ࡱ>  RTMNOPQIZfg~LbjbjVV4r<r<Cb: : 880_]$4$$$l%"% %giiiiii$he%l%l%%%$$lll%$$gl%gll'+$P׻d7%'lS08d\++(%%l%%%%%:l%%%8%%%%%%%%%%%%%: ? y:V=VAB5@AB2> >A2VB8 V =0C:8 #:@0W=8 >;B02AL:89 =0FV>=0;L=89 B5E=VG=89 C=V25@A8B5B V<5=V .@VO >=4@0BN:0 0D54@0 5:>=><VG=>W :V15@=5B8:8 01>@0B>@=89 ?@0:B8:C< V7 48AF8?;V=8 ((<VB0FV9=5 <>45;N20==O(( 4;O ABC45=BV2 A?5FV0;L=>ABV 6.050.100 ((:>=><VG=0 :V15@=5B8:0(( 45==>W D>@<8 =02G0==O  >;B020 2006 01>@0B>@=89 ?@0:B8:C< V7 48AF8?;V=8 ((<VB0FV9=5 <>45;N20==O(( 4;O ABC45=BV2 A?5FV0;L=>ABV 6.050.100 ((:>=><VG=0 :V15@=5B8:0(( 45==>W D>@<8 =02G0==O.  >;B020: >;B"#, 2006.  55 A. #:;040G: AB. 28:;040G . . !:@8;L=8:. V4?>2V40;L=89 70 28?CA:: 702. :0D54@8, 4. B. =., ?@>D5A>@ . . !025=:>. 5F5=75=B: :. 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Simulink ?@87=0G5=89 4;O <0B5<0B8G=>3> <>45;N20==O ;V=V9=8E V =5;V=V9=8E 48=0<VG=8E A8AB5< B0 ?@8AB@>W2, ?@54AB02;5=8E A2>TN DC=:FV>=0;L=>N 1;>:-AE5<>N, I> =07820TBLAO S-<>45;;N 01> ?@>AB> <>45;;N. @8 FL><C <>6;82V @V7=V 20@V0=B8 <>45;N20==O: C G0A>2V9 >1;0ABV, C G0AB>B=V9 >1;0ABV, 7 C?@02;V==O< ?>4VO<8, 7 28:>@8AB0==O< <5B>4C >=B5-0@;> (@50:FVO =0 2?;828 28?04:>2>3> E0@0:B5@C) B0 V=. 8:>@8AB>2CNG8 Simulink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atlab 4>72>;ONBL AB2>@N20B8 FV;89 @O4 3@0DVG=8E 2V:>=. # <5=N Edit 2V:=0 3@0DV:8 ?>@O4 V7 AB0=40@B=8<8 >?5@0FVO<8 @>1>B8 7 1CD5@>< >1<V=C T =87:0 =>28E :><0=4: Copy Figure  :>?VN20==O 3@0DV:0 C 1CD5@; Copy Options  :>?VN20==O >?FV9 3@0DV:0; Figure Properties  282545==O 2V:=0 2;0AB82>AB59 3@0DV:0; Axes Properties  282545==O 2V:=0 2;0AB82>AB59 >A59 3@0DV:0; Current Object Properties  282545==O 2V:=0 2;0AB82>AB59 ?>B>G=>3> >1(T:B0. >G8=0NG8 7 25@AVW Matlab 6.0, 7(O28;0AO 4@C30 ?0=5;L V=AB@C<5=BV2 V7 70A>10<8 D>@<0BC20==O B@828<V@=>W 3@0DV:8. &O ?0=5;L 282>48BLAO :><0=4>N View ( Camera Toolbar. $>@<0BC20==O B@828<V@=8E >1(T:BV2 2V41C20TBLAO 70 4>?><>3>N CO2=>W D>B>:0<5@8, G5@57 O:C A?>AB5@V30T<> 70 >1(T:B><. VW :=>?>: ?0=5;V V=AB@C<5=BV2 ?@>4C1;L>20=> :><0=40<8 <5=N Tools: Edit Plot  @5403C20==O 2;0AB82>AB59 3@0DV:0; Zoom In  71V;LH5==O <0AHB01C 3@0DV:0; Zoom Out  7<5=H5==O <0AHB01C 3@0DV:0; Rotate 3D  >15@B0==O C ?@>AB>@V; Move Camera  CAB0=>2:0 :0<5@8 >3;O4C; Camera Motion  CAB0=>2:0 ?5@5<VI5==O :0<5@8 >3;O4C; Camera Axes  CAB0=>2:0 :>>@48=0B=8E >A59 ?@8 @>1>BV 7 :0<5@>N; Camera Reset  A:840==O CAB0=>2>: :0<5@8; Basic Fiting  ?@>2545==O 0?@>:A8<0FVW B0 @53@5AVW; Data Statistics  >45@60==O AB0B8AB8G=8E 40=8E 4;O B>G>: 3@0DV:0. ><0=40 Basic Fitin 2V4:@820T 2V:=>, I> 40T 4>ABC? 4> :V;L:>E 284V2 0?@>:A8<0FVW B0 @53@5AVW: A?;09=>2>W, 5@<VB>2>W V ?>;V=><V0;L=>W V7 AB5?5=O<8 2V4 1(;V=V9=0 0?@>:A8<0FVO) 4> 10, C B><C G8A;V V7 AB5?5=5< 2 (:204@0B8G=89) B0 3 (:C1VG=89). # ?C=:BV Insert <5=N 3@0DVG=>3> 2V:=0 ?5@5410G5=V >?5@0FVW 2AB02:8 >A=>2=8E >1(T:BV2: ?V4?8A8 >A59, B8BC;L=89 ?V4?8A, ?V4?8A8 2 A5@548=V @8AC=:0, AB@V;:8, 2V4@V7:8 ?@O<>W, ;535=48 9 H:0;8 :>;L>@V2. @8:;04 1 >1C4C20B8 70;56=VABL sin(x), O:I> x T ?>A;V4>2=VABL G8A5; 2V4 1 4> 50. # 2V:=V Matlab 70?8ACT<> :><0=48: X=1:50; plot(X, sin(X), (o(); @8 ?>1C4>2V 40=>W DC=:FVW ?> B>G:0E =5<>6;82> AB25@46C20B8 ?@> WW D>@<C. ">G:8 @>7:840=V ?> ?>;N, V A:;040TBLAO 2@065==O ?@> 9<>2V@=5 WE @>7<VI5==O. !?@>10 0?@>:A8<0FVW ?>;V=><>< 8-3> AB5?5=O =5 40T ?>78B82=>3> @57C;LB0BC (@8A 1.1).  8A. 1.1. =B5@?>;OFVO A8=CA>W48 C 3@0DVG=><C 2V:=V 4=0: :0@B8=0 :0@48=0;L=> 7<V=8BLAO, :>;8 <8 70AB>ACT<> A?;09=>2C V=B5@?>;OFVN, O:0 T >4=8< V7 284V2 1030B>V=B5@20;L=>W V=B5@?>;OFVW (@8A 1.2).  8A. 1.2. @8:;04 A?;09=>2>W B0 5@<VB>2>W V=B5@?>;OFVW C 3@0DVG=><C 2V:=V #AB0=>2:0 ?@0?>@FO Show equations 282>48BL C 3@0DVG=><C 2V:=V 70?8A8 @V2=O=L @53@5AVW. 0 :><0=4>N Tools ( Data Statistics 282>48BLAO 2V:=> Data Statistics V7 =87:>N AB0B8AB8G=8E ?0@0<5B@V2. V4<VB82H8 ?@0?>@F5< B>9 G8 V=H89 ?0@0<5B@ C FL><C 2V:=V <>6=0 A?>AB5@V30B8 2V4?>2V4=C ?>1C4>2C =0 3@0DV:C, =0?@8:;04, ?>1C4>2C 25@B8:0;59 V7 <V=V<0;L=8<, A5@54=V< B0 <0:A8<0;L=8< 7=0G5==O< y V 3>@87>=B0;59 V7 <V=V<0;L=8<, A5@54=V< V <0:A8<0;L=8< 7=0G5==O< x. )>1 2825AB8 3@0DV: ?>E81:8, B@510 2AB0=>28B8 ?@0?>@5FL Plot residuals B0 C <5=N ?V4 F8< ?@0?>@F5< 281@0B8 B8? 3@0DV:0. @V< B>3>, >?FVTN Separate figure 7040TBLAO ?>1C4>20 3@0DV:0 ?>E81:8 2 >:@5<><C 2V:=V. =>4V =5>1EV4=> 2 >4=><C 2V:=V @>7<VAB8B8 45:V;L:0 :>>@48=0B=8E >A59 V7 @V7=8<8 3@0DV:0<8 B0:, I>1 2>=8 =5 =0:;040;8AO >48= =0 >48=. ;O FL>3> 28:>@8AB>2CNBL :><0=48: subplot  AB2>@NT =>2V >1(T:B8 :;0AC axes (?V42V:=0); subplot(m, n, p)  @>71820T 3@0DVG=5 2V:=> =0 m x n ?V42V:>=, ?@8 FL><C m  :V;L:VABL ?V42V:>= ?> 3>@87>=B0;V, n  :V;L:VABL ?V42V:>= ?> 25@B8:0;V, 0 p  =><5@ ?V42V:=0, 2 O:5 1C45 282>48B8AO ?>B>G=89 3@0DV: (?V42V:=0 2V4@0E>2CNBLAO ?>A;V4>2=> ?> @O4:0E); subplot (111) V clf reset  2840;OT 2AV ?V42V:=0 9 ?>25@B0T 3@0DVG=5 2V:=> C 728G09=89 AB0=. !;V4 2V4<VB8B8, I> 4;O 2AVE 3@0DV:V2 <>6;820 V=482V4C0;L=0 CAB0=>2:0 4>40B:>28E >1(T:BV2, =0?@8:;04, B8BC;L=8E =04?8AV2, ?V4?8AV2 >A59 B0 V=. @8:;04 2. >1C4C20B8 G>B8@8 3@0DV:8 @V7=>3> B8?C, I> @>7<VICNBLAO C @V7=8E ?V42V:=0E:  8A. 1.3. '>B8@8 3@0DV:8 @V7=>3> B8?C 2 >4=><C 2V:=V x=-5:0.1:5; >> subplot(2,2,1),plot(x,sin(x)) >> subplot(2,2,2),plot(sin(5*x),cos(2*x+0.2)) >> subplot(2,2,3),contour(peaks) >> subplot(2,2,4),surf(peaks) 0240==O 4> ;01>@0B>@=>W @>1>B8 0 4>?><>3>N ?0:5B0 MATLAB 28:>=0B8 707=0G5=V 4VW. 0@V0=B8 70240=L =02>4OBLAO =86G5 V 287=0G0NBLAO 70 2:07V2:>N 28:;040G0. 0@V0=B 1 0=> 25:B>@ V=(3, 1, 5, 1). 87=0G8B8: 4,5*V. 5:B>@, 5;5<5=B0<8 O:>3> T ?>A;V4>2=VABL 2V4 1 4> 50 7 :@>:>< 5, ?><=>68B8 =0 01A>;NB=5 7=0G5==O :><?;5:A=>3> G8A;0 5+4i. =09B8 >15@=5=C <0B@8FN 4;O <0B@8FV :  EMBED Equation.3 . 840;8B8 B@5BV9 AB>2?5FL <0B@8FV  EMBED Equation.3 . 1G8A;8B8 B0 2825AB8 C D>@<0BV ((Format short((:  EMBED Equation.3 . 0=0 45O:0 70;56=VABL y(x) 25:B>@0<8 :>>@48=0B WW B>G>:: X= (2, 4, 6, 8, 10, 12, 14), Y= (3.76, 4.4, 5.1, 5.56, 6, 6.3, 6.7). >1C4C20B8 ?>;V=><V0;L=C @53@5AVN (0?@>:A8<0FVN) 70;56=>ABV 4;O AB5?5=V2 ?>;V=><0 1, 2, 3 B0 6; ?>1C4C20B8 @V7=V B8?8 3@0DV:V2 ?>E81:8 0?@>:A8<0FVW; ?>1C4C20B8 3@0DV: ?>E81:8 2 >:@5<><C 2V:=V. ;O 7=0G5=L x, I> 7<V=NNBLAO C <560E 2V4  2 4> 10 V7 :@>:>< 0.1, ?>1C4C20B8 3@0DV:8 2 >4=><C 2V:=V 70 DC=:FVO<8 cos(4*x), sin(3*x+0.7), cos(x) B0 3@0DV:8 ?>25@E=V @V2=V2 V ?>25@E=V. 0@V0=B 2 0=> 25:B>@ V=(3, 1, 5, 1). 87=0G8B8: V + 10,4. =09B8 >15@=5=C <0B@8FN 4;O <0B@8FV : EMBED Equation.3 , 45  EMBED Equation.3 . 1G8A;8B8 B0 2825AB8 C D>@<0BV ((Format short((:  EMBED Equation.3 . 1G8A;8B8 45B5@<V=0=B8:  EMBED Equation.3 . 1G8A;8B8 45B5@<V=0=B8:  EMBED Equation.3 , 45  EMBED Equation.3 . 5E09 45O:0 70;56=VABL y(x) 7040=0 25:B>@0<8 :>>@48=0B WW B>G>: X = (1, 3, 5, 7, 9, 11, 13), Y = (3.75, 4.3, 5.1, 6.1, 6.3, 7.2, 7.5). # MatLab =0 3@0DV:C 2825AB8 ?>;V=><V0;L=C @53@5AVN (0?@>:A8<0FVN) 4;O AB5?5=V2 ?>;V=><0 1, 2 B0 3. 825AB8 3@0DV: ?>E81:8. ;O 7=0G5=L x, I> 7<V=NTBLAO C <560E 2V4  2 4> 20 V7 :@>:>< 0.2, ?>1C4C20B8 3@0DV:8 2 >4=><C 2V:=V 70 DC=:FVO<8 cos(3*x), sin(5*x+0.3), cos(x) B0 3@0DV:8 ?>25@E=V @V2=V2 V ?>25@E=V. 0@V0=B 3 0=> 25:B>@ V=(3, 1, 5, 1). 87=0G8B8: Cos(V); =09B8 =52V4><C <0B@8FN X V7 @V2=O=L:  EMBED Equation.3 . 1G8A;8B8 45B5@<V=0=B8:  EMBED Equation.3 , 45  EMBED Equation.3 . 840;8B8 4@C389 @O4>: <0B@8FV  EMBED Equation.3 . 5:B>@, 5;5<5=B0<8 O:>3> T ?>A;V4>2=VABL 2V4 1 4> 40 V7 :@>:>< 5, ?><=>68B8 =0 01A>;NB=5 7=0G5==O :><?;5:A=>3> G8A;0 7+3i. >1C4C20B8 70;56=VABL cos(x), O:I> x T ?>A;V4>2=VABL G8A5; 2V4 1 4> 30. 0AB>AC202H8 A?;09=>2C V=B5@?>;OFVN, 2825AB8 3@0DV: ?>E81:8. ;O 7=0G5=L x, I> 7<V=NTBLAO C <560E 2V4  3 4> 10 V7 :@>:>< 0.1, ?>1C4C20B8 3@0DV:8 2 >4=><C 2V:=V 70 DC=:FVO<8 cos(7*x), sin(3*x+0.8), cos(3*x) B0 3@0DV:8 ?>25@E=V @V2=V2 V ?>25@E=V. 0@V0=B 4 =09B8 >15@=5=C <0B@8FN 4;O <0B@8FV :  EMBED Equation.3 . 5:B>@, 5;5<5=B0<8 O:>3> T ?>A;V4>2=VABL 2V4 1 4> 30 V7 :@>:>< 2, ?><=>68B8 =0 01A>;NB=5 7=0G5==O :><?;5:A=>3> G8A;0 4+7i. 840;8B8 4@C389 AB>2?5FL <0B@8FV  EMBED Equation.3 . 1G8A;8B8 45B5@<V=0=B:  EMBED Equation.3 , 45  EMBED Equation.3 . =09B8 =52V4><C <0B@8FN X V7 @V2=O=L:  EMBED Equation.3 . 0=0 45O:0 70;56=VABL y(x) 25:B>@0<8 :>>@48=0B WW B>G>:: X= (2, 4, 6, 8, 10, 12, 14), Y= (3.76, 4.4, 5.1, 5.56, 6, 6.3, 6.7). >1C4C20B8 ?>;V=><V0;L=C @53@5AVN (0?@>:A8<0FVN) 70;56=>ABV 4;O AB5?5=V2 ?>;V=><0 1, 2, 3 B0 6; ?>1C4C20B8 @V7=V B8?8 3@0DV:V2 ?>E81:8 0?@>:A8<0FVW; ?>1C4C20B8 3@0DV: ?>E81:8 2 >:@5<><C 2V:=V. ;O 7=0G5=L x, I> 7<V=NTBLAO C <560E 2V4  2 4> 20 V7 :@>:>< 0.2, ?>1C4C20B8 3@0DV:8 2 >4=><C 2V:=V 70 DC=:FVO<8 cos(3*x), sin(5*x+0.3), cos(x) B0 3@0DV:8 ?>25@E=V @V2=V2 V ?>25@E=V. 0@V0=B 5 =09B8 >15@=5=C <0B@8FN 4;O <0B@8FV :  EMBED Equation.3 . =09B8 =52V4><C <0B@8FN X V7 @V2=O=L:  EMBED Equation.3 . 1G8A;8B8 45B5@<V=0=B:  EMBED Equation.3 , 45  EMBED Equation.3 . 1G8A;8B8 B0 2825AB8 C D>@<0BV ((Format short((:  EMBED Equation.3 . 5:B>@, 5;5<5=B0<8 O:>3> T ?>A;V4>2=VABL 2V4 1 4> 70 V7 :@>:>< 5, ?><=>68B8 =0 01A>;NB=5 7=0G5==O :><?;5:A=>3> G8A;0 6+8i. 5E09 45O:0 70;56=VABL y(x) 7040=0 25:B>@0<8 :>>@48=0B WW B>G>: X = (2, 4, 6, 8, 10), Y = (3.7, 4.4, 5.15, 5.6, 6.9). # MatLab =0 3@0DV:C 2825AB8 ?>;V=><V0;L=C @53@5AVN (0?@>:A8<0FVN) 4;O ;V=V9=>W, ?0@01>;VG=>W, :C1VG=>W @53@5AVW. 825AB8 3@0DV: ?>E81:8. ;O 7=0G5=L x, I> 7<V=NTBLAO C <560E 2V4  2 4> 10 V7 :@>:>< 0.1, ?>1C4C20B8 3@0DV:8 2 >4=><C 2V:=V 70 DC=:FVO<8 cos(4*x), sin(3*x+0.7), cos(x) B0 3@0DV:8 ?>25@E=V @V2=V2 V ?>25@E=V. 0@V0=B 6 =09B8 >15@=5=C <0B@8FN 4;O <0B@8FV :  EMBED Equation.3 . 5:B>@, 5;5<5=B0<8 O:>3> T ?>A;V4>2=VABL 2V4 1 4> 70 7 :@>:>< 10, ?><=>68B8 =0 01A>;NB=5 7=0G5==O :><?;5:A=>3> G8A;0 5+3i. 1G8A;8B8 B0 2825AB8 C D>@<0BV ((Format short((:  EMBED Equation.3 . 840;8B8 4@C389 @O4>: <0B@8FV  EMBED Equation.3 . =09B8 4>1CB>: 25:B>@V2: V=(3+2/(3+6), exp(7), sqrt(12)) B0 Y=(round(sin(5()), sqrt(14), 7+2/15) V ?