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Oscillation Mitigation for Sliding-Mode Observers in Sensorless Control of IPMSMs
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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/626773634c65f412596c8308/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/626773634c65f412596c8308/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Oscillation Mitig<span class="_ _0"></span>ation for Sliding<span class="_ _0"></span>-Mode Observers in </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1 ws1">Sensorless Control of IPMSMs</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls2 ws2">Yue Zhao, Wei<span class="_ _0"></span> Qiao </div><div class="t m0 x4 h4 y4 ff1 fs2 fc0 sc0 ls3 ws3">Department<span class="_ _0"></span> of Electrical Engineering </div><div class="t m0 x5 h4 y5 ff1 fs2 fc0 sc0 ls4 ws4">Un<span class="_ _0"></span>ive<span class="_ _0"></span>rsi<span class="_ _0"></span>ty<span class="_ _0"></span> of N<span class="_ _0"></span>ebr<span class="_ _0"></span>ask<span class="_ _0"></span>a-L<span class="_ _0"></span>in<span class="_ _0"></span>coln </div><div class="t m0 x6 h4 y6 ff1 fs2 fc0 sc0 ls5 ws5">Lincol<span class="_ _0"></span>n, NE 68588-<span class="_ _0"></span>0511 US<span class="_ _0"></span>A </div><div class="t m0 x7 h4 y7 ff1 fs2 fc0 sc0 ls6 ws6">yue.zh<span class="_ _0"></span>ao@husk<span class="_ _0"></span>ers.unl<span class="_ _0"></span>.edu; wqi<span class="_ _0"></span>ao@eng<span class="_ _0"></span>r.unl.edu </div><div class="t m0 x8 h3 y3 ff1 fs1 fc0 sc0 ls7 ws7">Long Wu </div><div class="t m0 x9 h4 y4 ff1 fs2 fc0 sc0 ls8 ws8">Pho<span class="_ _1"></span>enix In<span class="_ _1"></span>ter<span class="_ _1"></span>natio<span class="_ _1"></span>nal<span class="_ _1"></span> &#8211; A Jo<span class="_ _1"></span>hn De<span class="_ _1"></span>ere<span class="_ _1"></span> Compa<span class="_ _1"></span>n<span class="_ _1"></span>y </div><div class="t m0 xa h4 y5 ff1 fs2 fc0 sc0 ls9 ws9">1750 NDSU Res<span class="_ _0"></span>earch Park<span class="_ _0"></span> Dr. </div><div class="t m0 xb h4 y6 ff1 fs2 fc0 sc0 lsa wsa">Fargo, ND<span class="_ _0"></span> 58102 USA<span class="_ _0"></span> </div><div class="t m0 xc h4 y7 ff1 fs2 fc0 sc0 lsb ws7">WuLong@JohnDeere.com<span class="fc1 ls7"> </span></div><div class="t m0 xd h4 y8 ff1 fs2 fc0 sc0 ls7 ws7"> </div><div class="t m0 xe h5 y9 ff2 fs3 fc0 sc0 lsc ws7">Abstract<span class="ff3 lsd wsb">&#8212;Bac<span class="_ _1"></span>k electro<span class="_ _1"></span>magnetic force (EMF)-base<span class="_ _1"></span>d methods are<span class="_ _1"></span> </span></div><div class="t m0 xe h5 ya ff3 fs3 fc0 sc0 lse wsc">commonly use<span class="_ _1"></span>d for sens<span class="_ _1"></span>orless co<span class="_ _1"></span>ntrol of inte<span class="_ _1"></span>rior per<span class="_ _1"></span>manent </div><div class="t m0 xe h5 yb ff3 fs3 fc0 sc0 lsf wsd">magne<span class="_ _1"></span>t sy<span class="_ _1"></span>nchr<span class="_ _1"></span>ono<span class="_ _1"></span>us <span class="_ _1"></span>machi<span class="_ _1"></span>nes<span class="_ _1"></span> (IPM<span class="_ _1"></span>SM<span class="_ _1"></span>s) in medi<span class="_ _1"></span>um a<span class="_ _1"></span>nd hi<span class="_ _1"></span>gh </div><div class="t m0 xe h5 yc ff3 fs3 fc0 sc0 lsd wsb">speed range.