एक नियंत्रण प्रणाली का कुल स्थानांतरण फलन निम्नलिखित समीकरण द्वारा दिया गया है। अवकलन दर प्रतिक्रिया स्थिरांक Kt का मान ज्ञात कीजिए। (अवमंदन अनुपात 0.9 पर विचार करें)

C(s)R(s)=36s2+3.6s+36

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  1. 1
  2. 0.16
  3. 0.2
  4. 0.707

Answer (Detailed Solution Below)

Option 3 : 0.2
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अवधारणा:

द्वितीयक क्रम के ब्लॉक आरेख पर विचार करें जैसा कि नीचे दिखाया गया है:

F20 Tapesh S 25-5-2021 Swati D1

प्रणाली की प्रतिक्रिया है:

c(t)=1eζωnt1ζ2sin[(ωn1ζ2)t+θ]

प्रणाली का खुला-लूप स्थानांतरण फलन है:

G(s)=ωn2s(s+2ζωn)

बंद-लूप स्थानांतरण फलन है:

TF=ωn2s2+2ζωns+ωn2

गणना:

दी गई प्रणाली के लिए खुला-लूप स्थानांतरण फलन है:

G(s)=36s2+3.6s

दिखाए गए अनुसार अवकलन प्रतिक्रिया के साथ नई प्रणाली पर विचार करें:

F20 Tapesh S 25-5-2021 Swati D2

H(s)=G(s)1+ktG(s)s

H(s)=36s2+3.6s+36Kts

प्रणाली का कुल स्थानांतरण फलन है:

C(s)R(s)=H(s)1+H(s)

C(s)R(s)=36s2+3.6s+36Kts+36

मानक रूप की तुलना करने पर हमें मिलता है:

ωn = 6 और दिया गया ζ = 0.9

2(0.9)(6) = 3.6+36kt 

2(0.9)(6) = 3.6[1 + 10k

1 + 10k= 3

kt = 0.2

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