{\rtf1\adeflang1025\ansi\ansicpg1250\uc1\adeff0\deff0\stshfdbch0\stshfloch0\stshfhich0\stshfbi0\deflang1029\deflangfe1029\themelang1029\themelangfe0\themelangcs0{\fonttbl{\f0\fbidi \froman\fcharset238\fprq2{\*\panose 02020603050405020304}Times New Roman{\*\falt Times New Roman};}
{\f1\fbidi \fswiss\fcharset238\fprq2{\*\panose 020b0604020202020204}Arial;}{\f3\fbidi \froman\fcharset2\fprq2{\*\panose 05050102010706020507}Symbol;}{\f34\fbidi \froman\fcharset238\fprq2{\*\panose 02040503050406030204}Cambria Math;}
{\f36\fbidi \froman\fcharset238\fprq2{\*\panose 02040503050406030204}Cambria;}{\f37\fbidi \fswiss\fcharset238\fprq2{\*\panose 020f0502020204030204}Calibri;}{\f38\fbidi \fswiss\fcharset238\fprq2{\*\panose 020b0604030504040204}Tahoma;}
{\flomajor\f31500\fbidi \froman\fcharset238\fprq2{\*\panose 02020603050405020304}Times New Roman{\*\falt Times New Roman};}{\fdbmajor\f31501\fbidi \froman\fcharset238\fprq2{\*\panose 02020603050405020304}Times New Roman{\*\falt Times New Roman};}
{\fhimajor\f31502\fbidi \froman\fcharset238\fprq2{\*\panose 02040503050406030204}Cambria;}{\fbimajor\f31503\fbidi \froman\fcharset238\fprq2{\*\panose 02020603050405020304}Times New Roman{\*\falt Times New Roman};}
{\flominor\f31504\fbidi \froman\fcharset238\fprq2{\*\panose 02020603050405020304}Times New Roman{\*\falt Times New Roman};}{\fdbminor\f31505\fbidi \froman\fcharset238\fprq2{\*\panose 02020603050405020304}Times New Roman{\*\falt Times New Roman};}
{\fhiminor\f31506\fbidi \fswiss\fcharset238\fprq2{\*\panose 020f0502020204030204}Calibri;}{\fbiminor\f31507\fbidi \froman\fcharset238\fprq2{\*\panose 02020603050405020304}Times New Roman{\*\falt Times New Roman};}
{\f301\fbidi \froman\fcharset0\fprq2 Times New Roman{\*\falt Times New Roman};}{\f300\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr{\*\falt Times New Roman};}{\f302\fbidi \froman\fcharset161\fprq2 Times New Roman Greek{\*\falt Times New Roman};}
{\f303\fbidi \froman\fcharset162\fprq2 Times New Roman Tur{\*\falt Times New Roman};}{\f304\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew){\*\falt Times New Roman};}
{\f305\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic){\*\falt Times New Roman};}{\f306\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic{\*\falt Times New Roman};}
{\f307\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese){\*\falt Times New Roman};}{\f311\fbidi \fswiss\fcharset0\fprq2 Arial;}{\f310\fbidi \fswiss\fcharset204\fprq2 Arial Cyr;}{\f312\fbidi \fswiss\fcharset161\fprq2 Arial Greek;}
{\f313\fbidi \fswiss\fcharset162\fprq2 Arial Tur;}{\f314\fbidi \fswiss\fcharset177\fprq2 Arial (Hebrew);}{\f315\fbidi \fswiss\fcharset178\fprq2 Arial (Arabic);}{\f316\fbidi \fswiss\fcharset186\fprq2 Arial Baltic;}
{\f317\fbidi \fswiss\fcharset163\fprq2 Arial (Vietnamese);}{\f641\fbidi \froman\fcharset0\fprq2 Cambria Math;}{\f640\fbidi \froman\fcharset204\fprq2 Cambria Math Cyr;}{\f642\fbidi \froman\fcharset161\fprq2 Cambria Math Greek;}
{\f643\fbidi \froman\fcharset162\fprq2 Cambria Math Tur;}{\f646\fbidi \froman\fcharset186\fprq2 Cambria Math Baltic;}{\f647\fbidi \froman\fcharset163\fprq2 Cambria Math (Vietnamese);}{\f661\fbidi \froman\fcharset0\fprq2 Cambria;}
{\f660\fbidi \froman\fcharset204\fprq2 Cambria Cyr;}{\f662\fbidi \froman\fcharset161\fprq2 Cambria Greek;}{\f663\fbidi \froman\fcharset162\fprq2 Cambria Tur;}{\f666\fbidi \froman\fcharset186\fprq2 Cambria Baltic;}
{\f667\fbidi \froman\fcharset163\fprq2 Cambria (Vietnamese);}{\f671\fbidi \fswiss\fcharset0\fprq2 Calibri;}{\f670\fbidi \fswiss\fcharset204\fprq2 Calibri Cyr;}{\f672\fbidi \fswiss\fcharset161\fprq2 Calibri Greek;}
{\f673\fbidi \fswiss\fcharset162\fprq2 Calibri Tur;}{\f676\fbidi \fswiss\fcharset186\fprq2 Calibri Baltic;}{\f677\fbidi \fswiss\fcharset163\fprq2 Calibri (Vietnamese);}{\f681\fbidi \fswiss\fcharset0\fprq2 Tahoma;}
{\f680\fbidi \fswiss\fcharset204\fprq2 Tahoma Cyr;}{\f682\fbidi \fswiss\fcharset161\fprq2 Tahoma Greek;}{\f683\fbidi \fswiss\fcharset162\fprq2 Tahoma Tur;}{\f684\fbidi \fswiss\fcharset177\fprq2 Tahoma (Hebrew);}
{\f685\fbidi \fswiss\fcharset178\fprq2 Tahoma (Arabic);}{\f686\fbidi \fswiss\fcharset186\fprq2 Tahoma Baltic;}{\f687\fbidi \fswiss\fcharset163\fprq2 Tahoma (Vietnamese);}{\f688\fbidi \fswiss\fcharset222\fprq2 Tahoma (Thai);}
{\flomajor\f31510\fbidi \froman\fcharset0\fprq2 Times New Roman{\*\falt Times New Roman};}{\flomajor\f31509\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr{\*\falt Times New Roman};}
{\flomajor\f31511\fbidi \froman\fcharset161\fprq2 Times New Roman Greek{\*\falt Times New Roman};}{\flomajor\f31512\fbidi \froman\fcharset162\fprq2 Times New Roman Tur{\*\falt Times New Roman};}
{\flomajor\f31513\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew){\*\falt Times New Roman};}{\flomajor\f31514\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic){\*\falt Times New Roman};}
{\flomajor\f31515\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic{\*\falt Times New Roman};}{\flomajor\f31516\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese){\*\falt Times New Roman};}
{\fdbmajor\f31520\fbidi \froman\fcharset0\fprq2 Times New Roman{\*\falt Times New Roman};}{\fdbmajor\f31519\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr{\*\falt Times New Roman};}
{\fdbmajor\f31521\fbidi \froman\fcharset161\fprq2 Times New Roman Greek{\*\falt Times New Roman};}{\fdbmajor\f31522\fbidi \froman\fcharset162\fprq2 Times New Roman Tur{\*\falt Times New Roman};}
{\fdbmajor\f31523\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew){\*\falt Times New Roman};}{\fdbmajor\f31524\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic){\*\falt Times New Roman};}
{\fdbmajor\f31525\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic{\*\falt Times New Roman};}{\fdbmajor\f31526\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese){\*\falt Times New Roman};}
{\fhimajor\f31530\fbidi \froman\fcharset0\fprq2 Cambria;}{\fhimajor\f31529\fbidi \froman\fcharset204\fprq2 Cambria Cyr;}{\fhimajor\f31531\fbidi \froman\fcharset161\fprq2 Cambria Greek;}{\fhimajor\f31532\fbidi \froman\fcharset162\fprq2 Cambria Tur;}
{\fhimajor\f31535\fbidi \froman\fcharset186\fprq2 Cambria Baltic;}{\fhimajor\f31536\fbidi \froman\fcharset163\fprq2 Cambria (Vietnamese);}{\fbimajor\f31540\fbidi \froman\fcharset0\fprq2 Times New Roman{\*\falt Times New Roman};}
{\fbimajor\f31539\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr{\*\falt Times New Roman};}{\fbimajor\f31541\fbidi \froman\fcharset161\fprq2 Times New Roman Greek{\*\falt Times New Roman};}
{\fbimajor\f31542\fbidi \froman\fcharset162\fprq2 Times New Roman Tur{\*\falt Times New Roman};}{\fbimajor\f31543\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew){\*\falt Times New Roman};}
{\fbimajor\f31544\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic){\*\falt Times New Roman};}{\fbimajor\f31545\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic{\*\falt Times New Roman};}
{\fbimajor\f31546\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese){\*\falt Times New Roman};}{\flominor\f31550\fbidi \froman\fcharset0\fprq2 Times New Roman{\*\falt Times New Roman};}
{\flominor\f31549\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr{\*\falt Times New Roman};}{\flominor\f31551\fbidi \froman\fcharset161\fprq2 Times New Roman Greek{\*\falt Times New Roman};}
{\flominor\f31552\fbidi \froman\fcharset162\fprq2 Times New Roman Tur{\*\falt Times New Roman};}{\flominor\f31553\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew){\*\falt Times New Roman};}
{\flominor\f31554\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic){\*\falt Times New Roman};}{\flominor\f31555\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic{\*\falt Times New Roman};}
{\flominor\f31556\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese){\*\falt Times New Roman};}{\fdbminor\f31560\fbidi \froman\fcharset0\fprq2 Times New Roman{\*\falt Times New Roman};}
{\fdbminor\f31559\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr{\*\falt Times New Roman};}{\fdbminor\f31561\fbidi \froman\fcharset161\fprq2 Times New Roman Greek{\*\falt Times New Roman};}
{\fdbminor\f31562\fbidi \froman\fcharset162\fprq2 Times New Roman Tur{\*\falt Times New Roman};}{\fdbminor\f31563\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew){\*\falt Times New Roman};}
{\fdbminor\f31564\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic){\*\falt Times New Roman};}{\fdbminor\f31565\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic{\*\falt Times New Roman};}
{\fdbminor\f31566\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese){\*\falt Times New Roman};}{\fhiminor\f31570\fbidi \fswiss\fcharset0\fprq2 Calibri;}{\fhiminor\f31569\fbidi \fswiss\fcharset204\fprq2 Calibri Cyr;}
{\fhiminor\f31571\fbidi \fswiss\fcharset161\fprq2 Calibri Greek;}{\fhiminor\f31572\fbidi \fswiss\fcharset162\fprq2 Calibri Tur;}{\fhiminor\f31575\fbidi \fswiss\fcharset186\fprq2 Calibri Baltic;}
{\fhiminor\f31576\fbidi \fswiss\fcharset163\fprq2 Calibri (Vietnamese);}{\fbiminor\f31580\fbidi \froman\fcharset0\fprq2 Times New Roman{\*\falt Times New Roman};}
{\fbiminor\f31579\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr{\*\falt Times New Roman};}{\fbiminor\f31581\fbidi \froman\fcharset161\fprq2 Times New Roman Greek{\*\falt Times New Roman};}
{\fbiminor\f31582\fbidi \froman\fcharset162\fprq2 Times New Roman Tur{\*\falt Times New Roman};}{\fbiminor\f31583\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew){\*\falt Times New Roman};}
{\fbiminor\f31584\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic){\*\falt Times New Roman};}{\fbiminor\f31585\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic{\*\falt Times New Roman};}
{\fbiminor\f31586\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese){\*\falt Times New Roman};}}{\colortbl;\red0\green0\blue0;\red0\green0\blue255;\red0\green255\blue255;\red0\green255\blue0;\red255\green0\blue255;\red255\green0\blue0;
\red255\green255\blue0;\red255\green255\blue255;\red0\green0\blue128;\red0\green128\blue128;\red0\green128\blue0;\red128\green0\blue128;\red128\green0\blue0;\red128\green128\blue0;\red128\green128\blue128;\red192\green192\blue192;}{\*\defchp \fs22 }
{\*\defpap \ql \li0\ri0\sa200\sl276\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 }\noqfpromote {\stylesheet{\qj \li0\ri0\sb240\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 
\af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang2057\langfe1032\cgrid\langnp2057\langfenp1032 \snext0 \sqformat \spriority0 Normal;}{\s1\qj \li0\ri0\sb240\sl360\slmult1
\keepn\widctlpar\wrapdefault\aspalpha\aspnum\faauto\outlinelevel0\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang1033\langfe1032\cgrid\langnp1033\langfenp1032 \sbasedon0 \snext0 \slink15 \sqformat heading 1;}{
\s2\qc \li0\ri0\sb240\keepn\widctlpar\wrapdefault\aspalpha\aspnum\faauto\outlinelevel1\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang1033\langfe1032\cgrid\langnp1033\langfenp1032 \sbasedon0 \snext0 \slink16 \sqformat 
heading 2;}{\s3\qc \li0\ri0\sb240\keepn\widctlpar\wrapdefault\aspalpha\aspnum\faauto\outlinelevel2\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \ab\af0\afs24\alang1025 \ltrch\fcs0 \b\fs24\lang1033\langfe1032\cgrid\langnp1033\langfenp1032 
\sbasedon0 \snext0 \slink17 \sqformat heading 3;}{\s4\qc \li0\ri0\sb240\sl360\slmult1\keepn\widctlpar\wrapdefault\aspalpha\aspnum\faauto\outlinelevel3\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \ai\af0\afs24\alang1025 \ltrch\fcs0 
\i\fs24\lang1033\langfe1032\cgrid\langnp1033\langfenp1032 \sbasedon0 \snext0 \slink18 \sqformat heading 4;}{\s5\qc \li0\ri0\sb240\sl360\slmult1\keepn\widctlpar\wrapdefault\aspalpha\aspnum\faauto\outlinelevel4\adjustright\rin0\lin0\itap0 \rtlch\fcs1 
\ai\af0\afs24\alang1025 \ltrch\fcs0 \i\fs24\lang1033\langfe1032\cgrid\langnp1033\langfenp1032 \sbasedon0 \snext0 \slink19 \sqformat heading 5;}{\s6\qj \li0\ri0\sb120\sl480\slmult1
\keepn\widctlpar\wrapdefault\aspalpha\aspnum\faauto\outlinelevel5\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \ab\af0\afs24\alang1025 \ltrch\fcs0 \b\fs24\lang1033\langfe1032\cgrid\langnp1033\langfenp1032 \sbasedon0 \snext0 \slink20 \sqformat heading 6;}{
\s7\ql \li0\ri0\keepn\widctlpar\wrapdefault\aspalpha\aspnum\faauto\outlinelevel6\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \ai\af0\afs20\alang1025 \ltrch\fcs0 \i\fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 \sbasedon0 \snext0 \slink21 \sqformat 
heading 7;}{\s8\qj \li0\ri0\sb240\sa60\widctlpar\wrapdefault\aspalpha\aspnum\faauto\outlinelevel7\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \ai\af1\afs24\alang1025 \ltrch\fcs0 \i\f1\fs24\lang2057\langfe1032\cgrid\langnp2057\langfenp1032 
\sbasedon0 \snext0 \slink22 \sqformat heading 8;}{\s9\ql \li0\ri0\keepn\widctlpar\wrapdefault\aspalpha\aspnum\faauto\outlinelevel8\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \ai\af0\afs20\alang1025 \ltrch\fcs0 
\i\fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 \sbasedon0 \snext0 \slink23 \sqformat heading 9;}{\*\cs10 \additive \ssemihidden Default Paragraph Font;}{\*
\ts11\tsrowd\trftsWidthB3\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\trcbpat1\trcfpat1\tblind0\tblindtype3\tsvertalt\tsbrdrt\tsbrdrl\tsbrdrb\tsbrdrr\tsbrdrdgl\tsbrdrdgr\tsbrdrh\tsbrdrv \ql \li0\ri0\sa200\sl276\slmult1
\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \fs22\lang1029\langfe1029\cgrid\langnp1029\langfenp1029 \snext11 \ssemihidden \sunhideused Normal Table;}{\*\cs15 \additive \rtlch\fcs1 
\ab\af36\afs32 \ltrch\fcs0 \b\f36\fs32\lang2057\langfe0\kerning32\langnp2057\langfenp0 \sbasedon10 \slink1 \slocked Nadpis 1 Char;}{\*\cs16 \additive \rtlch\fcs1 \ab\ai\af36\afs28 \ltrch\fcs0 \b\i\f36\fs28\lang2057\langfe0\langnp2057\langfenp0 
\sbasedon10 \slink2 \slocked \ssemihidden Nadpis 2 Char;}{\*\cs17 \additive \rtlch\fcs1 \ab\af36\afs26 \ltrch\fcs0 \b\f36\fs26\lang2057\langfe0\langnp2057\langfenp0 \sbasedon10 \slink3 \slocked \ssemihidden Nadpis 3 Char;}{\*\cs18 \additive \rtlch\fcs1 
