Misalai Nau'in Tsawon Kudin Yawan Ƙarfin Daɗi?

Mai Tsawo Wani Yadda Ake Kula Sistem na Tsawon Idan?

Takardun Sistem na Tsawon Idan

Sistem na tsawon idan yana amfani da wani abu mai sada na likitoci don kula masu shirya da masu fitarwa, tare da neman hanyoyi na lokaci na idan.

Tsarin kula (kula masu shirya-masu fitarwa) wannan sistem na tsawo an bayyana kamar haka:

• K ita ce DC Gain (gain na DC na sistem na rikitar masu shirya zuwa uku na masu fitarwa)

• T ita ce tsarin lokaci na sistem (tsarin lokaci ita ce maida ya kula yadda sistem na tsawon idan ke jawo wa shirya na step unit).

Tsarin Kula na Sistem na Tsawon Idan

Tsarin kula yana nuna alaka daga masu fitarwa zuwa masu shirya na sistem na kontrol, don duk abubuwan masu shirya.

Poles na Tsarin Kula

Poles na tsarin kula suna cewa abubuwan Laplace Transform variable(s), wadanda suke sa tsarin kula zuwa infiniti.Denominata ta tsarin kula ita ce poles na function.

Zeros na Tsarin Kula

Zeros na tsarin kula suna cewa abubuwan Laplace Transform variable(s), wadanda suke sa tsarin kula zuwa zero.Nominator ta tsarin kula ita ce zeros na function.

Sistem na Tsawon Idan

A nan ne a yi tasiri game da sistem na tsawon idan baki daya. Sistem na tsawon idan yana ba ni wani takarda na yadda ake jawo wa shirya zuwa uku na masu fitarwa.Idan masu shirya ita ce unit step, R(s) = 1/s saboda haka masu fitarwa ita ce C(s). Tsarin gaba-gaban sistem na tsawon idan ita ce, i.e ita ce tsarin kula.

Akwai biyu poles, wanda batun ita ce pole na shirya a asalin s = 0 kuma wanda batun ita ce pole na sistem a s = -a, wanda ya fi a axis na negative a plot na poles.Na amfani da MATLAB’s pzmap command, zan iya tabbatar da poles da zeros na sistem, wadannan mummunan don kula alhakin da yake yi.A nan za mu yi inverse transform saboda haka total response zai zama wanda yake samu forced response da natural response.

Saboda pole na shirya a asalin, yana produce forced response kamar hakan da aka bayyana cewa yana ba shirya wanda yake yi forced response, kuma pole na sistem a -a yana produce natural response wanda yana cikin transient response na sistem.

Ba da damar yadda, tsarin gaba-gaban sistem na tsawon idan ita ce C(s) = 1-e-at wanda ita ce equal to forced response wanda ita ce “1” da natural response wanda ita ce equal to “e-at”. Abin da ake bukata shine parameter “a”.

Yawan abubuwan kamar likitoci ko inverse Laplace Transform, wadannan duka sun za su kula total response amma suka fi wasu lokaci da lafiya.

Amfani da poles, zeros, da wadannan abubuwan da yawa suka ba mu qualitative information don kula masu shirya, saboda hakan zan iya kula yadda ake jawo wa shirya da lokacin da sistem yake shiga uku na masu fitarwa.

Ba da haka, zan bayyana uku abubuwan transient response performance specifications, tsarin lokaci, rise time, da settling time game da sistem na tsawon idan.

Tsarin Lokaci na Sistem na Tsawon Idan

Tsarin lokaci yana nuna lokacin da step response ke jawo zuwa 63% ko 0.63 na uku na masu fitarwa. Ana kiran wannan da t = 1/a. Idan muke karfin tsarin lokaci, unit ita ce 1/seconds ko frequency.

Ana kira parameter “a” exponential frequency. Saboda derivative of e-at ita ce -a at t = 0. Saboda haka, tsarin lokaci ana kiran transient response specification game da sistem na tsawon idan.

Zan iya kula yadda ake jawo wa shirya ta haka da setting poles. Saboda haka, ya fi a pole dari imaginary axis, yadda ake jawo wa shirya ita ce faɗa. Saboda haka, muna iya set poles dari imaginary axis don kula yadda ake jawo wa shirya.

Rise Time na Sistem na Tsawon Idan

Rise time yana nuna lokacin da waveform ke jawo zuwa 0.1 zuwa 0.9 ko 10% zuwa 90% na uku na masu fitarwa. Don equation na rise time, muna iya put 0.1 da 0.9 a general first-order system equation respectively.

Don t = 0.1

Don t = 0.9

Daga baya 0.9 zuwa 0.1

A nan equation na rise time. Idan muna jan parameter "a", zan iya kula rise time wanda aka bayar da "a" a equation.

Settling Time na Sistem na Tsawon Idan

Settling time yana nuna lokacin da response ke jawo zuwa 2% na uku na masu fitarwa. Muna iya limit percentage zuwa 5% na uku na masu fitarwa. Duk percentages suna da muhimmanci.

Equation na settling time ita ce Ts = 4/a.

Bisa hankali da wadannan uku transient response specifications, zan iya kula step response wanda aka bayar da ita saboda hakan wadannan qualitative technique yana da muhimmanci game da order systems equations.

Kasuwancin Sistem na Tsawon Idan

Ba da damar yadda ake kula dukkan abubuwan da suka shafi 1st order control system, muna samu wadannan kasuwanci:

• Pole na input function yana produce form na forced response. Saboda hakan, pole a asalin yana produce step function a output.

• Pole na transfer function yana produce natural response. Ita ce pole na sistem.

• Pole a real axis yana produce exponential frequency na form e-at. Saboda hakan, ya fi a pole dari asalin, yadda ake jawo wa shirya ita ce faɗa.

• Fahimta poles da zeros yana ba mu iya haɗaƙar harkokin sistem da kula outputs da su da faɗa da inganci.