Question Paper: Control Systems : Question Paper May 2014 - Electronics & Telecomm. (Semester 4) | Mumbai University (MU)
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## 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)