## Principles of Control Systems - Dec 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.

### Answer any **five** of the following:-

**1 (a)** How to find gain margin and phase margin using bode plot?(4 marks)
**1 (b)** Compare open loop control system and closed loop control systems and give examples.(4 marks)
**1 (c) ** Compare two stability methods:-

(i) Root locus

(ii) Routh's criterion.(4 marks)
**1 (d)** Draw the step responses of a standard second order undamped, under damped and critically damped system. Also show pole locations of these systems.(4 marks)
**1 (e)** Define 'Type' and 'Order' of the system. Hence determine type and order of control system with

(4 marks)
**1 (f)** Explain Hurwitz stability criterion. What are its disadvantages?(4 marks)
**2 (a)** Find the transfer function C(s)/(R(s) using block diagram reduction technique.

(10 marks)
**2 (b)** Derive the expression for output response of standard second order under damped system.(10 marks)
**3 (a)** Consider the following block diagram shown. Draw its equivalent signal flow graph and find its transfer function C(s)/R(s) using masons gain rule.

(10 marks)
**3 (b)** Find all the error coefficients for unity feedback systems having transfer function as

Calculate the type of system in each case.

(a)

(b)

(10 marks)
**4 (a)** Using Rouths stability criterion, determine the number of roots on imaginary axis for the system

s^{6}+4s^{5}+3s^{4}-16s^{2}-64s-48=0

and comment on stability of given system.(10 marks)
**4 (b)** Sketch the root locus for the system having

Obtain the value of K when damping ratio = 0.5 from the root locus. (10 marks)
**5 (a)** Sketch the Bode plot for the system.

Comment on system stability. (10 marks)
**5 (b)** Sketch the polar plot for the system having transfer function

(10 marks)
**6 (a)** Sketch the nyquist plot for

G(s)H(s)=50/[(s+1)(s+2)]

And comment on closed loop stability of system.(10 marks)
**6 (b)** Derive the transfer function of armature controlled dc servomotor and obtain the resulting block diagram.(10 marks)

### Write short notes on the following:-

**7 (a)** Synchros.(7 marks)
**7 (b)** Correlation between time domain and frequency domain specifications.(7 marks)
**7 (c) ** PI and PD controllers.(7 marks)