## Control System Engineering - Jun 2014

### Electronics and Comm. Engg. (Semester 4)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1 (a)** Explain open loop and closed loop control system with suitable example &
gives its advantages and disadvantages.(7 marks)
**1 (b)** Find the transfer function of Fig.1 using Mason's gain formula.

IMAGE(7 marks)
**2 (a)** Explain the advantages of state space approach over classical methods and
obtain state variable equation.X=AX+BU and CX+DU Also draw the block diagram.(7 marks)
**2 (b)** Explain Rules for block diagram reduction technique.(7 marks)
**2 (c)** Write the differential equations for the mechanical system shown in Fig.2. Also
obtain an analogous electrical circuit based on force-current analogy.

IMAGE(7 marks)
**3 (a)** By means of Routh criterion, determine the stability of the system described by
characteristic equations.

(1) S^{4}+2S^{3}+8S^{2}+4S+3=0

(2) 3S^{4}+10S^{3}+5S^{2}+5S+2=0.(7 marks)
**3 (b)** Explain following terms with necessary diagrams.

(1) Delay Time (2) Rise Time (3) Peak Time

(4) Steady state error (5) Settling Time.(7 marks)
**3 (c)** Explain standard Test signals & derive equation of steady state error.(7 marks)
**3 (d)** A certain Feedback control system is described by the following transfer
Function

G(s) = K / S^{2} (S+20) (S+30) , H(s) =1

Determine steady state error coefficients & also determine the value of K to
limit the steady state error to 10 units due to input r(t) = 1+ 10t+20t^{2} .(7 marks)
**4 (a)** Discuss Nyquist's stability criterion.(7 marks)
**4 (b)** What are the Bode plots? With necessary diagrams explain the following terms.

(1) Gain cross over frequency

(2) Phase cross over frequency

(3) Gain Margin

(4) Phase Margin.(7 marks)
**4 (c)** Sketch the Root Locus of unity feedback control system with
G(s) = K/S(S+1)(S+3) and determine the value of K for Marginal stability.(14 marks)
**5 (a)** Write a short note on thermal system , its modeling and analysis for two
different inputs.(7 marks)
**5 (b)** Explain Rules for construction of Root Locus.(7 marks)
**5 (c)** What is Transfer function ? Discuss its properties, advantages & disadvantages
of it(7 marks)
**5 (d)** Find Polar Plots of G(s) = 1/ (1+P 1 S) (1+P_{2} S)(7 marks)