किसी निश्चित प्रणाली में अवस्था प्रतिरूप निम्नानुसार दिया गया है

D = 0 के साथ[X1X2]=[2342][X1X2]+[35]U और Y = [11][X1X2] है। इसका स्थानांतरण फलन ___________ होगा। 

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MPPKVVCL Indore JE Electrical 21 August 2018 Official Paper
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  1. [8s+1]s2+8
  2. [2s+43]s2+8
  3. [8s43]s2+8
  4. [2s1]s2+8

Answer (Detailed Solution Below)

Option 1 : [8s+1]s2+8
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Detailed Solution

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संकल्पना

एक अवस्था समिष्टि प्रतिरूप को निम्न रूप में दर्शाया गया है:

X˙=AX+BU

Y=CX+DU

जहाँ, A = प्रणाली आव्यूह

B = इनपुट आव्यूह

C = आउटपुट आव्यूह

D = डेटा स्थानांतरण आव्यूह

अवस्था समिष्ठि प्रतिरूप से स्थानांतरण फलन को निम्न के द्वारा दिया गया है:

Y(s)U(s)=C(sIA)1B+D

गणना

दिया गया है, A=[2342]

B=[35]

C=[11]

D = 0

(sIA)1=[s+2+34s2]1

(sIA)1=1s24+12[s23+4s+2]

(sIA)1=1s2+8[s23+4s+2]

(sIA)1B=1s2+8[s23+4s+2][35]

(sIA)1B=1s2+8[3s215s+22]

C(sIA)1B=1s2+8[11][3s215s+22]

C(sIA)1B=1s2+8[3s21+5s+22]

C(sIA)1B=[8s+1]s2+8

सही उत्तर विकल्प 1 है। 

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