Answer the following:

1 (a)
Define relative and absolute stability. State its significance.

5 M

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

5 M

1 (c)
Differentiate open and closed system.

5 M

1 (d)
Explain different types of models used in applications.

5 M

2 (a)
Obtain the transfer function of the following mechanical system.

10 M

2 (b)
Using Mason's gain formula, find C(s)/R(s)

10 M

3 (a)
Construct root locus for the following transfer function. Find range of K for system to be stable \( G(s)H(s)= \dfrac {K(S+13)}{S(S+3)(S+8)} \)

10 M

3 (b)
Check controllability and observability for the system \[ x= \begin{bmatrix}
1 &2 &1 \\0
&1 &3 \\1
&1 &1
\end{bmatrix}x+\begin{bmatrix}
1\\2
\\0
\end{bmatrix} \\ y= \begin{bmatrix}
1&3&1\end{bmatrix} \]

10 M

4 (a)
Sketch the bode plot for the system described by following transfer function. Also comment on stability \[ G(s)H(s)= \dfrac {0.4 (1+ 6S)}{S^2 (1+0.5S)} \]

10 M

4 (b)
Find the solution of following state equation \( x= \begin{bmatrix}
-5 &-6 \\1
&0 \end{bmatrix} x+ \begin{bmatrix}
1\\0\end{bmatrix} u \\
y=\begin{bmatrix}
1&1
\end{bmatrix} \)

10 M

5 (a)
State and prove properties of state transition matrix.

7 M

5 (b)
The characteristics equations for certain feedback systems are given below. Determine range of k for the system to be stable

i) S

ii) S

i) S

^{4}+20KS^{2}+5S^{2}+10S+15=0ii) S

^{2}+2KS^{2}+(K+2)+4=0
8 M

5 (c)
Explain what is robust control system. Also explain the need of robust control.

5 M

6 (a)
Explain the effects of P, I and D actions.

6 M

6 (b)
Explain the effect of addition off poles and zeros to the system.

7 M

6 (c)
Explain different time domain specifications.

7 M

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