## Principles of Control Systems - May 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 four:-

**1 (a)** Differentiate between feedback and feed forward control system.(5 marks)
**1 (b)** What is a compensator? Why is it required?(5 marks)
**1 (c)** What are the properties of state transition matrix?(5 marks)
**1 (d)** Explain the concept of absolute, relative and robust stability.(5 marks)
**1 (e)** Find the transfer function for following network.
(5 marks)
**2 (a)** Obtain the transfer function of the mechanical system.
(10 marks)
**2 (b)** Consider unity feedback control system with an open loop transfer function of - $$ G(s) =\dfrac {k(s+1)(s+2)}{(S+0.1)(s-1)} $$

i) Plot the root loci showing asymptotes, centroid break away point, the gain at which root locus crosses jw axis.

ii) Find value of gain for which a closed system is critically damped.(10 marks)
**3 (a)** A unity feedback control system is characterized by the open loop transfer function $$ G(s) = \dfrac {k(s+13)}{s(s+3)(s+7)} $$ using the Routh criterion, calculate the range of values of k for system to be stable.(10 marks)
**3 (b)** Write a note on advances in control systems.(10 marks)
**4 (a)** Obtain the state variable model of the transfer function- $$ \dfrac {Y(s)}{U(s)} = \dfrac {s^2 + 3s+3}{s^2 + 2^2s+3s+1} $$(10 marks)
**4 (b)** Sketch the Bode plot for the open loop transfer function given by - $$ G(s) \ H(s) = \dfrac {0.5 (1+5s)}{s^2 (1+0.5s)} $$(10 marks)
**5 (a)** Find rise time, setting time and peak overshoot for the system given by transfer function - $$ G(s) = \dfrac {25}{(s^2 + 8s +25)} $$(5 marks)
**5 (b)** Using Nyquist criterion, determine the closed loop system having following open loop transfer function is stable or not. If not, find the number of poles in right half of s plane- $$ G(s) \ H(s) = \dfrac {1+4s}{s^2 (1+s)(1+2s)} $$(5 marks)
**5 (c)** Check controllability and observability for the system- $$ x= \begin{bmatrix}1 &2 &1 \\0 &1 &3 \\1 &1 &1 \end{bmatrix} x+ \begin{bmatrix} 1\\0 \\2 \end{bmatrix} u \\ y = \begin{bmatrix}1 &3 &0 \end{bmatrix} x $$(10 marks)
**6 (a)** Explain the concept of on-off controller using example.(5 marks)
**6 (b)** Compare lead-lag compensator.(5 marks)
**6 (c)** Obtain the overall transfer function from signal flow graph.
(10 marks)