Zamani Da Rike Yanzu: Me Ke Nana? (Hadisi Da Tarihin Cikakken Hausa)

فیلڈ: Karkashin Kuliya da Dukkana

China

wani shine rise time

Wani Shine Rise Time?

Rise time yana nufin lokacin da alama ya dogara daga hanyar da aka sani zuwa hanyar da aka sani. A cikin ilimin analogi da digital, hanyoyi na biyu da hanyoyi na uku suna 10% da 90% na farkon ko kafin halayi. Saboda haka, rise time yana nuna lokacin da alama ya dogara daga 10% zuwa 90% na farkon halayi.

Rise time yana daya daga muhimman abubuwan da ke cikin ilimin analogi da digital. Yana bayyana lokacin da fadada ya dogara daga matsayin zuwa matsayin a cikin systemi na analogi, wanda yake da muhimmanci a cikin tattalin arziki. A cikin systemi na digital, rise time yana bayyana lokacin da alama ta yi a kan gaba daga matsayin zuwa matsayin.

A cikin ilimin kontrol, rise time yana nufin lokacin da fadada ya dogara daga X% zuwa Y% na farkon halayi. Ma'ana na X da Y yana canza a cikin tunanin systemi.

Rise time a cikin systemi na second-order da underdamped yana 0% zuwa 100%, a cikin systemi na critically damped yana 5% zuwa 95%, da a cikin systemi na overdamped yana 10% zuwa 90%.

Rise Time Equation

Don in tabbatar da bayanan a cikin ilimin domain na lokaci, za a duba systemi na first-order da second-order.

Saboda haka, don in tabbatar da formular da za a yi game da rise time, za a duba systemi na first-order da second-order.

Rise Time of a First Order System

Systemi na first-order yana nuna a cikin closed-loop transfer function masu.

$G(s) = \frac{1}{Ts+1} = \frac{b}{s+a}$

A cikin funktar hukuma, T yana nufin tsawon lokaci. Muhimman tsarin da na lokaci game da sistem ta farko suna tattara a cikin tsawon lokaci T.

Sau, za mu iya haɗa da cewa input na takaitaccen sistema ta gaba ce unit step function. Kuma ana nufin shi a cikin Laplace transform kamar;

$R(s) = \frac{1}{s}$

Saboda haka, signal na dacewacewa zan iya nufin a cikin;

$C(s) = G(s) R(s)$

$C(s) = \frac{1}{Ts+1} \times \frac{1}{s}$

$C(s) = \frac{\frac{1}{T}}{s+\frac{1}{T}} \times \frac{1}{s}$

$C(s) = \frac{\frac{1}{T}}{s(s+\frac{1}{T})}$

Ko kwallon wannan kudin da partial fraction.

$C(s) = \frac{A_1}{s} + \frac{A_2}{s+\frac{1}{T}}$

A nan, gane maɗalƙin A1 da A2;

$\frac{A_1}{s} + \frac{A_2}{s+\frac{1}{T}} = \frac{\frac{1}{T}}{s(s+\frac{1}{T})}$

$A_1 (s+\frac{1}{T}) + A_2 s = \frac{1}{T}$

Don s=0;

$A_1(0+\frac{1}{T}) + A_2 (0) = \frac{1}{T}$

$A_1 \frac{1}{T} = \frac{1}{T}$

$A_1 = 1$

Don s=-1/T;

$A_1(\frac{-1}{T} + \frac{1}{T}) + A_2 (\frac{-1}{T}) = \frac{1}{T}$

$A_1 (0) - A_2 \frac{1}{T} = \frac{1}{T}$

$A_2 = -1$

Saboda haka,

$C(s) = \frac{1}{s} + \frac{-1}{s+\frac{1}{T}}$

A lokacin da aka yi Laplace na baya;

$C(t) = L^{-1} \left[ \frac{1}{s} -\frac{1}{s+\frac{1}{T}} \right]$

$C(t) = 1-e^{\frac{-t}{T}}$

Duk da haka, zan yi kalkulushi da yake daɗi rise time bayan 10% zuwa 90% na ƙarin balo.