<span class="_ _1"></span> The featur<span class="_ _1"></span>e of hig<span class="_ _1"></span>h robustness to sy<span class="_ _1"></span>stem struct<span class="_ _1"></span>ure </div><div class="t m0 xe h5 yd ff3 fs3 fc0 sc0 ls10 wse">and pa<span class="_ _1"></span>ra<span class="_ _1"></span>mete<span class="_ _1"></span>r unc<span class="_ _1"></span>ert<span class="_ _1"></span>ainti<span class="_ _1"></span>es<span class="_ _1"></span> ma<span class="_ _1"></span>kes t<span class="_ _1"></span>he sl<span class="_ _1"></span>idi<span class="_ _1"></span>ng-<span class="_ _1"></span>mode <span class="_ _1"></span>obse<span class="_ _1"></span>rver<span class="_ _1"></span> </div><div class="t m0 xe h5 ye ff3 fs3 fc0 sc0 ls11 wsf">(SMO) a promising candidate for rotor <span class="_ _1"></span>position estimation. In a </div><div class="t m0 xe h5 yf ff3 fs3 fc0 sc0 ls12 ws10">practical dri<span class="_ _1"></span>ve system, because of phy<span class="_ _1"></span>sical li<span class="_ _1"></span>m<span class="_ _0"></span>itatio<span class="_ _1"></span>ns, e.g., </div><div class="t m0 xe h5 y10 ff3 fs3 fc0 sc0 ls13 ws11">samplin<span class="_ _0"></span>g frequenc<span class="_ _0"></span>y and com<span class="_ _0"></span>putational resou<span class="_ _0"></span>rce, it is cha<span class="_ _0"></span>llenging </div><div class="t m0 xe h5 y11 ff3 fs3 fc0 sc0 ls14 ws12">to obtain a <span class="_ _1"></span>perfect sinus<span class="_ _1"></span>oidal <span class="_ _1"></span>w<span class="_ _1"></span>aveform for the bac<span class="_ _1"></span>k EMF by<span class="_ _1"></span> a </div><div class="t m0 xe h5 y12 ff3 fs3 fc0 sc0 ls15 ws13">SMO, especiall<span class="_ _1"></span>y in high s<span class="_ _1"></span>peed range.<span class="_ _1"></span> As a result, the r<span class="_ _1"></span>otor </div><div class="t m0 xe h5 y13 ff3 fs3 fc0 sc0 ls16 ws14">position obtained<span class="_ _0"></span> from the estimated back EMF by usin<span class="_ _0"></span>g the </div><div class="t m0 xe h5 y14 ff3 fs3 fc0 sc0 ls17 ws15">trad<span class="_ _0"></span>itional invers<span class="_ _0"></span>e tangen<span class="_ _0"></span>t method<span class="_ _0"></span> will ha<span class="_ _0"></span>ve nonn<span class="_ _0"></span>egligible </div><div class="t m0 xe h5 y15 ff3 fs3 fc0 sc0 ls18 ws16">oscilla<span class="_ _0"></span>tions. This pap<span class="_ _0"></span>er propo<span class="_ _0"></span>ses a nov<span class="_ _0"></span>el algor<span class="_ _0"></span>ithm, which<span class="_ _0"></span> uses </div><div class="t m0 xe h5 y16 ff3 fs3 fc0 sc0 ls19 ws17">the estimated rotor speed as a feedbac<span class="_ _1"></span>k signal wi<span class="_ _1"></span>th th<span class="_ _0"></span>e </div><div class="t m0 xe h5 y17 ff3 fs3 fc0 sc0 ls12 ws18">convention<span class="_ _1"></span>al back EM<span class="_ _1"></span>F-based inve<span class="_ _1"></span>rse ta<span class="_ _1"></span>ngent method t<span class="_ _1"></span>o extract<span class="_ _1"></span> </div><div class="t m0 xe h5 y18 ff3 fs3 fc0 sc0 ls1a ws19">the rotor positio<span class="_ _1"></span>n. The pr<span class="_ _1"></span>oposed alg<span class="_ _1"></span>orith<span class="_ _1"></span>m can effectivel<span class="_ _1"></span>y </div><div class="t m0 xe h5 y19 ff3 fs3 fc0 sc0 ls1b ws1a">mitiga<span class="_ _0"></span>te the o<span class="_ _0"></span>scillation<span class="_ _0"></span> and <span class="_ _0"></span>improve <span class="_ _0"></span>the d<span class="_ _0"></span>ynamic<span class="_ _0"></span> performan<span class="_ _0"></span>ce of </div><div class="t m0 xe h5 y1a ff3 fs3 fc0 sc0 ls15 ws1b">the SMO for rotor position<span class="_ _1"></span> estimation. The prop<span class="_ _1"></span>osed algorit<span class="_ _1"></span>hm