Gurbin Locus na Kokarin Niyoyin Tattalin Arzikin IEE-Business

Takardar Da Yadda Ake Amfani Da Tekunin Root Locus

Tekunin root locus a cikin sistem na kontrol shi ne yadda amfani da rubutu don nuna yadda wani abubuwa na duniya ke iya taimaka wajen bayyana masu samun inganci da kuma al'adu na sistem ta kontrol.

Fadada Tekunin Root Locus

• Tekunin root locus a cikin sitem na kontrol ya zama zai iya amfani da shi daidai saboda hanyoyin mafi so kuɗi a cikin hanyoyin da suka bazu.

• Na amfani da tekunin root locus zan iya tabbatar da kyau yadda kowane babban muhimmiyar abubuwa na duniya ke iya taimaka wajen bayyana al'adu na kowane sistem.

• Tekunin root locus tana ba da hanyar da ya fi dace da duk fahimtar abubuwan da za su iya amfani da shi.

Wannan makala zai amfani da kalmomin da suka duba a cikin tekunin root locus wanda ake buƙata sakamako a cikin fahimta amsa.

• Taifuka Na Tushen Daga Tekunin Root Locus : 1 + G(s)H(s) = 0 tana ana son taifukan. Idan an yi tasiri ga taifukan kuma an sanar da dk/ds da take da zero, muna iya samun wurare da aka fara.

• Wurare Da Aka Fara : Idan akwai biyu da root loci sun fara zuwa pole kuma sun haɗa da ƙarin hukuma, idan suka sauya suka fara da ƙarin hukuma da suka haɗa suka fara da ƙarin hukuma. Ko wurare da aka fara a kan da ake samun wurare da suka fara da ƙarin hukuma 1 + G(s)H(s) = 0. Kyau na K tana zama mafi tsawo a wurare da branches na root loci suka fara. Wurare da aka fara zai iya zama mai sauƙi, mai asali ko kompleksi.

• Wurare Da Aka Sanya : Yadda ake sanya wurare da aka sanya a cikin plot ita ce: Root locus ya zama a kan biyu da zeros a kan axin gaba.

• Centre of Gravity : Ana kiran shi da centroid, wanda ake bayyana shi da wuraren da duka asymptotes suka fara. Lissafan, ana kula shi da ƙarin hukumar da poles da zeros a cikin transfer function idan an yi tasiri ga farkon hukumar da poles da zeros. Centre of gravity tana zama mai sauƙi, kuma ana kiran shi da σA.

A nan, 'N' tana nufin hukumar da poles, kuma 'M' tana nufin hukumar da zeros a cikin sistem.

• Asymptotes Na Root Loci : Asymptote tana fara zuwa centre of gravity ko centroid kuma tana haɗa zuwa infinity a kan ƙarin hukuma. Asymptotes tana ba da hanyar da root locus ke iya haɗa idan suka fara zuwa wurare da aka fara.

• Gargajiya Na Asymptotes : Asymptotes tana haɗa da gargajiya da axin gaba, wanda ake iya kula shi daga rukunin:

A nan, p = 0, 1, 2 ……. (N-M-1)

N tana nufin hukumar da poles

M tana nufin hukumar da zeros.

• Gargajiya Na Haɗa Ko Farawa : Ana kula gargajiya na haɗa idan akwai poles da suka fara da ƙarin hukuma a cikin sistem. Gargajiya na haɗa tana iya kula shi daga 180-{(sum of angles to a complex pole from the other poles)-(sum of angle to a complex pole from the zeros)}.

• Haɗuwar Root Locus Daga Axin Mai Tsabta : Don in samun wurare da root locus tana haɗa zuwa axin mai tsabta, ana iya amfani da Routh Hurwitz criterion. Idan an samu auxiliary equation, kuma kula kimanin K, za su iya samun wuraren da take haɗa.

• Gain Margin : Gain margin tana nufin kyau na kimanin gain factor da za su iya kula shi idan an yi tasiri ga kimanin gain factor. Lissafan, ana kula shi daga rukunin:

• Phase Margin : Phase margin tana iya kula shi daga rukunin:

• Symmetry Na Root Locus : Root locus tana symmetric zuwa x axis ko axin gaba.

• Yadda ake kula K a kan wurare da kake da root loci? Akwai biyu da hanyoyin kula K, har hanyar tana a bayyana a nan.

• Magnitude Criteria : A kan wurare da kake da root locus, muna iya amfani da magnitude criteria kamar haka:

An amfani da wannan rukunin muna iya kula K a kan wurare da ake buƙata.

• Amfani Da Root Locus Plot : Kimanin K a kan s a kan root locus tana a kula shi daga:

Root Locus Plot

Root locus plot, wanda tana cikin wannan tekunicen, tana bayyana masu samun inganci na sistem. Tana bayyana kimanin 'K' da za su iya taimaka wajen samun inganci, tana taimaka wajen system yadda zai yi aiki a cikin ƙarin hukumar da duniya.

A nan akwai abubuwan da ake buƙata don in samun root locus. Abubuwan tana a bayyana a nan:

• Tsakiyar da root locus tana zama : Idan an samu duka poles da zeros a kan plane, muna iya samun tsakiyar da root locus tana zama daga rukunin:Kawai segment tana zama a kan root locus idan ƙarin hukumar da poles da zeros a kan gabas na segment tana zama ɗaya.

• Yadda ake kula ƙarin hukumar da separate root loci ? : Ƙarin hukumar da separate root loci tana zama ƙarin hukumar da roots idan ƙarin hukumar da roots tana zama mafi yawan poles, ba haka ƙarin hukumar da separate root loci tana zama ƙarin hukumar da poles idan ƙarin hukumar da roots tana zama mafi yawan zeros.

Shiga Don In Samun Root Locus

Daga cikin abubuwan da ake bayyana, muna iya samun root locus plot zuwa kowane nau'o'i na sistem. A nan, ake bayyana shiga don in samun root locus.

• Samun duka roots da poles daga open loop transfer function kuma samun su a kan complex plane.

• Duka root loci tana fara zuwa poles inda K = 0 kuma tana haɗa zuwa zeros inda K tana haɗa zuwa infinity. Ƙarin hukumar da branches tana haɗa zuwa infinity tana zama farkon hukumar da poles da zeros na G(s)H(s).

• Samun tsakiyar da root loci tana zama daga rukunin a nan idan an samu M da N.

• Kula wurare da aka fara da wurare da aka sanya idan akwai.

• Samun asymptotes da centroid point a kan complex plane don root loci daga rukunin slope na asymptotes.

• A nan, kula gargajiya na haɗa da haɗuwar root loci zuwa axin mai tsabta.

• A nan, kula K daga hanyar da ake bayyana a nan.

Idan an yi waɗannan shiga, muna iya samun root locus plot zuwa kowane open loop transfer function.

• Kula gain margin.

• Kula phase margin.

• Muna iya magana game da samun inganci na sistem daga Routh Array.