Digital Data of Control System Cikakken Bayanan Kontrol

Digital Data Definition

A cikin na'urar daɗi mai yawa, data masu digital sun hada da abubuwa ko kuma samfurin bayanai na musamman wanda ke maimaita shaida a cikin format masu digital.

Sampling Process

Samplin shine yanayin kawo alama na tsohon analog zuwa alama na digital tun daga amfani da samplar, wanda yake koma da kuma ci gaba.

Tattalin samplin yana kawo alama na tsohon analog zuwa alama na digital tun daga amfani da switch, wanda ake kiran samplar, wanda yake koma da kuma ci gaba. Don samplar mai kyau, girman faduwar pulse na farko yana da tsari (kamar zero). A cikin na'urar daɗi, Z transformations yana da muhimmanci sosai, kamar haka Fourier transform a cikin na'urar daɗi masu tsawon lissafi. Yana iya duba Z transformations da amfani da su a cikin tushen bayanai.

Muna define z transform a haka

Idan, F(k) shine data masu daɗi

Z shine lambar mai faɗi

F (z) shine Fourier transform na f (k).

Abubuwan da suka fi sani game da z transformation suna rubuta ta haka

Linearity

Muna neman jamiyar funksiya biyu masu daɗi f (k) da g (k) kamar haka

idantaccen p da q su ne sabbin adadin da suka fi sani, don haka idan muna yi Laplace transform muna samun

Change of Scale: muna neman funksiya f(k), idan muna yi z transform muna samun

don haka muna samun da change of scale property

Shifting Property: Da haka wannan property

Don haka muna neman abubuwan da suka fi sani da z transforms da muna ba da shawarar maimakon readers da suka karanta wa:

Laplace transformation na wannan funksiya shine 1/s 2 kuma f(k) = kT. Don haka z transformation na wannan funksiya shine

Laplace transformation na wannan funksiya shine 2/s3 kuma f(k) = kT. Don haka z transformation na wannan funksiya shine

Laplace transformation na wannan funksiya shine 1/(s + a) kuma f(k) = e (-akT)

Don haka z transformation na wannan funksiya shine

Laplace transformation na wannan funksiya shine 1/(s + a) 2 kuma f(k) = Te-akT. Don haka z transformation na wannan funksiya shine

Laplace transformation na wannan funksiya shine a/(s 2 + a2) kuma f(k) = sin(akT). Don haka z transformation na wannan funksiya shine

Laplace transformation na wannan funksiya shine s/(s 2 + a2) kuma f(k) = cos(akT). Don haka z transformation na wannan funksiya shine

Yanzu ana buƙatar samun data nan kowane lokaci, wanda yana nufin kawo data masu daɗi zuwa form masu tsawon lissafi. Muna iya kawo data masu digital na na'urar daɗi zuwa form masu tsawon lissafi tun daga amfani da hold circuits wanda ake magana a cikin bayanan:

Hold Circuits: Wadannan su ne circuit's wanda suke kawo data masu daɗi zuwa data masu tsawon lissafi ko kuma data na baya. Yanzu akwai nau'o'i biyu masu hold circuits da suka bayyana a cikin bayanan:

Zero Order Hold Circuit

Bayanin diagram block na zero order hold circuit shine a haka:

Figure related to zero order hold.

A cikin diagram block muna bayyana input f(t) don circuit, idan muna koyar input signal zuwa wannan circuit yana kawo input signal zuwa form masu tsawon lissafi. Output na zero order hold circuit shine a haka.Yanzu muna son in tabbata transfer function na zero order hold circuit. Idan muna rubuta equation na output muna samun

idantaccen muna yi Laplace transform na equation na farko muna samun

Daga equation na farko muna iya tabbatar transfer function

Idan muna koyar s=jω muna iya rubuta bode plot na zero order hold circuit. Bayanin electrical na zero order hold circuit shine a haka, wanda yake da sampler da ya fara da resistor da kuma wannan combination yake fara da parallel combination da ya fara da resistor da capacitor.

GAIN PLOT – frequency response curve of ZOH

PHASE PLOT – frequency response curve of ZOH

First Order Hold Circuit

Bayanin diagram block na first order hold circuit shine a haka:

First Order Hold Circuit

A cikin diagram block muna bayyana input f(t) don circuit, idan muna koyar input signal zuwa wannan circuit yana kawo input signal zuwa form masu tsawon lissafi. Output na first order hold circuit shine a haka: Yanzu muna son in tabbata transfer function na first order hold circuit. Idan muna rubuta equation na output muna samun

idantaccen muna yi Laplace transform na equation na farko muna samun

Daga equation na farko muna iya tabbatar transfer function (1-e -sT)/s. idan muna koyar s=jω muna iya rubuta bode plot na zero order hold circuit.

Bode plot na first order hold circuit shine a haka wanda yake da magnitude plot da phase angle plot. Magnitude plot yana fara da magnitude value 2π/ωs.