Answer any one question from Q1 and Q2

1 (a)
Give the various terminology of electrical system and its analogous quantities based on force-current analogy.

6 M

1 (b)
Write the differential equations of system shown in Fig. 1. Also find \[ \dfrac {X_1 (s)} {F(s)} \]

6 M

2 (a)
Obtain transfer function of the system shown in Fig. 2:

6 M

2 (b)
The open loop transfer function of unity feedback system is \[ G(s) = \dfrac {k_1} {s(\tau s +1)} \ with \ k, \ \tau>0 \] with a given of k

_{1}, the peak overshoot was found to be 80%. if the overshoot is decreased up to 20% by new gain k_{2}find k_{2}in terms of k_{1}.
6 M

Answer any one question from Q3 and Q4

3 (a)
Using Routh's criteria, comment on the stability if characteristic equation is:

S2+s+1=0

S

^{5}+2s^{4}=3s^{3}+8s
4 M

3 (b)
Draw the Bode plot and obtain gain margin, phase margin, gain crossover frequency and phase crossover frequency if: \[ G(s)\cdot H(s)= \dfrac {50,000 (s+10)}{s(s+1)(s+500)}

8 M

4 (a)
\[ if\ G(s) H(s) = \dfrac {k}{s(s+1)(s+10)} \] sketch the complete Root locus and comment on the stability.

8 M

4 (b)
\[ If \ G(s) \ H(s)= \dfrac {1}{s(s+1)} \] Find Resonance peak and Resonance frequency,

4 M

Answer any one question from Q5 and Q6

5 (a)
Obtain transfer function of state model if: \[ A=\begin{bmatrix}
0 &1 &0 \\0
&0 &1 \\-6
&-11 &-6
\end{bmatrix}, \ B=\begin{bmatrix}
0\\0
\\1
\end{bmatrix}, \ C=\begin{bmatrix}
1 &0 &0
\end{bmatrix}, \ D=[0] \]

6 M

5 (b)
Find controllability and observability of the state model: \[ A=\begin{bmatrix}
1 &0 &1 \\0
&1 &1 \\1
& 1 &1
\end{bmatrix}, \ B=\begin{bmatrix}
1\\1
\\1
\end{bmatrix}, \ C=\begin{bmatrix}
1 &1 &1
\end{bmatrix}, \ D=[0]\]

7 M

6 (a)
Obtain state transition matrix if: \[ x= \begin{bmatrix} 0 &-1 \\-11 &-12 \end{bmatrix} x( \] using Laplace transformation.

6 M

6 (b)
With the help of general equation, explain concept of controllable canonical and observable canonical form of state space.

7 M

Answer any one question from Q7 and Q8

7 (a)
Enlist various terms in PID controller with sketch of output of P, PI, PD and PID controller for step input.

6 M

7 (b)
Find pulse transfer function of Fig. 3.

7 M

8 (a)
Explain any one application of PLC with ladder diagram.

6 M

8 (b)
Obtain unit step response of the system shown in Fig. 4

7 M

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