## 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)