@8A2>WB8 4@C3><C 5;5<5=BC 7=0G5==O  EMBED Equation.3 . 5E09 45O:0 70;56=VABL y(x) 7040=0 25:B>@0<8 :>>@48=0B WW B>G>: X = (1, 3, 5, 7, 9, 11, 13), Y = (3.75, 4.3, 5.1, 6.1, 6.3, 7.2, 7.5). # MatLab =0 3@0DV:C 2825AB8 ?>;V=><V0;L=C @53@5AVN (0?@>:A8<0FVN) 4;O AB5?5=V2 ?>;V=><0 1, 2 B0 3. 825AB8 3@0DV: ?>E81:8. ;O 7=0G5=L x, I> 7<V=NTBLAO C <560E 2V4  2 4> 20 V7 :@>:>< 0.2, ?>1C4C20B8 3@0DV:8 2 >4=><C 2V:=V 70 DC=:FVO<8 cos(3*x), sin(5*x+0.3), cos(x) B0 3@0DV:8 ?>25@E=V @V2=V2 V ?>25@E=V. 0@V0=B 7 =09B8 >15@=5=C <0B@8FN 4;O <0B@8FV :  EMBED Equation.3 , 45  EMBED Equation.3 . 5:B>@, 5;5<5=B0<8 O:>3> T ?>A;V4>2=VABL 2V4 1 4> 100 V7 :@>:>< 20, ?><=>68B8 =0 01A>;NB=5 7=0G5==O :><?;5:A=>3> G8A;0 4+3i. 840;8B8 B@5BV9 @O4>: <0B@8FV  EMBED Equation.3 . !B2>@VBL <03VG=C <0B@8FN @>7<V@>< 3x3 V 28:>=09B5 >?5@0FVN :>=:0B5=FVW, O:I>  EMBED Equation.3 . 8:>=09B5 >?5@0FVN :>=:0B5=FVW, O:I>  EMBED Equation.3 , 0  EMBED Equation.3 . 5E09 45O:0 70;56=VABL y(x) 7040=0 25:B>@0<8 :>>@48=0B WW B>G>: X = (2, 4, 6, 8, 10), Y = (3.7, 4.4, 5.15, 5.6, 6.9). # MatLab =0 3@0DV:C 2825AB8 ?>;V=><V0;L=C @53@5AVN (0?@>:A8<0FVN) 4;O ;V=V9=>W, ?0@01>;VG=>W, :C1VG=>W @53@5AVW. 825AB8 3@0DV: ?>E81:8. ;O 7=0G5=L x, I> 7<V=NTBLAO C <560E 2V4  3 4> 10 V7 :@>:>< 0.1, ?>1C4C20B8 3@0DV:8 2 >4=><C 2V:=V 70 DC=:FVO<8 cos(7*x), sin(3*x+0.8), cos(3*x) B0 3@0DV:8 ?>25@E=V @V2=V2 V ?>25@E=V. 0@V0=B 8 =09B8 =52V4><C <0B@8FN X V7 @V2=O=L:  EMBED Equation.3 . 1G8A;8B8 B0 2825AB8 C D>@<0BV ((Format short((:  EMBED Equation.3 . 1G8A;8B8 45B5@<V=0=B8:  EMBED Equation.3 , 45  EMBED Equation.3 . !B2>@VBL <03VG=C <0B@8FN @>7<V@>< 3x3 V 28:>=09B5 >?5@0FVN :>=:0B5=FVW, O:I>  EMBED Equation.3 . 8:>=09B5 >?5@0FVN :>=:0B5=FVW, O:I>  EMBED Equation.3 , 0  EMBED Equation.3 . >1C4C20B8 70;56=VABL sin(x), O:I> x T ?>A;V4>2=VABL G8A5; 2V4 1 4> 40. 0AB>AC202H8 A?;09=>2C V=B5@?>;OFVN, 2825AB8 3@0DV: ?>E81:8 2 >:@5<><C 2V:=V. ;O 7=0G5=L x, I> 7<V=NTBLAO C <560E 2V4  2 4> 10 V7 :@>:>< 0.1, ?>1C4C20B8 3@0DV:8 2 >4=><C 2V:=V 70 DC=:FVO<8 cos(4*x), sin(3*x+0.7), cos(x) B0 3@0DV:8 ?>25@E=V @V2=V2 V ?>25@E=V. 0@V0=B 9 =09B8 =52V4><C <0B@8FN X V7 @V2=O=L:  EMBED Equation.3 . 5:B>@, 5;5<5=B0<8 O:>3> T ?>A;V4>2=VABL 2V4 1 4> 60 V7 :@>:>< 6, ?><=>68B8 =0 01A>;NB=5 7=0G5==O :><?;5:A=>3> G8A;0 15+2i. !B2>@VBL <03VG=C <0B@8FN @>7<V@>< 3x3 V 28:>=09B5 >?5@0FVN :>=:0B5=FVW, O:I>  EMBED Equation.3 . =09B8 4>1CB>: 25:B>@V2: V=(2+2/(3+4), exp(5), sqrt (10)) B0 Y=(round(sin(3()), sqrt(12), 5+1/15) V ?@8A2>WB8 4@C3><C 5;5<5=BC 7=0G5==O  EMBED Equation.3 . 8:>=09B5 >?5@0FVN :>=:0B5=FVW, O:I>  EMBED Equation.3 , 0  EMBED Equation.3 . 5E09 45O:0 70;56=VABL y(x) 7040=0 25:B>@0<8 :>>@48=0B WW B>G>: X = (2, 4, 6, 8, 10), Y = (3.7, 4.4, 5.15, 5.6, 6.9). # MatLab =0 3@0DV:C 2825AB8 ?>;V=><V0;L=C @53@5AVN (0?@>:A8<0FVN) 4;O ;V=V9=>W, ?0@01>;VG=>W, :C1VG=>W @53@5AVW. 825AB8 3@0DV: ?>E81:8. ;O 7=0G5=L x, I> 7<V=NTBLAO C <560E 2V4  3 4> 10 7 :@>:>< 0.1, ?>1C4C20B8 3@0DV:8 2 >4=><C 2V:=V 70 DC=:FVO<8 cos(7*x), sin(3*x+0.8), cos(3*x) B0 3@0DV:8 ?>25@E=V @V2=V2 V ?>25@E=V. 0@V0=B 10 =09B8 =52V4><C <0B@8FN X V7 @V2=O=L: EMBED Equation.3 . 1G8A;8B8 B0 2825AB8 C D>@<0BV ((Format short((:  EMBED Equation.3 . 1G8A;8B8 45B5@<V=0=B8: EMBED Equation.3 , 45  EMBED Equation.3 . !B2>@VBL <03VG=C <0B@8FN @>7<V@>< 3x3 V 28:>=09B5 >?5@0FVN :>=:0B5=FVW, O:I>  EMBED Equation.3 . =09B8 4>1CB>: 25:B>@V2: V=(2+2/(3+4), exp(5), sqrt (10)) B0 Y=(round(sin(3()), sqrt(12), 5+1/15)  V ?@8A2>WB8 4@C3><C 5;5<5=BC 7=0G5==O  EMBED Equation.3 . >1C4C20B8 70;56=VABL cos(x), O:I> x T ?>A;V4>2=VABL G8A5; 2V4 1 4> 30. 0AB>AC202H8 A?;09=>2C V=B5@?>;OFVN, 2825AB8 3@0DV: ?>E81:8. ;O 7=0G5=L x, I> 7<V=NTBLAO C <560E 2V4  2 4> 20 V7 :@>:>< 0.2, ?>1C4C20B8 3@0DV:8 2 >4=><C 2V:=V 70 DC=:FVO<8 cos(3*x), sin(5*x+0.3), cos(x) B0 3@0DV:8 ?>25@E=V @V2=V2 V ?>25@E=V. >=B@>;L=V 70?8B0==O 0B8 287=0G5==O <>45;N20==O. 025AB8 ?@8:;048. )> @>7C<VNBL ?V4 V<VB0FV9=>N <>45;;N? /:V B8?8 D09;V2 E0@0:B5@=V 4;O MatLab? /:V :><0=48 28:>@8AB>2CNBL 4;O 2AB0=>2;5==O D>@<0BC G8A5; C MatLab? /:V >?5@0B>@8 70AB>A>2CNBL 4;O 287=0G5==O >?5@0FV9 =04 40=8<8? /: 70?8ACNBL :>=AB@C:FVN 4;O D>@<C20==O 7@>AB0NG>W ?>A;V4>2=>ABV G8A5; C MatLab? /:V >?5@0B>@8 28:>@8AB>2CNBL 4;O 287=0G5==O >?5@0FV9 =04 40=8<8? 01>@0B>@=0 @>1>B0 !2 82G5==O 1;>:V2 1V1;V>B5:8 Simulink. !B2>@5==O <>45;59. A=>2=V ?@89><8 ?V43>B>2:8 B0 @5403C20==O <>45;V 5B0 @>1>B8 02G8B8AO :>@8ABC20B8AO 1V1;V>B5:0<8 ?0:5B0 <>45;N20==O 48=0<VG=8E A8AB5< Simulink, =0;0HB>2C20B8 ?0@0<5B@8 A8AB5<8, 1C4C20B8 =09?@>ABVHV <>45;V, 28:>@8AB>2CNG8 1;>:8 1V1;V>B5: Sinks, Math, Signals & Systems. !B8A;V B5>@5B8G=V ?>2V4><;5==O ?@> A:;04 >A=>2=8E 1V1;V>B5: A8AB5<8 Simulink V1;V>B5:0 465@5; A83=0;V2 V 4VW Sources 0=0 1V1;V>B5:0 <VAB8BL ?V:B>3@0<8 465@5; A83=0;V2 B0 4VW. @8@>40 2?;82C <>65 1CB8 =09@V7=><0=VB=VH>N. 040;V :><?>=5=B8 1;>:V2 40=>W 1V1;V>B5:8 1C45<> =07820B8 ?@>AB> 465@5;0<8. Band-Limited White Noise  35=5@0B>@ ((1V;>3> HC<C(( 7 >1<56C20;L=>N A<C3>N; Chirp Signal  465@5;> 30@<>=VG=8E :>;820=L 7<V==>W G0AB>B8; Clock  35=5@0B>@ =5?5@5@2=>3> A83=0;C G0AC; Constant  465@5;> ?>ABV9=>W 25;8G8=8 (A:0;O@, 25:B>@, <0B@8FO); Digital Clock  F8D@>289 3>48==8:, 465@5;> 48A:@5B=>3> A83=0;C G0AC; From Workspace  48A:@5B=89 V<?C;LA=89 35=5@0B>@; From File  A;C68BL 4;O >45@60==O 40=8E V7 7>2=VH=L>3> D09;0, 40=V ?>28==V 1CB8 ?@54AB02;5=V C 283;O4V <0B@8FV; Pulse Generator  35=5@0B>@ V<?C;LA82=8E A83=0;V2; Ramp  71C46C20G, 35=5@0B>@ ;V=V9=> 7@>AB0NG>3> (A?040NG>3>) A83=0;C; Random Number  28?04:>25 G8A;>, 465@5;> 48A:@5B=>3> A83=0;C, 0<?;VBC40 O:>3> T 28?04:>2>N 25;8G8=>N, @>7?>4V;5=>N 70 =>@<0;L=8< 70:>=><; Repeating Sequence  ?5@V>48G=89 A83=0;, 35=5@0B>@ ?5@V>48G=>3> 48A:@5B=>3> A83=0;C 4>2V;L=>W D>@<8; Signal Generator  35=5@0B>@ A83=0;C, 35=5@0B>@ =5?5@5@2=>3> A83=0;C 4>2V;L=>W D>@<8; Sine Wave  35=5@0B>@ 30@<>=VG=8E :>;820=L (A8=CA>W40;L=89 2?;82); Step  B0:B, 465@5;> >48=8G=>3> 48A:@5B=>3> A83=0;C V7 7040=8<8 ?0@0<5B@0<8; Uniform Random Number  @V2=><V@=5 28?04:>25 G8A;>, 465@5;> 48A:@5B=>3> A83=0;C, 0<?;VBC40 O:>3> T @V2=><V@=> @>7?>4V;5=>N 28?04:>2>N 25;8G8=>N.  V1;V>B5:0 @5TAB@0FV9=8E ?@8;04V2 Sinks &O 1V1;V>B5:0 <VAB8BL 1;>:8 >45@6C20GV2 V=D>@<0FVW, WE I5 =07820NBL @5TAB@CNG8<8 :><?>=5=B0<8. >6=89 @53VAB@0B>@ <0T A2>T 2V:=> =0AB@>9:8. Display  5:@0=, ?@87=0G5=89 4;O 2V4>1@065==O G8A;>28E 7=0G5=L 25;8G8=; Scope  4>72>;OT C ?@>F5AV <>45;N20==O A?>AB5@V30B8 48=0<V:C 7<V=8 E0@0:B5@8AB8: A8AB5<8, I> =0A FV:02;OBL; Stop Simulation  1;>: 7C?8=5==O <>45;N20==O; Terminator To File  ?@8;04 70?8AC 40=8E C D09;; To Workspace  ?@8;04 70?8AC 2 7<V==C @>1>G>3> ?@>AB>@C; XY Graph  ?@87=0G5=89 4;O ?>1C4>28 3@0DV:V2 C A8AB5<V ?>;O@=8E :>>@48=0B.  V1;V>B5:0 <0B5<0B8G=8E 1;>:V2 Math (Math Operations) 0=0 1V1;V>B5:0 <VAB8BL 1;>:8, I> @50;V7CNBL 5;5<5=B0@=V (0;351@0WG=V B0 B@83>=><5B@8G=V) DC=:FVW, 0 B0:>6 >?5@0FVW <0B5<0B8G=>W ;>3V:8 V <>6CBL 1CB8 28:>@8AB0=V C <>45;V 1C4L-O:>W A8AB5<8. Abs  01A>;NB=5 7=0G5==O, D>@<CT 01A>;NB=5 7=0G5==O 2EV4=>3> A83=0;C; Algebraic Constraint  0;351@0WG=89 :>@V=L, ?@87=0G5=89 4;O ?>HC:C :>@5=V2 0;351@0WG=8E @V2=O=L. !C<VA=5 28:>@8AB0==O 2 S-<>45;V 45:V;L:>E B0:8E 1;>:V2 70157?5GCT @VH5==O A8AB5<8 0;351@0WG=8E @V2=O=L. Bitwise Logical Operator Combinatorial Logic  :><1V=0B>@8:0, 70157?5GCT ?5@5B2>@5==O 2EV4=>3> A83=0;C 2V4?>2V4=> 4> 7040=>W B01;8FV VAB8==>ABV; Complex to Magnitude-Angle  284V;5==O V7 :><?;5:A=>3> G8A;0 0<?;VBC48 V D078; Complex to Real-Imag  284V;5==O CO2=>W V 4V9A=>W G0AB8=8 :><?;5:A=>3> G8A;0; Dot Product  70157?5GCT A:0;O@=5 <=>65==O 42>E 25:B>@V2, I> ?>40NBLAO =0 2EV4; Gain  ?@8<=>6C20G, 28:>=CT @>;L ?@8<=>6C20G0 A83=0;V2, I> =04E>4OBL =0 2EV4; Logical Operator  ;>3VG=89 >?5@0B>@, <VAB8BL =01V@ ;>3VG=8E >?5@0B>@V2; Magnitude-Angle to Complex  ?5@5B2>@5==O 0<?;VBC48 V D078 C :><?;5:A=5 G8A;>; Math Function  <0B5<0B8G=0 DC=:FVO, 4>72>;OT 28:>@8AB>2C20B8 4;O ?5@5B2>@5==O 2EV4=>3> A83=0;C 5;5<5=B0@=V =5B@83>=><5B@8G=V DC=:FVW; Matrix Gain  <0B@8G=89 ?@8<=>6C20G, 28:>@8AB>2CTBLAO 4;O ?@8<=>65==O 2EV4=>3> A83=0;C =0 <0B@8FN (01> 25:B>@); MinMax  <V=V<C< 01> <0:A8<C<, 70157?5GCT ?>HC: <V=V<0;L=>3> 01> <0:A8<0;L=>3> 5;5<5=B0 2EV4=>3> 25:B>@0; Product  <=>65==O, 4>72>;OT <=>68B8 01> 4V;8B8 45:V;L:0 2EV4=8E A83=0;V2; Real-Imag to Complex  AB2>@5==O :><?;5:A=>3> G8A;0 7 CO2=>W V 4V9A=>W G0AB8=8; Relational Operator  >?5@0B>@ 2V4=>H5==O, @50;V7CT >?5@0FVW 2V4=>H5==O =04 42><0 2EV4=8<8 A83=0;0<8; Rounding Function  DC=:FVO >:@C3;5==O, <VAB8BL @V7=V DC=:FVW >:@C3;5==O 7=0G5=L  0<?;VBC48 2EV4=>3> A83=0;C; Sign  7=0:, 28:>=CT ?5@52V@:C 7=0:0 2EV4=>3> A83=0;C V D>@<CT >4=5 7 B@L>E 7=0G5=L (-1, O:I> 2EV4=89 7=0: <5=H5 =V6 0, 0, O:I> 2EV4=89 A83=0; 4>@V2=NT 0; 1, O:I> 2EV4=89 A83=0; 4>@V2=NT 0); Slider Gain  ?V4AB@>N20;L=89 ?@8<=>6C20G; Sum  4>4020==O, 28:>=CTBLAO 4>4020==O 2EV4=8E A83=0;V2; Trigonometric Function  B@83>=><5B@8G=0 DC=:FVO, 70157?5GCT ?5@5B2>@5==O 2EV4=>3> A83=0;C 70 4>?><>3>N >4=VTW 7 B@83>=><5B@8G=8E DC=:FV9.  5?5@5@2=V 1;>:8 Continuous  Derivative  A;C68BL 4;O 48D5@5=FVN20==O 2EV4=8E 40=8E (A83=0;V2), B>1B> 7=0E>465==O ?>EV4=>W A83=0;C; Integrator  A;C68BL 4;O V=B53@C20==O 2EV4=8E 40=8E (A83=0;V2); Memory  ?0<(OBL, 70?0<(OB>2CT 2EV4=89 A83=0; V 7<VICT 9>3> =0 >48= B0:B G0AC; State-Space  4>72>;OT 7040B8 ;V=50@87>20=C <0B@8G=C <>45;L-A8AB5<C; Transfer Fcn  AB2>@5==O ?5@54020;L=>W D-FVW H(s)=y(s)/u(s) C 283;O4V 2V4=>H5==O ?>;V=><V2 7040=>3> AB5?5=O; Transport Delay  70157?5GCT G0A>2C 70B@8<:C 2EV4=>3> A83=0;C =0 7040=89 G0A; Variable Transport Delay  <0T 420 2E>48: >48= 4;O 70B@8<:8 A83=0;C, 0 4@C389  4;O A83=0;C C?@02;V==O; 4>72>;OT AB2>@N20B8 70B@8<:C, 7040=C @V2=8< A83=0;C C?@02;V==O; Zero-Pole  A;C68BL 4;O AB2>@5==O ?5@54020;L=>W DC=:FVW V7 7040=8<8 ?>;NA0<8 V =C;O<8. V1;V>B5:0 ?V4A8AB5< V C?