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Control system miscellaneous

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Control system miscellaneous
  1. An electrical system and its signal-flow graph representation are shown in Fiures I and II respectively. The values of G2 and H, respectively, are
    1. Z3(s)
      		 ,
      -Z3(s)
      Z1(s) + Z2(s) + Z3(s)Z1(s) + Z3(s)
    2. -Z3(s)
      		 ,
      -Z3(s)
      Z2(s) - Z3(s) + Z4(s)Z1(s) + Z3(s)
    3. Z3(s)
      		 ,
      Z3(s)
      Z2(s) + Z3(s) + Z4(s)Z1(s) + Z3(s)
    4. -Z3(s)
      		 ,
      Z3(s)
      Z2(s) - Z3(s) + Z4(s)Z1(s) + Z3(s)
Correct Option: A

Applying loop rules to both the loops,

Vi (s) = I1 Z1 (s) + (I1 – I2) Z3 (s) ...(i)
I1 Z3 (s) = I2 Z2 (s) + I12 Z3 (s) + I2 Z4 (s) ...(ii)
From equation (i),

Vt
 =
- I2 Z1(s)
+ I1 .....(iii)
Z1(s) + Z3(s)Z1(s) + Z3(s)

From equation (ii),
I2 =
Z3(s) I1(s)
...(iv)
Z1(s) + Z2(s) + Z3(s)

From the given signal-flow graph, and from equation (iv), we get
I2
 = G2
I1

⇒ G2 =
Z3(s)
Z1(s) + Z2(s) + Z3(s)

From equation (iii),
H = -
Z3(s)
Z1(s) + Z3(s)


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