Question Paper: Control Systems : Question Paper Jun 2015 - Electronics & Telecom Engineering (Semester 4) | Pune University (PU)
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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)} $$Find Resonance peak and Resonance frequency,\lt/span\gt\ltspan class='paper-ques-marks'\gt(4 marks)\lt/span\gt \lt/span\gt -------------- \ltspan class='paper-comments'\gt ### Answer any one question from Q5 and Q6 \lt/span\gt\ltspan class='paper-question'\gt\ltspan class='paper-ques-desc'\gt\ltb\gt5 (a)\lt/b\gt Obtain transfer function of state model if:$$ 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)