Attempt any four:

1 (a)
Explain the effect of addition of pole and zero to the system.

5 M

1 (b)
Define gain margin and phase margin. Explain how these margins are used for stability analysis.

5 M

1 (c)
Difference open-loop and closed-loop systems.

5 M

1 (d)
Explain need of compensator.

5 M

1 (e)
State and prove properties of state transition matrix.

5 M

2 (a)
obtain the transfer function of the following electrical system.

10 M

2 (b)
Find the transfer function \[ \dfrac {c(s)}{R(s)} \] for the following system using block diagram reduction technique.

10 M

3 (a)
Obtain the state space model for the following mechanical system.

10 M

3 (b)
Obtain the solution of the system described by \[ x= \begin{bmatrix} 0 &1 \\ -2 & -4 \end{bmatrix} x + \begin{bmatrix}0\\2 \end{bmatrix} u \]

10 M

4 (a)
The open-loop transfer function of a unity feedback system is given by \[ G(s) = \dfrac {K}{(s+3)(s+5)(s^2+2s+2)} \] Plot the root loci. Find the points where the root loci cross the imaginary axis.

10 M

4 (b)
Construct the bode plot for the following transfer function. Comment on stability \[ G(s)= \dfrac {100}{s^2 (1+0.005s)(1+0.08s)(1+0.5s)} \]

10 M

5 (a)
Check controllability and observability for the system described by \[ x= \begin{bmatrix}0 &6 &-5 \\1 &0 &2 \\3 &2 &4 \end{bmatrix} x+ \begin{bmatrix}0\\1 \\2
\end{bmatrix} u \\ y = \begin{bmatrix} 1 &2 &3
\end{bmatrix}x \]

10 M

5 (b)
Derive the relationship between time and frequency domain specification of the system.

10 M

6 (a)
Write a short note on model predictive control.

5 M

6 (b)
Explain the features of P, I and D control actions

5 M

6 (c)
Find the range of K for the system to be stable

s

s

^{4}+7s^{3}+10s^{2}+2ks + k =0
5 M

6 (d)
Describe the Mason's gain formula with an example.

5 M

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