Control Systems - Dec 2012

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) Obtain the transfer function from the magnitude plot shown below:
(5 marks) 1 (b) What do you mean by steady state error? What information is contained in the specification K_v=1000?(5 marks) 1 (c) A unity feedback control system has an open loop transfer function
G(s)H(s)=K/[s(s²+4s+13)]. Determine:
(i) Centroid, Number and angle of Asymptotes.
(ii) Breakaway points, if any.(5 marks) 1 (d) Compare Absolute Stability and Relative Stability.(5 marks) 2 (a) Find the transfer function from the block diagram using block diagram reduction rules.
(10 marks) 2 (b) Derive the transfer function of field controlled dc servomotor.(10 marks) 3 (a) Construct the signal flow graph from the following set of equations and find the overall transmittance using Mason's Gain Formula.
x₂ = g₂₁x₁ + g₂₃x₃
x₃ = g₃₁x₁ + g₃₂x₂ + g₃₃x₃
x₄ = g₄₂x₂ + g₄₃x₃(10 marks) 3 (b) Sketch the root locus for a unity feedback control system with
G(s) = K/[s(s+1)(s+3)] and determine -
(i) K for marginal stability.
(ii) Frequency of oscillation for marginal stability.
(iii) K for damping ratio of 0.5.(10 marks) 4 (a) For a unity feedback system with open loop transfer function given below determine the range of K for stability
G(s) = K/[(s+2)(s+4)(s²+6s+25)](10 marks) 4 (b) Sketch the bode plot for
G(s)H(s) = 10/[s(1+0.1s)(1+0.5s)] and find
(i) Gain crossover frequency
(ii) Phasecrossover frequency
(iii) Gain margin
(iv) Phase margin.
Also comment on system stability.(10 marks) 5 (a) Derive the time response expression for a second order control system subjected to unit step input. (10 marks) 5 (b) Sketch the Nyquist plot for
G(s)H(s)=50/[(s+1)(s+2)]
and comment on the closed loop stability of the system.(10 marks) 6 (a) For a system with transfer function
G(s) = 16/[(s²+1.6s+16)]. Find:
(i) rise time
(ii) damped frequency of oscillation.
(iii) Peak time
(iv) peak overshoot
(v) Settling time.(10 marks) 6 (b) What is sensitivity? Explain the effect of system parameter variations on the sensitivity of open loop and closed loop control system.(10 marks)

Write shorts notes any two of the following:-

7 (a) Static error coefficients and steady state errors.(10 marks) 7 (b) Stepper motors.(10 marks) 7 (c) Error compensation techniques.(10 marks)