Question Paper: Control Systems : Question Paper May 2015 - Electronics & Telecomm. (Semester 4) | Mumbai University (MU)
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## Control Systems - May 2015

### Electronics & Telecomm. (Semester 4)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.

### Attempt the following:

1 (a) Differentiate open-loop and closed-loop systems. (5 marks)

1 (b) Explain Mason's gain formula. (5 marks)

1 (c) What is optimal control? What the advantages and disadvantages of optimal control. (5 marks)

1 (d) Define gain and phase margin. Explain how to find gain margin and phase margins using polar plot. (5 marks)

2 (a) Find the transfer function of the block diagram shown in figure by using block, diagram reduction method. (10 marks)

2 (b) Construct the root locus having following open loop transfer function. $$G(s)H(s) = \dfrac {K(s+4)} {(s+0.5)^2(s+2)}$$ Find range of K for the system to be stable. (10 marks)

3 (a) Find the transfer function of the electrical network shown in figure. Also obtain the state space model. (10 marks)

3 (b) Check whether the system is stable or not. $$S^6 + 3S^5 + 2S^4 + 9S^3 + 5S^2 + 12S + 20 = 0$$ (5 marks)

3 (c) State and prove properties of state transmission matrix. (5 marks)

4 (a) The open-loop transfer function of control system is $$G(s) H(s) = \dfrac {0.5s+1} {s(1+0.1s)(1+0.2s)}$$ Determine approximate value of gain and phase margins. (10 marks)

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 marks)

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 marks)

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

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

6 (a) Explain the correlation between time and frequency domain specifications. (8 marks)

6 (b) Derive the equation for solution of homogeneous system. (7 marks)

6 (c) Explain different time domain specifications. (5 marks)

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