\ab\af37\afs28 \ltrch\fcs0 \b\f37\fs28\lang2057\langfe0\langnp2057\langfenp0 \sbasedon10 \slink4 \slocked \ssemihidden Nadpis 4 Char;}{\*\cs19 \additive \rtlch\fcs1 \ab\ai\af37\afs26 \ltrch\fcs0 \b\i\f37\fs26\lang2057\langfe0\langnp2057\langfenp0 
\sbasedon10 \slink5 \slocked \ssemihidden Nadpis 5 Char;}{\*\cs20 \additive \rtlch\fcs1 \ab\af37 \ltrch\fcs0 \b\f37\lang2057\langfe0\langnp2057\langfenp0 \sbasedon10 \slink6 \slocked \ssemihidden Nadpis 6 Char;}{\*\cs21 \additive \rtlch\fcs1 \af37\afs24 
\ltrch\fcs0 \f37\fs24\lang2057\langfe0\langnp2057\langfenp0 \sbasedon10 \slink7 \slocked \ssemihidden Nadpis 7 Char;}{\*\cs22 \additive \rtlch\fcs1 \ai\af37\afs24 \ltrch\fcs0 \i\f37\fs24\lang2057\langfe0\langnp2057\langfenp0 
\sbasedon10 \slink8 \slocked \ssemihidden Nadpis 8 Char;}{\*\cs23 \additive \rtlch\fcs1 \af36 \ltrch\fcs0 \f36\lang2057\langfe0\langnp2057\langfenp0 \sbasedon10 \slink9 \slocked \ssemihidden Nadpis 9 Char;}{\s24\qj \li0\ri0\sb120\sl480\slmult1
\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang2057\langfe1032\cgrid\langnp2057\langfenp1032 \sbasedon0 \snext24 \slink25 Body Text 3;}{\*\cs25 \additive \rtlch\fcs1 
\af0\afs16 \ltrch\fcs0 \fs16\lang2057\langfe0\langnp2057\langfenp0 \sbasedon10 \slink24 \slocked \ssemihidden Z\'e1kladn\'ed text 3 Char;}{\s26\qc \li0\ri0\sb240\sl360\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 
\rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang1033\langfe1032\cgrid\langnp1033\langfenp1032 \sbasedon0 \snext0 \sqformat caption;}{\s27\qj \fi-283\li283\ri0\sb60\sa60\sl360\slmult1
\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin283\itap0 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang1033\langfe1032\cgrid\langnp1033\langfenp1032 \sbasedon0 \snext27 \sautoupd List Bullet;}{
\s28\qj \li0\ri0\sb240\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang1033\langfe1032\cgrid\langnp1033\langfenp1032 \sbasedon0 \snext28 \slink29 Body Text;}{\*\cs29 
\additive \rtlch\fcs1 \af0\afs24 \ltrch\fcs0 \fs24\lang2057\langfe0\langnp2057\langfenp0 \sbasedon10 \slink28 \slocked \ssemihidden Z\'e1kladn\'ed text Char;}{
\s30\qj \fi-1418\li0\ri0\sb120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang2057\langfe1032\cgrid\langnp2057\langfenp1032 \sbasedon0 \snext30 \slink31 Body Text 2;}{\*
\cs31 \additive \rtlch\fcs1 \af0\afs24 \ltrch\fcs0 \fs24\lang2057\langfe0\langnp2057\langfenp0 \sbasedon10 \slink30 \slocked \ssemihidden Z\'e1kladn\'ed text 2 Char;}{\s32\qc \li0\ri0\sb240\sl480\slmult1
\widctlpar\wrapdefault\hyphpar0\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \ab\af0\afs24\alang1025 \ltrch\fcs0 \b\fs24\lang1033\langfe1032\cgrid\langnp1033\langfenp1032 \sbasedon0 \snext32 \slink33 \sqformat Title;}{\*\cs33 \additive 
\rtlch\fcs1 \ab\af36\afs32 \ltrch\fcs0 \b\f36\fs32\lang2057\langfe0\kerning28\langnp2057\langfenp0 \sbasedon10 \slink32 \slocked N\'e1zev Char;}{\s34\qj \li0\ri0\sb240\widctlpar
\tqc\tx4153\tqr\tx8306\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang2057\langfe1032\cgrid\langnp2057\langfenp1032 \sbasedon0 \snext34 \slink35 footer;}{\*\cs35 \additive \rtlch\fcs1 
\af0\afs24 \ltrch\fcs0 \fs24\lang2057\langfe0\langnp2057\langfenp0 \sbasedon10 \slink34 \slocked \ssemihidden Z\'e1pat\'ed Char;}{\*\cs36 \additive \rtlch\fcs1 \af0 \ltrch\fcs0 \sbasedon10 page number;}{\s37\qj \li0\ri0\sb60\sa60\sl276\slmult1
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{\creatim\yr2013\mo6\dy17\hr13\min57}{\revtim\yr2017\mo12\dy5\hr15\min39}{\printim\yr2017\mo12\dy5\hr15\min37}{\version954}{\edmins4074}{\nofpages9}{\nofwords3281}{\nofchars19363}{\*\company WSEAS}{\nofcharsws22599}{\vern49167}}{\*\xmlnstbl {\xmlns1 http:
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{\*\wgrffmtfilter 2450}\ilfomacatclnup3\ltrpar \sectd \ltrsect\psz9\linex0\headery708\footery708\colsx708\endnhere\titlepg\sectdefaultcl\sftnbj {\*\pnseclvl1\pnucrm\pnstart1\pnindent720\pnhang {\pntxta .}}{\*\pnseclvl2\pnucltr\pnstart1\pnindent720\pnhang 
{\pntxta .}}{\*\pnseclvl3\pndec\pnstart1\pnindent720\pnhang {\pntxta .}}{\*\pnseclvl4\pnlcltr\pnstart1\pnindent720\pnhang {\pntxta )}}{\*\pnseclvl5\pndec\pnstart1\pnindent720\pnhang {\pntxtb (}{\pntxta )}}{\*\pnseclvl6\pnlcltr\pnstart1\pnindent720\pnhang 
{\pntxtb (}{\pntxta )}}{\*\pnseclvl7\pnlcrm\pnstart1\pnindent720\pnhang {\pntxtb (}{\pntxta )}}{\*\pnseclvl8\pnlcltr\pnstart1\pnindent720\pnhang {\pntxtb (}{\pntxta )}}{\*\pnseclvl9\pnlcrm\pnstart1\pnindent720\pnhang {\pntxtb (}{\pntxta )}}
\pard\plain \ltrpar\qc \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang2057\langfe1032\cgrid\langnp2057\langfenp1032 {\rtlch\fcs1 \ab\af0\afs32 \ltrch\fcs0 
\b\fs32\lang1033\langfe1032\langnp1033\insrsid396024\charrsid396024 Predictive Control }{\rtlch\fcs1 \ab\af0\afs32 \ltrch\fcs0 \b\fs32\lang1033\langfe1032\langnp1033\insrsid7686243\charrsid7686243 Dead-Time Processes}{\rtlch\fcs1 \ab\af0\afs32 
\ltrch\fcs0 \b\fs32\lang1033\langfe1032\langnp1033\insrsid396024\charrsid396024  }{\rtlch\fcs1 \ab\af0\afs32 \ltrch\fcs0 \b\fs32\lang1033\langfe1032\langnp1033\insrsid4849832 
\par }{\rtlch\fcs1 \ab\af0 \ltrch\fcs0 \b\lang1033\langfe1032\langnp1033\insrsid4849832 
\par }\pard \ltrpar\qc \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid12004563 {\rtlch\fcs1 \af0 \ltrch\fcs0 \lang1033\langfe1032\langnp1033\insrsid12004563\charrsid3358952 MAREK KUBAL\'c8\'cdK}{\rtlch\fcs1 \af0 
\ltrch\fcs0 \lang1029\langfe1032\langnp1029\insrsid12004563\charrsid3358952 ,}{\rtlch\fcs1 \af0 \ltrch\fcs0 \lang1033\langfe1032\langnp1033\insrsid12004563\charrsid3358952  VLADIM\'cdR BOB\'c1L
\par Tomas Bata University in Zl\'edn
\par Department of Process Control
\par }{\rtlch\fcs1 \af0 \ltrch\fcs0 \lang1045\langfe1032\langnp1045\insrsid12004563\charrsid3358952 Nad Str\'e1n\'ecmi 4511, 76005, Zl\'edn
\par CZECH REPUBLIC
\par kubalc}{\rtlch\fcs1 \af0 \ltrch\fcs0 \lang1045\langfe1032\langnp1045\insrsid12004563 ik@fai.utb.cz, bobal@fai.utb.cz, }{\rtlch\fcs1 \af0 \ltrch\fcs0 \lang1045\langfe1032\langnp1045\insrsid8001638 http://web.}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\lang1045\langfe1032\langnp1045\insrsid12004563\charrsid3358952 utb.cz/}{\rtlch\fcs1 \af0 \ltrch\fcs0 \lang1045\langfe1032\langnp1045\insrsid8001638 fai}{\rtlch\fcs1 \af0 \ltrch\fcs0 \lang1045\langfe1032\langnp1045\insrsid4849832\charrsid8001638 
\par }\pard \ltrpar\ql \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1045\langfe1032\langnp1045\insrsid4849832\charrsid8001638 
\par 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang1033\langfe1032\langnp1033\insrsid3803292 Abstract: - }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid7686243\charrsid4539580 One of the possible approaches to control of dead-time processes is application of predictive control methods. In technical practice often occur 
higher order processes when a design of an optimal controller leads to complicated control algorithms. One of the possibilities of control of such processes is their approximation by lower-order model with dead-time (time-delay). The first part of the pap
er deals with a design of an algorithm for predictive control of high-order processes which are approximated by }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid13335927 a }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid7686243\charrsid4539580 second-order model of the process with time-delay.}{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid7686243\charrsid4539580  }{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid7686243\charrsid4539580 The second part of the paper deals with a design of an an
alogical algorithm for predictive control of multivariable processes with time-delay. The predictive controllers are based on the recursive computation of predictions which was extended for the time-delay system. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid7686243\charrsid4539580 The designed control algorithms were verified by simulation.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid396024\charrsid4539580  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid7564043\charrsid4539580 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid4849832 
\par }\pard\plain \ltrpar\s28\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang1033\langfe1032\cgrid\langnp1033\langfenp1032 {\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 
\i\fs22\insrsid4849832 Key-Words: -}{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\insrsid4849832  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid744648 predictive}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang2057\langfe1032\langnp2057\insrsid7564043\charrsid7564043  control, }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid7686243 time-delay systems}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang2057\langfe1032\langnp2057\insrsid744648\charrsid744648 , transfer function models}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid744648 , matrix fraction models}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang2057\langfe1032\langnp2057\insrsid744648\charrsid744648  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4849832 
\par }\pard\plain \ltrpar\s6\qj \li0\ri0\keepn\widctlpar\wrapdefault\aspalpha\aspnum\faauto\outlinelevel5\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \ab\af0\afs24\alang1025 \ltrch\fcs0 \b\fs24\lang1033\langfe1032\cgrid\langnp1033\langfenp1032 {\rtlch\fcs1 
\ab0\af0\afs22 \ltrch\fcs0 \b0\fs22\lang2057\langfe1032\langnp2057\insrsid4849832 
\par }\pard\plain \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang2057\langfe1032\cgrid\langnp2057\langfenp1032 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid4849832 \sect }\sectd \ltrsect\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj \pard\plain \ltrpar\qj \li0\ri0\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 
\rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang2057\langfe1032\cgrid\langnp2057\langfenp1032 {\rtlch\fcs1 \ab\af0\afs28 \ltrch\fcs0 \b\fs28\lang1033\langfe1032\langnp1033\insrsid4849832 1\tab Introduction
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid6556543 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 
Some technological processes particularly in chemical industry are characterized by time-delays. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543 
Time-delays are mainly caused by the time required to transport mass, energy or information, but they can also be caused by processing time or accumulation. Time-delay may be defined as the time interval between the start of an eve}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\insrsid12738870 nt at one point in a system }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543 
and its resulting action at another point in the system. One older classification of techniques for the compensation of time-delayed processes is introduced in }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid11341759\charrsid11341759 [1}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid11341759 ]}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid11341759 ,}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid11341759\charrsid11341759 [2}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid11341759 ]}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid11341759  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543 
and newer overview of recent advances and open problems it is possible to find in }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid11341759 [3].}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543  }{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 
Processes with time-delay in general are difficult to control using standard feedback controllers. One of the possible approaches to control processes with time delay is model predictive control (MPC) }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid2249989\charrsid2249989 [4], [5}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid2249989 ], [6].}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543  The predictive control strategy includes a model of the process in the structure of the controller. The first time-delay compensation algorithm was proposed in }{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid15160134 [}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid15160134\charrsid15160134 7}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid15160134 ].}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 
 This control algorithm known as the Smith Predictor (SP) contained a dynamic model of the time-delay process and it can be considered as the first model predictive algorithm.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543  

\par }\pard \ltrpar\qj \fi284\li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid9397019 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543 When using most of other approaches}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\insrsid12859335 , the control actions are }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543 
based on past errors. MPC uses also future values of the reference signals. It is essentially based on discrete or sampled models of processes. Computation of appropriate control algorithms is then realized especially in the discrete domain. }{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 The basic idea of the generalized predictive control }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid3284503\charrsid3284503 [8], [9}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid3284503 ]}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543  is to use a model of a controlled process to predict a number of future out
puts of the process. A trajectory of future manipulated variables is given by solving an optimization problem incorporating a suitable cost function and constraints. Only the first element of the obtained control sequence is applied. The whole procedure i
s repeated in following sampling period. This principle is known as the receding horizon strategy.
