span>at<span class="_ _8"> </span>standstill<span class="_ _5"> </span>(<span class="_ _c"></span><span class="fc1">Briz<span class="_ _7"> </span>and<span class="_ _7"> </span>Degner<span class="_ _0"></span>,<span class="_ _7"> </span>201<span class="_ _2"></span>1<span class="fc0">).<span class="_ _5"> </span>Although</span></span></div><div class="t m6 x8 ha y36 ff1 fs7 fc0 sc0 ls0 ws0">FES<span class="_ _7"> </span>methods<span class="_ _8"> </span>ha<span class="_ _0"></span>ve<span class="_ _7"> </span>limitations<span class="_ _8"> </span>to<span class="_ _5"> </span>operate<span class="_ _7"> </span>close<span class="_ _8"> </span>to<span class="_ _5"> </span>zero<span class="_ _8"> </span>speed,<span class="_ _7"> </span>they</div><div class="t m6 x8 ha y37 ff1 fs7 fc0 sc0 ls0 ws0">hav<span class="_ _0"></span>e<span class="_ _4"> </span>been<span class="_ _1"> </span>expansiv<span class="_ _9"></span>ely<span class="_ _1"> </span>used<span class="_ _4"> </span>in<span class="_ _1"> </span>several<span class="_ _a"> </span>applications<span class="_ _1"> </span>that<span class="_ _4"> </span>do<span class="_ _1"> </span>not</div><div class="t m6 x8 ha y38 ff1 fs7 fc0 sc0 ls0 ws0">req<span class="_ _0"></span>uire<span class="_ _8"> </span>v<span class="_ _9"></span>ery<span class="_ _8"> </span>low-speed<span class="_ _7"> </span>operation<span class="_ _8"> </span>or<span class="_ _8"> </span>when<span class="_ _7"> </span>the<span class="_ _8"> </span>rot<span class="_ _9"></span>or<span class="_ _8"> </span>saliences<span class="_ _8"> </span>are</div><div class="t m6 x8 ha y39 ff1 fs7 fc0 sc0 ls0 ws0">inappropriate<span class="_ _7"> </span>for<span class="_ _8"> </span>HFSI<span class="_ _8"> </span>methods<span class="_ _7"> </span>(<span class="fc1">Pacas,<span class="_ _8"> </span>20<span class="_ _0"></span>1<span class="_ _2"></span>1<span class="fc0">).</span></span></div><div class="t m6 x9 ha y3a ff1 fs7 fc0 sc0 ls0 ws0">In<span class="_ _1"> </span>this<span class="_ _1"> </span>regard,<span class="_ _1"> </span>sliding<span class="_ _1"> </span>mode<span class="_ _1"> </span>(SM)<span class="_ _1"> </span>observers<span class="_ _1"> </span>have<span class="_ _1"> </span>become<span class="_ _1"> </span>a</div><div class="t m6 x8 ha y3b ff1 fs7 fc0 sc0 ls0 ws0">promising<span class="_ _8"> </span>alternative<span class="_ _a"> </span>for<span class="_ _8"> </span>FES<span class="_ _a"> </span>methods<span class="_ _a"> </span>applied<span class="_ _8"> </span>to<span class="_ _a"> </span>PMSMs<span class="_ _a"> </span>due<span class="_ _8"> </span>to</div><div class="t m6 x8 ha y3c ff1 fs7 fc0 sc0 ls0 ws0">the<span class="_ _d"> </span>observation<span class="_ _d"> </span>accuracy<span class="_ _3"> </span>and<span class="_ _d"> </span>the<span class="_ _d"> </span>robustness<span class="_ _d"> </span>with<span class="_ _d"> </span>respect<span class="_ _d"> </span>to</div><div class="t m6 x8 ha y3d ff1 fs7 fc0 sc0 ls0 ws0">bounded<span class="_ _3"> </span>disturbances<span class="_ _3"> </span>and<span class="_ _3"> </span>parameter<span class="_ _3"> </span>uncertainties<span class="_ _3"> </span>(<span class="fc1">Bernardes,</span></div><div class="t m6 x8 ha y3e ff1 fs7 fc1 sc0 ls0 ws0">Foletto<span class="_ _a"> </span>Montagner<span class="_ _9"></span>,<span class="_ _a"> </span>Grundling,<span class="_ _4"> </span>and<span class="_ _a"> </span>Pinheiro,<span class="_ _a"> </span>201<span class="_ _2"></span>4<span class="fc0">;<span class="_ _4"> </span></span>Hamida,<span class="_ _a"> </span>Glu-</div><div class="t m6 x8 ha y3f ff1 fs7 fc1 sc0 ls0 ws0">mineau,<span class="_ _3"> </span>and<span class="_ _3"> </span>De<span class="_ _3"> </span>Leon,<span class="_ _3"> </span>20<span class="_ _9"></span>1<span class="_ _9"></span>3<span class="fc0">;<span class="_ _3"> </span></span>Salgado,<span class="_ _3"> </span>Chairez,<span class="_ _3"> </span>Bandyopadh<span class="_ _9"></span>yay<span class="_ _9"></span>,</div><div class="t m6 x8 ha y40 ff1 fs7 fc1 sc0 ls0 ws0">Fridman,<span class="_ _7"> </span>and<span class="_ _7"> </span>Camacho,<span class="_ _8"> </span>20<span class="_ _9"></span>1<span class="_ _9"></span>4<span class="fc0">;<span class="_ _8"> </span></span>Slotine,<span class="_ _5"> </span>Hedrick,<span class="_ _8"> </span>and<span class="_ _7"> </span>Misaw<span class="_ _9"></span>a,<span class="_ _5"> </span>1<span class="_ _9"></span>986<span class="fc0">;</span></div><div class="t m6 x8 ha y41 ff1 fs7 fc1 sc0 ls0 ws0">Y<span class="_ _2"></span>an<span class="_ _a"> </span>and<span class="_ _a"> </span>Utkin,<span class="_ _a"> </span>20<span class="_ _c"></span>02<span class="fc0">).<span class="_ _a"> </span>Howev<span class="_ _9"></span>er,<span class="_ _8"> </span>it<span class="_ _a"> </span>is<span class="_ _a"> </span>well<span class="_ _a"> </span>known<span class="_ _8"> </span>that<span class="_ _a"> </span>the<span class="_ _a"> </span>major</span></div><div class="t m6 x8 ha y42 ff1 fs7 fc0 sc0 ls0 ws0">dra<span class="_ _0"></span>wback<span class="_ _8"> </span>in<span class="_ _7"> </span>SM<span class="_ _8"> </span>approach<span class="_ _7"> </span>is<span class="_ _8"> </span>the<span class="_ _8"> </span>chattering<span class="_ _7"> </span>phenomenon<span class="_ _8"> </span>(<span class="fc1">Levant,</span></div><div class="t m6 x8 ha y43 ff1 fs7 fc1 sc0 ls0 ws0">201<span class="_ _2"></span>0<span class="fc0">).<span class="_ _a"> </span>Thus,<span class="_ _8"> </span><span class="ff7">&#64257;</span>lters<span class="_ _a"> </span>and<span class="_ _8"> </span>continuous<span class="_ _a"> </span>switching<span class="_ _a"> </span>functions<span class="_ _a"> </span>ar<span class="_ _0"></span>e<span class="_ _a"> </span>often</span></div><div class="t m6 x8 ha y44 ff1 fs7 fc0 sc0 ls0 ws0">used<span class="_ _7"> </span>to<span class="_ _8"> </span>mitigate<span class="_ _5"> </span>the<span class="_ _8"> </span>chattering<span class="_ _7"> </span>(<span class="fc1">Hung,<span class="_ _8"> </span>Gao,<span class="_ _7"> </span>and<span class="_ _7"> </span>Hung,<span class="_ _5"> </span>1<span class="_ _9"></span>993<span class="fc0">;<span class="_ _8"> </span></span>Kim,</span></div><div class="t m6 x8 ha y45 ff1 fs7 fc1 sc0 ls0 ws0">Son,<span class="_ _6"> </span>and<span class="_ _5"> </span>Lee,<span class="_ _6"> </span>201<span class="_ _2"></span>1<span class="fc0">;<span class="_ _6"> </span></span>Yuan<span class="_ _6"> </span>et<span class="_ _6"> </span>al.,<span class="_ _5"> </span>20<span class="_ _0"></span>1<span class="_ _9"></span>3<span class="fc0">).<span class="_ _5"> </span>On<span class="_ _6"> </span>the<span class="_ _5"> </span>other<span class="_ _6"> </span>hand,<span class="_ _6"> </span>a<span class="_ _5"> </span>solution</span></div><div class="t m6 x8 ha y46 ff1 fs7 fc0 sc0 ls0 ws0">to<span class="_ _a"> </span>overcome<span class="_ _a"> </span>this<span class="_ _a"> </span>challenge,<span class="_ _a"> </span>without<span class="_ _a"> </span>compromising<span class="_ _a"> </span>the<span class="_ _a"> </span>observa-</div><div class="t m6 x8 ha y47 ff1 fs7 fc0 sc0 ls0 ws0">tion<span class="_ _8"> </span>performance,<span class="_ _a"> </span>is<span class="_ _8"> </span>to<span class="_ _a"> </span>use<span class="_ _8"> </span>high-order<span class="_ _8"> </span>sliding<span class="_ _a"> </span>mode<span class="_ _8"> </span>(HOSM)<span class="_ _a"> </span>ob-</div><div class="t m6 x8 ha y48 ff1 fs7 fc0 sc0 ls0 ws0">servers<span class="_ _a"> </span>(<span class="fc1">Lev<span class="_ _0"></span>ant,<span class="_ _8"> </span>1<span class="_ _2"></span>993<span class="fc0">,<span class="_ _a"> </span></span>20<span class="_ _c"></span>03<span class="fc0">).<span class="_ _a"> </span>HOSM<span class="_ _a"> </span>can<span class="_ _a"> </span>considerably<span class="_ _8"> </span>reduce<span class="_ _a"> </span>the</span></span></div><div class="t m6 x8 ha y49 ff1 fs7 fc0 sc0 ls0 ws0">chattering<span class="_ _4"> </span>keeping<span class="_ _1"> </span>the<span class="_ _1"> </span><span class="ff7">&#64257;</span>rst<span class="_ _4"> </span>order<span class="_ _4"> </span>SM<span class="_ _1"> </span>properties.<span class="_ _1"> </span>How<span class="_ _9"></span>ever<span class="_ _0"></span>,<span class="_ _1"> </span>this</div><div class="t m6 x8 ha y4a ff1 fs7 fc0 sc0 ls0 ws0">approach<span class="_ _8"> </span>r<span class="_ _9"></span>equires<span class="_ _8"> </span>to<span class="_ _7"> </span>determine<span class="_ _8"> </span>the<span class="_ _8"> </span>switching<span class="_ _8"> </span>function<span class="_ _7"> </span>derivative</div><div class="t m6 xa ha y4b ff1 fs7 fc0 sc0 ls0 ws0">Contents<span class="_ _8"> </span>lists<span class="_ _7"> </span>available<span class="_ _7"> </span>at<span class="_ _8"> </span><span class="fc1">ScienceDirect</span></div><div class="t m6 xb hb y4c ff8 fs7 fc0 sc0 ls3 ws0">journal<span class="_ _8"> </span>homepage:<span class="_ _7"> </span><span class="fc1 ls4">www.elsevier.com/locate/conengprac</span></div><div class="t m7 xc hc y4d ff1 fs8 fc0 sc0 ls0 ws0">Control<span class="_ _3"> </span>Engineering<span class="_ _d"> </span>Pr<span class="_ _9"></span>actice</div><div class="t m4 x1 h8 y4e ff1 fs4 fc1 sc0 ls0 ws0">http://dx.doi.org/10.