## Principles of Control Systems - May 2013

### 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.
**1 (a)** Obtain the transfer function of the lag network given in the figure below.

(5 marks)
**1 (b)** Explain how to find gain margin and phase margin from polar plot.(5 marks)
**1 (c)** Compare time response analysis with frequency response analysis.(5 marks)
**1 (d)** Explain various rules for block diagram reduction method to find out the transfer function.(5 marks)
**2 (a)** Find the total transfer function C/R using block diagram reduction technique for the figure below.

(10 marks)
**2 (b)** For a unity feedback control system the forward path transfer function is given by

Determine the steady state error of the system when the inputs are:-

(i) 5

(ii) 5t

(iii) 3t^{2}/2(10 marks)
**3 (a)** The characteristic equation for a certain feedback control system are given below. Determine the range of values of k for the system to be stable.

(i) s^{4}+20ks^{3}+5s^{2}+10s+15=0

(ii) s^{3}+2ks^{2}+(K+2)s+4=0(10 marks)
**3 (b)** Sketch the complete root locus for the system having open loop transfer function

(10 marks)
**4 (a)** A unity feedback system has open loop transfer function

Draw the bode plot and determine the gain margin and phase margin and state whether the system is stable or not?(10 marks)
**4 (b)** Sketch the polar plot and discuss the stability of the system represented by

(10 marks)
**5 (a)** Derive the value of K_{p} ,K_{v} and K_{p}a for type 0, type 1 and type 2 system.(5 marks)
**5 (b)** Show the location of poles of second order control system for various values of damping ratio. (5 marks)
**5 (c) ** A unity feedback system has open loop transfer function:

Using Nyquist stability criterion check whether the closed loop system is stable.If system is stable find gain margin and phase margin.(10 marks)
**6 (a)** Draw the diagram of basic lead and lag networks and derive their respective transfer functions.(10 marks)
**6 (b)** Explain different composite continuous controllers.(10 marks)

### Write shorts notes on the following:-

**7 (a)** Masons gain formula and its application.(5 marks)
**7 (b)** Stepper motor.(5 marks)
**7 (c) ** Effect of adding a zero to second order system.(5 marks)
**7 (d)** Synchro transmitter-receivers.(5 marks)