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+2t². 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)