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Muhimmiya na Tsarin Iko

Muhimmiya na Tsarin Iko?

Muhimmiya na tsari na nuna alaka daga fayilolin da suka fito a sistem na kontrolu zuwa fayilolin da suka fito. Diagramin bakiya shi ne bayanin sistem na kontrolu wanda ya amfani da bakiyoyi don nuna muhimmin tsari da sauyukoyi na nuna fayilolin da suka fito.

Muhimmiya na tsari shi ne tushen mai kyau wajen nuna sistem na dinamika da ba ta yiwuwa ba. Daga ilimin lissafi, muhimmin tsari shi ne funksiya da yake amfani da muhimmanci masu adadin kusa

Don kowane sistem na kontrolu, akwai fayilolin da ke fayilolin da ke fiye ko sabab da ke yi aiki a cikin muhimmin tsari don samun abubuwan da suka faru a cikin fayilolin da suka fito ko jawabi.

Saboda haka, alakan da ke duni daga fayilolin da suka fito zuwa fayilolin da suka fito ana gudanar da muhimmin tsari. A Laplace Transform, idan fayilolin da suka fito ana nufin da $R(s)$ da fayilolin da suka fito ana nufin da $C(s)$ .

Muhimmin tsari na sistem na kontrolu an nufin da shi ne nisbah na Laplace transform daga fayilolin da suka fito zuwa Laplace transform daga fayilolin da suka fito, tare da damar zama cewa duk takardun farkon da suka fito suna zero.

$\begin{align*} G(s)=\frac{C(s)}{R(s)}\end{align*}$

Miya ne DC Gain?

Funshin da nufin yana da duk fahimtoci mai kyau. Zai na cikin tashar da na gudanar da ita ya zama da shi ne kashi da ake kawo da ake kawo da shi a tashar da na gudanar da ita wanda ya zama da shi, wanda yake bayyana da lambar daga minus infinity zuwa plus infinity.

Idan an yi hakkin da na ciki da sautin da ake kawo da shi, za a samun tashar da na gudanar da ita a tashar da na gudanar da ita ya zama da shi.

Kalmomin DC gain suna da shi ne kashi da ake kawo da ake kawo da shi a tashar da na gudanar da ita zuwa sautin da ake kawo da shi.

DC gain yana da shi ne kashi da ake kawo da ake kawo da shi a tashar da na gudanar da ita zuwa sautin da ake kawo da shi. Kalmomin final value theorem suna nuna cewa DC gain yana da shi ne ma'anar funshin da ake kawo da shi a tafin 0 don funshin da suka gudanar da ita.

Yadda Ake Koyar Da Tashar Da Na Gudanar Da Ita Daga Tsarin Da Ya Kasa

Tartar da kungiyar tattalin kasa na tsarin kasa ita ce tartar da mafi yawan dawwama ta kungiyar tattalin kasa. Kungiyoyi na farko suna da muhimmanci a bayyana.

Don in fahimta masu hukuma da ke gudanar da zai iya kasance, ya kamata a duba funshin kafin kungiyar na farko daidai.

$\begin{align*}G(s)=\frac{G(s)}{R(s)} = \frac{b_{0}}{s+ a_{0}}\end{align*}$

$G(s)$ zai iya rubuta a haka

$\begin{align*}\frac{K}{\tau s+1} = \frac{b_{0}}{s+a_{0}}\end{align*}$

A nan,

$\begin{align*} a {0}=\frac{1}{\tau} \; \; \; \; b {0}=\frac{K}{\tau} \end{align*}$

$\tau$ tana da takardun lokaci. K tana da takardun zafin DC ko kuma zafin dawwama

Daidaitar Zafi na Zafin DC na Funtshen na Zafi

Zafi na DC shine yawan hanyoyin zafin dawwama ta gurbin zuwa zafin dawwamansa, ya'ni, zafin dawwama na tasirin unit step.

Don daidaitar zafi na DC na funtshen na zafi, za mu iya duba masu Linear Transform Inverse (LTI) na bazu da kuma fasahar.

Masu LTI na bazu tana da shi

(1) $\begin{equation*} G(s)=\frac{Y(s)}{U(s)}\end{equation*}$

Masu LTI na fasahar tana da shi

$\begin{equation*} G(z)=\frac{Y(z)}{U(z)}\end{equation*}$

Yara final value theorem don kalkulasar zafin dawwama na tasirin unit step.

