Attempt any five

1 (a)
Differentiate between open loop and closed loop control system.

4 M

1 (b)
Explain the Mason's Gain formula with reference to signal Flow Graph Technique.

4 M

1 (c)
Define and state the condition for controllability and observability for n

^{th}order MIMO system.
4 M

1 (d)
The characteristic equation for certain feedback control system is given below. Determine the range of value of K for the system to be stable.

S

S

^{3}+2ks^{2}+ (k+2)s+4=0
4 M

1 (e)
Define gain and phase margin. Draw approximate Bode plot for a stable system showing gain and phase margin.

4 M

1 (f)
Compare between Lead and Lay compensator.

4 M

2 (a)
Derive the output response for second order under-damped control system subjected to unit step input.

10 M

2 (b)
Find the transfer function C(S)/R(S) using Block diagram reduction Technique.

10 M

3 (a)
Find the Transfer function for the system show below.

4 M

3 (b)
What are the properties of state transition matrix?

4 M

3 (c)
For the system shown below, chose V

_{1}(t) and V_{2}(t) as state variales and write down the state equations satisfied by them. Bring these equations in the vector-matrix form

12 M

4 (a)
Examine the observability of the system given below using kalman's test. \[ \begin{bmatrix}x_1\\x_2 \\x_3 \end{bmatrix} = \begin{bmatrix}0 &1 &0 \\0 &0 &1 \\0 &-2 &-3 \end{bmatrix} \begin{bmatrix}x_1\\x_2 \\x_3 \end{bmatrix} = \begin{bmatrix}0\\0 \\1 \end{bmatrix} u = Ax+ Bu \]

8 M

4 (b)
Derive the expression for Peak resonant of a standard second order control system.

8 M

4 (c)
Explain the concept of ON/OFF controller.

4 M

5 (a)
For a unit feedback system the open loop transfer function is given by \[ G(S) = \dfrac {K}{S(S+2) (S^2+6S+25)} \] Sketch the root locus and find the value of K at which the system becomes unstable.

10 M

5 (b)
Explain Robust control and Adaptive control system.

10 M

6 (a)
Find polar plot for the transfer function given below \[ G(S) = \dfrac {1}{(1+S)(1+4S)} \]

5 M

6 (b)
Write a short note on PID controller.

5 M

6 (c)
Determine the stability of a system shown by following open loop transfer function using Nyquist criterion \[ G(s) \ H(s) = \dfrac {(4s+1)} {s^2 (s+1) (2s+1)} \]

10 M

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