\par Some technological processes in industry are characterized by high-order dynamic behaviour or large time constants which increase the difficulty of controlling it. However using the approximation of }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid14427478 a }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 higher-order process by }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid14427478 a }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 
lower-order model with time-delay provides simplification of the control algorithms. The paper then introduces a design and verification of an algorithm for predictive control of second order linear systems with}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid7240251  two steps}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543  time delay. A number of higher ord
er industrial processes can be approximated by this model.
\par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid6556543\charrsid6556543 Typical technological processes require the simultaneous control of several variables related to one system.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543  Each input may influence all system outputs. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid6556543\charrsid6556543 
The design of a controller for such a system must be quite sophisticated if the system is to be controlled adequately. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 
One of the most effective approaches to control of multivariable systems is }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543 model predictive control. An advantage of model predictive control is that multivariable systems can be 
handled in a straightforward manner. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 In technical practice also often occur multivariable processes with time delay.}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543  Typical examples of such processes are e.g. liquid storing tanks, distillation columns or some types of chemical reactors. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 The paper then d
eals also with a design of an analogical algorithm for predictive control of multivariable processes with time-delay. Both for control of the single input-single output and multivariable systems was applied the same approach. The predictive controllers ar
e based on}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1906509  input-output models. In case of the SISO control it is a transfer function model and in case of}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid9052933  the}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1906509  MIMO control the model is considered in the form of the matrix fraction.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid5912844  The models are used for }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 
a recursive computation of predictions which was extended for the time-delay system}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid5912844 s}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 .}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid11226861 
 In case of the input-output model it is not necessary to examine observability. Feasibility is ensured by a suitable setting of constraints.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1906509  }{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543  The proposed algorithms were verified by simulation.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid15205568\charrsid15205568  }{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid8004284 
\par }\pard \ltrpar\qj \fi284\li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid555478 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid13840179\charrsid8004284 
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\fs22\lang4105\langfe1032\langnp4105\insrsid13840179 
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\b\fs22\lang1033\langfe1032\langnp1033\insrsid16734106  of SISO System}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid135913 
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\fs22\lang4105\langfe1032\langnp4105\insrsid16341867         }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\up12\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 (2)}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543 
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1136461 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid14224697 
Model predictive control has an ability to deal with control difficulties such as nonlinearity,}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid12726072  constrained variables, time-de}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid14224697 l}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid12726072 ay}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid14224697  and also }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid8611692 control of unstable systems. A system described by transfer function 
(1) may be then also unstable i.e. with roots of the denominator outside the Unite Circle. The proposed predictive controller}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6449375  then}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid8611692 
 ensures BIBO (Bounded Input Bounded Output) stability of the }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6449375 whole }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid8611692 closed loop system}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid6449375  despite the fact that the controlled system is unstable}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid8611692 .}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid12726072  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid6556543\charrsid6556543 The model can be also written in the form
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\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid6556543                        }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang4105\langfe1032\langnp4105\insrsid16341867                      }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543 (3)
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1136461 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543 
A widely used model in general model predictive control is the CARIMA model which we can obtain from the nominal model (3) by adding a disturbance model
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\fs22\lang4105\langfe1032\langnp4105\insrsid2043655      }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543 (6)}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1136461 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 
The CARIMA model for time-delay system takes the form
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\rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \fs22\lang1033\langfe1032\cgrid\langnp1033\langfenp1032\insrsid6556543\charrsid6556543 {\object\objemb\objw3221\objh340{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000
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000004000000f0010100030000000000}{\result {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\dn10\lang1033\langfe1032\langnp1033\insrsid14958271\charrsid6556543 {\pict{\*\picprop\shplid1035{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLockAspectRatio}{\sv 1}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fRecolorFillAsPicture}{\sv 0}}{\sp{\sn fUseShapeAnchor}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fPreferRelativeResize}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}
{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fFakeMaster}{\sv 0}}{\sp{\sn fCameFromImgDummy}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw5680\pich600\picwgoal3220\pichgoal340\wmetafile8\bliptag-865011217\blipupi404{\*\blipuid cc70f9ef49e03d65d01dda552912a796}010009000003b903000002001c00000000000500000009020000000005000000020101000000050000000102ffffff00050000002e0118000000050000000b02
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\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid4607379           }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang4105\langfe1032\langnp4105\insrsid16341867            }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid6556543\charrsid6556543 (7)
\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid6556543 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543 where }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 
\i\fs22\insrsid6556543\charrsid6556543 d }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543 is the dead time. In our case }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\insrsid6556543\charrsid6556543 d }{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\insrsid6556543\charrsid6556543 is equal to 2.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid16734106\charrsid16734106  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6556543\charrsid15629775 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid13840179 {\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid10381471 2.2 }{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 
\b\fs22\lang1033\langfe1032\langnp1033\insrsid135913 Model}{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid10381471  of MIMO System}{\rtlch\fcs1 \af0 \ltrch\fcs0 \lang1033\langfe1032\langnp1033\insrsid135913 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid15737299 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10381471\charrsid10381471 
Let us consider a two input \endash  two output system. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471 The two \endash  input/two \endash  output (TITO) processes are }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid16349568 
very}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471  often encountered multivariable processes in practice and many processes with inputs/outputs beyond two can be treated as several TITO subsystems }{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10381471\charrsid12849150 [}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid12849150\charrsid12849150 10}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid10381471\charrsid12849150 ].}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10381471\charrsid10381471 
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1136461 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10381471\charrsid10381471 
A general transfer matrix of a two-input\endash two-output system with significant cross-coupling between the control loops is expressed as:
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\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10381471 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \fs22\lang1033\langfe1032\cgrid\langnp1033\langfenp1032\insrsid10381471\charrsid10381471 {\object\objemb\objw2020\objh660
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\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471        }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4474318         }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid4474318 (10}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10381471\charrsid10381471 )
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid3761268 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10381471\charrsid10381471 
It may be assumed that the transfer matrix can be transcribed to the following form of the matrix fraction:
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\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10381471 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \fs22\lang2057\langfe1032\cgrid\langnp2057\langfenp1032\insrsid10381471\charrsid10381471 {\object\objemb\objw3320\objh340
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\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10381471\charrsid10381471   and the matrices }{\pard\plain \ltrpar\qj \li0\ri0\sa120\widctlpar
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\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471                    }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4474318 
                     (12}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10381471\charrsid10381471 
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid3761268 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471 
As an example a model with polynomials of second degree was chosen. This model proved to be effective for control of several }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9644420 real }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid10381471\charrsid10381471 TITO processes }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid9457382\charrsid9457382 [11}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang4105\langfe1032\langnp4105\insrsid3611748\charrsid9457382 ]}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid9457382 ,}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471 
 where controllers based on a model with polynomials of the first degree failed. The model has sixteen parameters. The matrices }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\insrsid10381471\charrsid10381471 A}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid10381471\charrsid10381471  and }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\insrsid10381471\charrsid10381471 B}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471  are defined as follows}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10381471\charrsid10381471 
\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10381471 {\pard\plain \ltrpar\qj \li0\ri0\sa120\widctlpar
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\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471         }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4474318          (14}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10381471\charrsid10381471 
\par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10381471\charrsid10381471 the CARIMA model in the MIMO case is as follows 
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\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471                    }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4474318 
                   (16}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10381471\charrsid10381471 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1136461 {\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang1033\langfe1032\langnp1033\insrsid10381471\charrsid10381471 C}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid13727312  is a}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10381471\charrsid10381471  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid10381471\charrsid10381471 colouring polynomial matrix. For}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid13727312  purpose of simplification it was}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471 
 supposed to be equal to the identity matrix }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid3611748 [}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid3474563 4}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10381471\charrsid10381471 ]}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10381471\charrsid10381471 . }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid1136461 
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1136461 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1136461\charrsid1136461 
The nominal model with }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang1033\langfe1032\langnp1033\insrsid1136461\charrsid1136461 d}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1136461\charrsid1136461 
 steps of time-delay is considered as
\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1136461 {\pard\plain \ltrpar\qj \li0\ri0\sa120\widctlpar
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\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid1136461\charrsid1136461      }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4474318       (17}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid1136461\charrsid1136461 )}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid1136461\charrsid1136461 
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1136461 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1136461\charrsid1136461 
For the purpose of simplification it was considered}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1077468  an}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1136461\charrsid1136461 
 equal time-delay in all particular transfer functions of the transfer matrix. The CARIMA model for time-delay system then takes the form
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\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10381471 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10381471 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\rtlch\fcs1 \ab\af0\afs28 \ltrch\fcs0 \b\fs28\lang1033\langfe1032\langnp1033\insrsid1385489 3}{\rtlch\fcs1 \ab\af0\afs28 \ltrch\fcs0 
\b\fs28\lang1033\langfe1032\langnp1033\insrsid3081497 \tab }{\rtlch\fcs1 \ab\af0\afs28 \ltrch\fcs0 \b\fs28\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 Implementation of predictive controller }{\rtlch\fcs1 \ab\af0\afs28 \ltrch\fcs0 
\b\fs28\lang1033\langfe1032\langnp1033\insrsid4849832 
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The basic idea of MPC is to use a model of a controlled process to predict }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 N}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
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 future outputs of the process. A trajectory of future manipulated variables is given by solving an optimization problem incorporating a suitable cost function and constraints. Only the first element of the obtained control sequence is applied. The whole 
procedure is repeated in following sampling period. This principle is known as the receding horizon strategy. The computation of a control law of MPC is based on minimization of the following criterion 
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\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid10564841\charrsid10564841          }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid10564841              }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid4657411 (19}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10564841\charrsid10564841 )
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10564841 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10564841\charrsid10564841 where }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 
\b\i\fs22\insrsid10564841\charrsid10564841 e}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10564841\charrsid10564841 (}{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\insrsid10564841\charrsid10564841 k}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 +}{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 j}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 )}{\rtlch\fcs1 \af302\afs22 \ltrch\fcs0 \f302\fs22\insrsid10564841\charrsid10564841  is a vector of predicted control errors, \'c4}{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 
\b\i\fs22\insrsid10564841\charrsid10564841 u}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10564841\charrsid10564841 (}{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\insrsid10564841\charrsid10564841 k}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 +}{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 j}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 ) is a vector of future increments of the manipulated variable (for the system with two inputs and two outputs each vector has two elements), }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 
\i\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 N}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841  is a length of the prediction horizon, }{\rtlch\fcs1 \ai\af0\afs22 
\ltrch\fcs0 \i\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 N}{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang1033\langfe1032\sub\langnp1033\insrsid10564841\charrsid10564841 u}{\rtlch\fcs1 \af302\afs22 \ltrch\fcs0 
\f302\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841  is a length of the control horizon and \'eb is a weighting factor of control increments. 
