## Control Systems - May 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)** Define relative,absolute and robust stability of the system.(5 marks)
**1(b)** What is gain and phase margin?Explain how to find gain phase margin by using polar plot.(5 marks)
**1(c)** Differentiate open loop and closed loop system.(5 marks)
**1(d)** What is damping ratio? Show the location of roots in s plane for different values of damping ratio.(5 marks)
**2(a)** Derive the transfer function of electromechanical system shown in fig:
(10 marks)
**2(b)** Find the transfer function of the electrical network in figure
(10 marks)
**3(a)** Find the closed loop transfer of the system whose block diagrams is given in figure;
(10 marks)
**3(b)** State and prove properties of state transition matrix.(5 marks)
**3(c)** What is optimal control?Why optimal control is needed?(5 marks)
**4(a)** Construct a state model of the system shown infig
(10 marks)
**4(b)** Predict the controllability and observability for the system

[x=egin{bmatrix}
0 & 1 & 0\
3& 0& 2\
-12&-7 &-6
end{bmatrix}x +egin{bmatrix}
0\
0\
0
end{bmatrix}u$$\ltbr\gty=[1 2 0]dx\lt/span\gt\ltspan class='paper-ques-marks'\gt(10 marks)\lt/span\gt
\lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt5(a)\lt/b\gt Construct the root locus for the system having following open loop transfer function:\ltbr\gt[G(s)H(s)=dfrac{k}{(s+3)(s+5)(s^{2}+2s+2)}\lt/span\gt\ltspan class='paper-ques-marks'\gt(10 marks)\lt/span\gt
\lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt5(b)\lt/b\gt Construct the bode plot for the following transfer function:\ltbr\gt[G(s).H(s)=dfrac{10(s+10)}{s(s+10)(s+5)}$$(10 marks)
**6(a)** What is adaptive control? Explain one method of adaptive control.(7 marks)
**6(b)** Explain how the stability of the system can be analysed Using Nyquist Criterion.(7 marks)
**6(c)** Explain the time domain specifications.(6 marks)