Question Paper: Control Systems : Question Paper Dec 2014 - Electronics & Telecom Engineering (Semester 4) | Pune University (PU)
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## Control Systems - Dec 2014

### 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) Explain open loop and closed loop systems with real time example.(6 marks) 1 (b) A unity feedback system has open loop transfer function: $$G(s) = \dfrac {K} {s(s+10)}$$ Determine 'K' so that damping factor is 0.5. For this value of 'K' determine:
(1) Location of closed loop poles,
(2) Peak overshoot, and
(3) Peak time. Assume input is unit step
(6 marks)
2 (a) Find closed loop transfer function $$\dfrac {y(s)}{x(s)} \ if \ G_1 = G_2 = \dfrac {1}{s+1} \ and \ G_3=G_4=s+1, \ H_1=1$$ for system shown in Fig Q2 (a) using block diagram reduction technique. (6 marks) 2 (b) If open loop transfer function is $$G(s) = \dfrac {1}{s+1}$$, obtain unit step response. Also find output at time t=0,1,2,3,4,5. Assume unity feedback and G(s) is in closed loop.(6 marks)

### Answer any one question from Q3 and Q4

3 (a) Comment on stability using Routh criteria if characteristic equation is:
Q(s) = s5+2s4+3s3+4s2+5s+6=0
How many poles lie in right half of s-plane?
(4 marks)
3 (b) Construct Nyquist plot and find phase frequency and gain margin if: $$G(s)\cdot H(s) = \dfrac {1} {s(s+1)(s+2)}$$ Also comment on stability.(8 marks) 4 (a) $$If \ G(s) \ H(s)= \dfrac {k(s+2)}{s(s+1)(s+3)}.$$ construct root locus and comment on stability of system.(7 marks) 4 (b) Obtain resonance peak and resonance frequency if: $$G(s)\cdot H(s)= \dfrac {21} {s(s+5)} \ with \ H(s) =1$$(4 marks) 5 (a) Obtain controllable and observable canonical state model if: $$G(s) = \dfrac {y(s)}{u(s)} = \dfrac {s^3 + 2s^2 + 5s +1}{s^4 = 4s^3 + 4s^2 + 7s +2}$$(6 marks)

### Answer any one question from Q5 and Q6

5 (b) Find controllability and observability if: $$A=\begin{bmatrix} -2 &1 &0 \\1 &-3 &2 \\10 &0 &-8 \end{bmatrix}, \ B=\begin{bmatrix} 0\\0.1 \\1 \end{bmatrix}, \ C=\begin{bmatrix} 1 &0 &1 \end{bmatrix}, \ D=[0]$$(7 marks) 6 (a) List advantages of state space over transfer function.(6 marks) 6 (b) Obtain state transition matrix if: $$x= \begin{bmatrix} 0 &-3 \\1 &-4 \end{bmatrix} x(t)$$(7 marks)

### Answer any one question from Q7 and Q8

7 (a) Explain Ladder concept in PLC. Draw and explain different symbols used to construct ladder.(6 marks) 7 (b) Find pulse transfer function and impulse response for the system shown in Fig. Q. 7(b). (7 marks) 8 (a) Write PID equation. For unit step input sketch the response of P, I, D action of PID.(6 marks) 8 (b) Write a note on digital control system with help of suitable block diagram.(7 marks)