## Control Systems - Dec 2014

### 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.
**1 (a)** Compare open loop and closed loop system with suitable examples.
(5 marks)
**1 (b)** Draw the step response for an under-damped second order system with damping ratio 0.2, 1, 1.2 respectively.(5 marks)
**1 (c)** The transfer function of a system is given by $$ T(s)= \dfrac {k(s+6)} {s(s+2)(s+5)(s^2+7s+1^2)} $$

Determine i) Poles ii) Zeros iii) Characteristic equation(5 marks)
**1 (d)** Define Hurwitz stability criteria with its advantages and disadvantages. Give suitable example.(5 marks)
**2 (a)** Determine transfer function C(S)/R(CS) of the system shown in fig.
(10 marks)
**2 (b)** Using Masons gain formula, find C(S)/R(CS) of SFG shown in fig.
(10 marks)
**3 (a)** Show the pole zero location and the unit step response of the following second order control system-

i) Under-damped

ii) Over-damped

iii) Critical damped

iv) Undamped(10 marks)
**3 (b)** For the network shown in fig obtain -
i) Transfer function
ii) State variable model
(10 marks)
**4 (a)** Write the differential equation for the mechanical system shown in fig and explain force voltage analogy.
(10 marks)
**4 (b)** The open loop transfer function of a unity feedback system is given by [ G(S)=dfrac {K(s+9)}{s(s^2+4s+11)} ] Sketch the Root locus of the system.(10 marks)
**5 (a)** Sketch the polar for the open loop transfer function given by -

[ G(s) = dfrac {1}{s^2(1+s)(1+2s)} ](10 marks)
**5 (b)** A unity feedback system has [ G(s)=dfrac {40(s+2)}{s(s+1)(s+5)} ] Determine

i) Type of system

ii) All error coefficients

iii) Error for ramp I/P with magnitude-3.(10 marks)
**6 (a)** Sketch the bode plot for the following Transfer function [ G(s)=dfrac {75(1+0.25)}{s(s^2+16s+100)} ](10 marks)
**6 (b)** What is Adaptive Control? Explain any one adaptive control methods.(5 marks)
**6 (c)** Explain controllability and observability.(5 marks)