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n a vector form is given by
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\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid10564841\charrsid10564841                         }{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid10564841                                  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4657411 (20}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10564841\charrsid10564841 )
\par }\pard \ltrpar\qj \li0\ri0\sa240\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10564841 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 where }
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\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 
  is a vector of system predictions along the horizon of the length }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 N}{\rtlch\fcs1 \af302\afs22 \ltrch\fcs0 
\f302\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 , \'c4}{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 u}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841  is a vector of control increments, }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 y}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang1033\langfe1032\sub\langnp1033\insrsid10564841\charrsid10564841 0}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841  is the free response vector. }{\rtlch\fcs1 \ab\ai\af0\afs22 
\ltrch\fcs0 \b\i\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 G}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 
 is a matrix of the dynamics. It contains values of the step sequence. In SISO case it is given as}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10564841\charrsid10564841    
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\fs22\dn74\lang1036\langfe1032\langnp1036\insrsid14958271\charrsid16253453 {\pict{\*\picprop\shplid1057{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLockAspectRatio}{\sv 1}}{\sp{\sn pictureGray}{\sv 0}}
{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fRecolorFillAsPicture}{\sv 0}}{\sp{\sn fUseShapeAnchor}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}
{\sp{\sn fLine}{\sv 0}}{\sp{\sn fPreferRelativeResize}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fFakeMaster}{\sv 0}}{\sp{\sn fCameFromImgDummy}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw5609\pich2785\picwgoal3180\pichgoal1579\wmetafile8\bliptag-323494405\blipupi-538{\*\blipuid ecb7ddfbcd9451119581a4a952a6790c}
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08000000320a6a01e60c010000004c791c000000fb02c0fe000000000000bc02010000000402001054696d6573204e657720526f6d616e0010f11200278ba277
4091a5773d0f664f040000002d01000004000000f001010008000000320a40052c000100000047790a00000026060f000a00ffffffff0100000000001c000000
fb021000070000000000bc02000000ee0102022253797374656d004f3d0f664f00000a0038008a01000000000100000028f31200040000002d01010004000000f0010000030000000000}}}}}\sectd \ltrsect
\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4657411                     (21}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid16253453 )}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid10564841\charrsid10564841 
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa240\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10289250 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid10564841\charrsid10564841 
In TITO case the matrix }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang1036\langfe1032\langnp1036\insrsid10564841\charrsid10564841 G}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid10564841\charrsid10564841 
 takes the following form}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10564841\charrsid10564841 
\par }\pard \ltrpar\qj \li0\ri0\sa240\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10564841 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid14958271\charrsid10564841 
{\pict{\*\picprop\shplid1058{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLockAspectRatio}{\sv 1}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fRecolorFillAsPicture}{\sv 0}}
{\sp{\sn fUseShapeAnchor}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}
{\sp{\sn fLine}{\sv 0}}{\sp{\sn fPreferRelativeResize}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fFakeMaster}{\sv 0}}{\sp{\sn fCameFromImgDummy}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw4763\pich2716\picwgoal2700\pichgoal1540\wmetafile8\bliptag2123784020\blipupi708{\*\blipuid 7e965f5468af79e5d008bf9a6e628924}
010009000003ed02000002001c00000000000500000009020000000005000000020101000000050000000102ffffff00050000002e0118000000050000000b02
00000000050000000c02a009e0101200000026060f001a00ffffffff000010000000c0ffffffb4ffffffa0100000540900000b00000026060f000c004d617468
54797065000040021c000000fb02c0fe0000000000009001000000020002001053796d626f6c0000720a0afd40f11200b8a4f377c1a4f3772030f5777a0a66ed
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211001000000fa7908000000320ad303211001000000fa7908000000320aa302211001000000fa7908000000320a3b09211001000000fb7908000000320a7301
211001000000f97908000000320a9308770201000000ea7908000000320a6307770201000000ea7908000000320a3306770201000000ea7908000000320a0305
770201000000ea7908000000320ad303770201000000ea7908000000320aa302770201000000ea7908000000320a3b09770201000000eb7908000000320a7301
770201000000e97908000000320a20057201010000003d791c000000fb0220ff0000000000009001000000020002001053796d626f6c00007f0a0a7d40f11200
b8a4f377c1a4f3772030f5777a0a66ed040000002d01010004000000f001000008000000320a3109ac04010000002d791c000000fb0220ff0000000000009001
000000000402001054696d6573204e657720526f6d616e00b8a4f377c1a4f3772030f5777a0a66ed040000002d01000004000000f001010008000000320a3109
780f01000000307908000000320a31091b0501000000317908000000320a5107bc0c01000000307908000000320a9103c60701000000307908000000320a9103
750401000000317908000000320ab10177040100000030791c000000fb02c0fe0000000000009001000000000402001054696d6573204e657720526f6d616e00
b8a4f377c1a4f3772030f5777a0a66ed040000002d01010004000000f001000008000000320a0107020f01000000307908000000320a4103020f010000003079
08000000320a4103cb0901000000307908000000320a6101020f01000000307908000000320a610150070100000030791c000000fb02c0fe000000000000bc02
010000000402001054696d6573204e657720526f6d616e00b8a4f377c1a4f3772030f5777a0a66ed040000002d01000004000000f001010008000000320ae108
7d0e01000000477908000000320ae108ea0201000000477908000000320a0107c10b01000000477908000000320a4103cb0601000000477908000000320a4103
8f0301000000477908000000320a61017c0301000000477908000000320a20052c000100000047791c000000fb02c0fe00000000000090010000000204020010
4d54204578747261000a0a7f40f11200b8a4f377c1a4f3772030f5777a0a66ed040000002d01010004000000f001000008000000320ae108f30b010000004c79
08000000320ae1087809010000004c7908000000320ae108fd06010000004c7908000000320a01071a04010000004d7908000000320a21051b0f010000004d79
08000000320a2105f30b010000004f7908000000320a21057809010000004f7908000000320a21051a04010000004d7908000000320a4103f30b010000004c79
08000000320a6101f30b010000004c7908000000320a61017809010000004c791c000000fb0220ff0000000000009001010000000402001054696d6573204e65
7720526f6d616e00b8a4f377c1a4f3772030f5777a0a66ed040000002d01000004000000f001010008000000320a3109f303010000004e790a00000026060f00
0a00ffffffff0100000000001c000000fb021000070000000000bc02000000ee0102022253797374656d00ed7a0a66ed00000a0021008a0100000000010000005cf31200040000002d01010004000000f0010000030000000000}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid10564841\charrsid10564841             }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid16253453                 }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\up60\insrsid4657411 (22}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\up60\insrsid10564841\charrsid16253453 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1029\langfe1032\langnp1029\insrsid10564841\charrsid10564841 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid16253453 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 where sub-matrices }{
\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 G}{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang1033\langfe1032\sub\langnp1033\insrsid10564841\charrsid10564841 i}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841  have dimension 2x2 and contain values of the step sequence.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid2774790 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 
The criterion (12) can be written in a general vector form 
\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid16253453 {\pard\plain \ltrpar\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid16253453 
\rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \fs22\lang1036\langfe1032\cgrid\langnp1036\langfenp1032\insrsid10564841\charrsid10564841 {\object\objemb\objw2520\objh360{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300
000000000000000000120000
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ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000feffffff05000000feffffff0600000007000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c000000000000046000000000000000000000000e070
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0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000004000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000200ffffffffffffffffffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000600000000000000feffffff02000000fefffffffeffffff05000000060000000700000008000000090000000a0000000b0000000c0000000d0000000e0000000f000000100000001100000012000000130000001400000015000000160000001700000018000000feffffff1a00
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ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
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000000000000000000000000000000000000000000000000000000000000000000000000ffffffff030000000400000001000000ffffffff00000000000000005d1100007b020000120500000100090000038902000002001c00000000000500000009020000000005000000020101000000050000000102ffffff000500
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40f01200278ba2774091a57739146695040000002d01000008000000320a9e01490201000000287902004f006c0065005000720065007300300030003000000000000000000000000000000000000000000000000000000000000000000000000000000000000000180002010300000005000000ffffffff000000000000
000000000000000000000000000000000000000000000000000000000000040000003a050000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff00000000
0000000000000000000000000000000000000000000000000000000000000000190000009f000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001c000000fb023afebd00000000009001000000020402001053796d626f6c00774b150af8404b1b0040f01200278ba2774091a57739146695040000002d01010004000000f001000008000000320a
9e017b050100000029791c000000fb023afebd00000000009001000000020402001053796d626f6c0077cf140aa7604b1b0040f01200278ba2774091a57739146695040000002d01000004000000f001010008000000320a9e0195060100000028791c000000fb023afebd00000000009001000000020402001053796d62
6f6c00774b150af9404b1b0040f01200278ba2774091a57739146695040000002d01010004000000f001000008000000320a9e01c7090100000029791c000000fb02c0fe000000000000bc02010000000402001054696d6573204e657720526f6d616e0010f11200278ba2774091a57739146695040000002d0100000400
0000f001010008000000320aa001d60e01000000757908000000320aa001a70c01000000757908000000320aa001d70801000000777908000000320aa0011b0701000000797908000000320aa0018b0401000000777908000000320aa001cf020100000079791c000000fb02c0fe00000000000090010000000204020010
53796d626f6c00774b150afa404b1b0010f11200278ba2774091a57739146695040000002d01010004000000f001000008000000320aa001130e01000000447908000000320aa001e40b01000000447908000000320aa001490a010000002b7908000000320aa001ea07010000002d7908000000320aa0019e0301000000
2d7908000000320aa0014e01010000003d791c000000fb0240ff0000000000009001010000000402001054696d6573204e657720526f6d616e0010f11200278ba2774091a57739146695040000002d01000004000000f001010008000000320a10016d0d01000000547908000000320af200db050100000054791c000000
fb02c0fe0000000000009001010000000402001054696d6573204e657720526f6d616e0010f11200278ba2774091a57739146695040000002d01010004000000f001000008000000320aa0014a00010000004a791c000000fb02c0fe0000000000009001010000020402001053796d626f6c0077cf140aaa604b1b0010f1
1200278ba2774091a57739146695040000002d01000004000000f001010008000000320aa001300b010000006c791c000000fb02c0fe0000000000009001000000000402001054696d6573204e657720526f6d616e0010f11200278ba2774091a57739146695040000002d01010004000000f001000008000000320a8301
2c0701000000887908000000320a8301e0020100000088790a00000026060f000a00ffffffff0100000000001c000000fb021000070000000000bc02000000ee0102022253797374656d00953914669500000a0038008a01000000000000000028f31200040000002d01000004000000f001010003000000000000000000
00001c0000000200c1c2830000000000000050fe1900343a190000000000030101030a0a0112834a0002863d0003010000012287790006090000028612220287770000029628000296290000030f00000b11011283540000000a0301000001228779000609000002861222028777000002962800029629000002862b0002
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00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c4550494354005d11000085fdffff1a05000008005d117b020000
0100090000038902000002001c00000000000500000009020000000005000000020101000000050000000102ffffff00050000002e0118000000050000000b0200000000050000000c024002c00f1200000026060f001a00ffffffff000010000000c0ffffffa1ffffff800f0000e10100000b00000026060f000c004d61
746854797065000050001c000000fb023afebd00000000009001000000020402001053796d626f6c0077cf140aa6604b1b0040f01200278ba2774091a57739146695040000002d01000008000000320a9e0149020100000028791c000000fb023afebd00000000009001000000020402001053796d626f6c00774b150af8
404b1b0040f01200278ba2774091a57739146695040000002d01010004000000f001000008000000320a9e017b050100000029791c000000fb023afebd00000000009001000000020402001053796d626f6c0077cf140aa7604b1b0040f01200278ba2774091a57739146695040000002d01000004000000f00101000800
0000320a9e0195060100000028791c000000fb023afebd00000000009001000000020402001053796d626f6c00774b150af9404b1b0040f01200278ba2774091a57739146695040000002d01010004000000f001000008000000320a9e01c7090100000029791c000000fb02c0fe000000000000bc020100000004020010
54696d6573204e657720526f6d616e0010f11200278ba2774091a57739146695040000002d01000004000000f001010008000000320aa001d60e01000000757908000000320aa001a70c01000000757908000000320aa001d70801000000777908000000320aa0011b0701000000797908000000320aa0018b0401000000
777908000000320aa001cf020100000079791c000000fb02c0fe0000000000009001000000020402001053796d626f6c00774b150afa404b1b0010f11200278ba2774091a57739146695040000002d01010004000000f001000008000000320aa001130e01000000447908000000320aa001e40b01000000447908000000
320aa001490a010000002b7908000000320aa001ea07010000002d7908000000320aa0019e03010000002d7908000000320aa0014e01010000003d791c000000fb0240ff0000000000009001010000000402001054696d6573204e657720526f6d616e0010f11200278ba2774091a57739146695040000002d0100000400
0000f001010008000000320a10016d0d01000000547908000000320af200db050100000054791c000000fb02c0fe0000000000009001010000000402001054696d6573204e657720526f6d616e0010f11200278ba2774091a57739146695040000002d01010004000000f001000008000000320aa0014a00010000004a79
1c000000fb02c0fe0000000000009001010000020402001053796d626f6c0077cf140aaa604b1b0010f11200278ba2774091a57739146695040000002d01000004000000f001010008000000320aa001300b010000006c791c000000fb02c0fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e0010f11200278ba2774091a57739146695040000002d01010004000000f001000008000000320a83012c0701000000887908000000320a8301e0020100000088790a00000026060f000a00ffffffff0100000000001c000000fb021000070000000000bc02000000ee0102022253797374656d00953914669500000a00
38008a01000000000000000028f31200040000002d01000004000000f0010100030000000000}{\result {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\dn10\lang1036\langfe1032\langnp1036\insrsid14958271\charrsid16253453 
{\pict{\*\picprop\shplid1059{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLockAspectRatio}{\sv 1}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fRecolorFillAsPicture}{\sv 0}}
{\sp{\sn fUseShapeAnchor}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}
{\sp{\sn fLine}{\sv 0}}{\sp{\sn fPreferRelativeResize}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fFakeMaster}{\sv 0}}{\sp{\sn fCameFromImgDummy}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw4445\pich635\picwgoal2520\pichgoal360\wmetafile8\bliptag1129825201\blipupi-44{\*\blipuid 4357c3b16ad38be2f40bfeab98c2b0aa}
0100090000038902000002001c00000000000500000009020000000005000000020101000000050000000102ffffff00050000002e0118000000050000000b02
00000000050000000c024002c00f1200000026060f001a00ffffffff000010000000c0ffffffa1ffffff800f0000e10100000b00000026060f000c004d617468
54797065000050001c000000fb023afebd00000000009001000000020402001053796d626f6c0077cf140aa6604b1b0040f01200278ba2774091a57739146695
040000002d01000008000000320a9e0149020100000028791c000000fb023afebd00000000009001000000020402001053796d626f6c00774b150af8404b1b00
40f01200278ba2774091a57739146695040000002d01010004000000f001000008000000320a9e017b050100000029791c000000fb023afebd00000000009001
000000020402001053796d626f6c0077cf140aa7604b1b0040f01200278ba2774091a57739146695040000002d01000004000000f001010008000000320a9e01
95060100000028791c000000fb023afebd00000000009001000000020402001053796d626f6c00774b150af9404b1b0040f01200278ba2774091a57739146695
040000002d01010004000000f001000008000000320a9e01c7090100000029791c000000fb02c0fe000000000000bc02010000000402001054696d6573204e65
7720526f6d616e0010f11200278ba2774091a57739146695040000002d01000004000000f001010008000000320aa001d60e01000000757908000000320aa001
a70c01000000757908000000320aa001d70801000000777908000000320aa0011b0701000000797908000000320aa0018b0401000000777908000000320aa001
cf020100000079791c000000fb02c0fe0000000000009001000000020402001053796d626f6c00774b150afa404b1b0010f11200278ba2774091a57739146695
040000002d01010004000000f001000008000000320aa001130e01000000447908000000320aa001e40b01000000447908000000320aa001490a010000002b79
08000000320aa001ea07010000002d7908000000320aa0019e03010000002d7908000000320aa0014e01010000003d791c000000fb0240ff0000000000009001
010000000402001054696d6573204e657720526f6d616e0010f11200278ba2774091a57739146695040000002d01000004000000f001010008000000320a1001