is </div><div class="t m0 xe h5 y1b ff3 fs3 fc0 sc0 ls1c ws1c">validat<span class="_ _0"></span>ed by simulation<span class="_ _0"></span>s in MATLAB Sim<span class="_ _0"></span>ulink as <span class="_ _0"></span>well as </div><div class="t m0 xe h5 y1c ff3 fs3 fc0 sc0 ls1d ws1d">experi<span class="_ _1"></span>ments on a high-<span class="_ _1"></span>pow<span class="_ _1"></span>er IPMSM drive syste<span class="_ _1"></span>m. </div><div class="t m0 xe h5 y1d ff2 fs3 fc0 sc0 ls1e ws7">Key<span class="_ _0"></span>words&#8212;<span class="_ _0"></span><span class="ff3 ls1f ws1e">Interi<span class="_ _1"></span>or p<span class="_ _1"></span>erma<span class="_ _1"></span>ne<span class="_ _1"></span>nt <span class="_ _1"></span>magnet s<span class="_ _1"></span>ync<span class="_ _1"></span>hrno<span class="_ _1"></span>us ma<span class="_ _1"></span>chi<span class="_ _1"></span>ne </span></div><div class="t m0 xe h5 y1e ff3 fs3 fc0 sc0 ls20 ws1f">(IPMSM); oscillatio<span class="_ _0"></span>n mitiga<span class="_ _0"></span>tion; sensor<span class="_ _0"></span>less control; slidin<span class="_ _0"></span>g-mode </div><div class="t m0 xe h5 y1f ff3 fs3 fc0 sc0 ls21 ws20">observer (SM<span class="_ _1"></span>O); speed feedback<span class="ff2 ls22 ws7"> </span></div><div class="t m0 xf h4 y20 ff1 fs2 fc0 sc0 ls23 ws7">I.<span class="ff4 ls7"> <span class="_ _2"> </span><span class="ff1">I<span class="fs4 ls24">NTRODUCTION <span class="_ _1"></span></span> </span></span></div><div class="t m0 x10 h4 y21 ff1 fs2 fc0 sc0 ls25 ws21">Elect<span class="_ _0"></span>romech<span class="_ _0"></span>anical<span class="_ _0"></span> senso<span class="_ _0"></span>rs, e.g<span class="_ _0"></span>., resolv<span class="_ _0"></span>ers<span class="_ _0"></span>, optical<span class="_ _0"></span> enco<span class="_ _0"></span>ders<span class="_ _0"></span>, </div><div class="t m0 xe h4 y22 ff1 fs2 fc0 sc0 ls26 ws22">and hall-<span class="_ _0"></span>effe<span class="_ _0"></span>ct sens<span class="_ _0"></span>ors,<span class="_ _0"></span> are <span class="_ _0"></span>comm<span class="_ _0"></span>only u<span class="_ _0"></span>sed to <span class="_ _0"></span>obtain<span class="_ _0"></span> roto<span class="_ _0"></span>r </div><div class="t m0 xe h4 y23 ff1 fs2 fc0 sc0 ls23 ws23">posit<span class="_ _0"></span>ion<span class="_ _0"></span>s/s<span class="_ _0"></span>peeds<span class="_ _0"></span>, w<span class="_ _0"></span>h<span class="_ _0"></span>ich are<span class="_ _0"></span> in<span class="_ _0"></span>dis<span class="_ _0"></span>pensa<span class="_ _0"></span>bl<span class="_ _0"></span>e for h<span class="_ _0"></span>igh<span class="_ _0"></span>-p<span class="_ _0"></span>erf<span class="_ _0"></span>orma<span class="_ _0"></span>nce </div><div class="t m0 xe h4 y24 ff1 fs2 fc0 sc0 ls27 ws24">control<span class="_ _1"></span> of interior per<span class="_ _1"></span>manent magnet synchro<span class="_ _1"></span>nous machines </div><div class="t m0 xe h4 y25 ff1 fs2 fc0 sc0 ls28 ws25">(IPM<span class="_ _1"></span>SMs)<span class="_ _1"></span>. The <span class="_ _1"></span>use of t<span class="_ _1"></span>hese se<span class="_ _1"></span>nsors<span class="_ _1"></span> incre<span class="_ _1"></span>ases co<span class="_ _1"></span>st, s<span class="_ _1"></span>ize and </div><div class="t m0 xe h4 y26 ff1 fs2 fc0 sc0 ls29 ws26">wiring c<span class="_ _1"></span>omplexity of IP<span class="_ _1"></span>MSM dr<span class="_ _1"></span>ive systems. Mo<span class="_ _1"></span>reover, </div><div class="t m0 xe h4 y27 ff1 fs2 fc0 sc0 