Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

Solve any one question from Q.1(a,b) &Q.2(a,b)
1(a) Obtain the transfer function of system represented by the signal flow graph shown in figure no. 1.
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6 M
1(b) For the system with closed loop transfer function $$G(s)=\frac{25}{s^{2}+8s+25}$$/ determine damping factor, undamped natural frequency, rise time, peak time, peak overshoot and settling time with 2% tolerance band.
6 M

2(a) Obtain the transfer function of system represented by the block diagram shown in Figure No. 2.
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6 M
2(b) For the unity beedback system with open loop transfer function $G(s)=\frac{100\left ( s+2 \right )}{s\left ( s+5 \right )\left ( s+10 \right )}$ determine static error constants and steady state error if input is r(t) = 1 + t.
6 M

Solve any one question from Q.3(a,b) &Q.4(a,b)
3(a) Investigate the stability of a system having closed loop characteristics equation: $Q(s)=s^{3}+7s^{2}+10s+k=0 \ \text{and}\ \ \text{find} \ K_{mar}\ \text{and} \ W_{mar^{.}}$
4 M
3(b) For the unity feedback system with open loop transfer function $$G(s)= \frac{20}{s\left ( s+1\right )\left ( s+10 \right ),}$$/
sketch Nyquist plot and investigate stability.
8 M

4(a) Determine damping factor, undamped natrural frequency, resonant peak and resonant frequency for the system with closed loop transfer function:$G(s)= \frac{100}{s^{2}+10s+100}$
4 M
4(b) Sketch root locus of a system wih open loop transfer function $G(s)H(s)= \frac{K}{s\left ( s+4\right )\left ( s+6 \right ).}$
8 M

Solve any one question from Q.5(a,b) &Q.6(a,b)
5(a) Obtain controllable canonical and obserable canonical state models for the system with transfer function:$G(s)= \frac{s^{2}+3s+5}{s^{3}+5s^{2}+9}$
6 M
5(b) Investigate for complete state controllability and state observability of system with state space model matrices:
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7 M

6(a) Derive formula of state transition matrix and state any four properties.
7 M
6(b) Obtain physical variable state model of the system shown in Figure No.3.
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6 M

Solve any one question from Q.7(a,b) &Q.8(a,b)
7(a) Determine pulse transfer function of a system shown in Figure No.4, using first principle (starred Laplace transform)
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7 M
7(b) Sketch step and ramp reponses of P, PI & PID control actions.
6 M

8(a) Determine pulse transfer function shown in Figure No.5.
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7 M
8(b) Obtain ladder diagram for a 3-input two output system with boolean expressions: \begin{align*} Y_{1}=A\bar{B}C+A\ B\ \bar{C}\\ Y_{2}=\bar{A}\ \bar{B}\ \bar{C}+ A\ B.\end{align*}
6 M

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