Question Paper: Control Systems : Question Paper May 2014 - Electronics & Telecomm (Semester 4) | Pune University (PU)
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## Control Systems - May 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 the rules of block diagram reduction techniques.(6 marks) 1 (b) f peak overshoot is 16.3% and peak time is 0.3023 seconds. Determine:
(1) damping factor,
(2) undamped natural frequency and <br? (3)="" settling="" time="" (for="" 2%="" tolerance)="" of="" the="" system.&lt;="" a="">

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(6 marks)
2 (a) Find the closed loop transfer function $$\dfrac {C(s)} {R(s)}$$ of system shown in Fig. 1 using block diagram reduction technique.

(6 marks) 2 (b) $$If G(s) \ H(s) = \dfrac {25}{s(s+5)},$$ obtain damping factor, un-damped and damped natural frequency, rise time, peak time, and settling time.(6 marks)

### Answer any one question from Q3 and Q4

3 (a) Comment on the stability of a system using Routh's stability criteria whose characteristic equation is:
s4+2s3+4s2+6s+8=0.
How many poles of systems lie in right half of s-plane?
(4 marks)
3 (b) $$If G(s) \ H(s) = \dfrac {24} {s(s+2)(s+12)},$$ construct the Bode plot and calculate gain crossover frequency, phase crossover frequency, gain margin, phase margin and comment on stability.(8 marks) 4 (a) Open loop transfer function of unity feedback system is $$G(s) = \dfrac {K}{s(s+3)(s+5)}$$ Sketch the complete root locus and find marginal gain.(8 marks) 4 (b) $$If G(s) \ H(s) = \dfrac {1} {s(s+1)},$$ determine the value of:
i) Resonance Peak and
ii) Resonance frequency.
(4 marks)

### Answer any one question from Q5 and Q6

5 (a) State any three advantages of state space approach over classical approach. Derive an expression to obtain transfer function from state model.(7 marks) 5 (b) Find Controllability and Observability of the system given by state model: $$A= \begin{bmatrix} 1 &1 &5 \\1 &-2 &2 \\5 &2 &-8 \end{bmatrix}, \ B=\begin{bmatrix} 5 \\ 1\\10 \end{bmatrix}, \ C=\begin{bmatrix} 10 &15 &11 \end{bmatrix}, \ D=[0]$$(6 marks) 6 (a) Explain canonical controllable and observable state model with any example/transfer function.(6 marks) 6 (b) Obtain the state transition matrix for the system with state equation: $$[x]= \begin{bmatrix} 0 &1 \\-8 &-9 \end{bmatrix}$$ using Laplace transformation.(7 marks)

### Answer any one question from Q7 and Q8

7 (a) Explain application of programmable logic controller for elevator system with ladder diagram.(6 marks) 7 (b) Find the pulse transfer function and impulse response of the system shown in Fig. 2.

(7 marks) 8 (a) Write the equation of PID controller and explain role of each action in short.(6 marks) 8 (b) Obtain pulse transfer function of the system shown in Fig. 3 using first (Starred Laplace) principle.

(7 marks)