ls2a ws27">sensors are subj<span class="_ _1"></span>ected to high failure ra<span class="_ _1"></span>tes in harsh </div><div class="t m0 xe h4 y28 ff1 fs2 fc0 sc0 ls2b ws28">enviro<span class="_ _1"></span>nments, such a<span class="_ _1"></span>s high environment te<span class="_ _1"></span>mperature<span class="_ _1"></span>, high-</div><div class="t m0 xe h4 y29 ff1 fs2 fc0 sc0 ls2c ws29">speed op<span class="_ _1"></span>eratio<span class="_ _1"></span>n, and adve<span class="_ _1"></span>rse or hea<span class="_ _1"></span>vy load<span class="_ _1"></span>ing condi<span class="_ _1"></span>tions [1]. </div><div class="t m0 xe h4 y2a ff1 fs2 fc0 sc0 ls2d ws2a">To ove<span class="_ _0"></span>rcom<span class="_ _0"></span>e thes<span class="_ _0"></span>e draw<span class="_ _0"></span>back<span class="_ _0"></span>s, m<span class="_ _0"></span>uch<span class="_ _0"></span> research<span class="_ _0"></span> ef<span class="_ _0"></span>fort h<span class="_ _0"></span>as g<span class="_ _0"></span>one </div><div class="t m0 xe h4 y2b ff1 fs2 fc0 sc0 ls2e ws2b">into the<span class="_ _0"></span> develo<span class="_ _0"></span>pment of<span class="_ _0"></span> sens<span class="_ _0"></span>orless drives<span class="_ _0"></span> that h<span class="_ _0"></span>ave <span class="_ _0"></span>comparab<span class="_ _0"></span>le </div><div class="t m0 xe h4 y2c ff1 fs2 fc0 sc0 ls2f ws2c">or s<span class="_ _0"></span>im<span class="_ _0"></span>ilar<span class="_ _0"></span> dy<span class="_ _0"></span>nam<span class="_ _0"></span>ic p<span class="_ _0"></span>erf<span class="_ _0"></span>orma<span class="_ _0"></span>nce<span class="_ _0"></span> to<span class="_ _0"></span> sens<span class="_ _0"></span>or-<span class="_ _0"></span>base<span class="_ _0"></span>d <span class="_ _0"></span>driv<span class="_ _0"></span>es <span class="_ _0"></span>duri<span class="_ _0"></span>ng<span class="_ _0"></span> </div><div class="t m0 xe h4 y2d ff1 fs2 fc0 sc0 ls30 ws2d">last<span class="_ _0"></span> deca<span class="_ _0"></span>des. A<span class="_ _0"></span>mon<span class="_ _0"></span>g diff<span class="_ _0"></span>eren<span class="_ _0"></span>t r<span class="_ _0"></span>otor<span class="_ _0"></span> posi<span class="_ _0"></span>tion<span class="_ _0"></span>/s<span class="_ _0"></span>peed<span class="_ _0"></span> obse<span class="_ _0"></span>rv<span class="_ _0"></span>ers </div><div class="t m0 xe h4 y2e ff1 fs2 fc0 sc0 ls8 ws2e">used in sensorl<span class="_ _1"></span>ess control schemes, t<span class="_ _1"></span>he sliding-mode<span class="_ _1"></span> observer </div><div class="t m0 xe h4 y2f ff1 fs2 fc0 sc0 ls2a ws2f">(SMO)<span class="_ _1"></span> is a promising ca<span class="_ _1"></span>ndidat<span class="_ _1"></span>e. Gener<span class="_ _1"></span>ally spea<span class="_ _1"></span>king, a SMO is </div><div class="t m0 xe h4 y30 ff1 fs2 fc0 sc0 ls31 ws30">an observ<span class="_ _0"></span>er w<span class="_ _0"></span>hose in<span class="_ _0"></span>put is a <span class="_ _0"></span>discontin<span class="_ _0"></span>uous<span class="_ _0"></span> functi<span class="_ _0"></span>on of<span class="_ _0"></span> the er<span class="_ _0"></span>ror<span class="_ _0"></span> </div><div class="t m0 xe h4 y31 ff1 fs2 fc0 sc0 ls32 ws31">between<span class="_ _0"></span> the<span class="_ _0"></span> estim<span class="_ _0"></span>ated <span class="_ _0"></span>and m<span class="_ _0"></span>easur<span class="_ _0"></span>ed ou<span class="_ _0"></span>tputs<span class="_ _0"></span> [2]<span class="_ _0"></span>. If<span