6d0d01000000547908000000320af200db050100000054791c000000fb02c0fe0000000000009001010000000402001054696d6573204e657720526f6d616e00
10f11200278ba2774091a57739146695040000002d01010004000000f001000008000000320aa0014a00010000004a791c000000fb02c0fe0000000000009001
010000020402001053796d626f6c0077cf140aaa604b1b0010f11200278ba2774091a57739146695040000002d01000004000000f001010008000000320aa001
300b010000006c791c000000fb02c0fe0000000000009001000000000402001054696d6573204e657720526f6d616e0010f11200278ba2774091a57739146695
040000002d01010004000000f001000008000000320a83012c0701000000887908000000320a8301e0020100000088790a00000026060f000a00ffffffff0100
000000001c000000fb021000070000000000bc02000000ee0102022253797374656d00953914669500000a0038008a01000000000000000028f31200040000002d01000004000000f0010100030000000000}}}}}\sectd \ltrsect
\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid10564841\charrsid10564841            }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1036\langfe1032\langnp1036\insrsid16253453                      }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid4657411 (23}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 )
\par where }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 w}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 
 is a vector of the reference trajectory.  The criterion can be m}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid4657411 odified using the expression (19}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 ) to  
\par }{\pard\plain \ltrpar\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid16253453 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\fs22\lang1036\langfe1032\cgrid\langnp1036\langfenp1032\insrsid10564841\charrsid10564841 {\object\objemb\objw1920\objh340\objscalex99{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300000000000000000000100000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000feffffff05000000feffffff06000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c000000000000046000000000000000000000000e070
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0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000004000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000200ffffffffffffffffffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000600000000000000feffffff02000000fefffffffeffffff05000000060000000700000008000000090000000a0000000b0000000c0000000d0000000e0000000f0000001000000011000000feffffff13000000feffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
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0000000000000000000000000000000000000000000000000000000000000400000052030000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000001200000071000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000008000000320a8001450901000000487908000000320a8001ca0701000000757908000000320a8001320501000000757908000000320a800108030100000067791c000000fb02c0fe000000000000
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320a80014f01010000003d791c000000fb0240ff0000000000009001010000000402001054696d6573204e657720526f6d616e00b8f01200278ba2774091a577ac0e668a040000002d01000004000000f001010008000000320af000900801000000547908000000320af000c9030100000054791c000000fb02c0fe0000
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000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c4550494354003b0d0000a8fdffff3203000008003b0d58020000
0100090000039501000002001c00000000000500000009020000000005000000020101000000050000000102ffffff00050000002e0118000000050000000b0200000000050000000c022002000c1200000026060f001a00ffffffff000010000000c0ffffffa3ffffffc00b0000c30100000b00000026060f000c004d61
746854797065000050001c000000fb02c0fe000000000000bc02010000000402001054696d6573204e657720526f6d616e00b8f01200278ba2774091a577ac0e668a040000002d01000008000000320a8001020b01000000757908000000320a8001450901000000487908000000320a8001ca0701000000757908000000
320a8001320501000000757908000000320a800108030100000067791c000000fb02c0fe0000000000009001000000020402001053796d626f6c00776b0a0ac0204c1b00b8f01200278ba2774091a577ac0e668a040000002d01010004000000f001000008000000320a80013f0a01000000447908000000320a80010707
01000000447908000000320a80011a06010000002b7908000000320a80016f0401000000447908000000320a80014f01010000003d791c000000fb0240ff0000000000009001010000000402001054696d6573204e657720526f6d616e00b8f01200278ba2774091a577ac0e668a040000002d01000004000000f0010100
08000000320af000900801000000547908000000320af000c9030100000054791c000000fb02c0fe0000000000009001010000000402001054696d6573204e657720526f6d616e00b8f01200278ba2774091a577ac0e668a040000002d01010004000000f001000008000000320a80014a00010000004a791c000000fb02
c0fe0000000000009001000000000402001054696d6573204e657720526f6d616e00b8f01200278ba2774091a577ac0e668a040000002d01000004000000f001010008000000320a80014f020100000032790a00000026060f000a00ffffffff0100000000001c000000fb021000070000000000bc02000000ee01020222
53797374656d008aac0e668a00000a0038008a010000000001000000d0f21200040000002d01010004000000f0010000030000000000}{\result {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\dn10\lang1036\langfe1032\langnp1036\insrsid14958271\charrsid16253453 
{\pict{\*\picprop\shplid1060{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLockAspectRatio}{\sv 1}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fRecolorFillAsPicture}{\sv 0}}
{\sp{\sn fUseShapeAnchor}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}
{\sp{\sn fLine}{\sv 0}}{\sp{\sn fPreferRelativeResize}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fFakeMaster}{\sv 0}}{\sp{\sn fCameFromImgDummy}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex99\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw3387\pich600\picwgoal1920\pichgoal340\wmetafile8\bliptag-16624196\blipupi-688{\*\blipuid ff0255bcdc39b8be815f7ffaef9aad56}
0100090000039501000002001c00000000000500000009020000000005000000020101000000050000000102ffffff00050000002e0118000000050000000b02
00000000050000000c022002000c1200000026060f001a00ffffffff000010000000c0ffffffa3ffffffc00b0000c30100000b00000026060f000c004d617468
54797065000050001c000000fb02c0fe000000000000bc02010000000402001054696d6573204e657720526f6d616e00b8f01200278ba2774091a577ac0e668a
040000002d01000008000000320a8001020b01000000757908000000320a8001450901000000487908000000320a8001ca0701000000757908000000320a8001
320501000000757908000000320a800108030100000067791c000000fb02c0fe0000000000009001000000020402001053796d626f6c00776b0a0ac0204c1b00
b8f01200278ba2774091a577ac0e668a040000002d01010004000000f001000008000000320a80013f0a01000000447908000000320a80010707010000004479
08000000320a80011a06010000002b7908000000320a80016f0401000000447908000000320a80014f01010000003d791c000000fb0240ff0000000000009001
010000000402001054696d6573204e657720526f6d616e00b8f01200278ba2774091a577ac0e668a040000002d01000004000000f001010008000000320af000
900801000000547908000000320af000c9030100000054791c000000fb02c0fe0000000000009001010000000402001054696d6573204e657720526f6d616e00
b8f01200278ba2774091a577ac0e668a040000002d01010004000000f001000008000000320a80014a00010000004a791c000000fb02c0fe0000000000009001
000000000402001054696d6573204e657720526f6d616e00b8f01200278ba2774091a577ac0e668a040000002d01000004000000f001010008000000320a8001
4f020100000032790a00000026060f000a00ffffffff0100000000001c000000fb021000070000000000bc02000000ee0102022253797374656d008aac0e668a00000a0038008a010000000001000000d0f21200040000002d01010004000000f0010000030000000000}}}}}\sectd \ltrsect
\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid10564841\charrsid10564841                 }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1036\langfe1032\langnp1036\insrsid16253453                            }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid10564841\charrsid10564841 (}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang4105\langfe1032\langnp4105\insrsid4657411 24}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10564841\charrsid10564841 
\par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 where the gradient }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 g}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841  and the Hess matrix }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 H}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841  are defined by following expressions
\par }{\pard\plain \ltrpar\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid16253453 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\fs22\lang1036\langfe1032\cgrid\langnp1036\langfenp1032\insrsid10564841\charrsid10564841 {\object\objemb\objw1480\objh340{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300000000000000000000100000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000feffffff05000000feffffff06000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c000000000000046000000000000000000000000e070
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0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000004000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000200ffffffffffffffffffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000600000000000000feffffff02000000fefffffffeffffff05000000060000000700000008000000090000000a0000000b0000000c0000000d0000000e0000000f0000001000000011000000feffffff13000000feffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
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000000000000000000000000000000000000000000000000000000000000000000000000ffffffff030000000400000001000000ffffffff0000000000000000330a00005802000042030000010009000003a101000002001c00000000000500000009020000000005000000020101000000050000000102ffffff000500
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000000000000000000000000000000000000000000000000000000000000040000006a030000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000001200000076000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001c000000fb024efebd00000000009001000000020402001053796d626f6c007729160ad4c04b1b0040f01200278ba2774091a5775c156690040000002d01010004000000f001000008000000320a
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000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c455049435400330a0000a8fdffff4a0300000800330a58020000
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746854797065000050001c000000fb024efebd00000000009001000000020402001053796d626f6c00772c0e0a53804b1b0040f01200278ba2774091a5775c156690040000002d01000008000000320a7f01cc040100000028791c000000fb024efebd00000000009001000000020402001053796d626f6c007729160ad4
c04b1b0040f01200278ba2774091a5775c156690040000002d01010004000000f001000008000000320a7f01a2080100000029791c000000fb02c0fe000000000000bc02010000000402001054696d6573204e657720526f6d616e0010f11200278ba2774091a5775c156690040000002d01000004000000f00101000800
0000320a8001b20701000000777908000000320a8001560501000000797908000000320a8001070301000000477908000000320a80014f000100000067791c000000fb02c0fe0000000000009001000000020402001053796d626f6c007729160ad5c04b1b0010f11200278ba2774091a5775c156690040000002d010100
04000000f001000008000000320a8001c506010000002d7908000000320a80011602010000003d791c000000fb0240ff0000000000009001000000000402001054696d6573204e657720526f6d616e0010f11200278ba2774091a5775c156690040000002d01000004000000f001010008000000320ad001fb0501000000
30791c000000fb0240ff0000000000009001010000000402001054696d6573204e657720526f6d616e0010f11200278ba2774091a5775c156690040000002d01010004000000f001000008000000320af000130401000000547908000000320af00010010100000054790a00000026060f000a00ffffffff010000000000
1c000000fb021000070000000000bc02000000ee0102022253797374656d00905c15669000000a0038008a01000000000000000028f31200040000002d01000004000000f0010100030000000000}{\result {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\dn10\lang1036\langfe1032\langnp1036\insrsid14958271\charrsid16253453 {\pict{\*\picprop\shplid1061{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLockAspectRatio}{\sv 1}}{\sp{\sn pictureGray}{\sv 0}}
{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fRecolorFillAsPicture}{\sv 0}}{\sp{\sn fUseShapeAnchor}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}
{\sp{\sn fLine}{\sv 0}}{\sp{\sn fPreferRelativeResize}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fFakeMaster}{\sv 0}}{\sp{\sn fCameFromImgDummy}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw2611\pich600\picwgoal1480\pichgoal340\wmetafile8\bliptag65096918\blipupi-1412{\*\blipuid 03e14cd6ae1c62f7301e02294f04ae49}
010009000003a101000002001c00000000000500000009020000000005000000020101000000050000000102ffffff00050000002e0118000000050000000b02
00000000050000000c02200240091200000026060f001a00ffffffff000010000000c0ffffffa3ffffff00090000c30100000b00000026060f000c004d617468
54797065000050001c000000fb024efebd00000000009001000000020402001053796d626f6c00772c0e0a53804b1b0040f01200278ba2774091a5775c156690
040000002d01000008000000320a7f01cc040100000028791c000000fb024efebd00000000009001000000020402001053796d626f6c007729160ad4c04b1b00
40f01200278ba2774091a5775c156690040000002d01010004000000f001000008000000320a7f01a2080100000029791c000000fb02c0fe000000000000bc02
010000000402001054696d6573204e657720526f6d616e0010f11200278ba2774091a5775c156690040000002d01000004000000f001010008000000320a8001
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0000000000009001000000020402001053796d626f6c007729160ad5c04b1b0010f11200278ba2774091a5775c156690040000002d01010004000000f0010000
08000000320a8001c506010000002d7908000000320a80011602010000003d791c000000fb0240ff0000000000009001000000000402001054696d6573204e65
7720526f6d616e0010f11200278ba2774091a5775c156690040000002d01000004000000f001010008000000320ad001fb050100000030791c000000fb0240ff
0000000000009001010000000402001054696d6573204e657720526f6d616e0010f11200278ba2774091a5775c156690040000002d01010004000000f0010000
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\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid10564841\charrsid10564841                       }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid16253453                                 }{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid4657411 (26}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 )
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10289250 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 
Handling of constraints is one of main advantages of predictive control. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 
General formulation of predictive control with constraints is then as follows
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\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid10564841\charrsid10564841                 }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid526655                           }{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\insrsid4657411 (27}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10564841\charrsid10564841 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 
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\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid10564841\charrsid10564841                               }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid526655 
                                 }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4657411 (28}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid10564841\charrsid10564841 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang4105\langfe1032\langnp4105\insrsid10564841\charrsid10564841 
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa240\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10289250 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid4657411 The inequality (28}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10564841\charrsid10564841 ) expresses the constraints in a compact form.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10564841 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid3998603 {\rtlch\fcs1 \ab\af0\afs28 \ltrch\fcs0 \b\fs28\lang1033\langfe1032\langnp1033\insrsid3998603 4\tab }{\rtlch\fcs1 \ab\af0\afs28 
\ltrch\fcs0 \b\fs28\lang1033\langfe1032\langnp1033\insrsid3998603\charrsid3998603 Computation of predictions \endash  }{\rtlch\fcs1 \ab\af0\afs28 \ltrch\fcs0 \b\fs28\lang1033\langfe1032\langnp1033\insrsid16532164 SISO system}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid3998603 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid9918086 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9918086\charrsid9918086 An important}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid9918086\charrsid9918086  task is computation of predictions for arbitrary prediction and control horizons. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9918086\charrsid9918086 
Dynamics of most of processes requires horizons of length where it is not possible to compute predictions in a simple straightforward way. Recursive expressions for computation of the free response and the matrix }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 
\i\fs22\insrsid9918086\charrsid9918086 G}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9918086\charrsid9918086 
 in each sampling period had to be derived. There are several different ways of deriving the prediction equations for transfer function models. Some papers make use of Diophantine equations to form the prediction equations }{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\insrsid4197373\charrsid4197373 [12}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9918086\charrsid4197373 ].}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9918086\charrsid9918086  In }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid4197373\charrsid4197373 [13}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9918086\charrsid4197373 ]}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9918086\charrsid9918086 
 matrix methods are used to compute predictions. We derived a method for recursive computation of both the free response and the matrix of the dynamics.
\par }\pard \ltrpar\qj \fi284\li0\ri0\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10289250 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9918086\charrsid9918086 
Computation of the predictor for the time-delay system can be obtained by modifica
tion of the predictor for the corresponding system without a time-delay. At first we will consider the second order system without time-delay and then we will modify the computation of predictions for the time-delay system.
