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自動控制與實驗 Bode Plots
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Advantage of Working with Frequency Response in terms of Bode Plots zBode plots of systems in series (or tandem) simply add which is quite convenient. zBode’s important phase-gain relationship is given in terms of logarithms of phase and gain.
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Advantage of Working with Frequency Response in terms of Bode Plots zA much wider range of system behavior (from low to high frequency behavior) can be displayed on a single plot. zBode plots can be determined experimentally. zDynamic compensator design can be based entirely on Bode plots.
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Bode Form of the Transfer Function zBode form : all one zK 0 is transfer function magnitude at very low frequencies.
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Classes of terms of transfer functions z(1) z(2) z(3)
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Class1:singularities at the origin
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Class2: first-order term za) For zb) For zwe call the break point zbelow: magnitude is approximately constant 1 zabove: magnitude is like class 1
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Exp:
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phase za) For zb) For zc) For
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Exp:
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Class3:second order term zBreak point zPeak amplitude zmagnitude change slop +40dB or -40dB zphase change +180 0 or -180 0
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Matlab’s Bode Plots zbode(num,den)
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Example: G(s) U 0 sinωtY(t) U 0 ω/(s 2 + ω 2) Ĺ 1/(s 2 +s+3)
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Result: (response of G(s)=1/(s 2 +s+3) to sint )
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Example: zKG 1 =10/s(s 2 +0.4s+4) zKG 2 =0.01*(s 2 +0.01s+1)/s 2 [(s 2 /4)+0.02(s/2)+1] numG=0.01*[1 0.01 1] denG=[0.25 0.01 1 0 0] bode(numG,denG) numG=10 denG=[1 0.4 4 0] bode(numG,denG)
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