Solve any one question from Q1 and Q2

1 (a)
Consider the R-L-C network shown in Fig. 1:

i) Obtain transfer function if V

ii) Find the location of poles in terms of R, L and C.

iii) If R=1 MΩ, C=1 μF, L=1 mH. Is the location of poles of transfer function given in (i) are real? If yes, find the location.

i) Obtain transfer function if V

_{i}and V_{o}are input and output voltage respectively.ii) Find the location of poles in terms of R, L and C.

iii) If R=1 MΩ, C=1 μF, L=1 mH. Is the location of poles of transfer function given in (i) are real? If yes, find the location.

6 M

1 (b)
If \( G(s)= \dfrac {K}{s(s+64)} \) with H(s)=1, determine value of K so that damping factor is 0.5. For this value of 'K' determine:

i) Rise time, and

ii) Settling time.

Assume unit step input.

i) Rise time, and

ii) Settling time.

Assume unit step input.

6 M

2 (a)
Find \( \dfrac {C(s)}{R(s)} \) for the system shown in Fig. 2 using Block diagram rules.

6 M

2 (b)
The open loop transfer function of unity feedback system is:

\( G(s) = \dfrac {K}{s(\tau s+1)}, K, \tau > 0 \) with a given value of K, the peak overshoot was found to be 80%. Suppose peak overshoot is decreased to 20% by decreasing gain K. Find the new value of K (say K

\( G(s) = \dfrac {K}{s(\tau s+1)}, K, \tau > 0 \) with a given value of K, the peak overshoot was found to be 80%. Suppose peak overshoot is decreased to 20% by decreasing gain K. Find the new value of K (say K

_{2}) in terms of the old value.
6 M

Solve any one question from Q3 and Q4

3 (a)
Comment on stability of a system using Routh's criteria, if characteristics equation is D(s)=s

^{4}+5s^{3}+s^{2}+10+1. How many poles lies in Right of s-plane?
4 M

3 (b)
Construct Bode Plot and calculate GM, PM, W

_{gc}and W_{pc}if \( G(s) = \dfrac {200(s+20)}{s(2s+1)(s+40)} \) and H(s)=1.
8 M

4 (a)
Open loop transfer function of unity feedback system is \( G(s) = \dfrac {K}{s(s+2)(s+10)}. \) Sketch the complete root locus and comment on stability of system.

8 M

4 (b)
For unity feedback system with \( G(s) = \dfrac {100}{s(s+5)} \).

Determine:

i) Resonance peak

ii) Resonance frequency.

Determine:

i) Resonance peak

ii) Resonance frequency.

4 M

Solve any one question from Q5 and Q6

5 (a)
Enlist any two advantages of state space approach over transfer function. Obtain a state space representation in controllable and observable canonical form for the system \( G(s) = \dfrac {s+3}{s^2 + 3s +2} \)

6 M

5 (b)
Obtain the state space representation of system whose differential equation is: \[ \dfrac {d^2 y}{dt^3}+ 2 \dfrac {d^2 y}{dt^2}+ 3 \dfrac {dy}{dt}+ 6y = \dfrac {d^2u}{dt^2} - \dfrac {du}{dt}+ 2u. \] Also find controllability and observability of the system. Assume zero initial conditions.

7 M

6 (a)
Obtain state transition matrix if: \[ i) \ \dfrac {dx}{dt} = \begin{bmatrix}
0 &1 \\-1
&0
\end{bmatrix}x \\
ii) \ \dfrac {dx}{dt} = \begin{bmatrix}
0 &1 \\0
&0
\end{bmatrix} x \] using Laplace transformation.

6 M

6 (b)
Write a short note on 'state transition matrix and its properties'.

4 M

Solve any one question from Q7 and Q8

7 (a)
Advantage of digital control system over analog control systems.

4 M

7 (b)
Application of PLC (Programmable Logic Controller) in Elevator/List.

4 M

7 (c)
PID controllers and its operational characteristics.

5 M

8 (a)
Obtain pulse transfer function of the system shown in Fig. 3 with a=1.

6 M

8 (b)
Obtain pulse transfer function of system shown in Fig. 4

7 M

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