@02;V==O A83=0;0<8 Signals & Systems &5 >4=0 7 =091V;LH8E 1V1;V>B5: ?0:5B0 Simulink, >4=0: 2>=0 <VAB8BL 2 >A=>2=><C 4>AB0B=L> ?@>ABV 1;>:8: Bus Selector  70157?5GCT 281V@ 7040=8E A83=0;V2 V7 45:V;L:>E; Data Store Memory  70?8A 40=8E V7 7040=8< V<(O< C ?0<(OBL; Data Store Read  7G8BC20==O 40=8E V7 7040=8< V<(O<; Data Store Write  70?8A 7=0G5=L A83=0;V2 V7 7040=8< V<(O<; Data Type Conversion  ?5@5B2>@5==O 40=8E 4> 7040=>3> B8?C, 281@0=>3> V7 A?8A:C; Demux  @>74V;N20G, ?@>B8;56=89 1;>:C Mux; From  ?@89>< A83=0;C 2V4 1;>:0 Goto; Function-Call Generator; Goto; Goto Tag Visibility; Hit Crossing  V=48:0B>@ ?5@5B8=C, 4>72>;OT V45=B8DV:C20B8 <><5=B G0AC, :>;8 2EV4=89 A83=0; ((?5@5B8=0T(( 45O:5 7=0G5==O; IC; Matrix Concatenation  >1(T4=0==O A83=0;V2 C <0B@8FN; Merge  ?>3;8=0G, 2V418@0T V7 2EV4=8E A83=0;V2 >48=, 7=0G5==O O:>3> 1C;> >1G8;5=5 >AB0==V<; Mux  7<VHC20G, >1(T4=CT 2EV4=V A83=0;8 2 >48= 25:B>@=89 A83=0;; Probe  74V9A=NT 1V;LH 45B0;L=C ?5@52V@:C A83=0;V2, =V6 Signal Specification; Reshape; Selector ; Signal Specification  A;C68BL 4;O @>7?>4V;C A83=0;C =0 9>3> 2E>4V V 2840GV A?5F8DV:0FVW; Width  A83=0; V7 @V2=5<, I> 4>@V2=NT :V;L:>ABV 2EV4=8E A83=0;V2.  ;>:8 4;O <>45;N20==O =5;V=V9=8E A8AB5< Nonlinear (Discontinuities) !5@54 =5;V=V9=8E 1;>:V2 A;V4 2V4<VB8B8 1;>:8 7 B8?>28<8 =5;V=V9=>ABO<8, =0?@8:;04, C 283;O4V B8?>28E <0B5<0B8G=8E DC=:FV9, :><?>=5=B8 V450;L=8E V =5V450;L=8E >1<565=L. >2=> ?@54AB02;5=V V B0:V A:;04=V :><?>=5=B8, O: :20=B>2V A83=0;8 B0 V=. Backlash  ;NDB, 70157?5GCT CB@8<0==O 2EV4=>3> A83=0;C 2 45O:><C 7040=><C 4V0?07>=V Coulomb &Viscous Friction Dead Zone  <>45;NTBLAO ((<5@B20 7>=0((; 70<V=0 7=0G5==O 2EV4=>3> A83=0;C, I> 7=0E>48BLAO C 7040=><C 4V0?07>=V, =C;5<; Manual Switch  @CG=89 ?5@5<8:0G; Multiport Switch  1030B>2EV4=89 ?5@5<8:0G; Quantizer  :20=BCNG89 ?@8AB@V9; Rate Limiter  >1<56C20G H284:>ABV, ?@87=0G5=89 4;O :>=B@>;N 9 >1<565==O H284:>ABV 7<V=8 2EV4=>3> A83=0;C; Relay  @5;5; Saturation  =5;V=V9=89 ?@8AB@V9, 70AB>A>2CTBLAO 4;O >1<565==O A8=CA>W40;L=8E A83=0;V2; Switch  ?5@5<8:0G.  V1;V>B5:0 DC=:FV9 V B01;8FL Function & tables (User-Defined Functions) 0=89 1;>: ?@54AB02;5=89 42><0 :0B53>@VO<8: DC=:FVO<8 9 B01;8FO<8. ;>:8 DC=:FV9 4>72>;ONBL C2>48B8 C <>45;V ?@0:B8G=> 1C4L-O:V DC=:FVW, I> <0NBL 25;8:5 7=0G5==O C <0B5<0B8G=><C <>45;N20==V @V7=8E >1 T:BV2 B0 A8AB5<. ;>:8 B01;8FL 70157?5GCNBL 7040==O B01;8G=8E 40=8E V7 @V7=>N @>7<V@=VABN, 0 B0:>6 4>72>;ONBL 28:>@8AB>2C20B8 ;V=V9=C 9 A?;09=>2C V=B5@?>;OFVN B0 5:AB@0?>;OFVN 40=8E. &V 1;>:8 40NBL 7<>3C 5D5:B82=> 22>48B8 40=V 5:A?5@8<5=BV2 V 1C4C20B8 =0 WE >A=>2V ?@>ABV <>45;V ?@8AB@>W2 B0 A8AB5<:  Direct Look-Up Table (n-D); Interpolation (n-D) using PreLook-Up; Fcn  7040T DC=:FVW >4=VTW 7<V==>W u 01> @O4C 7<V==8E u(i); Look-Up Table  7040T C B01;8G=V9 D>@<V 45O:8E 40=8E, I> ?@54AB02;ONBL @O4 7=0G5=L DC=:FVW >4=VTW 7<V==>W; Look-Up Table (2-D); Look-Up Table (n-D); MATLAB Fcn  7040T DC=:FVW >4=VTW 7<V==>W u 01> @O4C 7<V==8E u(i) 70 ?@028;0<8, ?@89=OB8<8 4;O <>28 ?@>3@0<C20==O 107>2>W A8AB5<8; Polynomial  7040T AB5?5=5289 <=>3>G;5= P(u) C 283;O4V 25:B>@0 9>3> :>5DVFVT=BV2; PreLook-Up Index Search; S-Function; S-Function Builder; ;>:8 4;O <>45;N20==O 48A:@5B=8E A8AB5< 01> 48A:@5B=V :><?>=5=B8 Discrete 8A:@5B=V 1;>:8 ?@87=0G5=V 4;O AB2>@5==O <>45;59 48A:@5B=8E ?@8AB@>W2 42>E B8?V2: V7 48A:@5B=8< G0A>< B0 7 48A:@5B=8< AB0=><. &V 1;>:8 2:;NG0NBL C A515 ?@8AB@>W F8D@>2>W 70B@8<:8, 48A:@5B=>-G0A>289 V=B53@0B>@, 48A:@5B=89 DV;LB@ V V=. 5O:V 48A:@5B=V 1;>:8 <0NBL ?5@54020;L=V DC=:FVW, 0;5 28EV4=V A83=0;8 48A:@5B=8E 1;>:V2 <0NBL 48A:@5B=89 E0@0:B5@:  Discrete Transfer Fcn  1;>: 48A:@5B=>W ?5@54020;L=>W DC=:FVW; Discrete Zero-Pole  1;>: 7040==O 48A:@5B=>W >1;0ABV ?5@5E>4C; Discrete Filter  70AB>A>2CTBLAO 4;O AB2>@5==O 48A:@5B=>3> DV;LB@0, ?>@O4>: V 2;0AB82>ABV O:>3> 7040NBLAO ?>;V=><>< 2V4 4V;5==O 1/z C G8A5;L=8:C ?5@54020;L=>W E0@0:B5@8AB8:8; Discrete State-Space  1;>: D>@<C20==O 48A:@5B=>3> ?@>AB>@C AB0=C; Discrete-Time Integrator  70AB>A>2CTBLAO 4;O 48A:@5B=>3> V=B53@C20==O G0AC; 70728G09 2V= A;C68BL 4;O C?@02;V==O ;>3V:>N @>1>B8 <>45;V, =0?@8:;04, 4;O 7C?8=5==O ?@>F5AC <>45;N20==O 70 7040=8< 7=0G5==O< V=B53@0;0 G0AC; First-Order Hold  5:AB@0?>;OB>@ ?5@H>3> ?>@O4:C, 70B@8<CT 28EV4=89 A83=0; =0 7040=89 ?@><V6>: G0AC V 7040T ;V=V9=V 7<V=8 28EV4=>3> A83=0;C =0 :>6=><C B0:BV 48A:@5B870FVW;. Unit Delay 70157?5GCT 70B@8<:C 2EV4=>3> A83=0;C =0 >48= :@>: 5B0;>==>3> G0AC; Zero-Order Hold  5:AB@0?>;OB>@ =C;L>2>3> ?>@O4:C, 70B@8<CT 28EV4=89 A83=0; =0 7040=89 ?@><V6>: G0AC V 70;8H0T =57<V==8< 7=0G5==O 28EV4=>3> A83=0;C =0 :>6=><C B0:BV 48A:@5B870FVW. ?5@0FVW D>@<0BC20==O <>45;V. 5=N D>@<0BC20==O Format #?@02;V==O 2V4>1@065==O< ?V4?8AV2 V 283;O4>< 1;>:V2: Font  CAB0=>2:0 H@8DBC 4;O B5:AB>28E 70?8AV2; Text alignment  28@V2=N20==O B5:ABV2 C B5:AB>2><C 1;>FV; Flip name  @>7<VI5==O ?V4?8AC 725@EC G8 7=87C 1;>:0; Show/Hide name  2V4>1@065==O 01> ?@8E>2C20==O ?V4?8AC 1;>:0; Flip block  2V4>1@065==O 1;>:0 2V4=>A=> 25@B8:0;L=>W >AV; Rotate block  >15@B0==O 1;>:0 =0 900; Show drop shadow  ?>:07 BV=V 2V4 1;>:0. >:07 <VB>: 1;>:V2. #AB0=>2:0 :>;L>@V2. @8:;04 AB2>@5==O =09?@>ABVH8E <>45;59 @8:;04 1 >1C4C20B8 <>45;L 4;O A8=CA>W40;L=8E, B@8:CB=8E, ?@O<>:CB=8E A83=0;V2. >72(O70==O 1C4L-O:>W ?@>1;5<8 C A8AB5<V Simulink ?>28==> ?>G8=0B8AO 7 ?>AB0=>2:8 7040GV. # E>4V ?>AB0=>2:8 7040GV ?>B@V1=> 287=0G8B8AO 7 :><?>=5=B0<8, I> 1C4CBL 28:>@8AB0=V ?@8 <>45;N20==V. A=>2=V :><0=48 @5403C20==O <>45;V 7>A5@5465=V C <5=N Edit. B65, I>1 ?>1C4C20B8 <>45;L, 2V4:@8T<> ?CAB5 2V:=> 4;O =>2>W <>45;V (:=>?:0 ((Create a new model(( 2 ?0=5;V V=AB@C<5=BV2 1@0C75@0 1V1;V>B5: Simulink). >45;L <0T B0:89 283;O4:  8A. 2.1. >45;L 4;O A8=CA>W40;L=8E, B@8:CB=8E, ?@O<>:CB=8E A83=0;V2 #2545==O B5:AB>2>3> =04?8AC: #2545<> 703>;>2>: =0H>W <091CB=L>W <>45;V  ((Simple model(( (((@>AB0 <>45;L((). ;O FL>3> 4>AB0B=L> 2AB0=>28B8 :C@A>@ <8HV C ?>B@V1=5 <VAF5 V 42VGV :;0F=CB8 ;V2>N :=>?:>N <8HV. (O28BLAO ?@O<>:CB=0 @0<:0, 2 A5@548=V O:>W 7=0E>48BLAO <0@:5@. 04?8A8 22>4OBLAO 70 ?@028;0<8 @O4:>2>3> @540:B>@0. >7<VI5==O 1;>:V2 C 2V:=V <>45;V 7 @>74V;C Sources ?5@5BO3=CB8 70 4>?><>3>N <8HV B@8 465@5;0 A83=0;C: A8=CA>W40;L=89, ?@O<>:CB=89 (48A:@5B=89), ?8;>?>4V1=89. >BV< V7 @>74V;C Sinks ?5@5BO3=CB8 C 2V:=> <>45;V 1;>: >AF8;>3@0D0. ;O 1;>:V2 ?@8 <>45;N20==V <>6=0 70AB>A>2C20B8 :><0=48 <5=N Edit: !ut, Copy, Paste, Clear B0 V=. 0AB>A>2CNG8 FV :><0=48, <8 >45@68<> C @57C;LB0BV B@8 1;>:8 >AF8;>3@0D0: Scope, Scope1, Scope2. "5?5@ ?>B@V1=> 7(T4=0B8 28E>48 465@5; V7 2E>40<8 >AF8;>3@0DV2. ;O FL>3> 4>AB0B=L> 2:070B8 :C@A>@>< <8HV =0 ?>G0B>: 7(T4=0==O (28EV4 465@5;0), 0 ?>BV< ?@8 =0B8A=5==V :=>?:8 <8HV ?@>BO3=CB8 7(T4=0==O C 9>3> :V=5FL (2EV4 >AF8;>3@0D0). 0?CA: 45:V;L:>E <>45;59 >4=>G0A=> "5?5@ CA5 3>B>25 4;O >4=>G0A=>3> 70?CA:C <>45;59. )>1 >45@60B8 @57C;LB0B8 =5>1EV4=> 2AB0=>28B8 ?0@0<5B@8. # 2V:=V CAB0=>2:8 ?0@0<5B@V2 <>45;N20==O (2>=> 28:;8:0TBLAO :><0=4>N Simulation ( Simulation parameters& ) CAB0=>28<> ?0@0<5B@ Start time = 0, Stop time = 20. VA;O FL>3> ?>B@V1=> 70?CAB8B8 ?@>F5A <>45;N20==O :=>?:>N ((Start Simulation((. )>1 >45@60B8 >AF8;>3@0<8 2V4 :>6=>3> >AF8;>3@0D0, ?>B@V1=> WE 0:B82V7C20B8, 42VGV :;0F=CB8 ?> :>6=><C 7 =8E. B65, 28 <>65B5 10G8B8, I> 2AV B@8 <>45;V >4=>G0A=> ?@0FNNBL V >AF8;>3@0<8 ?@54AB02;ONBL B8<G0A>2V 70;56=>ABV A83=0;V2, O:V 28@>1;ONBL 465@5;0: A8=CA>W4C, ?@O<>:CB=V V<?C;LA8, B@8:CB=V V<?C;LA8. 15@565==O <>45;V >6=0 715@53B8 AB2>@5=C <>45;L 4;O ?>40;LH>3> 28:>@8AB0==O, ?>:07C 01> <>45@=V70FVW. ;O FL>3> 28:>@8AB>2CTBLAO :><0=40 Save 01> Save as <5=N File 2V:=0 @540:B>@0 <>45;59. >45;L 70?8ACTBLAO C 283;O4V D09;0 7 @>7H8@5==O< .mdl. @8:;04 2 >1C4C20B8 <>45;L @>1>B8 V450;L=>3> >1<56C20G0 =0?@C38 C :><?(NB5@=V9 <5@56V, =0 2EV4 O:>3> ?>40TBLAO A8=CA>W40;L=0 =0?@C30 7 0<?;VBC4>N 5 V G0AB>B>N 1 @04/A. >@>38 >1<565==O AB0=>2;OBL +0.5 B0 -0.5. # 40=><C 28?04:>2V >A=>2=8<8 1;>:0<8 1C4CBL 35=5@0B>@ A8=CA>W40;L=8E A83=0;V2 V 1;>: =5;V=V9=>ABV, I> <>45;NNBL ?5@54020;L=C E0@0:B5@8AB8:C >1<56C20G0. > F8E 1;>:V2 ?>B@V1=> 4>40B8 @5TAB@CNG89 1;>:  >AF8;>3@0D.  8A. 2.2. >45;L @>1>B8 V450;L=>3> >1<56C20G0 =0?@C38 ;O AB2>@5==O 40=>W <>45;V ?>B@V1=> 28:>=0B8 =0ABC?=V 4VW: 2V4:@8B8 2V:=> =>2>W <>45;V Simulink, =0B8A=C2H8 :=>?:C ((Create a new model((; V7 @>74V;C 1V1;V>B5:8 Sources ?5@5=5A5<> C 2V:=> <>45;V 465@5;> A8=CA>W40;L=>3> A83=0;C Sine Wave; V7 @>74V;C 1V1;V>B5:8 Nonlinear (Discontinuities) ?5@5=5A5<> C 2V:=> <>45;V =5;V=V9=89 1;>:  >1<56C20G Saturation; V7 @>74V;C 1V1;V>B5:8 Sinks ?5@5=5AB8 C 2V:=> <>45;V 1;>: >AF8;>3@0D0 Scope; 28:>=0B8 7(T4=0==O <V6 1;>:0<8; ?5@52V@8B8 CAB0=>2:C G0AC <>45;N20==O: Start time = 0, Stop time = 20; :;0F=C2H8 42VGV ?> 1;>:C Sine Wave, C 2V:=V ?0@0<5B@V2 465@5;0 A8=CA>W40;L=>3> A83=0;C 2AB0=>28B8 0<?;VBC4C, @V2=C 5; 70?CAB8B8 <>45;L =0 28:>=0==O, =0B8A=C2H8 :=>?:C ((Start Simulation((. !;V4 2V4<VB8B8, I> <>6=0 @>18B8 =0;0HBC20==O <0AHB01C >AF8;>3@0<. ;O 7<V=8 <0AHB01C 4>AB0B=L> :;0F=CB8 ?@02>N :=>?:>N <8HV C 2V:=V >AF8;>3@0<8. # :>=B5:AB=><C <5=N, I> 7(O28BLAO, ?>B@V1=>, 281@0B8 :><0=4C Axes Properties, O:0 A;C3CT 4;O 7040==O <0AHB01C >AF8;>3@0<8. 0?@8:;04, C 2V:=V 2;0AB82>AB59 >A59 B@510 7<V=8B8 7=0G5==O Y-min=-5 B0 Y-max=5 =0 7=0G5==O Y-min=-8 B0 Y-max=8. 0240==O 4> ;01>@0B>@=>W @>1>B8 0 4>?><>3>N 2:070=8E 1V1;V>B5: AB2>@8B8 <>45;V. 57C;LB0B8 ?>:070B8 70 4>?><>3>N 48A?;5O 9 >AF8;>3@0D0. @>18B8 ?V4?8A8 >1(T:BV2 <>45;59, ?@8 FL><C 28:>@8AB02H8 <5=N D>@<0BC20==O. 0@V0=B 1 !B2>@8B8 <>45;L 4;O 287=0G5==O AC<8 G8A5; (10, -3, 17). !B2>@8B8 <>45;L, >1(T4=02H8 2EV4=V A83=0;8 (10, 15, 3) 2 >48= 25:B>@=89 A83=0;, 71V;LH82H8 H8@8=C =5A:0;O@=8E ;V=V9 (Format( Wide nonscalar lines). !B2>@8B8 <>45;L 4;O @>72(O7C20==O A8AB5<8 0;351@0WG=8E @V2=O=L:  EMBED Equation.3  0@V0=B 2 >A;V48B8 ?>254V=:C <>45;V A8AB5<8 4@C3>3> ?