## Principles of Control Systems - Dec 2014

### Electronics Engineering (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 any five

**1 (a)** Differentiate between open loop and closed loop control system.(4 marks)
**1 (b)** Explain the Mason's Gain formula with reference to signal Flow Graph Technique.(4 marks)
**1 (c)** Define and state the condition for controllability and observability for n^{th} order MIMO system.(4 marks)
**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^{3}+2ks^{2}+ (k+2)s+4=0(4 marks)
**1 (e)** Define gain and phase margin. Draw approximate Bode plot for a stable system showing gain and phase margin.(4 marks)
**1 (f)** Compare between Lead and Lay compensator.(4 marks)
**2 (a)** Derive the output response for second order under-damped control system subjected to unit step input.(10 marks)
**2 (b)** Find the transfer function C(S)/R(S) using Block diagram reduction Technique.
(10 marks)
**3 (a)** Find the Transfer function for the system show below.
(4 marks)
**3 (b)** What are the properties of state transition matrix?(4 marks)
**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 marks)
**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 marks)
**4 (b)** Derive the expression for Peak resonant of a standard second order control system.(8 marks)
**4 (c)** Explain the concept of ON/OFF controller.(4 marks)
**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 marks)
**5 (b)** Explain Robust control and Adaptive control system.(10 marks)
**6 (a)** Find polar plot for the transfer function given below $$ G(S) = \dfrac {1}{(1+S)(1+4S)} $$(5 marks)
**6 (b)** Write a short note on PID controller.(5 marks)
**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 marks)