$C(t_{10}) = 0.10 \quad and \quad C(t_{90}) = 0.90$

$0.10 = 1 - e^{\frac{t_{10}}{T}}$

$e^{\frac{t_{10}}{T}} = 1-0.10$

$e^{\frac{t_{10}}{T}} = 0.9$

$\frac{-t_{10}}{T} = ln(0.9)$

$t_{10} = -T ln(0.9)$

$t_{10} = -T (-0.1053)$

$t_{10} = 0.1053T$

Hakuri;

$0.90 = 1 - e^{\frac{t_{90}}{T}}$

$e^{\frac{t_{90}}{T}} = 1 - 0.9$

$e^{\frac{t_{90}}{T}} = 0.1$

$\frac{-t_{90}}{T} = ln(0.1)$

$t_{90} = -T (-2.3025)$

$t_{90} = 2.3025T$

A nan, don lokacin da taka t_r;

$t_r = t_{90} - t_{10}$

$t_r = 2.3025T - 0.1053T$

$t_r = 2.197 T$

$t_r \approx 2.2T = \frac{2.2}{a}$

Wakar Tafiya na Sistem ta Dabba Biyu

A cikin sistem ta dabba biyu, wakar tafiya yana kula da 0% zuwa 100% don sistem mai tsawon hanyar, 10% zuwa 90% don sistem mai tsawon mafi, da 5% zuwa 95% don sistem mai tsawon kritikal.

A nan, za a tattaunawa masu kula da wakar tafiya don sistem ta dabba biyu. Da kuma likitoci don sistem ta dabba biyu shine;

$C(t) = 1-\frac{e^{-\zeta \omega_n t}}{\sqrt{1-\zeta^2}} sin(\omega_d t_r + \phi)$

Wakar tafiya yana nufin tr.

$C(t) = C(t_r) = 1$

$1 = 1 - \frac{e^{-\zeta \omega_n t}}{\sqrt{1-\zeta^2}} sin(\omega_d t_r + \phi)$

$\frac{e^{-\zeta \omega_n t}}{\sqrt{1-\zeta^2}} sin(\omega_d t_r + \phi) = 0$

$sin(\omega_d t_r + \phi) = 0$

$sin(\omega_d t_r + \phi) = sin(\pi)$

$(\omega_d t_r + \phi) = (\pi)$

$\omega_d t_r = \pi - \phi$

$t_r = \frac{\pi - \phi}{\omega_d}$

Amsa,

$\omega_d = \omega_n \sqrt{1-\zeta^2}$

$\phi = tan^{-1} (\frac{\sqrt{1-\zeta^2})}{\zeta}$

Saboda haka, tushen da naɗa na lokacin da takarda ya zama shine;

$t_r = \frac{\pi - tan^{-1} (\frac{\sqrt{1-\zeta^2})}{\zeta}}{\omega_n \sqrt{1-\zeta^2} }$

Yadda ake Kalkula Tushen Da Naɗa

Sistem ta Fadada Tsawo

Misali, za a bayyana tushen da naɗa na sistem ta fadada tsawo. Tushen da naɗa na sistem ta fadada tsawo yana nuna a cikin tushen da ake magana a nan.

$G(s) = \frac{5}{s+2}$

Samun da aka bincike ta hanyar tushen bayanin kan hanyar da na da ita.

$G(s) = \frac{b}{s+a}$

Saboda haka; a=2 da b=5;

Tushen bayanin kan hanyar da na da ita ce;

$t_r = \frac{2.2}{a}$

$t_r = \frac{2.2}{2}$

$t_r = 1.1 sec$

Sistem ta Farko na Tsakiyar Daɗi

Nemo lokacin da tsakiyar daɗi ya faruwa a sistem ta farko na tsakiyar daɗi da maƙashe tsakiya ta 5 rad/sec da kuma yawan daɗi 0.6.

$\omega_n = 5 rad/sec$

$\zeta = 0.6$

Zanen da tushen wakar zama na tafin yadda da dama:

$t_r = \frac{\pi - \phi}{\omega_d}$

Tana da ya kamata a samun yadda da dama ta ф da ωd.

$\phi = tan^{-1} \left( \frac{\sqrt{1-\zeta^2}}{\zeta} \right)$

$\phi = tan^{-1} \left( \frac{\sqrt{1-0.6 ^2}}{0.6} \right)$

$\phi = tan^{-1} \left( \frac{\sqrt{1-0.36}}{0.6} \right)$

$\phi = tan^{-1} \left( \frac{0.8}{0.6} \right)$

$\phi = tan^{-1} (1.33)$

$\phi = 0.9272 rad$

Daga nan za ωd,

$\omega_d = \omega_n \sqrt{1-\zeta^2}$

$\omega_d = 5 \times 0.8$

$\omega_d = 4 rad/sec$

Zaka iya a tsara wannan ma'a amsar da na bayan tsari;

$t_r = \frac{3.14-0.9272}{4}$

$t_r = \frac{2.2128}{4}$

$t_r = 0.5532 sec$

Miya kuma Ya Dacewa da Tsawo na Zama 10% zuwa 90%?

Babu wani abin da yake da zan iya shafi daidai cewa muna da yiwuwa da tsarin da ya dacewa da tsawo na zama 10% zuwa 90%.

