Solve any one question from Q.1(a,b)& Q.2(a,b)

1(a)
Explain open loop and closed loop systems with suitable examples.

6 M

1(b)
For a system with closed loop transfer function:\[G(s)=\frac{9}{\left ( s^2+4s+9 \right )}\] Determine rise time, peak time, peal overshoot, setting ime with 2% criterion.

6 M

2(a)
Determine \( \frac{C(s)}{D(s)}\)/ for the block diagram shown in Fig.1 using block diagram reduction:

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6 M

2(b)
For unity feedback system with open loop transfer function \(G(s)=\frac{k}{s\left ( s+5 \right )} \)/ determine k, peak overshoot, rise time, settling time with 2% criterion if damping factor is ξ=0.5.

6 M

Solve any one question from Q.3(a,b) & Q.4(a,b)

3(a)
Investigate the stability of system with characteristic equation: \[Q(s)=s^4+3s^3+4^s^2+3s+2=0.\]

4 M

3(b)
Draw Bode plot of a system with open loop transfer function\[G(s)\frac{100}{s\left ( s+2 \right )\left ( s+5 \right )}\]. Determine gain margin, phase margin, gain cross over frequency, phase cross over frequency and comments on stability.

8 M

4(a)
For an unity feedback system with open loop transfer function \( G(s)=\frac{4}{s\left ( s+2 \right )} \)/ determine damping factor, undamped natural frequency, resonant peak, resonant frequency.

4 M

4(b)
Sketch root locus of unity feedback system with open loop transfer function: \[G(s)=\frac{k}{s\left ( s+2 \right )\left ( s+6 \right )}\]

8 M

Solve any one question from Q.5(a,b) & Q.6(a,b)

5(a)
For a system with transfer function: \[G(s)\frac{2s^2+3s+1}{s^3+5s^2+7s+4}.\] Determine state model in controllable canonical and observable canonical form.

6 M

5(b)
Derive the expression for state transition matrix by Laplace transform method and state properties of state transition matrix.

7 M

6(a)
Determine the state transition matrix of:
\( A =\begin{bmatrix}
0 &1 \\
-4 & -5
\end{bmatrix} \)/ and abtain solution x(t) of state equation \(\dot{x}= Ax\ \text{if initial state is}\\x(0)=\begin{bmatrix}
1\\
0\end{bmatrix}. \)/

7 M

6(b)
Investigate state controllability and state obeservability if: \( A=\begin{bmatrix}
0 & 1 & 0\\
0& 0& 1\\
-4 & -6 & -8
\end{bmatrix}, B=\begin{bmatrix}
0\\
0\\
1\end{bmatrix},C=[1 \ 2\ 1].\)/

6 M

Solve any one question from Q.7(a,b) & Q.8(a,b)

7(a)
Explain PID controller with the help of its block diagram, equation and transfer function.

6 M

7(b)
Determine the pulse transfer function of the system shown in Fig.2 using first principles:

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7 M

8(a)
Sketch and explain block diagram of programmable logic controller (PLC).

6 M

8(b)
Determine the closed loop pulse transfer function \[\frac{C(z)}{R(z)}\] for the systme shown in Fig.3:

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7 M

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