## Control Systems - Dec 2013

### 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)** Define sensitivity of a control system. How can we reduce the sensitivity of a closed loop system.(5 marks)
**1 (b)** Explain Hurwitz stability criterion and its disadvantages.(5 marks)
**1 (c) ** Define the following terms related to second order system subjected to unit step input.

(i) Rise time

(ii) Peak time.

(iii) Peak overshoot

(iv) Delay time.

(v) Settling time.(5 marks)
**1 (d)** What are the advantages of a Nyquist plot.(5 marks)
**2 (a)** If the second order control system has transfer function

F(s) = s^{2} + 24s + 9.

If a step input is applied to it, determine time domain specifications. Also sketch time response.(10 marks)
**2 (b)** Find the range of K to make the system stable for a unity feedback system.

(10 marks)
**3 (a)** Determine the transfer functions C/R_{1} and C/R_{2} from the given system below. Also find C/R.

(10 marks)
**3 (b)** Find the transfer function of the following system using signal flow graph.

(10 marks)
**4 (a)** Draw the root locus for the system with

G(s)H(s) = K/[s(s+3)(s+6)]. Obtain the value of K when ?=0.6 from root locus. Also determine the value of K for marginal stability and critical damping.(10 marks)
**4 (b)** For a unity feedback system: G(s) = 200/[s(s+8)] and r(t)=2t, determine steady state error. If it is desired to reduce the existing error by 5%, find new value of gain of system.(10 marks)
**5 (a)** A unity feedback system has a loop gain

G(s)H(s)=60/[(s+4)(s^{2}+2s+5)]. Determine the system stability using Nyquist plot.(10 marks)
**5 (b)** Compare open loop control system and closed loop control system with at least 3 examples.(10 marks)
**6 (a)** Use Bode plot to determine the frequency response of system. H(s)=1 and

(10 marks)
**6 (b)** A unity feedback control system has

G(s) = K/[(s+4)^{3}]. Determine the range of K for system stability.(10 marks)

### Write shorts notes any **two** of the following:-

**7 (a)** Stepper motor construction and its applications in control system.(10 marks)
**7 (b)** State variable model with an example.(10 marks)
**7 (c) ** Error compensation techniques.(10 marks)