Bode Diagram Gain Margin da Phase Margin (Daga Rasa)

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Muhimmiya Bode Plot Da Nema

Muhimmiya Bode Plot Na?

Muhimmiya Bode plot shine wani graph da ake amfani da shi a fanni na kontrol na system don tabbatar da ingantaccen system na kontrol. Muhimmiya Bode plot yana nuna hanyar kuɗi a kan system ta hanyar labaran - Bode magnitude plot (wanda ya nuna hanyar kuɗi a decibels) da Bode phase plot (wanda ya nuna tasirin tari a darajoyi).

An kawo muhimmiya Bode plots a nan ne a shekarun 1930s da Hendrik Wade Bode a lokacin da ya yi aiki a Bell Labs a Amurka. Idan Bode plots sun bayar waɗannan hali mai tsabta don mari masu system, ba su iya ƙara hukumar da na transfer funtakai da singularities a kudancin abin da na farko (kamar da Nyquist stability criterion).

In fahimtar gain margins da phase margins ita ce muhimmiya don in fahimta Bode plots. Wannan ma'aikata su ne a cikin bayanin.

Gain Margin

Yawan Gain Margin (GM), yawan ingantaccen system. Gain margin yana nufin yadda za a iya ƙara ko rage gain bace ba zama system mai biyayi. Ana nuna shi a decibels (dB).

Zan iya karɓar gain margin daga Bode plot (kamar da aka nuna a diagram). Yana nuna wannan tun daga ƙarin magance (a Bode magnitude plot) da x-axis a fili da Bode phase plot = 180°. Wannan fili shine phase crossover frequency.

Ita ce muhimmiya in a fahimta cewa Gain da Gain Margin ba suwa ba duka. Duk da haka, Gain Margin shine negative na gain (a decibels, dB). Zan iya fahimta idan muna nuna formula ta Gain margin.

Gain Margin Formula

Formula Gain Margin (GM) zan iya nuna:

$\begin{align*} GM = 0 - G\ dB \end{align*}$

Daga G shine gain. Wannan shine magnitude (a dB) daga gida na magance a fili da phase crossover frequency.

A cikin misalidin da aka nuna a graph, Gain (G) shine 20. Saboda haka, idan muna amfani da formula ta gain margin, gain margin yana kasance 0 – 20 dB = -20 dB (mai biyayi).

Phase Margin

Yawan Phase Margin (PM), yawan ingantaccen system. Phase margin yana nufin yadda za a iya ƙara ko rage tari bace ba zama system mai biyayi. Ana nuna shi a darajoyi.

Zan iya karɓar phase margin daga Bode plot (kamar da aka nuna a diagram). Yana nuna wannan tun daga ƙarin magance (a Bode phase plot) da x-axis a fili da Bode magnitude plot = 0 dB. Wannan fili shine gain crossover frequency.

Ita ce muhimmiya in a fahimta cewa phase lag da Phase Margin ba suwa ba duka. Zan iya fahimta idan muna nuna formula ta phase margin.

Phase Margin Formula

Formula Phase Margin (PM) zan iya nuna:

$\begin{align*} PM = \phi - (- 180^{\circ}) \end{align*}$

Daga $\phi$ shine phase lag (wanda yake da lissafi ɗaya). Wannan shine tari daga gida na magance a fili da gain crossover frequency.

A cikin misalidin da aka nuna a graph, phase lag shine -189°. Saboda haka, idan muna amfani da formula ta phase margin, phase margin yana kasance -189° – (-180°) = -9° (mai biyayi).

Amsa, idan amplifier’s open-loop gain ya kare 0 dB a fili da tari lag -120°, phase lag -120°. Saboda haka, phase margin na wannan feedback system shine -120° – (-180°) = 60° (inganta).