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid9918086 {\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid9918086 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid3998603 {\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid11692753 4}{\rtlch\fcs1 \ab\af0\afs22 
\ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid3998603 .1 }{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid727258\charrsid727258 Computation of predictions }{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 
\b\fs22\lang1033\langfe1032\langnp1033\insrsid15140644 without time-delay}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid3998603 
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid7235830 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid11086775\charrsid11086775 
The difference equation of the CARIMA model without the unknown term can be expressed as:
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0a00ffffffff0100000000001c000000fb021000070000000000bc02000000ee0102022253797374656d00e6d70d66e600000a0038008a01000000000100000030f31200040000002d01010004000000f0010000030000000000}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang4105\langfe1032\langnp4105\insrsid2956925 
\par                                                                             }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid931497 (36}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid11086775\charrsid11086775 )
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10289250 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid11086775\charrsid11086775 
The coefficients of the matrices }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang1033\langfe1032\langnp1033\insrsid11086775\charrsid11086775 G}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid11086775\charrsid11086775 , }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang1033\langfe1032\langnp1033\insrsid11086775\charrsid11086775 P}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid11086775\charrsid11086775  and }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang1033\langfe1032\langnp1033\insrsid11086775\charrsid11086775 Q}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid11086775\charrsid11086775  for further predictions are computed recursively. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid11086775\charrsid11086775 
Based on the three previous predictions it is repeatedly computed the next row of the matrices }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\insrsid11086775\charrsid11086775 P}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid11086775\charrsid11086775  and }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\insrsid11086775\charrsid11086775 Q}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid11086775\charrsid11086775  in the following way:}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid11086775\charrsid11086775  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid11086775\charrsid11086775  
\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11086775 {\pard\plain \ltrpar\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11086775 
\rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \fs22\lang1033\langfe1032\cgrid\langnp1033\langfenp1032\insrsid11086775\charrsid11086775 {\object\objemb\objw2940\objh300{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300
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\ltrch\fcs0 \fs22\dn40\lang1033\langfe1032\langnp1033\insrsid14958271\charrsid2956925 {\pict{\*\picprop\shplid1074{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLockAspectRatio}{\sv 1}}{\sp{\sn pictureGray}{\sv 0}}
{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fRecolorFillAsPicture}{\sv 0}}{\sp{\sn fUseShapeAnchor}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}
{\sp{\sn fLine}{\sv 0}}{\sp{\sn fPreferRelativeResize}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fFakeMaster}{\sv 0}}{\sp{\sn fCameFromImgDummy}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw5503\pich1588\picwgoal3120\pichgoal900\wmetafile8\bliptag-1813230022\blipupi621{\*\blipuid 93ec4e3a5f2236e3fa25ead1b9b3c990}
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0000bc02000000ee0102022253797374656d00729116667200000a0038008a01000000000000000028f31200040000002d01000004000000f0010100030000000000}}}}}\sectd \ltrsect\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid11086775\charrsid11086775                    }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1275086   (38}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid11086775\charrsid11086775 )
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10289250 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid11086775\charrsid11086775 The recursion of the matrix }{\rtlch\fcs1 
\ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\insrsid11086775\charrsid11086775 G}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid11086775\charrsid11086775 
 is similar. The next element of the first column is repeatedly computed and the remaining columns are shifted. This procedure is performed repeatedly until the prediction horizon is achieved. If the control horizon is lower than the prediction 
horizon a number of columns in the matrix is reduced. Computation of a new element is performed as follows:
\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11086775 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid14958271\charrsid11086775 
{\pict{\*\picprop\shplid1075{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fPreferRelativeResize}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex89\picscaley91\piccropl0\piccropr0\piccropt0\piccropb0\picw5539\pich635\picwgoal3140\pichgoal360\wmetafile8\bliptag-1156519118\blipupi371{\*\blipuid bb10eb32287a42d7db6976cc3345ba36}
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000000010002001053796d626f6c0000cc0c0ac734e01200a8aaf377b1aaf3772030f577120d66e9040000002d01010004000000f001000009000000320a0000
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2b020083610003001b00000b01000200883200000101000a020083670003001b00000b010002008831000001010000000b00000026060f000c00ffffffff0100
0000000000001c000000fb021000070000000000bc02000000ee0102022253797374656d00e9120d66e900000a0021008a010000000000000000dce61200040000002d01000004000000f0010100030000000000}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1036\langfe1032\langnp1036\insrsid11086775\charrsid11086775                           }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1036\langfe1032\langnp1036\insrsid9707595  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\up12\lang1036\langfe1032\langnp1036\insrsid1275086 (39}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\up12\lang1036\langfe1032\langnp1036\insrsid11086775\charrsid9707595 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid11086775\charrsid15629775 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid3998603 {\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid11692753 4}{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 
\b\fs22\lang1033\langfe1032\langnp1033\insrsid3998603 .2 }{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid727258\charrsid727258 Computation of predictions }{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 
\b\fs22\lang1033\langfe1032\langnp1033\insrsid1275086 with time-delay}{\rtlch\fcs1 \af0 \ltrch\fcs0 \lang1033\langfe1032\langnp1033\insrsid3998603 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10289250 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid748572\charrsid748572 
In order to compute the control action it is necessary to determine the predictions from }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\insrsid748572\charrsid748572 d}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid748572\charrsid748572 +1 to }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang1033\langfe1032\langnp1033\insrsid748572\charrsid748572 d}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid748572\charrsid748572 +}{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang1033\langfe1032\langnp1033\insrsid748572\charrsid748572 N}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid748572\charrsid748572 .
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10289250 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid748572 The predictor (31}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\lang1029\langfe1032\langnp1029\insrsid748572\charrsid748572 ) }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid748572\charrsid748572 is then modified to}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid748572  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid539391 
\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid539391 {\pard\plain \ltrpar\qj \li0\ri0\sa120\widctlpar
\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid539391 \rtlch\fcs1 \af0\afs20\alang1025 \ltrch\fcs0 \fs20\lang2057\langfe1033\cgrid\langnp2057\langfenp1033\insrsid748572 {\object\objemb\objw4180\objh3100\objscaley122
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\sectd \ltrsect\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \fs20\lang2057\langfe1033\langfenp1033\insrsid748572  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang2057\langfe1033\langfenp1033\insrsid748572\charrsid748572 (40)}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1033\langfenp1033\insrsid748572 
\par }\pard \ltrpar\qj \fi284\li0\ri0\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10289250 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid2774790\charrsid2774790 
Recursive computation of the matrices is analogical to the recursive computation described in the previous section.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid2774790 
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10289250 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid2774790\charrsid2774790 The predictor modified for }{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\insrsid2774790 two steps of}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid2774790\charrsid2774790  time \endash delay is then given as follows}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid2774790 
\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid539391 {\pard\plain \ltrpar\qj \li0\ri0\sa120\widctlpar
\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid539391 \rtlch\fcs1 \af0\afs20\alang1025 \ltrch\fcs0 \fs20\lang2057\langfe1033\cgrid\langnp2057\langfenp1033\insrsid2774790 {\object\objemb\objw3760\objh1780\objscaley123
{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300000000000000000000240000
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\par 
\par }{\rtlch\fcs1 \ab\af0\afs28 \ltrch\fcs0 \b\fs28\lang1033\langfe1032\langnp1033\insrsid9182649 5\tab }{\rtlch\fcs1 \ab\af0\afs28 \ltrch\fcs0 \b\fs28\lang1033\langfe1032\langnp1033\insrsid3869619\charrsid3869619 Computation of predictions }{\rtlch\fcs1 
\ab\af0\afs28 \ltrch\fcs0 \b\fs28\lang1033\langfe1032\langnp1033\insrsid420512\charrsid3998603 \endash  }{\rtlch\fcs1 \ab\af0\afs28 \ltrch\fcs0 \b\fs28\lang1033\langfe1032\langnp1033\insrsid4129960 TIT}{\rtlch\fcs1 \ab\af0\afs28 \ltrch\fcs0 
\b\fs28\lang1033\langfe1032\langnp1033\insrsid420512 O system}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid9182649 
\par }{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid9182649 5.1 }{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid9182649\charrsid727258 Computation of predictions }{\rtlch\fcs1 
\ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid420512 without time delay}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid9182649 
\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid4129960 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960 The difference equation}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid3234516 s}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960  of the CARIMA model without the unknown term }{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid3234516 are as follows}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960 
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\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4129960 
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid6972631 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960 
These equations can be written into a matrix form
\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid4129960 {\pard\plain \ltrpar\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid4129960 
\rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \fs22\lang1033\langfe1032\cgrid\langnp1033\langfenp1032\insrsid4129960\charrsid4129960 {\object\objemb\objw3620\objh620{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000
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\fs22\insrsid4129960\charrsid4129960  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid339224 (20}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4129960\charrsid4129960 ) as follows
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\af0\afs22 \ltrch\fcs0 \fs22\dn42\lang1033\langfe1032\langnp1033\insrsid14958271\charrsid3428265 {\pict{\*\picprop\shplid1089{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLockAspectRatio}{\sv 1}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fRecolorFillAsPicture}{\sv 0}}{\sp{\sn fUseShapeAnchor}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
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{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fFakeMaster}{\sv 0}}{\sp{\sn fCameFromImgDummy}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw3246\pich1658\picwgoal1840\pichgoal940\wmetafile8\bliptag-602684075\blipupi-128{\*\blipuid dc13c555269b9e76c2cad35c5d7c3703}
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\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid3428265                                             (47}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid4129960\charrsid4129960 )
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid3428265 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4129960\charrsid4129960 
It is possible to divide computation of the predictions to recursion of the free response and recursion of the matrix of the dynamics. The free response vector predictions can be expressed as:}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid3428265 {\pard\plain \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid3428265 \rtlch\fcs1 
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\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4129960\charrsid4129960   }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid3428265 
                                                                           }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid3428265 (48}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960 )
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid3428265 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960 
The coefficients of the matrices }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960 P}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960 
 and }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960 Q}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960 
 for further predictions are computed recursively. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4129960\charrsid4129960 Based on the three previous predictions it is repeatedly computed the next row of the matrices }{\rtlch\fcs1 \ab\ai\af0\afs22 
\ltrch\fcs0 \b\i\fs22\insrsid4129960\charrsid4129960 P}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4129960\charrsid4129960  and }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\insrsid4129960\charrsid4129960 Q}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid4129960\charrsid4129960  in the following way:}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960 
\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid4129960 {\pard\plain \ltrpar\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid4129960 
\rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \fs22\lang1033\langfe1032\cgrid\langnp1033\langfenp1032\insrsid4129960\charrsid4129960 {\object\objemb\objw3320\objh660\objscalex96\objscaley97{\*\objclass Equation.3}{\*\objdata 01050000020000000b000000
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\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4129960\charrsid4129960         }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid5132831          }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid5132831 (52}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960 )
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid5132831 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid4129960\charrsid4129960 
The recursion of the matrix }{\rtlch\fcs1 \ab\ai\af0\afs22 \ltrch\fcs0 \b\i\fs22\lang4105\langfe1032\langnp4105\insrsid4129960\charrsid4129960 G}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid339224  is analogical}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid4129960\charrsid4129960 . }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid15606425 
The computation is similar as it was introduced in section 4.1.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid339224  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid15606425 It}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid4129960\charrsid4129960  is}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid15606425  apparent from equations (}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid5132831 53}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid15606425 ) and (}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid5132831 54}
{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid4129960\charrsid4129960 ).
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6603010000006a7908000000320a5c015f01010000006b791c000000fb02c0fe0000000000009001000000020002001053796d626f6c000082080a563cf11200
e8b1f377f1b1f3772040f577b80e66d7040000002d01010004000000f001000008000000320a3c03270101000000a37908000000320a5c014e18010000002b79
08000000320a5c018d16010000002d7908000000320a5c01ea12010000002b7908000000320a5c010f11010000002d7908000000320a5c019f0c010000002b79
08000000320a5c01c40a010000002d7908000000320a5c01fe08010000002b7908000000320a5c017604010000003d7908000000320a5c013d02010000002b79
1c000000fb02c0fe0000000000009001000000000402001054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577b80e66d7040000002d010000
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74000100000088791c000000fb02c0fe000000000000bc02010000000402001054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577b80e66d7
040000002d01010004000000f001000008000000320a5c01cd1302000000517908000000320a5c011c0f01000000757908000000320a5c019b0d010000005079
08000000320a5c010b0701000000757908000000320a5c01670501000000477908000000320a5c0163000100000079790a00000026060f000a00ffffffff0100
000000001c000000fb021000070000000000bc02000000ee0102022253797374656d00d7b80e66d700000a0021008a01000000000000000054f31200040000002d01000004000000f0010100030000000000}}}}}\sectd \ltrsect
\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid11891445  (55}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid4129960\charrsid4129960 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid3869619 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid9182649 {\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid9182649 5.2 }{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 
\b\fs22\lang1033\langfe1032\langnp1033\insrsid9182649\charrsid727258 Computation of predictions }{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\lang1033\langfe1032\langnp1033\insrsid420512 with time-delay}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\lang1033\langfe1032\langnp1033\insrsid9182649 
\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1059011 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1059011\charrsid1059011 
The predictor modified for a}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1059011 n arbitrary time \endash delay is }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid1059011\charrsid1059011 given as follows. 