class="_ _0"></span> a s<span class="_ _0"></span>lidi<span class="_ _0"></span>ng-</div><div class="t m0 xe h4 y32 ff1 fs2 fc0 sc0 ls33 ws32">mode mani<span class="_ _1"></span>fold is well de<span class="_ _1"></span>signed and<span class="_ _1"></span> when the state traj<span class="_ _1"></span>ector<span class="_ _1"></span>y </div><div class="t m0 xe h4 y33 ff1 fs2 fc0 sc0 ls34 ws33">reaches<span class="_ _0"></span> the m<span class="_ _0"></span>anif<span class="_ _0"></span>old, the<span class="_ _0"></span> slid<span class="_ _0"></span>ing m<span class="_ _0"></span>ode will b<span class="_ _0"></span>e enf<span class="_ _0"></span>orced. <span class="_ _0"></span>The </div><div class="t m0 xe h4 y34 ff1 fs2 fc0 sc0 ls2b ws34">dynamic be<span class="_ _1"></span>havior o<span class="_ _1"></span>f state trajector<span class="_ _1"></span>y under slidi<span class="_ _1"></span>ng mode only </div><div class="t m0 x11 h4 y35 ff1 fs2 fc0 sc0 ls35 ws35">depen<span class="_ _0"></span>ds<span class="_ _0"></span> on th<span class="_ _0"></span>e sli<span class="_ _0"></span>ding<span class="_ _0"></span> surf<span class="_ _0"></span>ac<span class="_ _0"></span>e and<span class="_ _0"></span> is<span class="_ _0"></span> not af<span class="_ _0"></span>fect<span class="_ _0"></span>ed<span class="_ _0"></span> by sy<span class="_ _0"></span>stem </div><div class="t m0 x11 h4 y36 ff1 fs2 fc0 sc0 ls36 ws36">structu<span class="_ _0"></span>re an<span class="_ _0"></span>d param<span class="_ _0"></span>eter un<span class="_ _0"></span>cert<span class="_ _0"></span>ainty<span class="_ _0"></span>. </div><div class="t m0 x12 h4 y37 ff1 fs2 fc0 sc0 ls37 ws37">Contro<span class="_ _1"></span>l systems with sl<span class="_ _1"></span>iding mode<span class="_ _1"></span> realizat<span class="_ _1"></span>ion are be<span class="_ _1"></span>coming </div><div class="t m0 x11 h4 y38 ff1 fs2 fc0 sc0 ls38 ws38">more<span class="_ _1"></span> and more trac<span class="_ _1"></span>tabl<span class="_ _1"></span>e due to the wide<span class="_ _1"></span>spread us<span class="_ _1"></span>e of digita<span class="_ _1"></span>l </div><div class="t m0 x11 h4 y39 ff1 fs2 fc0 sc0 ls39 ws39">contr<span class="_ _0"></span>ollers<span class="_ _0"></span> ov<span class="_ _0"></span>er the<span class="_ _0"></span> last f<span class="_ _0"></span>ew<span class="_ _0"></span> years<span class="_ _0"></span>. In <span class="_ _0"></span>a dis<span class="_ _0"></span>crete-<span class="_ _0"></span>tim<span class="_ _0"></span>e slidi<span class="_ _0"></span>ng<span class="_ _0"></span>-</div><div class="t m0 x11 h4 y3a ff1 fs2 fc0 sc0 lsa ws3a">mode <span class="_ _0"></span>con<span class="_ _0"></span>tr<span class="_ _0"></span>olle<span class="_ _0"></span>r o<span class="_ _0"></span>r <span class="_ _0"></span>obs<span class="_ _0"></span>erv<span class="_ _0"></span>er,<span class="_ _0"></span> in<span class="_ _0"></span> or<span class="_ _0"></span>der<span class="_ _0"></span> t<span class="_ _0"></span>o fa<span class="_ _0"></span>cili<span class="_ _0"></span>ta<span class="_ _0"></span>te<span class="_ _0"></span> com<span class="_ _0"></span>pu<span class="_ _0"></span>ter-</div><div class="t m0 x11 h4 y3b ff1 fs2 fc0 sc0 ls3a ws3b">based im<span class="_ _0"></span>plem<span class="_ _0"></span>entation,<span class="_ _0"></span> the contro<span class="_ _0"></span>l input<span class="_ _0"></span> is calcul<span class="_ _0"></span>ated<span class="_ _0"></span> once in<span class="_ _0"></span> </div><div class="t m0 x11 h4 y3c ff1 fs2 fc0 