ÿþ<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <html> <head> <title>#  -" '!   !  #  -     '/</title> <meta http-equiv="content-type" content="text/html;charset=windows-1251"> <link rel="stylesheet" type="text/css" href="master_style.css"> <meta name="ROBOTS" content="noindex, nofollow"> </head> <body> <h2 align="center"><b>#  -" '!   !  #  -     '/</b></h2> <h4 align="center"><br>Michal MALEK, Pavol MAKYS, Marek STULRAJTER</h4> <h4 align="center">B45;5=85 M;5:B@>B5E=8G5A:8E A8AB5<, #=825@A8B5B Zilina, Univerzitna 1, 010 26 Zilina, !;>20:8O</h4> <hr> <p><b>AB>G=8:</b>:POWER ENGINEERING AND ELECTRICAL ENGINEERING, VOL. 9, NO. 1</p> <hr> <p align="left"> 57N<5:  =0AB>OI55 2@5<O, ACI5AB2C5B =5A:>;L:> ?@8<5=5=89 2 >1;0AB8 M;5:B@>?@82>4>2 ?>;>65=8O, B0:8E :0: 2KA>:>A:>@>AB=>9 @57, 345 B@048F8>==K5 :0A:04=K5 AB@C:BC@K C?@02;5=8O >15A?5G820NB =54>AB0B>G=CN B>G=>ABL. >MB><C, 1K205B F5;5A>>1@07=> 87<5=8BL AB@C:BC@C C?@02;5=8O (=0?@8<5@, A?>A>1 A:>;L7OI53> C?@02;5=8O sliding mode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p> <p align="left"> ;NG52K5 A;>20 @54C?@02;5=85, A5@2>?@82>4, B>G=>ABL.</p> <p align="left"> -B0 AB0BLO - G0ABL ?>;=>9 B5<K ?>4 =0720=85< #?@02;5=85 -;5:B@8G5A:8<8 2830B5;O<8 A @54C?@02;5=85<. -B> B5<0B8G5A:8 A2O70=> A> AB0BL59 ?>4 =0720=85< 2545=85 2 #?@02;5=85 -;5:B@8G5A:8<8 2830B5;O<8 A @54C?@02;5=85< [1]. ;02=0O F5;L MB>9 AB0BL8 A>AB>8B 2 B><, GB>1K ?>:070BL, :0: 8A?>;L7>20BL A0<K5 >1I85 AB@C:BC@K 2 >1;0AB8 :><<5@G5A:8E M;5:B@8G5A:8E 42830B5;59, 8E >A>15==>AB8 8 2>7<>6=>AB8 =0AB@>9:8. K45;5= @0745;, >?8AK20NI89 >3@0=8G5=8O, :>B>@K5 <>3CB ?>O28BLAO ?@8 @50;870F88 M;5:B@8G5A:8E ?@82>4>2.  :>=F5 ?>:070=K 284K =5:>B>@KE 4@C38E <5B>4>2 ?@54C?@02;5=8O.</p> <p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p> <img src="images/ris0-1.gif" border="0" hspace="10" vspace="10"> (1)<br> <p>A AC<<0@=>9 >H81:>9 (2).</p> <img src="images/ris0-2.gif" border="0" hspace="10" vspace="10"> (2)<br> <img src="images/ris-1.gif" border="0" hspace="10" vspace="10"><br> <p align="left"> 8AC=>: 1  !B@C:BC@=0O AE5<0 C?@02;5=8O ?>;>65=85< A ?@54C?@02;5=85< ?> A:>@>AB8 8 CA:>@5=8N</p> <p align="left"> 0: MB> <>65B 1KBL 70<5G5=> ?> 2K@065=8N 1, CA8;5=85 ?@54C?@02;5=8O ?> A:>@>AB8 KFFÉ <>65B ?>2;8OBL =0 CA8;5=85 ?@54C?@02;5=8O ?> CA:>@5=8N KFFµ. @8=8<0O 548=8G=>5 CA8;5=85 KFFÉ, CA8;5=85 :>=BC@0 CA:>@5=8O KFFµ 1C45B @02=> J (<><5=B 8=5@F88).</p> <p align="left"> >?@>A - B>, :0: >= 70B@>=5B >H81:C, =01;N405<C1 2 AB@C:BC@5 A ?@54C?@02;5=85< ?> A:>@>AB8. B25B ?@54>AB028B <>45;8@>20=85, ?@>2545==>5 A>3;0A=> 1;>:-AE5<5 8A. 1. A5 2>7<>6=K5 2>7459AB28O ?@>8;;NAB@8@>20=K =0 8A. 2. 0<5G5=>, GB> =5>1E>48<>5 ;8=59=>5 C25;8G5=85 A:>@>AB8 A;54C5B 70 AB@C:BC@>9 157 ;N1>3> ?@54C?@02;5=8O A ?