\par }{\pard\plain \ltrpar\qj \li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1059011 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\fs22\lang1033\langfe1032\cgrid\langnp1033\langfenp1032\insrsid1059011\charrsid1059011 {\object\objemb\objw2140\objh940{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300000000000000000000140000
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ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000feffffff05000000feffffff060000000700000008000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c000000000000046000000000000000000000000d02b
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000000000000000000000000030000000600000000000000feffffff02000000fefffffffeffffff05000000060000000700000008000000090000000a0000000b0000000c0000000d0000000e0000000f000000100000001100000012000000130000001400000015000000160000001700000018000000190000001a00
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ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
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0000bc02010000000402001054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577d70f6631040000002d01000004000000f001010008000000320a4003ff0b01000000797908000000320a4003020a01000000757908000000320a4003590801000000477908000000320a2005f4000100000079790800
0000320a4003ea0001000000797908000000320a600108010100000079791c000000fb02c0fe0000000000009001000000020002001053796d626f6c00006e100a523cf11200e8b1f377f1b1f3772040f577d70f6631040000002d01010004000000f001000008000000320a4003ea0a010000002b7908000000320a4003
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010000006b7908000000320a4003720501000000647908000000320a4003e601010000006b7908000000320a6001540501000000647908000000320a60010402010000006b790a00000026060f000a00ffffffff0100000000001c000000fb021000070000000000bc02000000ee0102022253797374656d0031d70f6631
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090000030100000112836b0002862b000288310002862b00128364000002962800029629000000012287790006090000030100000112836b0002862b000288320002862b00128364000002962800029629000000012287790006090000030100000112836b0002862b000288330002862b00128364000002962800029629
000000000002965b0002965d000002863d0002874700028594030287750002862b0002877900030f01000b0102883000001100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c455049435400bf0e000086f9ffffc20600000800bf0e7a060000
0100090000035d03000002001c00000000000500000009020000000005000000020101000000050000000102ffffff00050000002e0118000000050000000b0200000000050000000c02e005600d1200000026060f001a00ffffffff000010000000c0ffffffbdffffff200d00009d0500000b00000026060f000c004d61
746854797065000050011c000000fb024efebd00000000009001000000020002001053796d626f6c0000ff100a242cef1200e8b1f377f1b1f3772040f577d70f6631040000002d01000008000000320a5f01a2010100000028791c000000fb024efebd00000000009001000000020002001053796d626f6c00006e100a4e
2cef1200e8b1f377f1b1f3772040f577d70f6631040000002d01010004000000f001000008000000320a5f0121060100000029791c000000fb024efebd00000000009001000000020002001053796d626f6c0000ff100a252cef1200e8b1f377f1b1f3772040f577d70f6631040000002d01000004000000f00101000800
0000320a3f0384010100000028791c000000fb024efebd00000000009001000000020002001053796d626f6c00006e100a4f2cef1200e8b1f377f1b1f3772040f577d70f6631040000002d01010004000000f001000008000000320a3f033f060100000029791c000000fb024efebd000000000090010000000200020010
53796d626f6c0000ff100a262cef1200e8b1f377f1b1f3772040f577d70f6631040000002d01000004000000f001010008000000320a1f058e010100000028791c000000fb024efebd00000000009001000000020002001053796d626f6c00006e100a502cef1200e8b1f377f1b1f3772040f577d70f6631040000002d01
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00009001000000000402001054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577d70f6631040000002d01010004000000f001000008000000320a2005b10301000000337908000000320a0405050101000000887908000000320a4003b10301000000327908000000320a2403fb000100000088790800
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6631040000002d01010004000000f001000008000000320a4003ea0a010000002b7908000000320a40033f0901000000447908000000320a40036807010000003d7908000000320afa04950601000000fa7908000000320aca03950601000000fa7908000000320a9a02950601000000fa7908000000320a840595060100
0000fb7908000000320a6a01950601000000f97908000000320afa04400001000000ea7908000000320aca03400001000000ea7908000000320a9a02400001000000ea7908000000320a8405400001000000eb7908000000320a6a01400001000000e97908000000320a20057b04010000002b7908000000320a2005ce02
010000002b7908000000320a40038504010000002b7908000000320a4003c402010000002b7908000000320a60016704010000002b7908000000320a6001e202010000002b791c000000fb02c0fe0000000000009001010000000402001054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577d70f6631
040000002d01000004000000f001010008000000320a2005680501000000647908000000320a2005f001010000006b7908000000320a4003720501000000647908000000320a4003e601010000006b7908000000320a6001540501000000647908000000320a60010402010000006b790a00000026060f000a00ffffffff
0100000000001c000000fb021000070000000000bc02000000ee0102022253797374656d0031d70f663100000a0021008a01000000000100000054f31200040000002d01010004000000f0010000030000000000}{\result {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\dn42\lang1033\langfe1032\langnp1033\insrsid14958271\charrsid1059011 {\pict{\*\picprop\shplid1098{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLockAspectRatio}{\sv 1}}{\sp{\sn pictureGray}{\sv 0}}
{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fRecolorFillAsPicture}{\sv 0}}{\sp{\sn fUseShapeAnchor}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}
{\sp{\sn fLine}{\sv 0}}{\sp{\sn fPreferRelativeResize}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fFakeMaster}{\sv 0}}{\sp{\sn fCameFromImgDummy}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw3775\pich1658\picwgoal2140\pichgoal940\wmetafile8\bliptag644896959\blipupi107{\*\blipuid 267058bf125f515e54c925bdb462a1bc}
0100090000035d03000002001c00000000000500000009020000000005000000020101000000050000000102ffffff00050000002e0118000000050000000b02
00000000050000000c02e005600d1200000026060f001a00ffffffff000010000000c0ffffffbdffffff200d00009d0500000b00000026060f000c004d617468
54797065000050011c000000fb024efebd00000000009001000000020002001053796d626f6c0000ff100a242cef1200e8b1f377f1b1f3772040f577d70f6631
040000002d01000008000000320a5f01a2010100000028791c000000fb024efebd00000000009001000000020002001053796d626f6c00006e100a4e2cef1200
e8b1f377f1b1f3772040f577d70f6631040000002d01010004000000f001000008000000320a5f0121060100000029791c000000fb024efebd00000000009001
000000020002001053796d626f6c0000ff100a252cef1200e8b1f377f1b1f3772040f577d70f6631040000002d01000004000000f001010008000000320a3f03
84010100000028791c000000fb024efebd00000000009001000000020002001053796d626f6c00006e100a4f2cef1200e8b1f377f1b1f3772040f577d70f6631
040000002d01010004000000f001000008000000320a3f033f060100000029791c000000fb024efebd00000000009001000000020002001053796d626f6c0000
ff100a262cef1200e8b1f377f1b1f3772040f577d70f6631040000002d01000004000000f001010008000000320a1f058e010100000028791c000000fb024efe
bd00000000009001000000020002001053796d626f6c00006e100a502cef1200e8b1f377f1b1f3772040f577d70f6631040000002d01010004000000f0010000
08000000320a1f0535060100000029791c000000fb0220ff0000000000009001000000000402001054696d6573204e657720526f6d616e00e8b1f377f1b1f377
2040f577d70f6631040000002d01000004000000f001010008000000320a9003a30c0100000030791c000000fb02c0fe00000000000090010000000004020010
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08000000320a0405050101000000887908000000320a4003b10301000000327908000000320a2403fb0001000000887908000000320a6001ac03010000003179
08000000320a440119010100000088791c000000fb02c0fe000000000000bc02010000000402001054696d6573204e657720526f6d616e00e8b1f377f1b1f377
2040f577d70f6631040000002d01000004000000f001010008000000320a4003ff0b01000000797908000000320a4003020a01000000757908000000320a4003
590801000000477908000000320a2005f40001000000797908000000320a4003ea0001000000797908000000320a600108010100000079791c000000fb02c0fe
0000000000009001000000020002001053796d626f6c00006e100a523cf11200e8b1f377f1b1f3772040f577d70f6631040000002d01010004000000f0010000
08000000320a4003ea0a010000002b7908000000320a40033f0901000000447908000000320a40036807010000003d7908000000320afa04950601000000fa79
08000000320aca03950601000000fa7908000000320a9a02950601000000fa7908000000320a8405950601000000fb7908000000320a6a01950601000000f979
08000000320afa04400001000000ea7908000000320aca03400001000000ea7908000000320a9a02400001000000ea7908000000320a8405400001000000eb79
08000000320a6a01400001000000e97908000000320a20057b04010000002b7908000000320a2005ce02010000002b7908000000320a40038504010000002b79
08000000320a4003c402010000002b7908000000320a60016704010000002b7908000000320a6001e202010000002b791c000000fb02c0fe0000000000009001
010000000402001054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577d70f6631040000002d01000004000000f001010008000000320a2005
680501000000647908000000320a2005f001010000006b7908000000320a4003720501000000647908000000320a4003e601010000006b7908000000320a6001
540501000000647908000000320a60010402010000006b790a00000026060f000a00ffffffff0100000000001c000000fb021000070000000000bc02000000ee0102022253797374656d0031d70f663100000a0021008a01000000000100000054f31200040000002d01010004000000f0010000030000000000}}}}}
\sectd \ltrsect\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1059011\charrsid1059011                     }{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1059011                   (56}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1059011\charrsid1059011 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid1059011 
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10749830 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10749830\charrsid10749830 
The computation of }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10749830 the }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10749830\charrsid10749830 free response is then modified to

\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1059011 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid10749830\charrsid1059011 
\par }\pard \ltrpar\qj \li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid4982630 {\pard\plain \ltrpar\qj \li0\ri0\sa120\widctlpar
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\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1059011\charrsid1059011    }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid4982630                                                                           }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1059011\charrsid1059011 (}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid4982630 57}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1059011\charrsid1059011 )
\par }\pard \ltrpar\qj \fi284\li0\ri0\sa120\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid4982630 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid1059011\charrsid1059011 
The computation of the forced response is again given by equation (}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\insrsid4982630 53}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid1059011\charrsid1059011 )
\par }\pard\plain \ltrpar\s28\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid9716655 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang1033\langfe1032\cgrid\langnp1033\langfenp1032 {\rtlch\fcs1 \ab\af0\afs28 
\ltrch\fcs0 \b\fs28\insrsid8207408 6 Simulation }{\rtlch\fcs1 \ab\af0\afs28 \ltrch\fcs0 \b\fs28\insrsid3549040 Verification }{\rtlch\fcs1 \ab\af0\afs28 \ltrch\fcs0 \b\fs28\insrsid6977908 
\par }\pard \ltrpar\s28\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid6977908 {\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\insrsid13893676 6}{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\insrsid10961081 .1 }{
\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\insrsid6835649 SISO control}{\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\insrsid10961081  
\par }\pard \ltrpar\s28\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid12393850 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 
As simulation examples were chosen a fifth order linear system described by following transfer function
\par }\pard \ltrpar\s28\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11223673 {\pard\plain \ltrpar
\s28\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11223673 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \fs22\lang1033\langfe1032\cgrid\langnp1033\langfenp1032\insrsid490045\charrsid490045 
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\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045       }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid11223673                }{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\up18\insrsid4862203\charrsid11223673 (59}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\up18\insrsid490045\charrsid11223673 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 
\par }\pard \ltrpar\s28\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11736403 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 The systems were identified by model (}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4862203 6}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9206495 ) using off-line LSM}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid16335468  (least squares method)}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid9206495  [14}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 ]. System (}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4862203 58}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 
) was approximated by 
\par }\pard \ltrpar\s28\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid11223673 {\pard\plain \ltrpar
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\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw1515\pich529\picwgoal859\pichgoal300\wmetafile8\bliptag-915173917\blipupi2306{\*\blipuid c9738de31650ad6cf27383a4cc0f6ca6}
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\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 . The step responses of models}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4862203 
 (58) and (59}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 ) together with discrete step respo}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4862203 nses of their approximations (60) and (61}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\insrsid490045\charrsid490045 ) are in the following figures
\par }\pard \ltrpar\s28\qj \li0\ri0\sb240\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid490045 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1029\langfe1032\langnp1029\insrsid14958271\charrsid490045 {\*\shppict
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\af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 
\par Fig.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9728384  1}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045  Step responses of models}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9728384  (58}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\insrsid490045\charrsid490045 ) and (}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid14507566 60}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 )
\par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1029\langfe1032\langnp1029\insrsid14958271\charrsid490045 {\*\shppict{\pict{\*\picprop\shplid1106{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
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\af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 
\par Fig}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9728384 . 2}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045  Step responses of model}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid14507566 s (59}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\insrsid490045\charrsid490045 ) and (}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid14507566 61}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 )
\par }\pard \ltrpar\s28\qj \fi284\li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid4347537 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 Control responses are in figures}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\insrsid9728384  3, 4, 5 and 6}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 .}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid490045\charrsid490045 
\par }\pard \ltrpar\s28\qj \fi284\li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid4347537 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid490045\charrsid490045 
The tuning parameters that are lengths of the prediction and control horizons and the weighting coefficient }{\rtlch\fcs1 \ai\af302\afs22 \ltrch\fcs0 \i\f302\fs22\lang2057\langfe1032\langnp2057\insrsid490045\charrsid490045 \'eb}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid490045\charrsid490045  were tuned exper
imentally. There is a lack of clear theory relating to the closed loop behavior to design parameters. The length of the prediction horizon, which should cover the important part of the step response, was in both cases set to }{\rtlch\fcs1 \ai\af0\afs22 
\ltrch\fcs0 \i\fs22\lang2057\langfe1032\langnp2057\insrsid490045\charrsid490045 N}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid490045\charrsid490045  = 40. The length of the control horizon was also set to }{\rtlch\fcs1 
\ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang2057\langfe1032\langnp2057\insrsid490045\charrsid490045 N}{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang2057\langfe1032\sub\langnp2057\insrsid490045\charrsid490045 u}{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 
\i\fs22\lang2057\langfe1032\langnp2057\insrsid490045\charrsid490045  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid490045\charrsid490045 = 40. The coefficient }{\rtlch\fcs1 \ai\af302\afs22 \ltrch\fcs0 
\i\f302\fs22\lang2057\langfe1032\langnp2057\insrsid490045\charrsid490045 \'eb}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid490045\charrsid490045  was taken as equal to 0,5.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid490045\charrsid490045 
\par }\pard \ltrpar\s28\qj \li0\ri0\sb240\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid490045 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid14958271\charrsid490045 {\*\shppict
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\fs22\insrsid490045\charrsid490045 )
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\af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 
\par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid3744392 Fig. 4}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045  Control of model }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid3744392 (60}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid490045\charrsid490045 ) \endash manipulated variable
\par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid14958271\charrsid490045 {\*\shppict{\pict{\*\picprop\shplid1109{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
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\af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 
\par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid3744392 Fig. 5}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045  Control of model (}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid3744392 61}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid490045\charrsid490045 )
\par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid14958271\charrsid490045 {\*\shppict{\pict{\*\picprop\shplid1110{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
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\af0\afs22 \ltrch\fcs0 \fs22\insrsid490045\charrsid490045 
\par }\pard \ltrpar\s28\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid6829075 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid3744392 Fig. 6}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang2057\langfe1032\langnp2057\insrsid490045\charrsid490045  Control of model (}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid15823919 61}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang2057\langfe1032\langnp2057\insrsid490045\charrsid490045 ) \endash manipulated variable}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid490045  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang2057\langfe1032\langnp2057\insrsid6829075 
\par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid12652420 
\par }\pard \ltrpar\s28\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid12652420 {\rtlch\fcs1 \ab\af0\afs22 \ltrch\fcs0 \b\fs22\insrsid12652420 6.2 TITO control 
\par }\pard \ltrpar\s28\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid14751192 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid537753 A}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid7083720  TITO}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid537753\charrsid537753  system with two steps of time-delay
\par }{\pard\plain \ltrpar\s28\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid14751192 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