(3) $\begin{equation*} L\left ( y_{step(t)} \right )=G(s)\frac{1}{s}\end{equation*}$

(4) $\begin{equation*}DC\; \; Gain = \lim_{t\rightarrow \infty }y_{step(t)}\end{equation*}$

(5) $\begin{equation*} DC\; \; Gain = \lim_{s\rightarrow 0 }s\left [ G(s)\frac{1}{s} \right ]\end{equation*}$

$G(s)$ yana da zama da duk masu shiga suna cikin kofin tsohon fadin

Saboda haka,

(6) $\begin{equation*}DC\; \; Gain = \lim_{s\rightarrow 0 }s\left [ G(s)\right ]\end{equation*}$

Zaɓin kimiyyar takaitaccen da ake amfani da shi wajen sistema LTI mai tsarki ya zama

(7) $\begin{equation*}\frac{y(\infty)}{u(\infty)} = G(s)_{s=0}=G(0)\end{equation*}$

Zaɓin kimiyyar takaitaccen da ake amfani da shi wajen sistema LTI mai yawan karamin sauyi ya zama

(8) $\begin{equation*}\frac{y(\infty)}{u(\infty)} = G(z)_{z=1}=G(1)\end{equation*}$

Duk da kowane, idan tattalin yadda na iya haɗa, zaɓuɓɓukan zai shafi $\infty$ .

Na'urar da cikakken ci gaba da ci gaba ta faruwar da ci gaba ta fadada kan ya kamata da ita ce da aka samu daga ci gaba ta faruwar. Wannan na'ura ce mai sauƙiwa don duk tattalin yadda na iya haɗa da tattalin yadda ba na iya haɗa.

Haruffar da Tattalin Yadda Na Iya Haɗa a Tattalin Yadda Na Iya Haɗa

A tattalin yadda na iya haɗa ko ‘s’ domain, an yi haruffa (1) ta hanyar haruffar da 's'.

(9) $\begin{equation*}\frac{\dot{Y(s)}}{U(s)}= sG(s)\end{equation*}$

idandaza $\dot{Y(s)}$ shine Laplace transform of $\dot{y(t)}$

Haruffar da Tattalin Yadda Ba Na Iya Haɗa

An samu haruffar da tattalin yadda ba na iya haɗa ta hanyar farkon sauki.

(10) $\begin{equation*}\dot{y(k)}=\frac{y_{k}-y_{k-1}}{T}\end{equation*}$

(11) $\begin{equation*}\dot{Y(z)}=\frac{Y(z)-z^{-1}Y(z)}{T}\end{equation*}$

(12) $\begin{equation*}\dot{Y(z)}=Y(z)\left [\frac{ ^{1-z^{-1}}}{T} \right ]\end{equation*}$

(13) $\begin{equation*}\dot{Y(z)}=Y(z)\left [\frac{z-1}{T_{z}} \right ]\end{equation*}$

Saboda haka don kawo yawan alama a matsayin tsari, ana bukata a duba $\frac{z-1}{T_{z}}$

Misalai na Nau'i a Neman Gaini na DC

Misali 1

Amsa funksiya na ilimi mai tsauri,

$\begin{align*} H(s) =\frac{Y(s)}{U(s)} = \frac{12}{(s+2)(s+10)}\end{align*}$

Don neman gaini na DC (gaini na gaba daya) na funksiya na ilimi mai tsauri, ya kamata a yi amfani da hukuma na nau'in tsari

$\begin{align*}\lim_{t\rightarrow \infty}y(t)= \lim_{s\rightarrow 0}s\times \frac{12}{(s+2)(s+10)}\end{align*}$

$\begin{align*}\lim_{t\rightarrow \infty}y(t)= \lim_{s\rightarrow 0}s\times \frac{12}{2\times 3}=2\end{align*}$

A nan da DC gain ta zama tushen yawan daga cikin tsawon yawan karamin hukuma na birnin zuwa unit step input.

DC Gain = $\frac{2}{1}=2$

Saboda haka, ya danganta a lura cewa bayanin DC Gain ta haɗa da waƙoƙi masu ƙasa mai girma.

Misali 2

Bayyana DC gain ta wannan tushen

$\begin{align*}G(s)=\frac{K}{\tau s+1}\end{align*}$

Jawaban langkah bagi persamaan transfer di atas adalah

$\begin{align*}y_{step}(t)=L^{-1}\left [\frac{K}{(\tau s+1)s} \right ]\end{align*}$

$\begin{align*}y_{step}(t)=L^{-1}\left [ K\left ( \frac{1}{s}-\frac{\tau }{\tau s+1} \right ) \right ]\end{align*}$

Sada, amfani da teorem na gaba don samun kasuwancin DC.

$\begin{align*}y_{ss}=\lim_{t\rightarrow \infty }y_{step}(t)= \lim_{s\rightarrow 0}\frac{K}{(\tau s+1)s}s = K\end{align*}$

Bayanin: Tambayata asalin, babban ra'ayin zai iya tabbacin, idama za'a karin shiga wanda ke take tsara, ido ka ko take shiga.

Ba da kyau kuma kara mai rubutu!

Makarantarƙi:

Sistematun Gari

Sistemin Kontrola

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