sc0 ls3b ws3c">ever<span class="_ _1"></span>y sampling period and is held co<span class="_ _1"></span>nstant during this interva<span class="_ _1"></span>l. </div><div class="t m0 x11 h4 y3d ff1 fs2 fc0 sc0 ls3c ws3d">Beca<span class="_ _1"></span>use of a fini<span class="_ _1"></span>te samp<span class="_ _1"></span>ling freq<span class="_ _1"></span>uency, t<span class="_ _1"></span>he stat<span class="_ _1"></span>e traje<span class="_ _1"></span>ctory is </div><div class="t m0 x11 h4 y3e ff1 fs2 fc0 sc0 ls3d ws3e">unable t<span class="_ _0"></span>o exactly<span class="_ _0"></span> m<span class="_ _0"></span>ove along<span class="_ _0"></span> the sli<span class="_ _0"></span>ding su<span class="_ _0"></span>rfac<span class="_ _0"></span>e, w<span class="_ _0"></span>hich will<span class="_ _0"></span> </div><div class="t m0 x11 h4 y3f ff1 fs2 fc0 sc0 ls3e ws3f">give <span class="_ _0"></span>only a sli<span class="_ _0"></span>ding-lik<span class="_ _0"></span>e <span class="_ _0"></span>or quas<span class="_ _0"></span>i-sliding-<span class="_ _0"></span>mode<span class="_ _0"></span> motion<span class="_ _0"></span> [3],<span class="_ _0"></span> [4]<span class="_ _0"></span>. </div><div class="t m0 x12 h4 y40 ff1 fs2 fc0 sc0 ls3f ws40"> <span class="_ _3"></span>In s<span class="_ _0"></span>everal<span class="_ _0"></span> <span class="_ _0"></span>previou<span class="_ _0"></span>s w<span class="_ _0"></span>ork<span class="_ _0"></span>s, th<span class="_ _0"></span>e SMO h<span class="_ _0"></span>as b<span class="_ _0"></span>een <span class="_ _0"></span>applie<span class="_ _0"></span>d f<span class="_ _0"></span>or<span class="_ _0"></span> </div><div class="t m0 x11 h4 y41 ff1 fs2 fc0 sc0 ls40 ws41">sensorl<span class="_ _1"></span>ess control of PM<span class="_ _1"></span>SM drives [5]-[8]. T<span class="_ _1"></span>he SMO uses a </div><div class="t m0 x11 h4 y42 ff1 fs2 fc0 sc0 ls3e ws3f">discontinu<span class="_ _0"></span>ous c<span class="_ _0"></span>ontrol <span class="_ _0"></span>(i.e<span class="_ _0"></span>., a s<span class="_ _0"></span>witch<span class="_ _0"></span>ing f<span class="_ _0"></span>unction) t<span class="_ _0"></span>o estim<span class="_ _0"></span>ate <span class="_ _0"></span>the </div><div class="t m0 x11 h4 y43 ff1 fs2 fc0 sc0 ls41 ws42">back <span class="_ _0"></span>EMF b<span class="_ _0"></span>ased<span class="_ _0"></span> on<span class="_ _0"></span> the e<span class="_ _0"></span>rro<span class="_ _0"></span>rs of<span class="_ _0"></span> the<span class="_ _0"></span> sta<span class="_ _0"></span>tor cu<span class="_ _0"></span>rr<span class="_ _0"></span>ent es<span class="_ _0"></span>timati<span class="_ _0"></span>on<span class="_ _0"></span>. </div><div class="t m0 x11 h4 y44 ff1 fs2 fc0 sc0 ls42 ws43">However<span class="_ _1"></span>, in these works a<span class="_ _1"></span> high sampling fre<span class="_ _1"></span>quency, e.<span class="_ _1"></span>g., 20 </div><div class="t m0 x11 h4 y45 ff1 fs2 fc0 sc0 ls43 ws44">kHz, is commo<span class="_ _1"></span>nly used, and the spe<span class="_ _1"></span>ed range is not wide </div><div class="t m0 x11 h4 y46 ff1 fs2 fc0 sc0 ls44 ws45">enough.