Answer any one question from Q1 and Q2

1 (a)
Explain the rules of block diagram reduction techniques.

6 M

1 (b)
f peak overshoot is 16.3% and peak time is 0.3023 seconds. Determine:

(1) damping factor,

(2) undamped natural frequency and

(1) damping factor,

(2) undamped natural frequency and

6 M

2 (a)
Find the closed loop transfer function \[ \dfrac {C(s)} {R(s)} \] of system shown in Fig. 1 using block diagram reduction technique.

6 M

2 (b)
\[ If G(s) \ H(s) = \dfrac {25}{s(s+5)},\] obtain damping factor, un-damped and damped natural frequency, rise time, peak time, and settling time.

6 M

Answer any one question from Q3 and Q4

3 (a)
Comment on the stability of a system using Routh's stability criteria whose characteristic equation is:

s

How many poles of systems lie in right half of s-plane?

s

^{4}+2s^{3}+4s^{2}+6s+8=0.How many poles of systems lie in right half of s-plane?

4 M

3 (b)
\[ If G(s) \ H(s) = \dfrac {24} {s(s+2)(s+12)}, \] construct the Bode plot and calculate gain crossover frequency, phase crossover frequency, gain margin, phase margin and comment on stability.

8 M

4 (a)
Open loop transfer function of unity feedback system is \[ G(s) = \dfrac {K}{s(s+3)(s+5)} \] Sketch the complete root locus and find marginal gain.

8 M

4 (b)
\[ If G(s) \ H(s) = \dfrac {1} {s(s+1)}, \] determine the value of:

i) Resonance Peak and

ii) Resonance frequency.

i) Resonance Peak and

ii) Resonance frequency.

4 M

Answer any one question from Q5 and Q6

5 (a)
State any three advantages of state space approach over classical approach. Derive an expression to obtain transfer function from state model.

7 M

5 (b)
Find Controllability and Observability of the system given by
state model: \[ A= \begin{bmatrix}
1 &1 &5 \\1
&-2 &2 \\5
&2 &-8
\end{bmatrix}, \ B=\begin{bmatrix}
5 \\ 1\\10
\end{bmatrix}, \ C=\begin{bmatrix}
10 &15 &11
\end{bmatrix}, \ D=[0] \]

6 M

6 (a)
Explain canonical controllable and observable state model with any example/transfer function.

6 M

6 (b)
Obtain the state transition matrix for the system with state equation: \[ [x]= \begin{bmatrix}
0 &1 \\-8
&-9
\end{bmatrix} \] using Laplace transformation.

7 M

Answer any one question from Q7 and Q8

7 (a)
Explain application of programmable logic controller for elevator system with ladder diagram.

6 M

7 (b)
Find the pulse transfer function and impulse response of the system shown in Fig. 2.

7 M

8 (a)
Write the equation of PID controller and explain role of each action in short.

6 M

8 (b)
Obtain pulse transfer function of the system shown in Fig. 3 using first (Starred Laplace) principle.

7 M

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