Question Paper: Feedback Control System Question Paper - May 2017 - Instrumentation Engineering (Semester 4) - Mumbai University (MU)
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Feedback Control System - May 2017

MU Instrumentation Engineering (Semester 4)

Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

Solve any four question from Q.1(a, b, c, d, e)

1(a) Compare open loop and closed system. 5 marks

1(b) Explain principle of superposition and homogeneity. 5 marks

1(c) Explain regenerative feedback. 5 marks

1(d) Explain co-rrelation between time and frequency reponse. 5 marks

1(e) What is the effect of adding a zero to a system 5 marks

2(a) A unity feedback control system has an open loop transfer function G(s)ks(s2+4s+13)G(s)ks(s2+4s+13) G(s)\frac{k}{s\left ( s^{2} +4s+13\right )}/ sketch the roof locus plot of the system. Find the value of k and frequency at which the root loci cross the jw axis. 5 marks

2(b) Obtain the overall transfer functions C/R from the signal flow graph shown in figure.
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5 marks

3(a) Write the differential equations governing the behaviour of mechanical system shown in figure. Also obtain an analogous electrical circuit based on force-current analogy.
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5 marks

3(b) Sketch the Bode plot and determine the gain cross over frequency for the transfer function given below. G(s)=75(1+0.2s)s(s2+16s+13)G(s)=75(1+0.2s)s(s2+16s+13) G(s)=\frac{75\left ( 1+0.2s \right )}{s\left ( s^{2} +16s+13\right )} / 5 marks

4(a)(i) Sketch the polar plot of transfer function given below. G(s)=1(1+s)(1+2s)G(s)=1(1+s)(1+2s) G(s)=\frac{1}{\left ( 1+s \right )\left ( 1+2s \right )} / 5 marks

4(a)(ii) Explain any one thermal system and also write its difference equation. 5 marks

4(b) Using the block diagram reduction techniques find the closed loop transfer function of the system given below
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5 marks

5(a) The characteristic equations for a certain feedback control system are given below. Determine the range of k for system to be stable.
&i)s^{3}+2ks^{2}+\left ( 2+k \right )s+4 = 0 \\&ii) s^{4}+20ks^{3}+5s^{2}+10s+15 =0&i)s^{3}+2ks^{2}+\left ( 2+k \right )s+4 = 0 \\&ii) s^{4}+20ks^{3}+5s^{2}+10s+15 =0 &i)s^{3}+2ks^{2}+\left ( 2+k \right )s+4 = 0 \\ &ii) s^{4}+20ks^{3}+5s^{2}+10s+15 =0 /
5 marks

5(b) The closed loop transfer function of the C(s)R(s)=ω2ns2+2ωnξns+ω2nC(s)R(s)=ωn2s2+2ωnξns+ωn2 \frac{C(s)}{R(s)}=\frac{\omega _{n}^{2}}{s^{2}+2\omega _{n}\xi ns+\omega _{n}^{2}} /
obtain the equation of output response c(t) for the unit step input for underdamped condition.
5 marks

6(a) i) Explain the dominent condition
ii) Explain Nquist stability criterion
5 marks

6(b) For the system represented by the following equations find the transfer functions X(s) U(s) by signal flow graph technique. <merror><mtext>&x=x_{1}+\beta _{3}u \&x_{1}=-a_{1}x_{1}+x_{2}+\beta _{2}u\&x_{2}=-a_{2}x_{1}+\beta 1\mu</mtext></merror></math>" role="presentation" style="font-size: 125%; text-align: center; position: relative;">&x=x_{1}+\beta _{3}u \
&x_{1}=-a_{1}x_{1}+x_{2}+\beta _{2}u\
&x_{2}=-a_{2}x_{1}+\beta 1\mu
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><merror><mtext>&x=x_{1}+\beta _{3}u \&x_{1}=-a_{1}x_{1}+x_{2}+\beta _{2}u\&x_{2}=-a_{2}x_{1}+\beta 1\mu</mtext></merror></math>
<script type="math/tex; mode=display" id="MathJax-Element-6">&x=x_{1}+\beta _{3}u \ &x_{1}=-a_{1}x_{1}+x_{2}+\beta _{2}u\ &x_{2}=-a_{2}x_{1}+\beta 1\mu </script>
5 marks

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