Amma a cikin yawanci, ana samun da ya dacewa da tsawo bayan wannan halayen.

Ana amfani da wannan halaye saboda adadin tsawon da suka fi sani da kuma adadin tsawon da suka fi gaba suna da nasarorin da suke so kuɗi.

Misali, zaɓi hanyar daɗi da aka yi:

Wannan yadda zama da maɗalitaccen kimanin da suka fi shi hanyar da yaɗuwa har zuwa lokacin da ta samu ƙarin bayanin da suka fi.

Babu wani abin da za a iya yi don in tafi “wakar ƙaramin haɗuwa” daga lokacin da bayanin ya zama da maɗalitaccen kimanin, saboda wannan bai ba daidaito da wakar da aka ƙara waɗanda bayanin ya ƙara a nan (da yaɗuwar da wani abu mai haɗuwa ta faruwa a farkon Tr).

A kan ƙarin bayanin, na amfani da 90% tun daga 100% saboda yawancin bayanan ba suka samu ƙarin bayanin da suka fi.

Duk da cewa hakan ne da ita ce da grafikin logaritmiki, ba zan iya samu 100%, amma gradinta grafikin ya ƙara a ƙarin lokaci.

Don haka, domin kaɗan: wasu wurare da suke magance suna da tsari masu gajeruwa a kan gabashin da ƙarin bayanin.

Amma a kan tsari na ƙaramin haɗuwa, duk wurare suna da tsari masu ƙaramin haɗuwa. Kuma ƙara 10% zuwa 90% na ƙaramin haɗuwa yana ba da adadin da yaɗuwa a kan yawancin wurare.

Saboda haka, a kan ƙarin lokaci, na ƙara wakar ƙaramin haɗuwa daga 10% zuwa 90%.

Wakar Ƙaramin Haɗuwa vs Wakar Ƙaramin Yauje

Wakar ƙaramin yauje yana nufin wakar da bayanin ke ƙara (duba) daga ƙarin bayanin (X) zuwa ƙarin bayanin (Y).

A kan ƙarin lokaci, ƙarin bayanin mai yawa (X) yana zama 90% na ƙarin bayanin mai muhimmanci kuma ƙarin bayanin na ƙarin yana zama 10% na ƙarin bayanin mai muhimmanci. Daɗiɗa na nuna wakar ƙaramin yauje a kan ta haka.

rise time vs fall time — Wakar Ƙaramin Haɗuwa vs Wakar Ƙaramin Yauje

Don haka, a kan ƙarin lokaci, wakar ƙaramin yauje yana iya ƙunshi da wakar ƙaramin haɗuwa, duk da cewa a kan haka an ƙara shi.

Amma ya fi ingantaccen da wannan lokacin da karamin lokaci ba na iya duba daidai.

Idan kana da tsirriyar tufafi (kamar sin tufafi), karamin lokaci da karamin lokaci suna da shi gaba.

Babu nasarorin da ya haɗa da karamin lokaci da karamin lokaci. Duk wadannan abubuwa suna da muhimmanci a cikin bincike da sabon arziki da elektronika.

Karamin Lokaci da Fadada

Don bincike da alamun tufafi, ake amfani da oscilloscope. Idan ana sani da karamin lokacin alamun, za a iya samun fadada alamun don bincike.

Wannan zai taimaka muka zuba oscilloscope da fadada mai yawa ko kadan. Kuma zai bayar da natijoyi masu daidai a cikin oscilloscope.

Idan ana sani da karamin lokacin alamun, za a iya samun yadda oscilloscope zai rage alamun da taɓa da karamin lokacin.

Nasarorin da ke haɗa da fadada (BW) da karamin lokaci (tr) an yi a cikin rubutu a nan.

$BW \approx \frac{0.35}{t_r}$

An yi wannan rubutu a nan idan ana sani da karamin lokacin alamun a kan 10% zuwa 90% daga ƙarin balin.

Fadada na iya zama a cikin MHz ko GHz, kuma karamin lokaci a cikin μs ko ns.

Idan amplifiers da ake amfani da su a cikin oscilloscope suna da hanyar frequency response mai yawa, na iya samun natija mai daidai da numeratore 0.35.

Amma duk wadanda suke da oscilloscopes suna da roll-off mai yawa don bayar da frequency response mai daidai a cikin passband. A cikin wannan halin, numeratore ya zama 0.45 ko da yawa.

Misali, idan karamin kare da dama ta shiga oscilloscope, yana da 10-90% rise time da 1ns. Me yadda zai iya cewa bandwidth na oscilloscope?

Idan an sanya waɗannan lambar zuwa formula ta haka,

$BW = \frac{3.5}{10^{-9}} = 3.5 \times 10^{-9} = 350MHz$