<span class="_ _2"></span>10<span class="_ _9"></span>1<span class="_ _0"></span>6/j.conengprac.201<span class="_ _2"></span>6.0<span class="_ _c"></span>4.003</div><div class="t m4 x1 h8 y4f ff1 fs4 fc0 sc0 ls0 ws0">0967-0661/<span class="ff3">&amp;<span class="_ _5"> </span></span>201<span class="_ _2"></span>6<span class="_ _7"> </span>Elsevier<span class="_ _5"> </span>Ltd.<span class="_ _5"> </span>All<span class="_ _5"> </span>rights<span class="_ _7"> </span>reserved.</div><div class="t m8 xd hd y50 ff9 fs9 fc0 sc0 ls0 ws0">&#9734;</div><div class="t m4 xe h8 y51 ff1 fs4 fc0 sc0 ls0 ws0">This<span class="_ _8"> </span>wor<span class="_ _0"></span>k<span class="_ _8"> </span>w<span class="_ _0"></span>as<span class="_ _8"> </span>supported<span class="_ _7"> </span>in<span class="_ _8"> </span>part<span class="_ _8"> </span>by<span class="_ _7"> </span>Coordination<span class="_ _8"> </span>of<span class="_ _8"> </span>Impro<span class="_ _9"></span>vement<span class="_ _8"> </span>of<span class="_ _8"> </span>Higher</div><div class="t m4 x1 h8 y52 ff1 fs4 fc0 sc0 ls0 ws0">Education<span class="_ _5"> </span>Personnel<span class="_ _5"> </span>(CAPES)<span class="_ _7"> </span>and<span class="_ _5"> </span>by<span class="_ _7"> </span>National<span class="_ _5"> </span>Council<span class="_ _5"> </span>for<span class="_ _7"> </span>Scienti<span class="ff7">&#64257;</span>c<span class="_ _5"> </span>and<span class="_ _7"> </span>T<span class="_ _9"></span>echnolo-</div><div class="t m4 x1 h8 y53 ff1 fs4 fc0 sc0 ls0 ws0">gical<span class="_ _5"> </span>Development<span class="_ _5"> </span>(CNPq).</div><div class="t m9 xd he y54 ff3 fsa fc0 sc0 ls0 ws0">n</div><div class="t m4 xe h8 y55 ff1 fs4 fc0 sc0 ls0 ws0">Corresponding<span class="_ _5"> </span>author<span class="_ _0"></span>.</div><div class="t m4 x7 h6 y56 ff4 fs4 fc0 sc0 ls0 ws0">E-mail<span class="_ _5"> </span>addresses:<span class="_ _5"> </span><span class="ff1 fc1">cassio.baratieri@gmail.com<span class="_ _5"> </span><span class="fc0">(C.L.<span class="_ _7"> </span>Baratieri),</span></span></div><div class="t m4 x1 h8 y57 ff1 fs4 fc1 sc0 ls0 ws0">humberto.ctlab.ufsm.br@gmail.com<span class="_ _5"> </span><span class="fc0">(H.<span class="_ _5"> </span>Pinheiro).</span></div><div class="t m4 xf h8 y58 ff1 fs4 fc1 sc0 ls0 ws0">Control<span class="_ _5"> </span>Engineering<span class="_ _5"> </span>Practice<span class="_ _5"> </span>52<span class="_ _5"> </span>(201<span class="_ _9"></span>6)<span class="_ _7"> </span>59<span class="_"> </span><span class="ffa">&#8211;<span class="_ _c"> </span></span>69</div><a class="l" rel='nofollow' onclick='return false;'><div class="d ma"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d ma"></div></a><a class="l" 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