<span class="_ _1"></span> In some pr<span class="_ _1"></span>actica<span class="_ _1"></span>l applica<span class="_ _1"></span>tions, e.g.,<span class="_ _1"></span> the gener<span class="_ _1"></span>ators in </div><div class="t m0 x11 h4 y47 ff1 fs2 fc0 sc0 ls45 ws46">electric<span class="_ _0"></span> vehicles<span class="_ _0"></span>, w<span class="_ _0"></span>hen consi<span class="_ _0"></span>dering<span class="_ _0"></span> the<span class="_ _0"></span> sw<span class="_ _0"></span>itching losses<span class="_ _0"></span>, dri<span class="_ _0"></span>ve </div><div class="t m0 x11 h4 y48 ff1 fs2 fc0 sc0 ls7 ws47">size, an<span class="_ _0"></span>d EMI <span class="_ _0"></span>issues, the<span class="_ _0"></span> PWM f<span class="_ _0"></span>requency<span class="_ _0"></span> w<span class="_ _0"></span>ill be relati<span class="_ _0"></span>vely </div><div class="t m0 x11 h4 y49 ff1 fs2 fc0 sc0 ls26 ws48">lower, n<span class="_ _0"></span>ormally<span class="_ _0"></span> less than<span class="_ _0"></span> 10 k<span class="_ _0"></span>Hz. Low<span class="_ _0"></span> sapling fr<span class="_ _0"></span>equency<span class="_ _0"></span> and<span class="_ _0"></span> </div><div class="t m0 x11 h4 y4a ff1 fs2 fc0 sc0 ls46 ws49">high spee<span class="_ _0"></span>d w<span class="_ _0"></span>ill m<span class="_ _0"></span>ake the<span class="_ _0"></span> app<span class="_ _0"></span>licati<span class="_ _0"></span>on of<span class="_ _0"></span> a dis<span class="_ _0"></span>crete-t<span class="_ _0"></span>ime S<span class="_ _0"></span>MO </div><div class="t m0 x11 h4 y4b ff1 fs2 fc0 sc0 ls3b ws4a">more c<span class="_ _1"></span>hallenging. </div><div class="t m0 x12 h4 y4c ff1 fs2 fc0 sc0 ls47 ws4b">In the app<span class="_ _1"></span>lica<span class="_ _1"></span>tio<span class="_ _1"></span>ns where the bac<span class="_ _1"></span>k EMF i<span class="_ _1"></span>s estimat<span class="_ _1"></span>ed from a </div><div class="t m0 x11 h4 y4d ff1 fs2 fc0 sc0 ls33 ws4c">discre<span class="_ _1"></span>te-ti<span class="_ _1"></span>me SMO using a low sam<span class="_ _0"></span>pli<span class="_ _1"></span>ng freque<span class="_ _1"></span>ncy, the </div><div class="t m0 x11 h4 y4e ff1 fs2 fc0 sc0 ls3e ws4d">waveform<span class="_ _0"></span> of<span class="_ _0"></span> the <span class="_ _0"></span>estimate<span class="_ _0"></span>d <span class="_ _0"></span>back<span class="_ _0"></span> EMF w<span class="_ _0"></span>ill h<span class="_ _0"></span>ave <span class="_ _0"></span>distorti<span class="_ _0"></span>ons, </div><div class="t m0 x11 h4 y4f ff1 fs2 fc0 sc0 ls48 ws4e">which incl<span class="_ _1"></span>ude both pha<span class="_ _1"></span>se shift and magnitud<span class="_ _1"></span>e variat<span class="_ _1"></span>ion. The </div><div class="t m0 x11 h4 y50 ff1 fs2 fc0 sc0 ls45 ws4f">degree <span class="_ _0"></span>of the <span class="_ _0"></span>distorti<span class="_ _0"></span>on w<span class="_ _0"></span>ill becom<span class="_ _0"></span>e larger w<span class="_ _0"></span>hen<span class="_ _0"></span> the sam<span class="_ _0"></span>pling </div><div class="t m0 x11 h4 y51 ff1 fs2 fc0 sc0 ls49 ws50">freq<span class="_ _1"></span>uency decr<span class="_ _1"></span>ea<span class="_ _1"></span>ses. As a result, conve<span class="_ _1"></span>ntiona<span class="_ _1"></span>l angle ex<span class="_ _1"></span>traction </div><div class="t m0 x11 h4 y52 ff1 fs2 fc0 sc0 ls3e ws51">methods,<span class="_ _0"></span> e.g.