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\fs22\lang2057\langfe1032\langnp2057\insrsid4153360                   }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid12870820 (62}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang2057\langfe1032\langnp2057\insrsid537753\charrsid537753 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid537753\charrsid537753 
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\af0\afs22 \ltrch\fcs0 \fs22\insrsid537753\charrsid537753 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid5005073  was chosen as an example}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid537753\charrsid537753  
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\ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid4153360                   }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4153360 (65}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid5005073\charrsid5005073 )
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\ltrch\fcs0 \fs22\insrsid10749830 the }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid5005073\charrsid5005073 free response }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid14822987 was}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid5005073\charrsid5005073  then modified to
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0100000000001c000000fb021000070000000000bc02000000ee0102022253797374656d00fb8e0e66fb00000a0038008a0100000000020000002cf31200040000002d01020004000000f0010100030000000000}}}}}\sectd \ltrsect
\psz9\sbknone\linex0\headery708\footery708\cols2\colsx567\endnhere\titlepg\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4153360 
\par }\pard \ltrpar\s28\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid12472848 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4153360 
                                                                             (66}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid5005073\charrsid5005073 )}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid12472848 
\par }\pard \ltrpar\s28\qj \fi284\li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid8654501 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid537753\charrsid537753 Control r}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid12412402 esponses are in Fig.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid8654501  7 }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid537753\charrsid537753 and}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid12412402  Fig.}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid8654501  8}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid537753\charrsid537753 .}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang4105\langfe1032\langnp4105\insrsid537753\charrsid12472848 
\par }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid537753\charrsid537753 The length of the prediction horizon was set to }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 
\i\fs22\lang2057\langfe1032\langnp2057\insrsid537753\charrsid537753 N}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid537753\charrsid537753  = 10. The length of the control horizon was also set to }{\rtlch\fcs1 
\ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang2057\langfe1032\langnp2057\insrsid537753\charrsid537753 N}{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\fs22\lang2057\langfe1032\sub\langnp2057\insrsid537753\charrsid537753 u}{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 
\i\fs22\lang2057\langfe1032\langnp2057\insrsid537753\charrsid537753  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid537753\charrsid537753 = 10. The coefficient }{\rtlch\fcs1 \ai\af302\afs22 \ltrch\fcs0 
\i\f302\fs22\lang2057\langfe1032\langnp2057\insrsid537753\charrsid537753 \'eb}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid537753\charrsid537753  was taken as equal to 0,5.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid537753\charrsid537753 
\par }\pard \ltrpar\s28\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid12472848 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1029\langfe1032\langnp1029\insrsid10112999\charrsid537753 {\*\shppict
{\pict{\*\picprop\shplid1116{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLockAspectRatio}{\sv 1}}{\sp{\sn fLockPosition}{\sv 0}}{\sp{\sn fLockAgainstSelect}{\sv 0}}{\sp{\sn fLockAgainstGrouping}{\sv 0}}
{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fRecolorFillAsPicture}{\sv 0}}{\sp{\sn fUseShapeAnchor}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn wzName}{\sv Obr\'e1zek 1}}{\sp{\sn fLayoutInCell}{\sv 1}}
{\sp{\sn fHidden}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex57\picscaley57\piccropl0\piccropr0\piccropt0\piccropb0\picw14817\pich11113\picwgoal8400\pichgoal6300\pngblip\bliptag1721225947{\*\blipuid 6697d2db74a5010009d63d4961df8096}
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111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111040000002701ffff030000000000}}}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\insrsid537753\charrsid537753 
\par }\pard \ltrpar\s28\qj \li0\ri0\sa120\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid14825474 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid8654501 Fig. 8}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid8654501\charrsid490045  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\insrsid537753\charrsid537753 Simulation results \endash  manipulated variable.}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \fs22\insrsid12652420\charrsid490045 
\par }\pard\plain \ltrpar\qj \li0\ri0\widctlpar\tx284\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid6835918 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang2057\langfe1032\cgrid\langnp2057\langfenp1032 {\rtlch\fcs1 
\ab\af0\afs28 \ltrch\fcs0 \b\fs28\lang1033\langfe1032\langnp1033\insrsid6835918 7\tab Conclusions 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid734940 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid3021278\charrsid3021278 The algorithm for control of 
the higher-order processes based on model predictive control was designed. The higher-order process was approximated by the second-order model with time delay. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\lang1033\langfe1032\langnp1033\insrsid3021278\charrsid3021278 The predictive controller is based on the recursive computation of predictions by direct use of the CARIMA model. The computation of predictions was extended for the time-delay system. }{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid3021278\charrsid3021278 The control of two modifications of the higher-order processes (stable and non-minimum phase) were verified by simulation. The simulation verification provided good co
ntrol results. Asymptotic tracking of the reference signal was achieved in both cases. The control of non-minimum phase system was rather sensitive to tuning parameters. Experimental tuning of the controller was more complicated in this case.}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6422538  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid1064064\charrsid1064064 The}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6422538  analogical }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\fs22\insrsid1064064\charrsid1064064 algorithm for control of the multivariable time-delay systems was}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6422538  also}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid1064064\charrsid1064064  designed. }{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid4539580 The control of the}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid1064064\charrsid1064064  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid14825474\charrsid14825474 two \endash  input/two 
\endash  output }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid1064064\charrsid1064064 system with two steps of time-delay was verified by simulation.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid6422538 
 Good simulation control results were achieved.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid12979781  Further research can be focused on an extension of t}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid5733969 he proposed method for control of 2-D
 (two-Dimensional) discrete time systems. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid1064064\charrsid6422538 
\par }\pard \ltrpar\qj \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\insrsid9716655\charrsid9716655      }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 
\i\fs22\lang1033\langfe1032\langnp1033\insrsid4849832 
\par References:
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1029\langfe1032\langfenp1032\insrsid7805266 \hich\af0\dbch\af0\loch\f0 [1]\tab}}\pard\plain \ltrpar\s40\qj \fi-426\li426\ri0\widctlpar
\jclisttab\tx426\wrapdefault\aspalpha\aspnum\faauto\ls9\adjustright\rin0\lin426\itap0\pararsid3804655 \rtlch\fcs1 \af1\afs24\alang1025 \ltrch\fcs0 \f1\fs24\lang2057\langfe1032\cgrid\langnp2057\langfenp1032 {\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1029\langfe1032\langnp1029\insrsid7805266 A. O\rquote Dwyer,}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid6759120\charrsid6759120 
 Classification of techniques for the compensation of time delayed processes. Part 1: P}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid6759120 arameter optimised controllers,}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1029\langfe1032\langnp1029\insrsid6759120\charrsid6759120  }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\lang1029\langfe1032\langnp1029\insrsid6759120\charrsid6759120 
Proc. Of the 3rd IMACS/IEE International Multiconference on Circuits, Systems, Communications and Computers}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid7805266 , Athens, Greece, 1999, }{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid6759120\charrsid6759120 176-186.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid6759120\charrsid6759120 
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1029\langfe1032\langfenp1032\insrsid7805266 \hich\af0\dbch\af0\loch\f0 [2]\tab}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid7805266 A. O
\rquote Dwyer, }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid7805266\charrsid7805266 Classification of techniques for the compensation of time delayed processes. Part 2: Stru}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1029\langfe1032\langnp1029\insrsid7805266 cturally optimised controllers, }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid7805266\charrsid7805266  }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 
\i\f0\fs22\lang1029\langfe1032\langnp1029\insrsid7805266\charrsid7805266 Proc. of the 3rd IMACS/IEE International Multiconference on Circuits, Systems,Communications and Computers}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1029\langfe1032\langnp1029\insrsid7805266 , Athens, Greece, 1999, }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid7805266\charrsid7805266 187-198.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1033\langfe1032\langnp1033\insrsid7805266\charrsid7805266 
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1029\langfe1032\langfenp1032\insrsid12984446 \hich\af0\dbch\af0\loch\f0 [3]\tab}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid12984446 
J. P. Richard, }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid12984446\charrsid12984446 Time-delay systems: an overview of some recent advances}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1029\langfe1032\langnp1029\insrsid12984446  and open problems, }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\lang1029\langfe1032\langnp1029\insrsid12984446\charrsid12984446 Automatica}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1029\langfe1032\langnp1029\insrsid12984446 , }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid12984446\charrsid12984446 39,}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1029\langfe1032\langnp1029\insrsid12984446  2003, }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid12984446\charrsid12984446  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1029\langfe1032\langnp1029\insrsid12984446 1667-1694}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid12984446\charrsid12984446 .}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1033\langfe1032\langnp1033\insrsid12984446\charrsid5128139 
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1029\langfe1032\langfenp1032\insrsid3017141\charrsid223716 \hich\af0\dbch\af0\loch\f0 [4]\tab}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1029\langfe1032\langnp1029\insrsid3017141\charrsid223716 E. F. Camacho, C. Bordons, }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\lang1029\langfe1032\langnp1029\insrsid3017141\charrsid223716 Model Predictive Control, }{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid3017141\charrsid223716 Springer-Verlag, London, 2004.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid3017141\charrsid2364648 
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\langfenp1032\insrsid3017141\charrsid10233064 \hich\af0\dbch\af0\loch\f0 [5]\tab}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\insrsid3017141\charrsid10233064 M. Morari, J. H. Lee, Model predictive control: past, present and future. }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\insrsid3017141\charrsid10233064 Computers and Chemical Engineering, }{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \f0\fs22\insrsid3017141\charrsid10233064 23, 1999, 667-682.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid3017141\charrsid3424057 
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\langfenp1032\insrsid3017141\charrsid11304205 \hich\af0\dbch\af0\loch\f0 [6]\tab}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\insrsid3017141\charrsid11304205 J. Mikle\'9a & M. Fikar, }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\insrsid3017141\charrsid11304205 Process Modelling, Optimisation and Control.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\insrsid3017141\charrsid11304205  (Berlin: Springer-Verlag, 2008).}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid3017141\charrsid2700222 
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1029\langfe1032\langfenp1032\insrsid2700222\charrsid2700222 \hich\af0\dbch\af0\loch\f0 [7]\tab}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1029\langfe1032\langnp1029\insrsid2700222\charrsid2700222 O. J. Smith. Closed control of loops. }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\lang1029\langfe1032\langnp1029\insrsid2700222\charrsid2700222 Chem. Eng. Progress}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid2700222 , 53, 1957, }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid2700222\charrsid2700222 217-219.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1033\langfe1032\langnp1033\insrsid2700222\charrsid12652807 
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\langfenp1032\insrsid14241979\charrsid3553988 \hich\af0\dbch\af0\loch\f0 [8]\tab}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\insrsid14241979\charrsid3553988 D. W. Clarke, C. Mohtadi, P. S. Tuffs, Generalized predictive control, part I: the basic algorithm. }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\insrsid14241979\charrsid3553988 Automatica}{\rtlch\fcs1 
\af0\afs22 \ltrch\fcs0 \f0\fs22\insrsid14241979\charrsid3553988 , 23, 1987, 137-148.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid14241979 
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang2057\langfe1032\langnp2057\langfenp1032\insrsid14241979\charrsid3553988 \hich\af0\dbch\af0\loch\f0 [9]\tab}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\insrsid14241979\charrsid3553988 D. W. Clarke, C. Mohtadi, P. S. Tuffs, Generalized predictive control, part II: extensions and interpretations. }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\insrsid14241979\charrsid3553988 Automatica}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\insrsid14241979\charrsid3553988 , 23, 1987, 149-160.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid14241979\charrsid14572602 
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\langfenp1032\insrsid14572602\charrsid14572602 \hich\af0\dbch\af0\loch\f0 [10]\tab}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1033\langfe1032\langnp1033\insrsid14572602\charrsid14572602 F. G. Shinskey, }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\lang1033\langfe1032\langnp1033\insrsid14572602\charrsid14572602 Process Control System,}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid14572602\charrsid14572602  4th ed.; McGraw-Hill. New York, 1996.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid14572602 
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1029\langfe1032\langfenp1032\insrsid9457382 \hich\af0\dbch\af0\loch\f0 [11]\tab}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid9457382 
M. Kubal\'e8\'edk, M., V. Bob\'e1l, }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\insrsid9457382\charrsid556286 Adaptive Control of Coupled Drives Apparatus Based on Polynomial Theory. In }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1029\langfe1032\langnp1029\insrsid9457382\charrsid556286 Proc. IMechE Vol. 220 Part I: }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\lang1029\langfe1032\langnp1029\insrsid9457382\charrsid556286 J. Systems and Control Engineering}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid9457382\charrsid556286 , 220(I7),}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid9457382  2006,}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1029\langfe1032\langnp1029\insrsid9457382\charrsid556286  641-654.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid9457382\charrsid2631046 
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\langfenp1032\insrsid2631046\charrsid2631046 \hich\af0\dbch\af0\loch\f0 [12]\tab}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1033\langfe1032\langnp1033\insrsid2631046\charrsid2631046 W.H. Kwon, H. Choj, D.G. Byun, S. Noh,}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid4197373  }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1029\langfe1032\langnp1029\insrsid2631046\charrsid2631046 Recursive solution of generalized predictive control and its equivalence to rec}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1029\langfe1032\langnp1029\insrsid4197373 
eding horizon tracking control.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid2631046\charrsid2631046  }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\lang1033\langfe1032\langnp1033\insrsid2631046\charrsid2631046 
Automatica}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid2631046\charrsid2631046 , 28(6), }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid4197373 1992, }{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid2631046\charrsid2631046 1235\endash 1238.}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid2631046 
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\langfenp1032\insrsid4197373\charrsid4197373 \hich\af0\dbch\af0\loch\f0 [13]\tab}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1033\langfe1032\langnp1033\insrsid4197373\charrsid4197373 J. A. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\insrsid4197373\charrsid4197373 Rossiter, }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\insrsid4197373\charrsid4197373 
Model Based Predictive Control: a Practical Approach}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\insrsid4197373\charrsid4197373  (CRC Press, 2003).}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1033\langfe1032\langnp1033\insrsid4197373\charrsid9206495 
\par {\listtext\pard\plain\ltrpar \s40 \rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \fs22\lang1033\langfe1032\langnp1033\langfenp1032\insrsid9206495\charrsid9206495 \hich\af0\dbch\af0\loch\f0 [14]\tab}}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1033\langfe1032\langnp1033\insrsid9206495\charrsid9206495 V. Bob\'e1l, M. Kubal\'e8\'edk, P. Chalupa and P. }{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid9206495 Dost\'e1l, }{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid9206495\charrsid9206495 Identificati}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid9206495 on and Digital Control of Higher}{\rtlch\fcs1 \af0\afs22 
\ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid9206495\charrsid9206495 -Order Proc}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid9206495 esses Using Predictive Strategy}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1033\langfe1032\langnp1033\insrsid9206495\charrsid9206495 . }{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\lang1033\langfe1032\langnp1033\insrsid9206495\charrsid9206495 Proceedings of 26}{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 
\i\f0\fs22\lang1033\langfe1032\super\langnp1033\insrsid9206495\charrsid9206495 th}{\rtlch\fcs1 \ai\af0\afs22 \ltrch\fcs0 \i\f0\fs22\lang1033\langfe1032\langnp1033\insrsid9206495\charrsid9206495  European Conference on Modelling and Simulation}{
\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid9206495 , 2012, 426-433}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 \f0\fs22\lang1033\langfe1032\langnp1033\insrsid9206495\charrsid9206495 .}{\rtlch\fcs1 \af0\afs22 \ltrch\fcs0 
\f0\fs22\lang1033\langfe1032\langnp1033\insrsid9206495 
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