>@O4:C vdp.mdl, I> 7=0E>48BLAO C ?0?FV MatLab/Toolbox/Simulink/Simdemos/Simgeneral 4;O V=H>W =5;V=V9=>ABV, =0?@8:;04: f(u)=1-exp(u); f(u)=1-1.1*exp(u). 0=C <>45;L 4>?>2=8B8 3@0D>?>1C4C20G5<, 2E>48 O:>3> ?V4:;NG8B8 4> 28EV4=8E ?>@BV2 Out1 B0 Out2. >72(O7>: A8AB5<8 0;351@0WG=8E @V2=O=L EMBED Equation.3 T >?B8<0;L=8< ?;0=><. =09B8 <0:A8<0;L=5 7=0G5==O FV;L>2>W DC=:FVW F = 3x + 8y. !B2>@8B8 <>45;L (@57C;LB0B8 2825AB8 =0 5:@0=8, 28:>@8AB0B8 >AF8;>3@0D 4;O 3@0DVG=>3> 7>1@065==O 7<V==8E). !B2>@8B8 <>45;L 4;O @>72(O7C20==O A8AB5<8 0;351@0WG=8E @V2=O=L, 70AB>AC202H8 1;>: Algebraic Constraint (@57C;LB0B8 2825AB8 =0 5:@0=, 28:>@8AB0B8 >AF8;>3@0D 4;O 3@0DVG=>3> 7>1@065==O 7<V==8E):  EMBED Equation.3 . 0@V0=B 3 !B2>@8B8 <>45;L 4;O 287=0G5==O AC<8 G8A5; (20, -30, 17). >1C4C20B8 <>45;L @>1>B8 V450;L=>3> >1<56C20G0 ?V:V2 =0?@C38 C :><?(NB5@=V9 <5@56V, =0 2EV4 O:>3> ?>40TBLAO A8=CA>W40;L=0 =0?@C30 7 0<?;VBC4>N 20 V G0AB>B>N 1 @04/A. >@>38 >1<565==O AB0=>2;OBL +0.5 B0 -0.5. 0;0HBC20B8 <0AHB01 >AF8;>3@0<8. !B2>@8B8 <>45;L 4;O @>72(O7C20==O A8AB5<8 0;351@0WG=8E @V2=O=L (@57C;LB0B8 2825AB8 =0 5:@0=8, 28:>@8AB0B8 >AF8;>3@0D 4;O 3@0DVG=>3> 7>1@065==O 7<V==8E):  EMBED Equation.3  0@V0=B 4 !B2>@8B8 <>45;L 4;O @>72(O7C20==O A8AB5<8 0;351@0WG=8E @V2=O=L (@57C;LB0B8 2825AB8 =0 5:@0=8, 28:>@8AB0B8 >AF8;>3@0D 4;O 3@0DVG=>3> 7>1@065==O 7<V==8E):  EMBED Equation.3 . >A;V48B8 <>45;L =5;V=V9=>3> 5;5<5=B0 V7 7>=>N =5GCB;82>ABV (((<5@B20 7>=0(() ?@8 2EV4=><C A8=CA>W40;L=><C A83=0;V. 0;0HBC20B8 <0AHB01 >AF8;>3@0<8. 8:>@8AB0B8 1V1;V>B5:8 Sources, Nonlinear (Discontinuities). !B2>@8B8 <>45;L 4;O 287=0G5==O 4>1CB:C G8A5; (13, -40, 17). 0@V0=B 5 !B2>@8B8 <>45;L 4;O @>72(O7C20==O A8AB5<8 0;351@0WG=8E @V2=O=L (@57C;LB0B8 2825AB8 =0 5:@0=8, 28:>@8AB0B8 >AF8;>3@0D 4;O 3@0DVG=>3> 7>1@065==O 7<V==8E): EMBED Equation.3 . >A;V48B8 <>45;L V450;L=>3> :20=BCNG>3> ?@8AB@>N ?@8 2EV4=><C A8=CA>W40;L=><C A83=0;V. 0;0HBC20B8 <0AHB01 >AF8;>3@0<8. 8:>@8AB0B8 1V1;V>B5:8 Sources, Nonlinear (Discontinuities). !B2>@8B8 <>45;L 4;O @>72(O7C20==O @V2=O==O, 70AB>AC202H8 1;>: Algebraic Constraint (@57C;LB0B ?>:070B8 =0 5:@0=V 48A?;5O, 0 3@0DVG=5 7>1@065==O =0 5:@0=V >AF8;>3@0D0):  EMBED Equation.3 . 0@V0=B 6 >1C4C20B8 DV3C@C VAA06C (:>;820==O <0OB=8:0) ?@8 ?>74>26=VE B0 ?>?5@5G=8E A8=CA>W40;L=8E :>;820==OE V7 G0AB>B0<8 1 V 2 F. 8:>@8AB0B8 1V1;V>B5:8 Sources, Sinks. 57C;LB0B 2825AB8 =0 2V@BC0;L=89 3@0D>?>1C4C20G. >72(O7>: A8AB5<8 0;351@0WG=8E @V2=O=L EMBED Equation.3 T >?B8<0;L=8< ?;0=><. =09B8 <0:A8<0;L=5 7=0G5==O FV;L>2>W DC=:FVW F = 4x + 9y. !B2>@8B8 <>45;L (@57C;LB0B8 2825AB8 =0 5:@0=8, 28:>@8AB0B8 >AF8;>3@0D 4;O 3@0DVG=>3> 7>1@065==O 7<V==8E). !B2>@8B8 <>45;L 4;O @>72(O7C20==O @V2=O==O, 70AB>AC202H8 1;>: Algebraic Constraint (@57C;LB0B ?>:070B8 =0 5:@0=V 48A?;5O, 0 3@0DVG=5 7>1@065==O =0 5:@0=V >AF8;>3@0D0):  EMBED Equation.3 . 0@V0=B 7 >1C4C20B8 D07>289 ?>@B@5B A8=CA>W48 (2 O:>ABV x A;C68BL A83=0;, 0 2 O:>ABV y  ?>EV4=0 FL>3> A83=0;C), ?@8 FL><C 28:>@8AB02H8 1V1;V>B5:8 Sources, Sinks, Continuous. 57C;LB0B8 2825AB8 =0 2V@BC0;L=89 3@0D>?>1C4C20G. # ?>A;V4>2=>ABV G8A5; [3, 5, 18, 30, 6, 3.7] 7=09B8 <0:A8<0;L=5 G8A;>, ?@8 FL><C 70AB>AC202H8 1V1;V>B5:8 Sources, Sinks, Math (Math Operations). 57C;LB0B8 2825AB8 =0 48A?;59. >72(O7>: A8AB5<8 0;351@0WG=8E @V2=O=L EMBED Equation.3 T >?B8<0;L=8< ?;0=><. =09B8 <0:A8<0;L=5 7=0G5==O FV;L>2>W DC=:FVW F = 12x + 5y. !B2>@8B8 <>45;L (@57C;LB0B8 2825AB8 =0 5:@0=8, 28:>@8AB0B8 >AF8;>3@0D 4;O 3@0DVG=>3> 7>1@065==O 7<V==8E). 0@V0=B 8 >A;V48B8 <>45;L @50;L=>3> @5;59=>3> 5;5<5=B0 ?@8 2EV4=><C A8=CA>W40;L=><C A83=0;V, ?@8 FL><C 28:>@8AB0B8 1V1;V>B5:8 Sources, Sinks, Discontinuitiues. 57C;LB0B8 2825AB8 =0 >AF8;>3@0D. # ?>A;V4>2=>ABV G8A5; [3, 5, 18, 30, 6, 3.7] 7=09B8 <0:A8<0;L=5 G8A;>, ?@8 FL><C 28:>@8AB02H8 1V1;V>B5:8 Sources, Sinks, Math (Math Operations). 57C;LB0B8 2825AB8 =0 48A?;59. !B2>@8B8 <>45;L 4;O @>72(O7C20==O @V2=O==O, 70AB>AC202H8 1;>: Algebraic Constraint (@57C;LB0B ?>:070B8 =0 5:@0=V 48A?;5O, 0 3@0DVG=5 7>1@065==O =0 5:@0=V >AF8;>3@0D0):  EMBED Equation.3 . 0@V0=B 9 0 4>?><>3>N 1V1;V>B5: Sources, Sinks, Function & tables (User-Defined Functions) AB2>@8B8 A83=0; B8?C  EMBED Equation.3 . 57C;LB0B 2825AB8 =0 >AF8;>3@0D. # ?>A;V4>2=>ABV G8A5; [4, 10, 18, 25, 6, 3.5] 7=09B8 <V=V<0;L=5 G8A;>, ?@8 FL><C 28:>@8AB02H8 1V1;V>B5:8 Sources, Sinks, Math (Math Operations). 57C;LB0B8 2825AB8 =0 48A?;59. 8:>=09B5 ;>3VG=5 <=>65==O 42>E 25:B>@V2 [0 0 1 1 1] B0 [0 1 1 0 1]. 0@V0=B 10 >:070B8 D07>289 ?>@B@5B 70BCE0NG8E :>;820=L 284C  EMBED Equation.3 . 8:>@8AB0B8 1V1;V>B5:8 Sources, Sinks, Function & tables (User-Defined Functions), Continuous. 57C;LB0B 2825AB8 =0 2V@BC0;L=89 3@0D>?>1C4C20G. =09B8 287=0G5=89 V=B53@0;  EMBED Equation.3  <5B>4>< B@0?5FV9. 57C;LB0B8 2825AB8 =0 48A?;59, 0 3@0DVG=5 7>1@065==O ?>:070B8 =0 2V@BC0;L=><C >AF8;>3@0DV. 8:>=09B5 ;>3VG=5 <=>65==O 42>E 25:B>@V2 [0 0 1 1 1 0] B0 [0 1 1 0 1]. 4. >=B@>;L=V 70?8B0==O 0B8 ?>=OBBO :>=F5?BC0;L=>W <>45;V. /:0 A8AB5<0 =07820TBLAO AB0B8G=>N? 025AB8 ?@8:;04. /:0 A8AB5<0 =07820TBLAO 48=0<VG=>N? 025AB8 ?@8:;04. /:V VA=CNBL B8?8 48=0<VG=8E A8AB5<? 025AB8 ?@8:;048. ;O G>3> ?@87=0G5=89 1;>: Display (5:@0=)? /:V 4VW 4>72>;OT 28:>=C20B8 1;>: Scope? 0B8 E0@0:B5@8AB8:C 1V1;V>B5FV <0B5<0B8G=8E 1;>:V2 Math (Math Operations). 025AB8 ?@8:;048 =09?@>ABVH8E <>45;59. 01>@0B>@=0 @>1>B0 !3 !B2>@5==O B0 4>A;V465==O <>45;V :V=F52>3> 02B><0B0 '0AB8=0 1 5B0 @>1>B8 02G8B8AO AB2>@N20B8 <>45;V ?@>AB8E :V=F528E 02B><0BV2, 28:>@8AB>2CNG8 1V1;V>B5:8 ?0:5B0 <>45;N20==O 48=0<VG=8E A8AB5<  Simulink. @8:;048 AB2>@5==O =09?@>ABVH8E <>45;59 @8:;04 1 @8?CAB8<>, I> V=D>@<0FVO, O:0 20A FV:028BL, <>65 7=0E>48B8AO 2 =B5@=5BV =0 >4=><C V7 42>E Web-2C7;V2 (=0725<> WE 4;O 287=0G5=>ABV !09B1 B0 !09B 2). 8O282H8 HC:0=C V=D>@<0FVN, 28 7020=B06CTB5 WW =0 A2V9 :><?(NB5@; O:I> V=D>@<0FVO <VAB8BLAO =0 >1>E 2C7;0E, B> 2 O:>ABV 465@5;0 28ABC?0T !09B1 (1C45<> 22060B8, I> 2V= 2V4@V7=OTBLAO :@0I>N >@30=V70FVTN 40=8E). @8?CAB8<> B0:>6, I> 2 1C4L-O:><C 28?04:C 28 ?>28==V ?>2V4><8B8 ?@> @57C;LB0B8 ?>HC:C A2>T<C H5D>2V. >20 945 ?@> >?8A ?>254V=:8 ;N48=8 (:V=F52>3> 45B5@<V=>20=>3> 02B><0B0) ?@8 ?>HC:C V=D>@<0FVW 2 =B5@=5B. !B2>@8B8 <>45;L. >OA=5==O 4> 28:>=0==O ?@8:;04C 1: 2V4:@8B8 1V1;V>B5:C Math V ?5@5BO3=CB8 1;>: Combinatorial Logic C ?>;5 <>45;N20==O; 4>40B8 C <>45;L 1;>:8, I> 2V4?>2V40NBL 42>< Web-2C7;0<, :>B@V ?>7=0G8<> O: Site1, Site2. 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"><C :>6=89 V7 =8E 1C45 ?@54AB02;5=89 1;>:>< Constant V7 @>74V;C Sources. @C389 1;>: (Constant1) <>6=0 >45@60B8 <5B>4>< :>?VN20==O. ;O FL>3> ?>B@V1=> ?><VAB8B8 :C@A>@ <8HV =0 1;>: Constant V =0B8A=CB8 ?@02C :=>?:C <8HV. !?@020 2V4 C:07V2=8:0 7(O28BLAO 1V;89 E@5AB8:. 5 2V4?CA:0NG8 :=>?:8 <8HV, ?5@5<VAB8B8 2:07V2=8: C BC B>G:C ?>;O <>45;N20==O, :C48 ?>B@V1=> 2AB028B8 =0ABC?=89 1;>: Constant; 4;O 1V;LH>W =0>G=>ABV <>45;V 70<V=8B8 AB0=40@B=V V<5=0 1;>:V2 =0 =>2V, 0 A0<5: Viziter, Site1, Site2. @8<VB:0: 2AV 1;>:8 C 1;>:-4V03@0<V >1>2(O7:>2> ?>28==V <0B8 V<(O  01> 70?@>?>=>20=5 Simulink, 01> ?@87=0G5=5 @>7@>1=8:>< <>45;V; B><C =5 <>6=0 7@>18B8 1;>: ((157V<5==8<((, 28:>@8AB>2CNG8 :;02VHC Del 01> Backspace; 1;>: Combinatorial Logic <0T BC >A>1;82VABL, I> =0 9>3> 2EV4 <>65 ?>ABC?0B8 ;8H5 >48= A83=0;, 0 Viziter ?>28=5= >45@60B8 V=D>@<0FVN ?@> AB0= >1>E 2C7;V2, B><C =5>1EV4=> >1(T4=0B8 420 A83=0;8 2 >48=. ;O FL>3> ?>B@V1=> @>7<VAB8B8 1;>: Mux (7<VHC20G) V7 @>74V;C Signal Routing; 7<V=8B8 B01;8FN VAB8==>ABV 1;>:0 Viziter, ?0@0<5B@ Truth table (B01;8FO VAB8==>ABV) 7040B8 =0ABC?=8< G8=><: [0 0 1; 0 1 1; 1 0 1; 1 0 1]. 040NBLAO ;8H5 7=0G5==O 28EV4=>3> A83=0;C; 4;O 2V4>1@065==O @57C;LB0BV2 @>1>B8 <>45;V 28:>@8AB0B8 1;>: Display (5:@0=) V7 @>74V;C Sinks; 7=0G5==O :>=AB0=B Site1, Site2 AB028<> @V2=8< 0 (B>1B> 1C45<> 22060B8, I> 6>45= 2C7>; =5 <VAB8BL ?>B@V1=C V=D>@<0FVN); 7(T4=09B5 1;>:8 V 70?CABVBL <>45;L =0 28:>=0==O; 715@53B8 <>45;L 70 4>?><>3>N :><0=48 File ( Save as ?V4 V<5=5<, =0?@8:;04, Choice1. # AB2>@5=V9 <>45;V ?@0:B8G=> 2AV 1;>:8 28:>@8AB>2C20;8AO 7 ?0@0<5B@0<8, 2AB0=>2;5=8<8 70 70<>2G0==O<. @8:;04 2 # ?>1C4>20=V9 <>45;V 7<V=8B8 ?0@0<5B@8 A50=AC <>45;N20==O: 2AB0=>2VBL 25;8G8=C :@>:C <>45;N20==O @V2=>N 1, CAB0=>2VBL 7=0G5==O :V=F52>3> G0AC @V2=8< 1, 7<V=8B8 7=0G5==O :>=AB0=B Site1, Site2. >OA=5==O 4> 28:>=0==O ?@8:;04C 2: # 2V:=V 1;>:-4V03@0<8 <>45;V 2V4:@89B5 <5=N Simulation (<>45;N20==O) V 2815@VBL :><0=4C Simulation parameters (?0@0<5B@8) ( Solver (@>7@0EC=>:) V C @>7:@820NG><C A?8A:C Type 2815@VBL 20@V0=B Fixed-step (DV:A>20=89 :@>:). # ?>;5 Fixed step size (25;8G8=0 DV:A>20=>3> :@>:C) 2AB0=>2VBL 25;8G8=C :@>:C <>45;N20==O @V2=>N 1. <V=VBL 7=0G5==O C ?>;V Stop time (:V=F5289 G0A), =0?@8:;04 1.  8A. 3.1. 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AB0=>28B8 25;8G8=C DV:A>20=>3> :@>:C <>45;N20==O 1. 0@V0=B 3 !B2>@8B8 <>45;L ?>254V=:8 ;N48=8 (:V=F52>3> 45B5@<V=>20=>3> 02B><0B0) ?@8 ?>HC:C V=D>@<0FVW 2 Internet. @8?CAB8<>, I> V=D>@<0FVO, O:0 FV:028BL ;N48=C, 7=0E>48BLAO 2 Internet =0 ?5@H><C 2C7;V 2 >1AO7V 5 109B, 0 =0 4@C3><C  7 109B. 8O282H8 HC:0=C V=D>@<0FVN, :>@8ABC20G 7020=B06CT WW =0 A2V9 :><?(NB5@. # 1C4L-O:><C 28?04:>2V 2V= ?>28=5= ?>2V4><8B8 ?@> @57C;LB0B8 ?>HC:C A2>T<C :5@V2=8FB2C. 5@5410G8B8 715@565==O @57C;LB0BV2 <>45;N20==O C @>1>GC >1;0ABL MatLab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x x x]. # ?5@H><C @>7@O4V: 1  :>@8ABC20G =5 70@5TAB@>20=89, 0  70@5TAB@>20=89; C 4@C3><C @>7@O4V: 1  4>72>;5=> :C?C20B8, 0  =5 4>72>;5=> :C?C20B8; B@5BV9 @>7@O4 A;C68BL 4;O ?>2V4><;5==O ;VG8;L=8:0 ?@> 2V42V4C20==O A09B0. 57C;LB0B8 2825AB8 =0 48A?;59. 0@V0=B 6 >7@>18B8 <>45;L 10=:><0B0 (:V=F52>3> 45B5@<V=>20=>3> 02B><0B0), O:89 ?@89<0T @VH5==O ?@> 2840GC 3>BV2:8 ?@8 ?@028;L=> 22545=><C ?V=-:>4V B0 =0O2=>ABV AC<8, O:0 ?>B@V1=0 :;VT=BC. 2060B8, I> 0  V=D>@<0FVO =5?