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>[/itex]" 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>[/itex]
<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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