<span class="_ _0"></span>, the<span class="_ _0"></span> inve<span class="_ _0"></span>rse tan<span class="_ _0"></span>gent m<span class="_ _0"></span>ethod <span class="_ _0"></span>and an<span class="_ _0"></span>gle <span class="_ _0"></span>tracki<span class="_ _0"></span>ng </div><div class="t m0 x11 h4 y53 ff1 fs2 fc0 sc0 ls46 ws52">observer, w<span class="_ _0"></span>ill hav<span class="_ _0"></span>e an <span class="_ _0"></span>oscillati<span class="_ _0"></span>on pro<span class="_ _0"></span>blem, w<span class="_ _0"></span>hich resu<span class="_ _0"></span>lts in<span class="_ _0"></span> </div><div class="t m0 x11 h4 y54 ff1 fs2 fc0 sc0 ls4a ws53">degra<span class="_ _0"></span>dation<span class="_ _0"></span> of the<span class="_ _0"></span> dy<span class="_ _0"></span>nami<span class="_ _0"></span>c perfo<span class="_ _0"></span>rm<span class="_ _0"></span>ance of th<span class="_ _0"></span>e SMO an<span class="_ _0"></span>d lar<span class="_ _0"></span>ge </div><div class="t m0 x11 h4 y55 ff1 fs2 fc0 sc0 ls34 ws54">noise an<span class="_ _0"></span>d err<span class="_ _0"></span>ors in<span class="_ _0"></span> the<span class="_ _0"></span> estim<span class="_ _0"></span>ated rot<span class="_ _0"></span>or <span class="_ _0"></span>position<span class="_ _0"></span>. <span class="_ _0"></span> </div><div class="t m0 x12 h4 y56 ff1 fs2 fc0 sc0 ls2a ws55">This p<span class="_ _1"></span>aper propo<span class="_ _1"></span>ses a <span class="_ _1"></span>novel e<span class="_ _1"></span>stimated <span class="_ _1"></span>speed fe<span class="_ _1"></span>edback </div><div class="t m0 x11 h4 y57 ff1 fs2 fc0 sc0 ls3d ws56">algorithm<span class="_ _0"></span>, w<span class="_ _0"></span>hich will w<span class="_ _0"></span>ork togeth<span class="_ _0"></span>er w<span class="_ _0"></span>ith th<span class="_ _0"></span>e conventi<span class="_ _0"></span>onal<span class="_ _0"></span> </div><div class="t m0 x11 h4 y58 ff1 fs2 fc0 sc0 ls33 ws57">inver<span class="_ _1"></span>se tangent method<span class="_ _1"></span> for rotor po<span class="_ _1"></span>sition extrac<span class="_ _1"></span>tion. This </div><div class="t m0 x11 h4 y59 ff1 fs2 fc0 sc0 ls7 ws47">method w<span class="_ _0"></span>ill h<span class="_ _0"></span>ave a f<span class="_ _0"></span>ilte<span class="_ _0"></span>ring <span class="_ _0"></span>eff<span class="_ _0"></span>ect t<span class="_ _0"></span>o the <span class="_ _0"></span>estim<span class="_ _0"></span>ated <span class="_ _0"></span>position,<span class="_ _0"></span> </div><div class="t m0 x11 h4 y5a ff1 fs2 fc0 sc0 ls4b ws58">and m<span class="_ _0"></span>itigate th<span class="_ _0"></span>e p<span class="_ _0"></span>osition <span class="_ _0"></span>oscillati<span class="_ _0"></span>on cau<span class="_ _0"></span>sed <span class="_ _0"></span>by the<span class="_ _0"></span> low<span class="_ _0"></span> </div><div class="t m0 x11 h4 y5b ff1 fs2 fc0 sc0 ls4c ws59">sampling fre<span class="_ _0"></span>quency. The<span class="_ _0"></span> proposed os<span class="_ _0"></span>cillati<span class="_ _0"></span>on mitig<span class="_ _0"></span>ation </div><div class="t m0 x11 h4 y5c ff1 fs2 fc0 sc0 ls2e ws2b">algorithm<span class="_ _0"></span> is v<span class="_ _0"></span>alidated<span class="_ _0"></span> by<span class="_ _0"></span> simulations<span class="_ _0"></span> in <span class="_ _0"></span>MA<span class="_ _0"></span>TLAB Simulin<span class="_ _0"></span>k as </div><div class="t m0 x11 h4 y5d ff1 fs2 fc0 sc0 ls48 ws5a">well as exper<span class="_ _1"></span>iments on a high-po<span class="_ _1"></span>wer (155 kW) IPMSM drive </div><div class="t m0 x11 h4 y5e ff1 fs2 fc0 sc0 ls4d ws5b">system for<span class="_ _1"></span> off-road hyb<span class="_ _1"></span>rid electri<span class="_ _1"></span>c vehicles<span class="_ _1"></span>. </div><div class="t m0 x10 h6 y5f ff5 fs5 fc0 sc0 ls7 ws7">978-1-4673-1408-4/12/$31.00 &#169;2012 IEEE</div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>
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