@028;L=0, 1  ?@028;L=0 V=D>@<0FVO. >2V4><;OB8 :;VT=B0 ?@> 74V9A=5==O >?5@0FVW 2840GV 3>BV2:8 9 >?5@0B>@0 I>4> :>@8ABC20==O 02B><0B>< C 1C4L-O:><C 28?04:>2V. =D>@<0FVN 70?8AC20B8 C D09; MatLab. 0@V0=B 7 >7@>18B8 <>45;L ?@8AB@>N (:V=F52>3> 02B><0B0), 2AB0=>2;5=>3> =0 :>=25T@V, O:89 :>=B@>;NT H8@8=C V 4>268=C 45B0;59 B0 WE 2V4A>@B>2CT =0  1@0:>20=V 9  O:VA=V . 5>1EV4=> 4>40B:>2> ?>2V4><8B8 >?5@0B>@C ?@> ?0@0<5B@8 45B0;V. 2060B8, I> 0  >7=0:0 O:>ABV, 1  =0O2=VABL 1@0:C. 57C;LB0B8 2825AB8 =0 48A?;59. 0@V0=B 8 >7@>18B8 <>45;L ?@8AB@>N (:V=F52>3> 02B><0B0), 2AB0=>2;5=>3> =0 :>=25T@V, O:89 :>=B@>;NT ?>74>26=V9 V ?>?5@5G=89 @>7<V@ 45B0;59 B0 WE 2V4A>@B>2CT =0  1@0:>20=V 9  O:VA=V . >B@V1=> 4>40B:>2> ?>2V4><8B8 >?5@0B>@C ?@> ?0@0<5B@8 45B0;V. 2060B8, I> 0  7=0: O:>ABV, 1  =0O2=VABL 1@0:C. 57C;LB0B8 2825AB8 C @>1>GC >1;0ABL MatLab. 0@V0=B 9 >7@>18B8 <>45;L ?@8AB@>N (:V=F52>3> 02B><0B0), 2AB0=>2;5=>3> C 28A>B=><C 1C48=:>2V, O:89 :>=B@>;NT @>1>BC B@L>E ;VDBV2. 2B><0B ?>28=5= 2V4:@820B8 425@V B>3> ;VDB0, I> @0=VH5 ?@81C2 4> :;VT=B0. 2060B8, I> 0  ;VDB =5 ?@81C2, 1  ;VDB ?@81C2. /:I> ?@81C;> >4=>G0A=> 45:V;L:0 ;VDBV2, B> ?>28==V 2V4:@820B8AO 425@V ?5@H>3> ;VDB0 70 @>7@O4=VABN. >2V4><;5==O =04A8;0B8 >?5@0B>@C. 57C;LB0B8 2V4>1@060B8 =0 48A?;5W. 0@V0=B 10 >7@>18B8 <>45;L ?@8AB@>N (:V=F52>3> 02B><0B0), 2AB0=>2;5=>3> C 28A>B=><C 1C48=:>2V, O:89 :>=B@>;NT @>1>BC B@L>E ;VDBV2. 2B><0B ?>28=5= 2V4:@820B8 425@V B>3> ;VDB0, :>B@89 @0=VH5 ?@81C2 4> :;VT=B0. 2060B8, I> 0  ;VDB =5 ?@81C2, 1  ;VDB ?@81C2. /:I> ?@81C;> >4=>G0A=> 45:V;L:0 ;VDBV2, B> ?>28==V 2V4:@820B8AO 425@V ?5@H>3> ;VDB0 70 @>7@O4=VABN. >2V4><;5==O =04A8;0B8 >?5@0B>@C. 57C;LB0B8 70?8A0B8 C @>1>GC >1;0ABL MatLab G5@57 >AF8;>3@0D. >=B@>;L=V 70?8B0==O 1. /:V 5B0?8 2:;NG0T ?>1C4>20 :>=F5?BC0;L=>W <>45;V? 2. )> O2;OT A>1>N V<VB0FV9=89 5:A?5@8<5=B? 3. /:V A8AB5<8 VA=CNBL 70 C<>20<8 ?5@5E>4C 7 >4=>3> AB0=C 2 V=H89? 4. /:V ?0@0<5B@8 =0;0HBC20==O <0T 1;>: To Workspace? 5. /:89 <0T 7<VAB @>1>G0 >1;0ABL ?VA;O 715@565==O @57C;LB0BV2 <>45;N20==O? 6. 5 <>6=0 2AB0=>28B8 ?0@0<5B@8 <>45;V? 7. )> O2;OT A>1>N <>45;L :V=F52>3> 02B><0B0? 025AB8 ?@8:;048. 8. >OA=8B8 @>1>BC V =0;0HBC20==O 1;>:0 Combinatorial Logic. 9. >OA=8B8 =0;0HBC20==O ?0@0<5B@V2 2V:=0 Simulation parameters. 01>@0B>@=0 @>1>B0 !4 >A;V465==O <>45;V :V=F52>3> 02B><0B0 '0AB8=0 2 1. 5B0 @>1>B8 02G8B8AO AB2>@N20B8 1V;LH A:;04=V <>45;V :V=F528E 02B><0BV2, 28:>@8AB>2CNG8 1V1;V>B5:8 ?0:5B0 <>45;N20==O 48=0<VG=8E A8AB5<  Simulink. 2. @8:;048 AB2>@5==O S-<>45;59 @8:;04 1 !B2>@8B8 <>45;L ?>254V=:8 ;N48=8 (:V=F52>3> 45B5@<V=>20=>3> 02B><0B0) ?@8 ?>HC:C V=D>@<0FVW 2 Internet. @8?CAB8<>, I> V=D>@<0FVO, O:0 FV:028BL :;VT=B0, 7=0E>48BLAO 2 Internet =0 ?5@H><C 2C7;V 2 >1AO7V 4 109B8, 0 =0 4@C3><C  2 109B8. 8O282H8 HC:0=C V=D>@<0FVN, 2V= 7020=B06CT WW =0 A2V9 :><?(NB5@; O:I> V=D>@<0FVO <VAB8BLAO =0 >1>E 2C7;0E, B> 2 O:>ABV 465@5;0 28ABC?0T !09B1 (1C45<> 22060B8, I> F59 A09B 28@V7=OTBLAO :@0I>N >@30=V70FVTN 40=8E). @8?CAB8<> B0:>6, I> 2 1C4L-O:><C 28?04:C :;VT=B ?>28=5= ?>2V4><8B8 ?@> @57C;LB0B8 ?>HC:C A2>T<C :5@V2=8:>2V. 5@5410G8B8 715@565==O @57C;LB0BV2, >45@60=8E ?V4 G0A A50=AC <>45;N20==O, 2 @>1>GC >1;0ABL 70 4>?><>3>N 1;>:0 Scope. >OA=5==O 4> 28:>=0==O ?@8:;04C 1: >1C4C9B5 <>45;L =0ABC?=>3> 283;O4C, ?@8 FL><C B01;8FO VAB8==>ABV 1;>:0 Combinatorial Logic 1C45 ?@54AB02;5=0 25:B>@>< [0 0 1; 0 2 1; 4 0 1; 4 0 1]:  8A. 4.1. 15@565==O @57C;LB0BV2 <>45;N20==O 70 4>?><>3>N 1;>:0 Scope 2) V4:@89B5 2V:=> 1;>:0 Scope. 25@=VBL C203C, I> 3@0=8FV 28<V@N20==O ?> >AV G0AC (?> >AV 01AF8A) 71V30NBLAO 7 V=B5@20;>< <>45;N20==O, 2AB0=>2;5=>3> 4;O <>45;N20==O (2V4 0 4> 1). 0?CABVBL <>45;L =0 28:>=0==O. # 2V:=V 7(O2;OBLAO ?@O<V, I> 2V4?>2V40NBL 7=0G5==O< 5;5<5=BV2 28EV4=>3> 25:B>@0. 0 70<>2GC20==O< 40=V, I> 282>4OBLAO C 2V:=V Scope, =5 715@V30NBLAO. 3) ;O 715@565==O @57C;LB0BV2 ?>B@V1=> 7<V=8B8 CAB0=>2:8. ;O FL>3> C 2V:=V Scope =0B8A=CB8 :=>?:C Parameters. 0 2:;04FV Data history 4V0;>3>2>3> 2V:=0 2AB0=>28B8 2V4<VB:C Save data to workspase (715@565==O 40=8E C @>1>GV9 >1;0ABV), ?@8 FL><C AB0=5 4>ABC?=8< ?>;5 Variable name (V<(O 7<V==>W). =0G5==O =0 5:@0=V ?>28==V <0B8 B0:89 283;O4:  8A. 4.2. #AB0=>2:0 ?0@0<5B@V2 715@565==O @57C;LB0BV2 <>45;N20==O !CBBT2>N 7@CG=VABN 70AB>AC20==O 1;>:0 Scope 4;O 715@565==O @57C;LB0BV2 <>45;N20==O T B5, I> D>@<0B <0B@8FV Data 71V30TBLAO 7 D>@<0B>< 40=8E, :>B@V 28:>@8AB>2CNBLAO C 1;>FV From Workspase (22545==O 40=8E V7 @>1>G>W >1;0ABV). 4) 15@53B8 <>45;L ?V4 V<5=5<, =0?@8:;04, Choice4. @8:;04 2 #@0E>2CNG8 C<>2C ?5@H>3> 70240==O, ?@8?CAB8<>, I> :;VT=B =04A8;0T ?>2V4><;5==O A2>T<C :5@V2=8:C =5 2V4@07C, 0 G5@57 45O:89 G0A, =5>1EV4=89 4;O 7020=B065==O =0 :><?(NB5@ 7=0945=>W V=D>@<0FVW. V4?>2V4=> >1AO3 709=OB>3> 48A:>2>3> ?@>AB>@C ?@8 FL><C 71V;LHCTBLAO =0 25;8G8=C 70?8A0=>W ?>@FVW 40=8E. !B2>@8B8 <>45;L. >OA=5==O 4> 28:>=0==O ?@8:;04C 2: 1) >1C4C20B8 S-<>45;L, ?@87=0G5==O O:>W 1C45 2:;NG0B8 B0:V 4VW: 020=B065==O 7 @>1>G>W >1;0ABV @57C;LB0BV2 @>1>B8 <>45;V Choice4. 81V@ 2C7;0, V=D>@<0FVO 7 O:>3> 1C45 70?8A0=0 =0 :><?(NB5@. 1V;LH5==O >1AO3C 709=OB>3> 48A:>2>3> ?@>AB>@C =0 25;8G8=C 70?8A0=>W ?>@FVW 40=8E. 0B@8<:0 A83=0;C, I> V<VBCT ?>2V4><;5==O, =0 7040=89 V=B5@20; G0AC. ;O ?>1C4>28 40=>W <>45;V A:>@8AB0T<>AO =0ABC?=8<8 4>40B:>28<8 1;>:0<8: From Workspace (V7 1V1;V>B5:8 Sources)  7G8BC20==O 40=8E V7 @>1>G>W >1;0ABV. Demux (V7 1V1;V>B5:8 Signal Routing)  70157?5GCT @>74V;5==O 2EV4=>3> 25:B>@=>3> A83=0;C =0 A:;04>2V 9>3> :><?>=5=B8. Switch (V7 1V1;V>B5:8 Signal Routing)  ?5@5<8:0G. Relational Operator (V7 1V1;V>B5:8 Math Operations)  >?5@0B>@ 2V4=>H5==O, 4>72>;OT 281@0B8 2C7>;, 7 O:>3> 1C45 7020=B06C20B8AO V=D>@<0FVO. Sum (V7 1V1;V>B5:8 Math Operations)  4>4020==O, >1G8A;NTBLAO >1AO3 709=OB>3> 48A:>2>3> ?@>AB>@C. Transport Delay (V7 1V1;V>B5:8 Continuous)  70157?5GCT 70B@8<:C V<VBCNG>3> ?>2V4><;5==O =0 7040=89 V=B5@20; G0AC. Display  4>72>;OT ?>10G8B8 @57C;LB0B @>1>B8 <>45;V. >45;L <0B8<5 B0:89 283;O4:  8A. 4.3. >1C4>20 S-<>45;V 4> 70240==O 2 2) 0;03>48B8 2=CB@VH=V ?0@0<5B@8 1;>:V2, I> 2E>4OBL 4> A:;04C <>45;V. ;O @>1>B8 FVTW <>45;V 2 O:>ABV 28EV4=8E 40=8E T @57C;LB0B8 @>1>B8 <>45;V Choice4. )>1 <0B@8FO Data AB0;0 4>ABC?=>N 1;>:C From Workspace, =5>1EV4=> 2:070B8 WW V<(O 2 O:>ABV ?0@0<5B@0 1;>:0. ?5@0B>@ 2V4=>H5==O Relational Operator 4>72>;OT 7(OAC20B8, =0 O:><C 7 2C7;V2 <VAB8BLAO 1V;LH89 >1AO3 V=D>@<0FVW, 0 1;>: Switch 70157?5GCT ?5@5A8;0==O 2V4?>2V4=>3> A83=0;C =0 2EV4 1;>:0 Sum. ?5@0B>@ 2V4=>H5==O >= 2818@0TBLAO 2 @>7:@820NG><C A?8A:C 2V:=0 ?0@0<5B@V2 =0;03>465==O 1;>:0 V 2V4>1@060TBLAO 2 A5@548=V 1;>:0.  8A. 4.4. V:=> =0;03>465==O 1;>:0 Switch # ?>;5 Threshold (?>@V3), O:5 287=0G0T ?>@V3 A?@0FN20==O 1;>:0, 2AB0=>2;NT<> 7=0G5==O 1. &5 >7=0G0T, I> O:I> >1AO3 V=D>@<0FVW C 1;>FV Site1 1V;LH89, =V6 C 1;>FV Site2, B> =0 2EV4 1;>:0 Sum =04E>48BL A83=0; V7 ?5@H>3> V=D>@<0FV9=>3> 2E>4C 1;>:0 Switch; C ?@>B8;56=><C @07V ?5@5A8;0TBLAO A83=0; V7 4@C3>3> V=D>@<0FV9=>3> 2E>4C, @V2=89 >1AO3C V=D>@<0FVW C 1;>FV Site2.  8A. 4.5. V:=> =0;03>465==O 1;>:0 Sum 4;O 40=>W <>45;V ;>: Transport Delay 70B@8<CT A83=0;, O:89 =04E>48BL =0 9>3> 2EV4 =0 >48= :@>: <>45;L=>3> G0AC. > 70:V=G5==V 40=>3> V=B5@20;C =0 28EV4 1;>:0 2840TBLAO 7=0G5==O, V<VBCNG5 ?>2V4><;5==O H5DC (B@5BV9 5;5<5=B 25:B>@=>3> A83=0;C, 7G8B0=89 V7 @>1>G>W >1;0ABV). 0;03>48<> ?0@0<5B@8 <>45;V Send, 281@02H8 :><0=4C 2 <5=N Simulation( Simulation parameters.  8A. 4.6. #AB0=>2;5==O ?0@0<5B@V2 <>45;V 0?CABVBL =0 28:>=0==O A?>G0B:C <>45;L Choice4, 0 ?>BV< Send. >@V2=O9B5 7=0G5==O, 282545=V C 2V:=0E 1;>:0 Display <>45;V Choice4 7 ?>:070==O<8 1;>:V2 <>45;V Send. /:I> 2>=8 71V30NBLAO, B> 2A5 7@>1;5=> ?@028;L=>. 0 5:@0=V 1;>:0 Scope 2V4>1@06CNBLAO <><5=B8 D>@<C20==O A83=0;V2 =0 2E>40E 1;>:V2 Display, Display1. ;O 2V4>1@065==O 42>E 3@0DV:V2 =0;03>48<> 2;0AB82>ABV 1;>:0 =0ABC?=8< G8=><:  8A. 4.7. #AB0=>2:0 ?0@0<5B@V2 C 1;>FV Scope (Number of axes=2  :V;L:VABL 3@0DV:V2)  8A. 4.8. V03@0<0 @>1>B8 <>45;V Send (725@EC  70?8A =0 48A:, 7=87C  ?>2V4><;5==O H5DC) 3. 0240==O 4;O A0<>ABV9=>3> 28:>=0==O 0@V0=B 1 !B2>@8B8 <>45;L ?>254V=:8 ;N48=8 (:V=F52>3> 45B5@<V=>20=>3> 02B><0B0) ?@8 ?>HC:C V=D>@<0FVW 2 Internet. @8?CAB8<>, I> V=D>@<0FVO, O:0 FV:028BL ;N48=C, 7=0E>48BLAO 2 Internet =0 ?5@H><C 2C7;V 2 >1AO7V 5 109B, 0 =0 4@C3><C  2 109B. 5E09 :>@8ABC20G =04A8;0T ?>2V4><;5==O A2>T<C H5DC =5 2V4@07C, 0 G5@57 45O:89 G0A, =5>1EV4=89 4;O 7020=B065==O =0 :><?(NB5@ 7=0945=>W V=D>@<0FVW (?@8 FL><C 28:>@8AB0B8 1;>: Transport Delay). 0 :><?(NB5@ 7020=B06CTBLAO V=D>@<0FVO 7 B>3> 1;>:0, =0 O:89 2>=0 ?@89H;0 C 1V;LH><C >1AO7V (28:>@8AB0B8 1;>: Switch  ?5@5<8:0G). 57C;LB0B 2V4>1@078B8 =0 5:@0=0E 48A?;5W2 V ?>:070B8 3@0DVG=C V=B5@?@5B0FVN 70 4>?><>3>N >AF8;>3@0DV2. 0@V0=B 2 !B2>@8B8 <>45;L ?>254V=:8 ;N48=8 (:V=F52>3> 45B5@<V=>20=>3> 02B><0B0) ?@8 ?>HC:C V=D>@<0FVW 2 Internet. @8?CAB8<>, I> V=D>@<0FVO, O:0 FV:028BL ;N48=C, 7=0E>48BLAO 2 Internet =0 ?5@H><C 2C7;V 2 >1AO7V 4 109B8, 0 =0 4@C3><C  3 109B8. 5E09 :>@8ABC20G =04A8;0T ?>2V4><;5==O A2>T<C H5DC =5 2V4@07C, 0 G5@57 45O:89 G0A, ?>B@V1=89 4;O 7020=B065==O =0 :><?(NB5@ 7=0945=>W V=D>@<0FVW (?@8 FL><C 28:>@8AB0B8 1;>: Transport Delay). 57C;LB0B 2V4>1@078B8 =0 5:@0=0E 48A?;5W2 V ?>:070B8 3@0DVG=C V=B5@?@5B0FVN 70 4>?><>3>N >AF8;>3@0DV2. 0@V0=B 3 !B2>@8B8 <>45;L ?>254V=:8 ;N48=8 (:V=F52>3> 45B5@<V=>20=>3> 02B><0B0) ?@8 ?>HC:C V=D>@<0FVW 2 Internet. @8?CAB8<>, I> V=D>@<0FVO, O:0 FV:028BL ;N48=C, 7=0E>48BLAO 2 Internet =0 ?5@H><C 2C7;V 2 >1AO7V 10 109B, 0 =0 4@C3><C  7 109B. 5E09 :>@8ABC20G =04A8;0T ?>2V4><;5==O A2>T<C H5DC =5 2V4@07C, 0 G5@57 45O:89 G0A, =5>1EV4=89 4;O 7020=B065==O =0 :><?(NB5@ 7=0945=>W V=D>@<0FVW (?@8 FL><C 28:>@8AB0B8 1;>: Transport Delay). 0 :><?(NB5@ 7020=B06CTBLAO V=D>@<0FVO 7 B>3> 1;>:0, =0 O:89 2>=0 ?@89H;0 C 1V;LH><C >1AO7V (28:>@8AB0B8 1;>: Switch  ?5@5<8:0G). 