MU Control Systems - May 2015 Exam Question Paper

MU Electronics and Telecom Engineering (Semester 4)
Control Systems
May 2015

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

Attempt the following:

1 (a) Differentiate open-loop and closed-loop systems.

5 M

1 (b) Explain Mason's gain formula.

5 M

1 (c) What is optimal control? What the advantages and disadvantages of optimal control.

5 M

1 (d) Define gain and phase margin. Explain how to find gain margin and phase margins using polar plot.

5 M

2 (a) Find the transfer function of the block diagram shown in figure by using block, diagram reduction method.

10 M

2 (b) Construct the root locus having following open loop transfer function.

G (s) H (s) = \frac{K (s + 4)}{(s + 0.5)^{2} (s + 2)}

$G(s)H(s) = \dfrac {K(s+4)} {(s+0.5)^2(s+2)}$ Find range of K for the system to be stable.

10 M

3 (a) Find the transfer function of the electrical network shown in figure. Also obtain the state space model.

10 M

3 (b) Check whether the system is stable or not.

S^{6} + 3 S^{5} + 2 S^{4} + 9 S^{3} + 5 S^{2} + 12 S + 20 = 0

$S^6 + 3S^5 + 2S^4 + 9S^3 + 5S^2 + 12S + 20 = 0$

5 M

3 (c) State and prove properties of state transmission matrix.

5 M

4 (a) The open-loop transfer function of control system is

G (s) H (s) = \frac{0.5 s + 1}{s (1 + 0.1 s) (1 + 0.2 s)}

$G(s) H(s) = \dfrac {0.5s+1} {s(1+0.1s)(1+0.2s)}$ Determine approximate value of gain and phase margins.

10 M

4 (b) "For the system described by the following state equation, determine the step response of the system.

$\dot {x} = \begin{bmatrix}-2 &1 \\1 &-2 \end{bmatrix}x + \begin{bmatrix} 1\\1 \end{bmatrix}u; \ \ y=[0 \ 1]u$ "

10 M

5 (a) "Determine the controllability and observability properties of the following system

$\dot {x} = \begin{bmatrix} 1 &1 &0 \\0 &-2 &1 \\0 &0 &-1 \end{bmatrix}x + \begin{bmatrix}0\\1 \\-2 \end{bmatrix}u; \ \ y=[1 \ 0 \ ]x$ "

10 M

5 (b) Write a short note on stability analysis using Nyquist ctriterior.

5 M

5 (c) Write a short note on adaptive control.

5 M

6 (a) Explain the correlation between time and frequency domain specifications.

8 M

6 (b) Derive the equation for solution of homogeneous system.

7 M

6 (c) Explain different time domain specifications.

5 M

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