Zadanie 1
Dla układu
proszę wyznaczyć  z wykorzystaniem wykresów (charakterystyk) Bode go  zapas modułu i zapas fazy.
i=Sqrt[-1];
K=0.4;
wn=Sqrt[10];
ksi=1/Sqrt[10];
Ga[w_]:=K
Gb[w_]:=(1+i*w)
Gc[w_]:=1/(i*w)
Gd[w_]:=1/(1+i*w*0.2)
Ge[w_]:=1/(1+(2/Sqrt[10])*(i*w/Sqrt[10])+(i*w/Sqrt[10])^2)
fi[w_]:=0-90+(ArcTan[w]-ArcTan[0.2*w]-ArcTan[(1-(w/wn)^2),(2*ksi*w/wn)])*180/Pi
(a)
LogLinearPlot[20*Log10[Abs[Ga[w]]],{w,0.1,100},GridLines->Automatic, PlotStyle->Thick,
PlotLabel->"M: Ga(w)=K"]
LogLinearPlot[Arg[Ga[w]]*180/Pi,{w,0.1,100},GridLines->Automatic, PlotStyle->Thick,
PlotLabel->"fi: Ga(w)=K"]
M: GaH�wL�=K
0
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fi: GaH�wL�=K
1.0
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0.0
-0.5
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(b)
Show[{LogLinearPlot[20*Log10[Abs[Gb[w]]],{w,0.1,100},GridLines->Automatic, PlotStyle-
>Thick, PlotLabel->"M: Gb(w)=(1+i*w)"],
ListLogLinearPlot[{{0.1,0},{1,0},{100,40}},Joined->True, PlotStyle-
>{Red,Dashed,Thick}]}]
LogLinearPlot[Arg[Gb[w]]*180/Pi,{w,0.1,100},GridLines->Automatic, PlotStyle->Thick,
PlotLabel->"fi: Gb(w)=(1+i*w)"]
M: GbH�wL�=H�1+i*wL�
40
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fi: GbH�wL�=H�1+i*wL�
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(c)
LogLinearPlot[20*Log10[Abs[Gc[w]]],{w,0.1,100},GridLines->Automatic, PlotStyle->Thick,
PlotLabel->"M: Gc(w)=1/(i*w)"]
LogLinearPlot[Arg[Gc[w]]*180/Pi,{w,0.1,100},GridLines->Automatic, PlotStyle->Thick,
PlotLabel->"fi: Gc(w)=1/(i*w)"]
M: GcH�wL�=1��H�i*wL�
20
10
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fi: GcH�wL�=1��H�i*wL�
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(d)
Show[{LogLinearPlot[20*Log10[Abs[Gd[w]]],{w,0.1,100},GridLines->Automatic, PlotStyle-
>Thick, PlotLabel->"M: Gd(w)=1/(1+i*w*0.2)"],ListLogLinearPlot[{{0.1,0},{5,0},{500,-
40}},Joined->True, PlotStyle->{Red,Dashed,Thick}]}]
LogLinearPlot[Arg[Gd[w]]*180/Pi,{w,0.1,100},GridLines->Automatic, PlotStyle->Thick,
PlotLabel->"fi: Gd(w)=1/(1+i*w*0.2)"]
M: GdH�wL�=1��H�1+i*w*0.2L�
0
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fi: GdH�wL�=1��H�1+i*w*0.2L�
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(e)
Show[{LogLinearPlot[20*Log10[Abs[Ge[w]]],{w,0.1,100},GridLines->Automatic, PlotStyle-
>Thick, PlotLabel->"M:
Ge(w)=1/(1+(2/Sqrt[10])*(i*w/Sqrt[10])+(i*w/Sqrt[10])^2)"],ListLogLinearPlot[{{0.1,0},
{Sqrt[10],0},{Sqrt[10]*100,-80}},Joined->True, PlotStyle->{Red,Dashed,Thick}]}]
LogLinearPlot[Arg[Ge[w]]*180/Pi,{w,0.1,100},GridLines->Automatic, PlotStyle->Thick,
PlotLabel->"fi: Ge(w)=1/(1+(2/Sqrt[10])*(i*w/Sqrt[10])+(i*w/Sqrt[10])^2)"]
M: GeH�wL�=1��H�1+H�2��Sqrt@�10D�L�*H�i*w��Sqrt@�10D�L�+H�i*w��Sqrt@�10D�L�^2L�
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fi: GeH�wL�=1��H�1+H�2��Sqrt@�10D�L�*H�i*w��Sqrt@�10D�L�+H�i*w��Sqrt@�10D�L�^2L�
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(Wykresy zbiorcze)
Show[{LogLinearPlot[20*Log10[Abs[Ga[w]*Gb[w]*Gc[w]*Gd[w]*Ge[w]]],{w,0.1,100},GridLines
->Automatic, PlotStyle->Thick, PlotLabel->"M:
G(w)=Ga(w)*(Gb(w)*Gc(w)*Gd(w)*Ge(w)"],ListLogLinearPlot[{{0.1,20+20*Log10[K]},{1,20*Lo
g10[K]},{Sqrt[10],20*Log10[K]},{5,20*Log10[K]-40*Log10[5/Sqrt[10]]},{500,20*Log10[K]-
40*Log10[5/Sqrt[10]]-120}},Joined->True, PlotStyle->{Red,Dashed,Thick}]}]
LogLinearPlot[Arg[Ga[w]*Gb[w]*Gc[w]*Gd[w]*Ge[w]]*180/Pi,{w,0.1,100},GridLines-
>Automatic, PlotStyle->Thick, PlotLabel->"fi: G(w)=Ga(w)*(Gb(w)*Gc(w)*Gd(w)*Ge(w)"]
M: GH�wL�=GaH�wL�*H�GbH�wL�*GcH�wL�*GdH�wL�*GeH�wL�
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fi: GH�wL�=GaH�wL�*H�GbH�wL�*GcH�wL�*GdH�wL�*GeH�wL�
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Show[{LogLinearPlot[(Arg[Ga[w]] + Arg[Gb[w]] + Arg[Gc[w]] + Arg[Gd[w]] +
Arg[Ge[w]])*180/Pi, {w, 0.1, 100}, GridLines -> Automatic, PlotStyle -> {Red, Thick}],
ListLogLinearPlot[{{0.1, fi[0.1]}, {0.2, fi[0.2]}, {0.5, fi[0.5]}, {1, fi[1]}, {2,
fi[2]}, {Sqrt[10], fi[Sqrt[10]]}, {4, fi[4]}, {5, fi[5]}, {10, fi[10]}, {33, fi[33]},
{100, fi[100]}}, Joined -> True], ListLogLinearPlot[{{0.1, fi[0.1]}, {0.2, fi[0.2]},
{0.5, fi[0.5]}, {1, fi[1]}, {2, fi[2]}, {Sqrt[10], fi[Sqrt[10]]}, {4,fi[4]}, {5,
fi[5]}, {10, fi[10]}, {33, fi[33]}, {100, fi[100]}}]}]
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M: GH�wL�=GaH�wL�*H�GbH�wL�*GcH�wL�*GdH�wL�*GeH�wL�
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ODPOWIEDy

Z porównania charakterystyk amplitudowej i fazowej:
Zapas modułu  około 10dB, zapas fazy  ok. 100�.