57C;LB0B 2V4>1@078B8 =0 5:@0=0E 48A?;5W2 V ?>:070B8 3@0DVG=C V=B5@?@5B0FVN 70 4>?><>3>N >AF8;>3@0DV2. 0@V0=B 4 !B2>@8B8 <>45;L ?>254V=:8 ;N48=8 (:V=F52>3> 45B5@<V=>20=>3> 02B><0B0) ?@8 ?>HC:C V=D>@<0FVW 2 Internet. @8?CAB8<>, I> V=D>@<0FVO, O:0 FV:028BL ;N48=C, 7=0E>48BLAO 2 Internet =0 ?5@H><C 2C7;V 2 >1AO7V 5 109B, 0 =0 4@C3><C  2 109B. 5E09 :>@8ABC20G =04A8;0T ?>2V4><;5==O A2>T<C H5DC =5 2V4@07C, 0 G5@57 45O:89 G0A, =5>1EV4=89 4;O 7020=B065==O =0 :><?(NB5@ 7=0945=>W V=D>@<0FVW (?@8 FL><C 28:>@8AB0B8 1;>: Transport Delay). 0 :><?(NB5@ 7020=B06CTBLAO V=D>@<0FVO 7 B>3> 1;>:0, =0 O:89 2>=0 ?@89H;0 C 1V;LH><C >1AO7V (28:>@8AB0B8 1;>: Switch  ?5@5<8:0G). V4?>2V4=> >1AO3 709=OB>3> 48A:>2>3> ?@>AB>@C ?@8 FL><C 71V;LHCTBLAO =0 25;8G8=C 70?8A0=>W ?>@FVW 40=8E. 57C;LB0B 2V4>1@078B8 =0 5:@0=0E 48A?;5W2 V ?>:070B8 3@0DVG=C V=B5@?@5B0FVN 70 4>?><>3>N >AF8;>3@0DV2. 0@V0=B 5 5E09 <0T<> =0A>A=C AB0=FVN, 4> A:;04C O:>W 2E>4OBL B@8 =0A>A8, 2AB0=>2;5=V =0 @V7=V9 3;818=V. "8A: 2>48 4;O 2AVE =0A>AV2 22060TBLAO >4=0:>28<. '0A 2V4 C<8:0==O =0A>A0 4> ?>40GV 2>48 4;O ?5@H>3> AB0=>28BL 3 A., 4;O 4@C3>3>  5 A., 4;O B@5BL>3>  8 A. ?5@0B>@ 70;56=> 2V4 @V2=O 2>48 C A25@4;>28=V 2<8:0T 1-9, 2-9 01> 3-9 =0A>A. !B2>@8B8 <>45;L (:V=F52>3> 45B5@<V=>20=>3> 02B><0B0), 70 O:>N <>6=0 ?>:070B8 2<8:0==O =0A>AV2 V 2825AB8 G0A>2C 4V03@0<C @>1>B8 =0A>AV2 =0 >AF8;>3@0D. 0@V0=B 6 !B2>@8B8 <>45;L 02B><0B8G=>W :>@>1:8 ?5@540G 02B><>1V;O (:V=F52>3> 45B5@<V=>20=>3> 02B><0B0), 70 4>?><>3>N O:>W 2V41C20TBLAO @>73V= V7 7040=>N H284:VABN =0 B@L>E ?5@540G0E (1</A, 5</A, 7</A). =D>@<0FVO ?@> 22V<:=5=C ?5@540GC =04E>48BL C F8D@>2><C :>4V. @8 <>45;N20==V 28:>@8AB0B8 1;>:8 Swich, Combinatorial Logic B0 4;O <>45;N20==O ?@>F5AC @>73>=C 1;>: Ramp. =D>@<0FVN 2825AB8 =0 >AF8;>3@0D. 0@V0=B 7 5E09 <0T<> 420 2848 @5AC@AV2, O:V 28:>@8AB>2CNBLAO B0 ?>=>2;NNBLAO V7 45O:>N ?5@V>48G=VABN (1 HB/A, 5 HB/A). >@8ABC20GC =5>1EV4=> 28:>@8AB>2C20B8 B>9 @5AC@A, O:>3> =091V;LH5 C 40=89 <><5=B G0AC. !B2>@8B8 <>45;L (:V=F5289 45B5@<V=>20=89 02B><0B), O:0 2V4>1@060T ?>254V=:C :>@8ABC20G0. 57C;LB0B 2V4>1@078B8 =0 >AF8;>3@0DV. 0@V0=B 8 !B2>@8B8 <>45;L (:V=F5289 45B5@<V=>20=89 02B><0B), O:0 >1G8A;NT @59B8=3 ?V4?@8T<AB20 70 @V2=O==O< !09DC;V=0 V 048:>20  EMBED Equation.3 , 45 EMBED Equation.3  02B><0B ?>28=5= 284020B8 @VH5==O ?@> 704>2V;L=89 G8 =5704>2V;L=89 AB0= ?V4?@8T<AB20. 57C;LB0B8 2825AB8 =0 48A?;59. 0@V0=B 9 !B2>@8B8 <>45;L (:V=F5289 45B5@<V=>20=89 02B><0B), O:0 40T >FV=:C DV=0=A>2>3> AB0=C ?V4?@8T<AB20 70 @V2=O==O< ><0=0 VA0  EMBED Equation.3 , 45  EMBED Equation.3  >1>@>B=89 :0?VB0;/AC<0 0:B82V2;  EMBED Equation.3   >?5@0FV9=89 ?@81CB>:/AC<0 0:B82V2;  EMBED Equation.3   =5@>7?>4V;5=89 ?@81CB>:/AC<0 0:B82V2;  EMBED Equation.3   2;0A=89 :0?VB0;/70?>78G5=89 :0?VB0;. 5;8G8=0 Z <0T 3@0=8G=5 7=0G5==O 0,037. 2B><0B ?>28=5= 284020B8 >FV=:C ?V4?@8T<AB20 =0 48A?;59. 0@V0=B 10 !B2>@8B8 <>45;L 02B><0B8G=>W :>@>1:8 ?5@540G 02B><>1V;O (:V=F52>3> 45B5@<V=>20=>3> 02B><0B0), 70 4>?><>3>N O:>W 2V41C20TBLAO @>73V= V7 7040=>N H284:VABN =0 B@L>E ?5@540G0E (2</A, 6</A, 10</A). =D>@<0FVO ?@> 22V<:=5=C ?5@540GC =04E>48BL C F8D@>2><C :>4V. (284:VABL >1<568B8 4> 40 :</3>4, 60 :</3>4, 80 :</3>4. @8 AB2>@5==V <>45;V 28:>@8AB0B8 1;>:8 Swich, Combinatorial Logic, 0 4;O <>45;N20==O ?@>F5AC @>73>=C  1;>: Ramp. =D>@<0FVN 2825AB8 =0 >AF8;>3@0D. 01>@0B>@=0 @>1>B0 !5 >45;N20==O 28?04:>28E ?>4V9 '0AB8=0 1 1. 5B0 @>1>B8 5B>N 40=>W ;01>@0B>@=>W @>1>B8 T <>45;N20==O 28?04:>28E ?>4V9 70 4>?><>3>N 1;>:V2 Simulink. 2. @8:;048 AB2>@5==O S-<>45;59 @8:;04 1 >1C4C20B8 <>45;L 28?04:>2>W ?>4VW, I>1 28?04:>25 G8A;> ?>B@0?8;> C 4V0?07>= [0; 0.4]. >OA=5==O 4> 28:>=0==O ?@8:;04C 1: 0=0 <>45;L <0T B0:89 283;O4:  8A. 5.1. >45;N20==O 28?04:>2>W ?>4VW V7 7040=>N 2V@>3V4=VABN =0AB0==O  8A. 5.2. 0@0<5B@8 =0;03>465==O 1;>:0 Uniform Random Number 4;O <>45;V Minimum  =86=O 3@0=8FO 4V0?07>=C; Maximum  25@E=O 3@0=8FO; Sample time  5B0;>==89 G0A, C 40=><C 28?04:>2V 4>72>;OT 704020B8 :V;L:VABL 28?04:>28E G8A5;, I> 1C4CBL AD>@<>20=V 1;>:>< <>45;N20==O ?V4 G0A V=B5@20;C <>45;N20==O. @8 7=0G5==V, I> 4>@V2=NT 0, =>25 28?04:>25 G8A;> 35=5@CTBLAO G5@57 :>6=V 0,02 >48=8FV G0AC <>45;N20==O; Initial seed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x (-1,0736) +  x 0,0579. /:I> @57C;LB0B Z 28O2;OTBLAO 2V4(T<=8<, B> 2V@>3V4=VABL 10=:@CBAB20 =525;8:0. >40B=5 7=0G5==O Z C:07CT =0 28A>:C 2V@>3V4=VABL 10=:@CBAB20. >45;L <0T B0:89 283;O4:  8A. 5.3. 2>D0:B>@=0 <>45;L >FV=:8 9<>2V@=>ABV 10=:@CBAB20 ?V4?@8T<AB20 ?  2V@>3V4=0 7<V==0. =0G5==O WW 7040<> 70 4>?><>3>N 1;>:0 Uniform Random Number, O:89 @>7<VICTBLAO C 1V1;V>B5FV Souces (1V1;V>B5:0 465@5; B0 A83=0;V2). &5 71C@N20;L=0 25;8G8=0 (28:>=CT 71C@N20;L=C 4VN, B>1B> ?>@CHCT CAB0=>2;5=89 @568<, C=>A8BL 7<V=8 C A8AB5<C). A>1;82VABN FL>3> 1;>:0 T B5, I> 2V= C :>6=><C A50=AV <>45;N20==O 35=5@CT >4=C V BC 6 ?>A;V4>2=VABL 28?04:>28E G8A5;. 7  FN 7<V==C <8 ?@54AB028<> O: 465@5;> 4VW C 283;O4V >48=>:>3> ?5@5?04C Step (7=0E>48BLAO C 1V1;V>B5FV Souces). !B028<> F59 1;>: O: 704020;L=C 4VN 4;O 4>A;V465==O 48=0<VG=>W A8AB5<8, B>1B> 4>A;V46CT<>, O: A8AB5<0 @503CT =0 AB@81:>?>4V1=C 4VN 2EV4=>3> A83=0;C. # 1V1;V>B5FV Math (<0B5<0B8G=V 1;>:8) 7=0E>48<> 1;>: Gain (<=>6=8:). &59 1;>: 28:>=CT @>;L ?@8<=>6C20G0 A83=0;C, I> =04E>48BL =0 9>3> 2EV4. B65, =0 AC<0B>@ ?>28==> =04V9B8 B@8 A83=0;8: ?, 7, :>=AB0=B0 (-0,3877). 8EV4=89 A83=0; (@57C;LB0B) <8 ?>28==V ?>@V2=OB8 7 0 4;O B>3>, I>1 287=0G8B8 ABC?V=L 10=:@CBAB20. ;O FL>3> 28:>@8AB>2CT<> 1;>: Relational Operator. 57C;LB0B @>1>B8 =0H>W <>45;V <8 <>65<> A?>AB5@V30B8 =0 2V7C0;L=><C >AF8;>3@0DV Scope, O:89 7=0E>48BLAO C 1V1;V>B5FV @5TAB@0FV9=8E ?@8;04V2. V= 4>72>;OT ?@54AB028B8 @57C;LB0B8 <>45;N20==O C 283;O4V B8<G0A>28E 4V03@0< B8E 01> V=H8E ?@>F5AV2. /:I> @57C;LB0B Z 28O2;OTBLAO 2V4(T<=8<, B> 2V@>3V4=VABL 10=:@CBAB20 =525;8:0. >40B=5 7=0G5==O Z C:07CT =0 28A>:C 2V@>3V4=VABL 10=:@CBAB20. A>1;82VABN 1;>:0 Uniform Random Number T B5, I> 2V= C :>6=><C A50=AV <>45;N20==O 35=5@CT >4=C V BC A0<C ?>A;V4>2=VABL 28?04:>28E G8A5;. ;O 7<V=8 35=5@CNG>W ?>A;V4>2=>ABV =5>1EV4=> 2@CG=C 7<V=N20B8 7=0G5==O 9>3> ?0@0<5B@0 Initial seed (?>G0B:>25 7=0G5==O). @8 ?@>2545==V 25;8:>W :V;L:>ABV 5:A?5@8<5=BV2 V7 <5B>N =0:>?8G5==O AB0B8AB8G=8E 40=8E F5 =5 4C65 7@CG=>. "><C 4;O 35=5@C20==O 28?04:>28E ?>4V9 <>6=0 28:>@8AB0B8 1;>: Fnc (DC=:FVO) V7 1V1;V>B5:8 User-Defined Functions. 3. 0240==O 4;O A0<>ABV9=>3> 28:>=0==O 0@V0=B 1 >1C4C20B8 <>45;L 28?04:>2>W ?>4VW, I>1 28?04:>25 G8A;> ?>?0;> C 4V0?07>= [0; 0.4]. >6=5 28?04:>25 G8A;> ?>28==> DV:AC20B8AO =0 5:@0=V. @8 ?>1C4>2V <>45;V 28:>@8AB0B8 1;>: Fnc (DC=:FVO) V7 1V1;V>B5:8 User-Defined Functions; ?@8 =0;03>465==V 40=>3> 1;>:0 ?>B@V1=> 725@=CB8AO 4> 35=5@0B>@0 28?04:>28E G8A5; unifrnd (A, B), 45  V B  3@0=8FV 4V0?07>=C @>7?>4V;5==O 28?04:>28E G8A5;. 0@V0=B 2 >1C4C20B8 <>45;L 28?04:>2>W ?>4VW, I>1 28?04:>25 G8A;> ?>?040;> C 4V0?07>= [0; 0.5]. >6=5 28?04:>25 G8A;> <0T DV:AC20B8AO =0 5:@0=V 48A?;5O. @8 <>45;N20==V 28?04:>2>W ?>4VW 28:>@8AB0B8 1;>: Fnc, 0 2 O:>ABV ?0@0<5B@0 =0;03>465==O FL>3> 1;>:0 28:>@8AB0B8 DC=:FVN unifrnd(0, 1). 0@V0=B 3 >1C4C20B8 <>45;L 28?04:>2>W ?>4VW, I>1 28?04:>25 G8A;> ?>B@0?;O;> C 4V0?07>= [0; 0.7]. >6=5 28?04:>25 G8A;> ?>28==5 DV:AC20B8AO =0 5:@0=V 48A?;5O. @8 <>45;N20==V 28?04:>2>W ?>4VW 28:>@8AB0B8 1;>: Fnc, 0 2 O:>ABV ?0@0<5B@0 =0;03>465==O FL>3> 1;>:0  DC=:FVN unifrnd(0, 1). 57C;LB0B 2V4>1@078B8 =0 5:@0=0E 48A?;5W2. 0@V0=B 4 C45<> 22060B8, I> =0O2=VABL V=D>@<0FVW =0 1C4L-O:><C 7 42>E 2C7;V2  28?04:>20 ?>4VO. @V< B>3>, ?@8?CAB8<>, I> =0O2=VABL V 2V4?>2V4=VABL V=D>@<0FVW =0 :>6=><C 2C7;V  @V2=><V@=0 ?>4VO (B>1B> WE 2V@>3V4=VABL AB0=>28BL 0,5). 8O282H8 V=D>@<0FVN, :>@8ABC20G 7020=B06CT WW =0 A2V9 :><?(NB5@. # 1C4L-O:><C 28?04:>2V 2V= ?>28=5= ?>2V4><8B8 ?@> V=D>@<0FVN A2>T<C :5@V2=8FB2C. @8 <>45;N20==V 28?04:>2>W ?>4VW 28:>@8AB0B8 1;>: Fnc, 0 2 O:>ABV ?0@0<5B@0 =0;03>465==O FL>3> 1;>:0  DC=:FVN unifrnd(0, 1). 57C;LB0B 2V4>1@078B8 =0 5:@0=0E 48A?;5W2 V ?>:070B8 3@0DVG=C V=B5@?@5B0FVN 70 4>?><>3>N >AF8;>3@0D0. 0@V0=B 5 !B2>@8B8 <>45;L ?>254V=:8 ;N48=8 (:V=F52>3> 45B5@<V=>20=>3> 02B><0B0) ?@8 ?>HC:C V=D>@<0FVW 2 Internet. @8?CAB8<>, I> V=D>@<0FVO, O:0 FV:028BL ;N48=C, 7=0E>48BLAO 2 Internet =0 42>E 2C7;0E. C45<> 22060B8, I> =0O2=VABL V=D>@<0FVW =0 1C4L-O:><C 7 42>E 2C7;V2  28?04:>20 ?>4VO. 8O282H8 V=D>@<0FVN, :>@8ABC20G 7020=B06CT WW =0 A2V9 :><?(NB5@. # 1C4L-O:><C 28?04:>2V 2V= ?>28=5= ?>2V4><8B8 ?@> V=D>@<0FVN A2>T<C :5@V2=8FB2C. @8 <>45;N20==V 28?04:>2>W ?>4VW 28:>@8AB0B8 1;>: Fnc, 0 2 O:>ABV ?0@0<5B@0 =0;03>465==O FL>3> 1;>:0  DC=:FVN unifrnd(0, 1). 57C;LB0B 2V4>1@078B8 =0 5:@0=0E 48A?;5W2 V ?>:070B8 3@0DVG=C V=B5@?@5B0FVN 70 4>?><>3>N >AF8;>3@0DV2. 0@V0=B 6 !B2>@8B8 <>45;L ?>254V=:8 ;N48=8 (:V=F52>3> 45B5@<V=>20=>3> 02B><0B0) ?@8 ?>HC:C V=D>@<0FVW 2 Internet. @8?CAB8<>, I> V=D>@<0FVO, O:0 FV:028BL ;N48=C, 7=0E>48BLAO 2 Internet =0 42>E 2C7;0E. C45<> 22060B8, I> =0O2=VABL V=D>@<0FVW =0 1C4L-O:><C 7 42>E 2C7;V2  28?04:>20 ?>4VO. @V< B>3>, ?@8?CAB8<>, I> =0O2=VABL V 2V4?>2V4=VABL V=D>@<0FVW =0 :>6=><C 2C7;V  @V2=><V@=0 ?>4VO (B>1B> WW 2V@>3V4=VABL AB0=>28BL 0,5). 8O282H8 V=D>@<0FVN, :>@8ABC20G 7020=B06CT WW =0 A2V9 :><?(NB5@. # 1C4L-O:><C 28?04:>2V 2V= ?>28=5= ?>2V4><8B8 ?@> V=D>@<0FVN A2>T<C :5@V2=8FB2C. @8 <>45;N20==V 28?04:>2>W ?>4VW 28:>@8AB0B8 1;>: Fnc, 0 2 O:>ABV ?0@0<5B@0 =0;03>465==O FL>3> 1;>:0  DC=:FVN unifrnd(0, 1). 57C;LB0B 2V4>1@078B8 =0 5:@0=0E 48A?;5W2 V ?>:070B8 3@0DVG=C V=B5@?@5B0FVN 70 4>?><>3>N >AF8;>3@0DV2. 0@V0=B 7 5E09 ?>B@V1=> 7 Internet 7020=B068B8 =0 6>@AB:89 48A: D09;, I> <0T >1AO3 300 109B. 020=B065==O 2545BLAO ?0@0;5;L=> V7 42>E 2C7;V2, H284:VABL C :0=0;V 7<V=NTBLAO 28?04:>28< G8=>< 2V4 0,5 1VB/A 4> 1 1VB/A. @8 FL><C 7020=B065==O ?@8?8=8B8, O:I> @>7<V@ D09;0 AB0=5 =5 <5=H =V6 300 109B. >7<V@ >B@8<0=>3> D09;0 2825AB8 =0 48A?;59 V ?