## Control Systems - Dec 2015

### Electronics & Telecomm. (Semester 4)

TOTAL MARKS: 80

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Assume data if required.

(4) Figures to the right indicate full marks.
**1 (a)** Define rise time.(5 marks)
**1 (b)** Define gain margin and phase margin.(5 marks)
**1 (c)** What are the difficulties encountered in applying Routh stability criterion?(5 marks)
**1 (d)** Find out response of give system for a unit step I/P.
(5 marks)
**2 (a)** Obtain the transfer function of the mechanical system shown in Fig. 11A (i).
(10 marks)
**2 (b)** Draw a signal flow graph for the system shown in fig 11a (ii) and hence obtain the transfer function using Mason's gain formula.
(10 marks)
**3 (a)** Derive the expression for step response of second-order under damped system.(10 marks)
**3 (b)** Find the impulse response of the second order system whose transfer function $ G(s) = \dfrac {9}{(s^2 + 4s+ 9)} $(10 marks)
**4 (a)** A unity feedback system is characterized by an open loop transfer function $ G(s) = \dfrac {K} {s(s+10)}. $ Determine the gain K so that the system will have a damping ratio of 0.5. For this values of K determine settling time peak over shoot and time to peak over shoot for a unit step input.(10 marks)
**4 (b)** An unity feedback system is given as $ G(s) = \dfrac {1} {s(s+1)}. $ The input to the system is described by r(t)=4+6t+2t^{2}. Find the generalized error coefficients and the steady state error.(10 marks)
**5 (a)** Sketch the Bedplate showing the magnitude in dB and phase angle in degree as a function of log frequency for the transfer function given by $ G(s) = \dfrac {10} {s(1+0.5s) (1+0.1s)} $ and hence determine the gain margin and the phase margin of the system.(10 marks)
**5 (b)** Sketch the root locus for n unity feedback system with open loop transfer function $ G(s) = \dfrac {K}{s(s^2 + 8s + 32)}. $(10 marks)
**6 (a)** Using Routh Hurwitz criterion for the unity feedback system with open loop transfer function $ G(s) = \dfrac {K}{s(s+1) (s+2) (s+5)} $ find

i) the range of k for stability

ii) the value of k for marginally stable

iii) the actual location of the closed loop poles when the system is marginally stable.(10 marks)
**6 (b)** Explain controllably and observably.(10 marks)