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Control Systems - Jun 2015
Electronics & Telecom Engineering (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.
Answer any one question from Q1 and Q2
1 (a) Give the various terminology of electrical system and its analogous quantities based on force-current analogy.(6 marks) 1 (b) Write the differential equations of system shown in Fig. 1. Also find $$ \dfrac {X_1 (s)} {F(s)} $$ (6 marks) 2 (a) Obtain transfer function of the system shown in Fig. 2: (6 marks) 2 (b) The open loop transfer function of unity feedback system is $$ G(s) = \dfrac {k_1} {s(\tau s +1)} \ with \ k, \ \tau>0 $$ with a given of k1, the peak overshoot was found to be 80%. if the overshoot is decreased up to 20% by new gain k2 find k2 in terms of k1.(6 marks)
Answer any one question from Q3 and Q4
3 (a) Using Routh's criteria, comment on the stability if characteristic equation is:
S5+2s4=3s3+8s<ssup>2+s+1=0</ssup>(4 marks)
3 (b) Draw the Bode plot and obtain gain margin, phase margin, gain crossover frequency and phase crossover frequency if: $$ G(s)\cdot H(s)= \dfrac {50,000 (s+10)}{s(s+1)(s+500)}\lt/span\gt\ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt
\lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt4 (a)\lt/b\gt $$ if\ G(s) H(s) = \dfrac {k}{s(s+1)(s+10)} $$ sketch the complete Root locus and comment on the stability.\lt/span\gt\ltspan class='paper-ques-marks'\gt(8 marks)\lt/span\gt
\lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt4 (b)\lt/b\gt $$ If \ G(s) \ H(s)= \dfrac {1}{s(s+1)} $$ Find Resonance peak and Resonance frequency,\lt/span\gt\ltspan class='paper-ques-marks'\gt(4 marks)\lt/span\gt
\lt/span\gt
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\ltspan class='paper-comments'\gt
### Answer any one question from Q5 and Q6
\lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt5 (a)\lt/b\gt Obtain transfer function of state model if: $$ A=\begin{bmatrix}
0 &1 &0 \0
&0 &1 \-6
&-11 &-6
\end{bmatrix}, \ B=\begin{bmatrix}
0\0
\1
\end{bmatrix}, \ C=\begin{bmatrix}
1 &0 &0
\end{bmatrix}, \ D=[0] $$\lt/span\gt\ltspan class='paper-ques-marks'\gt(6 marks)\lt/span\gt
\lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt5 (b)\lt/b\gt Find controllability and observability of the state model: $$ A=\begin{bmatrix}
1 &0 &1 \0
&1 &1 \1
& 1 &1
\end{bmatrix}, \ B=\begin{bmatrix}
1\1
\1
\end{bmatrix}, \ C=\begin{bmatrix}
1 &1 &1
\end{bmatrix}, \ D=[0]$$\lt/span\gt\ltspan class='paper-ques-marks'\gt(7 marks)\lt/span\gt
\lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt6 (a)\lt/b\gt Obtain state transition matrix if: $$ x= \begin{bmatrix} 0 &-1 \-11 &-12 \end{bmatrix} x( $$ using Laplace transformation.(6 marks)
6 (b) With the help of general equation, explain concept of controllable canonical and observable canonical form of state space.(7 marks)
Answer any one question from Q7 and Q8
7 (a) Enlist various terms in PID controller with sketch of output of P, PI, PD and PID controller for step input.(6 marks) 7 (b) Find pulse transfer function of Fig. 3. (7 marks) 8 (a) Explain any one application of PLC with ladder diagram.(6 marks) 8 (b) Obtain unit step response of the system shown in Fig. 4 (7 marks)