>:070B8 G0A>2C 4V03@0<C ?@>?CA:=>W 740B=>ABV :0=0;C 72(O7:C. 0@V0=B 8 5E09 2V41C20TBLAO ?0@0;5;L=5 7020=B065==O D09;V2 V7 42>E 2C7;V2. (284:VABL C :0=0;V 7<V=NTBLAO 28?04:>28< G8=>< 2V4 0,5 1VB/A 4> 1 1VB/A. =D>@<0FVN 70?8AC20B8 =0 6>@AB:89 48A:, O:89 70?>2=5=89 500 109B0<8 V=D>@<0FVW. 5>1EV4=> ?>:070B8 G0A>2C 4V03@0<C ?@>?CA:=>W 740B=>ABV :0=0;C 2 V=B5@20;V 2V4 0 4> 500 A <>45;L=>3> G0AC, 0 B0:>6 7030;L=C :V;L:VABL 70?8A0=>W V=D>@<0FVW. 0@V0=B 9 >1C4C20B8 <>45;L >FV=N20==O 2V@>3V4=>ABV 10=:@CBAB20 ?V4?@8T<AB20 =0 >A=>2V Z-@0EC=:C B0 4>A;V48B8 40=C <>45;L (<>45;L ;LB<0=0). # 7030;L=><C 283;O4V V=45:A :@548B>A?@><>6=>ABV (Z-@0EC=>:) <0T 283;O4 Z=1,2*K1+1,4*K2+3,3*K3+0,6*K4+K5, 45 K1  >1>@>B=89 :0?VB0;/AC<0 0:B82V2; K2  =5@>7?>4V;5=89 4>EV4/AC<0 0:B82V2; K3  >?5@0FV9=89 4>EV4/AC<0 0:B82V2; K4  @8=:>20 20@BVABL 0:FV9/ 701>@3>20=VABL; K5  28@CG:0/AC<0 0:B82V2. ( 57C;LB0B8 1030B>G8A;5==8E @>7@0EC=:V2 ?> <>45;V ;LB<0=0 ?>:07CNBL, I> Z <>65 ?@89<0B8 7=0G5==O 2 <560E 2V4 [-14,+22], ?@8 FL><C ?V4?@8T<AB20, 4;O O:8E Z > 2,99, ?>?040NBL C G8A;> DV=0=A>2> ABV9:8E, 4;O O:8E Z < 1,81  157AC<=V2=>, =5A?@><>6=V, 0 V=B5@20; [1,81-2,99] 287=0G0T 7>=C =5287=0G5=>ABV). 57C;LB0B8 2825AB8 =0 >AF8;>3@0D. 0@V0=B 10 >1C4C20B8 <>45;L >FV=N20==O 2V@>3V4=>ABV 10=:@CBAB20 ?V4?@8T<AB20 =0 >A=>2V Z-@0EC=:C B0 4>A;V48B8 FN <>45;L (<>45;L ;LB<0=0 4;O :><?0=V9, 0:FVW O:8E =5 1C;8 ?>?C;O@=V =0 1V@6V) Z=0,717*X1+0,847*X2+3,107*X3+0,42*X4+0,995*X5, 45 X1  >1>@>B=89 :0?VB0;/AC<0 0:B82V2; X2  =5@>7?>4V;5=89 4>EV4/AC<0 0:B82V2; X3  >?5@0FV9=89 4>EV4/AC<0 0:B82V2; X4  10;0=A>20 20@BVABL 0:FV9/ 701>@3>20=VABL; X5  28@CG:0/AC<0 0:B82V2. (@0=8G=5 7=0G5==O 4;O FVTW D>@<C;8  1,23). 57C;LB0B8 2825AB8 =0 >AF8;>3@0D. 4. >=B@>;L=V 70?8B0==O 1. # G><C ?>;O30T ACBL <5B>4C >=B5-0@;>? 2. >OA=8B8, I> >7=0G0T 28A;V2 ((8?04:>20 ?>4VO 2V41C;0AO((? 025AB8 ?@8:;048. 3. /:V VA=CNBL A?>A>18 >B@8<0==O 28?04:>28E G8A5;? 4. /:V ?5@52038 <0T B01;8G=89 A?>AV1 35=5@C20==O ?>A;V4>2=>ABV 28?04:>28E G8A5; ? 5. /:V =54>;V:8 <0T B01;8G=89 A?>AV1 35=5@C20==O ?>A;V4>2=>ABV 28?04:>28E G8A5; ? 6. /:V ?5@52038 <0T DV78G=89 <5B>4 35=5@C20==O ?>A;V4>2=>ABV 28?04:>28E G8A5;? 7. >OA=8B8 35=5@C20==O @V2=><V@=>W 28?04:>2>W ?>A;V4>2=>ABV G8A5; 70 4>?><>3>N <C;LB8?;V:0B82=>3> :>=3@C5=B=>3> <5B>4C ;8H:V2. 8. /:C @>;L C =02545=8E ?@8:;040E <>45;59 2V4V3@0T 1;>: Uniform Random Number? 9. /:C @>;L C =02545=8E ?@8:;040E <>45;59 2V4V3@0T 1;>: Step? 10. /:V >A=>2=V E0@0:B5@8AB8:8 35=5@>20=8E ?>A;V4>2=>AB59 28?04:>28E G8A5; B0 O:V <5B>48 WE ?V4B25@465==O? 01>@0B>@=0 @>1>B0 !6 >45;N20==O 28?04:>28E ?>4V9 '0AB8=0 2 1. 5B0 @>1>B8 5B>N 40=>W ;01>@0B>@=>W @>1>B8 T AB2>@5==O <>45;59 7 V<VB0FVTN 28?04:>28E ?>4V9 B0 70AB>AC20==O 1;>:0 Hit Crossing. 2. @8:;048 AB2>@5==O S-<>45;59 @8:;04 1 >1C4C20B8 <>45;L 28?04:>2>W ?>4VW, O:0 4>72>;OT ?V4@0EC20B8 :V;L:VABL ?>?040=L 28?04:>28E G8A5;, @V2=><V@=> @>7?>4V;5=8E =0 V=B5@20;V [0; 8] ?@8 ?>@>3>2><C 7=0G5==V, I> 4>@V2=NT 4. >1C4C20B8 <>45;L. >OA=5==O 4> 28:>=0==O ?@8:;04C 1. 040=0 <>45;L <0T B0:89 283;O4:  8A. 6.1. >45;N20==O 28?04:>2>W ?>4VW 70 4>?><>3>N 1;>:0 Hit Crossing ;O 1;>:0 Hit Crossing <8 2AB0=>28<> =0ABC?=V 7=0G5==O ?0@0<5B@V2: # ?>;5 Hit Crossing offset (?>@V3 ?5@5B8=C) 22545<> 7=0G5==O 4 (?>@>3>25 7=0G5==O). # @>7:@820NG><C A?8A:C Hit Crossing direction (=0?@02;5==O ?5@5B8=C) 2815@5<> 20@V0=B rising (7@>AB0==O). 5HB0 1;>:V2 28:>=CNBL B0:V DC=:FVW: Matlab Fnc  35=5@CT ?>A;V4>2=VABL 28?04:>28E G8A5;, @V2=><V@=> @>7?>4V;5=8E =0 V=B5@20;V [0, 8] (unifrnd(0, 8)). Discrete-Time Integrator (48A:@5B=89 AC<0B>@ G0AC) 7=0E>48BLAO C 1;>FV Discrete  ?V4@0E>2CT :V;L:VABL @50;V70FV9 ?>4VW, I> FV:028BL =0A. Display (5:@0=)  282>48BL @57C;LB0B ?V4@0EC=:C. Scope (V=48:0B>@)  4>72>;OT A?>AB5@V30B8 70 @>1>B>N 1;>:0 Hit Crossing.  8A. 6.2. 0;03>465==O 1;>:0 Matlab Fnc @8:;04 2 >1C4C20B8 <>45;L, O:0 4>72>;OT ?V4@0E>2C20B8 :V;L:VABL ?>B@0?;O=L 45O:>W >7=0:8 2 V=B5@20; [2; 5]. >OA=5==O 4> 28:>=0==O ?@8:;04C 2 >1>B0 40=>W 1;>:-4V03@0<8 >A=>20=0 =0 28:>@8AB0==V 42>E 1;>:V2 Hit Crossing. 5@H89 V7 =8E <0T Hit Crossing offset  7 B0 Hit Crossing direction  falling (A?04), 4;O 4@C3>3> 7=0G5==O F8E ?0@0<5B@V2 @V2=V 2V4?>2V4=> Hit Crossing offset  3 V Hit Crossing direction  rising (7@>AB0==O). # <>45;V 4>40B:>2> 28:>@8AB0T<> 1;>: Logical Operator (;>3VG=89 >?5@0B>@), O:89 @50;V7CT DC=:FVN ;>3VG=>3> 4>4020==O. >1C4C20B8 <>45;L. 040=0 <>45;L <0T B0:89 283;O4:  8A. 6.3. >45;N20==O ?>?040==O 28?04:>2>W 25;8G8=8 C 7040=89 V=B5@20; @8:;04 3 5E09 <0T<> >1G8A;N20;L=C A8AB5<C, I> <VAB8BL 420 48A:>28E =0:>?8GC20G0 T<=VABN: 2.1 109B (=0725<> 9>3> HD1) B0 4.3 109B (=0725<> 9>3> HD2). 0=V =04E>4OBL =0 :>6=89 V7 =8E 2V4 A2>3> 465@5;0. 1AO3 =0ABC?=>W ?>@FVW V=D>@<0FVW T 28?04:>2>N 25;8G8=>N, @>7?>4V;5=>N 70 =>@<0;L=8< 70:>=><. ;O ?5@H>3> 465@5;0 70:>= @>7?>4V;5==O 28?04:>28E 25;8G8= <0T ?0@0<5B@8 m1=70, v1=5; 4;O 4@C3>3> 465@5;0  m2=120, v2=10. >B@V1=> ?>@V2=OB8 5D5:B82=VABL 70AB>AC20==O =0:>?8GC20GV2. # O:>ABV ?>:07=8:0 5D5:B82=>ABV 281@0B8 :>5DVFVT=B 28:>@8AB0==O 48A:>2>3> ?@>AB>@C  V. &O 25;8G8=0 <>65 1CB8 @>7@0E>20=0 O: 2V4=>H5==O >1AO3C ?0<(OBV, 28:>@8AB0=>3> =0 V=B5@20;V <>45;N20==O, 4> ?>2=>W T<=>ABV =0:>?8GC20G0. >1C4C20B8 <>45;L. >OA=5==O 4> 28:>=0==O ?@8:;04C 3 040=0 <>45;L <0T B0:89 283;O4:  8A. 6.4. >45;L @>1>B8 =0:>?8GC20GV2 >OA=8<> @>1>BC ?5@H>3> =0:>?8GC20G0. ;>: Matlab Fnc 2V4V3@0T @>;L 465@5;0 40=8E. # O:>ABV ?0@0<5B@0 =0;03>465==O 1;>:0 2:070=> V<(O 35=5@0B>@0 =>@<0;L=>3> @>7?>4V;5==O 7 2V4?>2V4=8<8 0@3C<5=B0<8: normrnd(70, 5). ;>: Discrete-Time Integrator (48A:@5B=89 AC<0B>@ G0AC) 28:>=CT 4>4020==O 40=8E, ?>ABC?0NG8E 2V4 465@5;0 C =0:>?8GC20G. #AV ?0@0<5B@8 <0NBL 7=0G5==O, 2AB0=>2;5=V 70 70<>2GC20==O<. ;>: Fnc (DC=:FVO) 70157?5GCT @>7@0EC=>: V (>1G8A;N20;L=5 7=0G5==O 282>48BLAO 2 A5@548=V 1;>:0) 4;O ?>B>G=>3> 7=0G5==O <>45;L=>3> G0AC. ;>: Display (5:@0=)  282>48BL =0 5:@0= >1G8A;5=5 7=0G5==O V. @8 7025@H5==V V=B5@20;C <>45;N20==O 2>=> ?@54AB02;OT A>1>N 3>B>2C >FV=:C 40=>3> ?>:07=8:0 4;O =0:>?8GC20G0 HD1. 5@54 70?CA:>< <>45;V 4>FV;L=> 2AB0=>28B8 A?>AV1 28<V@N20==O G0AC <>45;N20==O, 281@02H8 Simulation parameters ( Solver ( Type ( Fixed-step. @V< B>3>, 1060=> 701>@>=8B8 2840GC ?>?5@5465=L ?@> =5?V4:;NG5=V ?>@B8 1;>:V2. ;O FL>3> =0 2:;04FV Diagnostics (4V03=>AB8:0) 284V;VBL ?>4VN Unconnected block output V 2AB0=>2VBL ?5@5<8:0G None (V3=>@C20B8). 3. 0240==O 4;O A0<>ABV9=>3> 28:>=0==O 0@V0=B 1 >1C4C20B8 <>45;L 28?04:>2>W ?>4VW, O:0 4>72>;OT ?V4@0EC20B8 :V;L:VABL ?>?040=L 45O:>W >7=0:8 2 V=B5@20; [2; 6]. 50;V7C20B8 F5 70 4>?><>3>N 1;>:0 Hit Crossing (V=48:0B>@0 ?5@5B8=C). @8 <>45;N20==V 28?04:>2>W ?>4VW 28:>@8AB0B8 1;>: Matlab Fnc, 0 2 O:>ABV ?0@0<5B@0 9>3> =0;03>465==O  DC=:FVN unifrnd(0, 8). # <>45;V 4>40B:>2> 28:>@8AB0B8 1;>: Logical Operetor (;>3VG=89 >?5@0B>@), O:89 @50;V7CT DC=:FVN ;>3VG=>3> 4>4020==O. 57C;LB0B 2V4>1@078B8 =0 5:@0=0E 48A?;5O V ?>:070B8 3@0DVG=C V=B5@?@5B0FVN 70 4>?><>3>N >AF8;>3@0D0. 0@V0=B 2 >1C4C20B8 <>45;L 28?04:>2>W ?>4VW, O:0 4>72>;OT ?V4@0EC20B8 :V;L:VABL ?>?040=L 45O:>W >7=0:8 2 V=B5@20; [1; 7]. 50;V7C20B8 F5 70 4>?><>3>N 1;>:0 Hit Crossing (V=48:0B>@0 ?5@5B8=C). @8 <>45;N20==V 28?04:>2>W ?>4VW 28:>@8AB0B8 1;>: Matlab Fnc, 0 2 O:>ABV ?0@0<5B@0 9>3> =0;03>465==O  DC=:FVN unifrnd(0, 8). # <>45;V 4>40B:>2> 28:>@8AB0B8 1;>: Logical Operetor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m=50, v=3. V4@0EC20B8 5D5:B82=VABL 70AB>AC20==O =0:>?8GC20G0 (2 O:>ABV ?>:07=8:0 5D5:B82=>ABV 281@0B8 :>5DVFVT=B 28:>@8AB0==O 48A:>2>3> ?@>AB>@C  Ki). @8 <>45;N20==V 28?04:>2>W ?>4VW 28:>@8AB0B8 1;>: Matlab Fnc, 0 2 O:>ABV ?0@0<5B@0 =0;03>465==O FL>3> 1;>:0  DC=:FVN normrnd 7 C:070=8<8 28I5 ?0@0<5B@0<8. 57C;LB0B 2V4>1@078B8 =0 5:@0=V 48A?;5O. 0@V0=B 5 >1C4C20B8 <>45;L 28?04:>2>W ?>4VW, O:0 4>72>;OT ?V4@0EC20B8 :V;L:VABL ?>B@0?;O=L 28?04:>28E G8A5;, @V2=><V@=> @>7?>4V;5=8E =0 V=B5@20;V [0; 12] ?@8 ?>@>3>2><C 7=0G5==V, I> 4>@V2=NT 5. 0@V0=B 6 5E09 <0T<> >1G8A;N20;L=C A8AB5<C, I> <VAB8BL =0:>?8GC20G T<=VABN 2,1 109B. 0=V =04E>4OBL =0 F5 465@5;>. 1AO3 =0ABC?=>W ?>@FVW V=D>@<0FVW T 28?04:>2>N 25;8G8=>N, @>7?>4V;5=>N 70 =>@<0;L=8< 70:>=><, V <0T ?0@0<5B@8: m=70, v=5. =B5@20; G0AC <V6 ACAV4=V<8 ?>2V4><;5==O<8 T 28?04:>2>N 25;8G8=>N, @>7?>4V;5=>N 70 7040=8< 70:>=><, B0 <0T ?0@0<5B@8: m=10, v=4. C45<> 22060B8, I> 70?8A V=D>@<0FVW =0 =0:>?8GC20G 2V41C20TBLAO <8BBT2> V 25;8G8=0 ?@8@>I5==O <>45;L=>3> G0AC 287=0G0TBLAO BV;L:8 ?@><V6:>< G0AC 4> ?>O28 =0ABC?=>W ?>@FVW V=D>@<0FVW. >B@V1=> ?>1C4C20B8 <>45;L 4;O 2AB0=>2;5==O 5D5:B82=>ABV 70AB>AC20==O =0:>?8GC20G0 V B@820;>ABV V=B5@20;C <>45;N20==O @>1>B8 =0:>?8GC20G0. 57C;LB0B8 2825AB8 =0 48A?;5W, 0 3@0DV: 2V4>1@065==O <>45;L=>3> G0AC ?>:070B8 =0 >AF8;>3@0DV. 0@V0=B 7 !B2>@8B8 <>45;L =5?5@5@2=>3> <5@56=>3> DV;LB@0, I> 7040=89 48D5@5=FV9=8< @V2=O==O<  EMBED Equation.3 . 2060B8, I> =0 A8=CA>W40;L=89 A83=0; 4VT C :0=0;V 72(O7:C HC< V7 B0:8<8 ?0@0<5B@0<8: Sample time = 0,01, Min=-0,5, Max=0,5. 57C;LB0B8 2V4>1@078B8 =0 >AF8;>3@0DV. 0@V0=B 8 !B2>@8B8 <>45;L =5?5@5@2=>3> <5@56=>3> DV;LB@0, :>B@89 7040=89 48D5@5=FV9=8< @V2=O==O<  EMBED Equation.3 . 2060B8, I> =0 A8=CA>W40;L=89 A83=0; 4VT C :0=0;V 72(O7:C HC< V7 =0ABC?=8<8 ?0@0<5B@0<8: Sample time = 0,01, Min=-0,7, Max=0,7. 57C;LB0B8 2V4>1@078B8 =0 >AF8;>3@0DV. 0@V0=B 9 5E09 <0T<> >1G8A;N20;L=C A8AB5<C, I> <VAB8BL =0:>?8GC20G T<=VABN 3,6 109B. 0=V =04E>4OBL =0 F5 465@5;>. 1AO3 =0ABC?=>W ?>@FVW V=D>@<0FVW T 28?04:>2>N 25;8G8=>N, @>7?>4V;5=>N 70 =>@<0;L=8< 70:>=><, V <0T ?0@0<5B@8: m=80, v=3. =B5@20; G0AC <V6 ACAV4=V<8 ?>2V4><;5==O<8 T 28?04:>2>N 25;8G8=>N, @>7?>4V;5=>N 70 7040=8< 70:>=><, B0 <0T ?0@0<5B@8: m=20, v=6. C45<> 22060B8, I> 70?8A V=D>@<0FVW =0 =0:>?8GC20G 2V41C20TBLAO <8BBT2> B0 25;8G8=0 ?@8@>I5==O <>45;L=>3> G0AC 287=0G0TBLAO BV;L:8 ?@><V6:>< G0AC 4> ?>O28 =0ABC?=>W ?>@FVW V=D>@<0FVW. >B@V1=> ?