>AB>O==>9 7045@6:>9. 2545=85 ?@54C?@02;5=8O ?> A:>@>AB8 ?@82>48B : 0==C;8@>20=8N 7045@6:8, => =0?@>B82 ?@>8AE>48B ?5@5@53C;8@>20=85. -B> ?@>8AE>48B 87-70 =5A>25@H5==>3> ?@>A;56820=8O CA:>@5=8O, :>B>@>5 @02=> =C;N, :>340 A:>@>ABL 7040=8O 4>AB8305B CAB>9G82>3> A>AB>O=8O. >A;5 22545=8O ?@54C?@02;5=8O ?> CA:>@5=8N 2KH5C?><O=CB>5 =565;0B5;L=>5 ?5@5@53C;8@>20=85 C<5=LH5=> 4> <8=8<C<0.  MB>< A;CG05 A:>@>ABL =0@0AB05B 157 ?>AB>O==>9 7045@6:8 B0: 65 :0: 157 ?5@5@53C;8@>20=8O.</p> <p align="left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p> <img src="images/ris-2.gif" border="0" hspace="10" vspace="10"><br> <p align="left"> 8AC=>: 2  5@5E>4=K5 ?@>F5AAK ?> A:>@>AB8 ?@8 @53C;8@>20=88 ?>;>65=8O A  @53C;OB>@>< A:>@>AB8 2 @07;8G=KE @568<0E.</p> <p align="left"> ">340 7040=8O A:>@>AB8 8 ?>;>65=8O ?@>AB> 2KG8A;5=K ?CB5< 8=B53@8@>20=8O 7040=8O CA:>@5=8O.</p> <p align="left">  >1I5<, G5< 2KH5 ?>@O4>: ?@54C?@02;5=8O 8 @07<5@ 25:B>@0 7040=8O :8=5<0B8G5A:8E ?5@5<5==KE A2O70==KE A ?@54C?@02;5=85<, B5< =865 ?@8ACBAB285 2KA>:8E G0AB>B 2 2KE>4=>< A83=0;5 8 A;54>20B5;L=> A83=0;5 >H81:8, :>B>@K5 >:07K20NB ?>;>68B5;L=>5 2;8O=85 =0 ?5@5E>4=CN DC=:F8N A8AB5<K.</p> <p align="left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p> <img src="images/ris-3.gif" border="0" hspace="10" vspace="10"><br> <p align="left"> 8AC=>: 3  !B@C:BC@=0O AE5<0 C?@02;5=8O ?>;>65=85< A ?@54C?@02;5=85< 8 PDF @53C;OB>@>< A:>@>AB8</p> <p align="left">5@540B>G=0O DC=:F8O, 4;O AE5<K =0 8A. 3. 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MB>9 AB0BL5 1K;0 ?>AB02;5=0 F5;L 8AA;54>20BL =5:>B>@K5 D0:BK >B=>A8B5;L=> 25B259 ?@54C?@02;5=8O, 8A?>;L7C5<KE 2 :><<5@G5A:8E ?@82>40E. #:070=>, GB> =C6=> CG8BK20BL 8 GB> ?>4;568B @0AA<>B@5=8N ?@8 ?@>5:B8@>20=88 A8AB5<K ?@82>40 A 25B2O<8 ?@54C?@02;5=8O (MB> - ?@82>4 ?>78F8>=8@>20=8O A 2KA>:>9 B>G=>ABLN), 345 =5 B>;L:> ?>;>65=85, => B0:65 8 53> ?@>872>4=K5 2K=C645=K A;54>20BL 70 7040==K<8 25;8G8=0<8. 0AA<>B@5=85 ?5@5<5==KE >H81:8 >AB02;5=> 4;O 4@C38E ?C1;8:0F89. </p> <h4>8B5@0BC@0</h4> <ol> <li>MALEK, M., MAKYS, P., STULRAJTER, M.: An introduction to feedforward control of Electrical Drives [in slovak], AEEE, 2010, Vol.8, No.3.</li> <li>KALAS, V.: Servomechanizmy a automatizované pohony I, Edicne stredisko SVST, Bratislava, 1974.</li> <li>PHELAN, R.M.: Pseudo-Derivative Feedback (PDF) Control, UCRL - 51036, University of California, Lawrence Livermore Laboratory, 1971.</li> <li>DODDS, S. J., VITTEK, J.: Robust Position Control with Induction Motor, EPE-EMC, September 2000, Kosice, vol. 6, s.35-40.</li> <li>,M.: Position control of a servodrive with permanent magnet synchronous motor with direct torque and flux control, Dissertation work, University of Zilina, 2008.</li> </ol> </body> </html>