>1C4C20B8 <>45;L 4;O 2AB0=>2;5==O 5D5:B82=>ABV 70AB>AC20==O =0:>?8GC20G0 V 287=0G5==O B@820;>ABV V=B5@20;C <>45;N20==O @>1>B8 =0:>?8GC20G0. 57C;LB0B8 2825AB8 =0 48A?;5W, 0 3@0DV: 2V4>1@065==O <>45;L=>3> G0AC ?>:070B8 =0 >AF8;>3@0DV. 0@V0=B 10 >1C4C20B8 <>45;L, O:0 4>72>;OT ?V4@0E>2C20B8 :V;L:VABL ?>?040=L 45O:>W >7=0:8 2 V=B5@20; [2; 5]. 57C;LB0B 2825AB8 =0 48A?;59, 0 =0 >AF8;>3@0DV 2V4>1@078B8 3@0DV:. 4. >=B@>;L=V 70?8B0==O 1. /:V =54>;V:8 <0T DV78G=89 <5B>4 35=5@C20==O ?>A;V4>2=>ABV 28?04:>28E G8A5;? 2. /:V ?5@52038 <0T ?@>3@0<=89 <5B>4 35=5@C20==O ?>A;V4>2=>ABV 28?04:>28E G8A5;? 3. /:>N :><0=4>N 28:;8:0TBLAO 35=5@0B>@ 28?04:>2>W =5?5@5@2=>W 25;8G8=8, @V2=><V@=> @>7?>4V;5=>W C 7040=><C V=B5@20;V 2 ?0:5BV MatLab? 4.  O:8E 1;>:0E ?@8 <>45;N20==V 28?04:>2>W ?>4VW <>65 1CB8 2:070=0 DC=:FVO unifrnd(0,1) O:>ABV ?0@0<5B@0 =0;03>465==O ? 5. (OAC20B8 DC=:FV>=C20==O 35=5@0B>@0 28?04:>28E G8A5; V7 @V2=><V@=8< @>7?>4V;><. 6. (OAC20B8 DC=:FV>=C20==O 35=5@0B>@0 28?04:>28E G8A5; V7 =>@<0;L=8< 70:>=>< @>7?>4V;C. 7. (OAC20B8 A?>AV1 <>45;N20==O 28?04:>28E 25;8G8= V7 4>2V;L=8< @>7?>4V;><. 8. /:C @>;L C =02545=8E ?@8:;040E <>45;59 2V4V3@0T 1;>: Hit Crossing? 9. /:C @>;L C =02545=8E ?@8:;040E <>45;59 2V4V3@0T 1;>: Discrete-Time Integrator? 01>@0B>@=0 @>1>B0 !7 #?@02;V==O G0A>< <>45;N20==O 1. 5B0 @>1>B8 82G8B8 <>6;82>ABV 4>A;V4=8:0 7 C?@02;V==O <>45;L=8< 5:A?5@8<5=B>< 70 4>?><>3>N 1;>:0 Stop Simulation (7C?8=5==O <>45;N20==O) V7 @>74V;C Sinks, 0 B0:>6 <>45;N20==O =5?5@5@2=8E A8AB5< ?@8 7<V=V <>45;L=>3> G0AC 7 ?>ABV9=8< :@>:><. 2. @8:;048 AB2>@5==O S-<>45;59 @8:;04 1 0 >A=>2V <>45;V (;01>@0B>@=0 @>1>B0 ! 6, ?@8:;04 3) AB2>@8B8 <>45;L @>1>B8 =0:>?8GC20GV2 HD1 B0 HD2 7 28:>@8AB0==O< 1;>:0 Stop Simulation. #<>2>N 70:V=G5==O A50=AC <>45;N20==O T 28G5@?0==O T<=>ABV E>G0 1 >4=>3> 7 =0:>?8GC20GV2 (O:I> =0:>?8GC20G 70?>2=5=89, B> V EMBED Equation.3 1). >1C4C20B8 <>45;L. >OA=5==O 4> 28:>=0==O ?@8:;04C 1. 040=0 <>45;L <0T B0:89 283;O4:  8A. 7.1. 8:>@8AB0==O 1;>:0 Stop Simulation A:V;L:8 =0:>?8GC20GV 70?>2=NNBLAO 4>AB0B=L> ?>2V;L=>, B> @0FV>=0;L=> 2AB0=>28B8 V=B5@20; <>45;N20==O =01030B> 1V;LH8<, =V6 70 70<>2GC20==O<. 0?@8:;04, 7=0G5==O ?0@0<5B@0 Stop time 4>@V2=NT inf (Simulation(Simulation parameters).  8A. 7.2. 0;03>465==O ?0@0<5B@0 Stop time 8 <>65B5 2?52=8B8AO C ((4>AB@>:>2><C(( 7025@H5==V A50=AC <>45;N20==O, ?5@53;O=C2H8 25:B>@ 7=0G5=L G0AC tout, O:89 715@V30TBLAO C @>1>GV9 >1;0ABV MalLab (482. @8A. 7.3).  8A. 7.3. 0;03>465==O ?0@0<5B@V2 <>45;N20==O  8A. 7.4. 5:B>@ 7=0G5=L G0AC tout C @>1>GV9 >1;0ABV MatLab @8 <>45;N20==V A:;04=8E A8AB5< 1C20T =5>1EV4=> 7040B8 45:V;L:0 @V7=8E C<>2 70:V=G5==O 5:A?5@8<5=BC.  B0:8E 28?04:0E C A:;04 S-<>45;V <>65 2:;NG0B8AO 45:V;L:0 1;>:V2 Stop Simulation, :>6=89 7 O:8E ?>2(O70=89 V7 A2>TN >7=0:>N 7025@H5==O A50=AC. @8:;04 2 0 >A=>2V <>45;V (;01>@0B>@=0 @>1>B0 ! 7, ?@8:;04 1) AB2>@8B8 <>45;L @>1>B8 =0:>?8GC20GV2 HD1 B0 HD2 7 28:>@8AB0==O< 1;>:0 Stop Simulation. @8 @>1>BV =0:>?8GC20G0 A50=A ?>28=5= 7025@HC20B8AO =5 ;8H5 ?@8 28G5@?0==V 9>3> T<=>ABV, 0;5 V ?@8 35=5@0FVW ?>2V4><;5==O, @>7<V@ O:>3> ?5@528ICT 7040=89 ?>@V3. >1C4C20B8 <>45;L. >OA=5==O 4> 28:>=0==O ?@8:;04C 2 040=0 <>45;L <0T B0:89 283;O4:  8A. 7.5. 0AB>AC20==O 1;>:0 Stop Simulation 70 =0O2=>ABV 45:V;L:>E C<>2  8A. 7.6. 0;03>465==O ?5@H>3> 1;>:0 Hit Crossing (?5@528I5==O 4>268=8 ?>2V4><;5==O)  8A. 7.7. 0;03>465==O 4@C3>3> 1;>:0 Hit Crossing (28G5@?0==O T<=>ABV =0:>?8G5==O) ;O V45=B8DV:0FVW 2:070=8E ?>4V9 28:>@8AB>2CNBL 1;>:8 Hit Crossing (V=48:0B>@ ?5@5B8=C), ?@87=0G5==O O:8E ?>OA=NNBL WE V<5=0. ;O 2V7C0;V70FVW ?@8G8=8 70:V=G5==O A50=AC 1;>:8 Stop Simulation 72(O70=V 7 1;>:0<8 Display (5:@0=). =0G5==O ((1((, I> 282>48BLAO C 1;>FV Display, 2:07CT =0 2V4?>2V4=C ?@8G8=C 7025@H5==O <>45;N20==O. @8:;04 3 5E09 45O:89 ;VB0: @CE0TBLAO ?@O<>;V=V9=> 7 ?>ABV9=>N H284:VABN, 0 48A?5BG5@, O:89 70 =8< AB568BL, ?>28=5= 225AB8 V=D>@<0FVN ?@> ;VB0: 4> B>3>, O: 2V= ?5@5B=5 7040=89 @C1V6. ;O 287=0G5=>ABV 1C45<> 22060B8, I> C <>45;V 25;8G8=8 <0NBL B0:V 7=0G5==O: H284:VABL ;VB0:0  900 :</3>4; 2V4AB0=L 4> @C156C  12,5 :<; H284:VABL C2545==O V=D>@<0FVW  1 A8<2>; 70 A5:C=4C; 4>268=0 B5:ABC  50 A8<2>;V2. >1C4C20B8 <>45;L. >OA=5==O 4> 28:>=0==O ?@8:;04C 3 040=0 <>45;L <0T B0:89 283;O4:  8A. 7.8. >45;L @CEC ;VB0:0 )>1 @50;V7C20B8 F59 <5E0=V7< C AB2>@5=V9 <>45;V 4>AB0B=L> AB0=40@B=8E 70A>1V2 C?@02;V==O 5:A?5@8<5=B0<8 C 4V0;>3>2><C 2V:=V Simulation Parameters (?0@0<5B@8 <>45;N20==O). @> =8E 265 7304C20;>AO @0=VH5, 0;5 <8 @>73;O=5<> WE I5 @07 =0 :>=:@5B=><C ?@8:;04V.  8A. 7.9. #AB0=>2;5==O ?0@0<5B@0 Sample time 5@H =V6 CAB0=>28B8 ?0@0<5B@8 <>45;N20==O, <8 ?>28==V 28:>=0B8 B0:C ?@>F54C@C: ?@825AB8 H284:VABL ;VB0:0 V @>1>BC >?5@0B>@0 4> T48=>3> <0AHB01C G0AC; 281@0B8 25;8G8=C :@>:C ?@8@>ABC <>45;L=>3> G0AC; 287=0G8B8 >?B8<0;L=C B@820;VABL V=B5@20;C <>45;N20==O. 8@060T<> H284:VABL ;VB0:0 C :</A V >45@6CT<> 0,25 :</A. 818@0T<> :@>: ?@8@>ABC <>45;L=>3> G0AC (t A. B65, 22>48<> =0ABC?=V ?0@0<5B@8 <>45;N20==O: C ?>;V Stop time (:V=F5289 G0A)  50; C A?8A:C Type (B8?)  Fixed-step (DV:A>20=89 :@>:); C ?>;V Fixed step size (25;8G8=0 DV:A>20=>3> :@>:C)  2. AB0==V9 ?0@0<5B@ ?>B@51CT 4>40B:>2>3> ?>OA=5==O: 4;O 2AVE 1;>:V2, O:V <0NBL ?0@0<5B@ Sample Time (5B0;>==89 G0A), 2V= B0:>6 ?>28=5= 1CB8 @V2=8< 2. 8:>=02H8 A50=A <>45;N20==O, >45@6CT<> 2V4?>2V4L =0 ?>AB02;5=5 @0=VH5 70?8B0==O: 48A?5BG5@ CAB830T 225AB8 ?>B@V1=C V=D>@<0FVN. ;5 B0:89 @57C;LB0B <>6=0 >45@60B8 =5 702648. 06;82C @>;L 2V4V3@0T 281V@ :@>:C <>45;N20==O , B>1B> (t . 0?@8:;04, ?@8 Fixed step size = 3 48A?5BG5@ =5 2AB830T 225AB8 ?>2V4><;5==O. 3. 0240==O 4;O A0<>ABV9=>3> 28:>=0==O 0@V0=B 1 5E09 <0T<> >1G8A;N20;L=C A8AB5<C, I> <VAB8BL =0:>?8GC20G T<=VABN 2,1 109B. >2V4><;5==O 28?04:>2>W 4>268=8, 25;8G8=0 O:8E >?8ACTBLAO =>@<0;L=8< 70:>=>< V7 ?0@0<5B@0<8 m=70, v=5, =04E>4OBL =0 =0:>?8GC20G. !50=A @>1>B8 =0:>?8GC20G0 ?>28=5= 7025@HC20B8AO ?@8 28G5@?0==V 9>3> T<=>ABV. 5E09 G0A 70?8AC 1 109B0 ?>2V4><;5==O 7=0E>48BLAO C <560E  EMBED Equation.3 A, @>7?>4V;5=>N @V2=><V@=>. >B@V1=> ?>1C4C20B8 <>45;L 4;O 287=0G5==O 5D5:B82=>ABV 70AB>AC20==O =0:>?8GC20G0 V 287=0G5==O B@820;>ABV V=B5@20;C <>45;N20==O @>1>B8 =0:>?8GC20G0. 57C;LB0B8 2825AB8 =0 48A?;5W 0@V0=B 2 5E09 VA=CT 420 10=:8, 2 O:8E :C@A 20;NB8 2AB0=>2;5=89 =0 @V2=V 0,128% B0 0,13% 2V4 @V2=O :C@AC =0FV>=0;L=>3> 10=:C. >1>2V :>;820==O :C@AC 4;O ?5@H>3> 10=:C AB0=>2;OBL  EMBED Equation.3 , 0 4;O 4@C3>3>  EMBED Equation.3 . 87=0G8B8 <><5=B G0AC B0 10=:, C O:><C <>6=0 >1<V=OB8 20;NBC 70 =09283V4=VH8< :C@A><. 060=89 ?>@>3>289 :C@A AB0=>28BL 6,87. >1C4C20B8 <>45;L V @57C;LB0B8 ?>:070B8 =0 48A?;5W. 0@V0=B 3 5E09 VA=CT 420 10=:8, 2 O:8E @VG=89 2V4A>B>: 45?>78B=>3> 2:;04C AB0=>28BL 3% B0 2,7%, ?@8 FL><C :>;820==O 2V4A>B:0 4;O ?5@H>3> 10=:C AB0=>28BL  EMBED Equation.3 3@=. 7V 100 3@=., 0 4;O 4@C3>3>  EMBED Equation.3 3@=. 7V 100 3@=. 70 @V:. 87=0G8B8 <><5=B G0AC B0 10=:, C O:><C :;VT=B <>65 283V4=> 7=OB8 :>HB8. 060=89 ?>@>3>289 2V4A>B>: 3,3%. >1C4C20B8 <>45;L V @57C;LB0B8 ?>:070B8 =0 48A?;5W. 0@V0=B 4 >1C4C20B8 040?B82=C <>45;L ?@>3=>7C20==O V=25AB8FV9 (<>45;L @C3;52AL:>3> 4;O =0@>4=>3> 3>A?>40@AB20 #!! ), O:0 28@060TBLAO B0:>N D>@<C;>N:  EMBED Equation.3 , 45  EMBED Equation.3   >1AO3 :0?VB0;L=8E 2:;045=L =0 4CHC =0A5;5==O;  EMBED Equation.3   G8A5;L=VABL =0A5;5==O;  EMBED Equation.3   =0FV>=0;L=89 4>EV4;  EMBED Equation.3  ?0@0<5B@8. 57C;LB0B8 ?>:070B8 =0 48A?;5W. 0@V0=B 5 5E09 =0 A:;04 702575=> B@8 2848 B>20@V2 C :V;L:>ABV 10, 12, 13 >4. @8?CAB8<>, I> =0 ?5@H89 B>20@ ?>?8B :>;820TBLAO C <560E 1- 5, =0 4@C389  1-3, 0 =0 B@5BV9  1-6 >4. 70 4>1C. >1C4C20B8 <>45;L DC=:FV>=C20==O A:;04C, ?@8 FL><C @>1>B0 <>45;V ?>28==0 ?@8?8=OB8AO 2 B><C 28?04:C, O:I> =0 A:;04V 70:V=GCTBLAO E>G0 1 >48= V7 284V2 B>20@C. 57C;LB0B8 ?@> :V;L:VABL ?@>40=8E B>20@V2 ?>:070B8 =0 48A?;5W. >40B:>2> 2825AB8 V=D>@<0FVN ?@> B>20@, O:89 ?@>40=>. 4. >=B@>;L=V 70?8B0==O /:V VA=CNBL A?>A>18 7<V=8 <>45;L=>3> G0AC? )> >7=0G0T <>45;N20==O G0AC 70 >A>1;828< AB0=><? )> >7=0G0T <>45;N20==O G0AC 7V 7<V==8< :@>:><?  O:8E 28?04:0E 28:>@8AB>2CNBL 1;>: Stop Simulation? 8<>38 4> >D>@<;5==O 72VBC ?@> ;01>@0B>@=V @>1>B8 2VB ?@> ;01>@0B>@=V @>1>B8 ?>28=5= <VAB8B8: B8BC;L=89 0@:CH; <5BC @>1>B8; 70240==O; =04@C:>20=V =0 :><?(NB5@V <>45;V; @57C;LB0B8, 28A=>2:8. 2VB >D>@<;NTBLAO =0 0@:CH0E ?0?5@C 4 7 >4=VTW AB>@>=8. @8 >D>@<;5==V 1060=> 28:>@8AB>2C20B8 H@8DB Times 14-3> :53;O 7 >48=8G=8< V=B5@20;>< <V6 @O4:0<8. !E5<8 <>45;59 F5=B@CNBLAO ?> H8@8=V AB>@V=:8. "5<8 @5D5@0BV2 >1C4>20 V<VB0FV9=>W <>45;V ?@89=OBBO @VH5=L V7 28:>@8AB0==O< :V;L:>E :@8B5@VW2. >1C4>20 V<VB0FV9=>W <>45;V @CEC D>=4V2 =0 ?V4?@8T<AB2V. >1C4>20 V<VB0FV9=>W <>45;V C?@02;V==O DV=0=A>28<8 ?>B>:0<8 :><5@FV9=>3> 10=:C. >1C4>20 V<VB0FV9=>W <>45;V D>@<C20==O @0FV>=0;L=>W AB@C:BC@8 465@5; DV=0=AC20==O V=25AB8FV9. <VB0FV9=5 <>45;N20==O @878:V2 V=25AB8FV9=8E ?@>5:BV2. >1C4>20 V<VB0FV9=>W <>45;V >FV=N20==O 5D5:B82=>ABV ;V78=3C. >1C4>20 V<VB0FV9=>W <>45;V 25:A5;L=>3> >1V3C. A=>2=V 0A?5:B8 V<VB0FV9=>3> <>45;N20==O. A=>2=V 5B0?8 ?>1C4>28 V<VB0FV9=>W <>45;V. 0H8==0 V<VB0FVO 2 5:>=><V:>->@30=V70FV9=8E A8AB5<0E. <VB0FV9=0 <>45;L 48A:@5B=>3> 28@>1=8G>3> ?@>F5AC. <VB0FV9=0 <>45;L :5@C20==O 70?0A0<8. VB5@0BC@0 1. VB;V=AL:89 . . >45;N20==O 5:>=><V:8: 02G. ?>AV1=8:.  .: #, 2003.  408 A. 2. C;LBO52 . 87C0;L=>5 <>45;8@>20=85 2 A@545 MATLAB: #G51=. :C@A.  !1: 8B5@, 2000.  432 A.: 8;. LO:>=>2 . Simulink 4. !?5F80;L=K9 A?@02>G=8:. !1: 8B5@, 2002. 528 A.: 8;. 4. V35;L . . 0B5<0B8G=V <5B>48 @8=:>2>W 5:>=><V:8: 02G0;L=89 ?>AV1=8:.  .: >=4>@, 2003.  158 A. 5. !8B=8: . $., @;5=:> .!. <VB0FV9=5 <>45;N20==O: 02G. ?>AV1=8:.  .: #, 1998.  232A. 6. 0B5<0B8G5A:85 <>45;8 B@0=AD>@<0F8>==>9 M:>=><8:8: #G51=>5 ?>A>185 /".!. ;510=>20, .. 052=520, .. !B@868G5=:>, .!. C@LO=>20, .. 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