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Control Systems - Jun 2014
Electronics & Communication (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.
1 (a) Explain with examples open loop and closed loop control system. List merits and demerits of both.(10 marks)
1 (b) Draw the electrical network based on torque-current analogy give all the performance equation for the Fig. Q1(b).
(10 marks)
2 (a) Obtain the T.F. of the system using block diagram reduction method.
(10 marks)
2 (b) Obtain the transfer function using signal flow graph. By Mason's gain formula.
(10 marks)
3 (a) Draw the transient response characteristics of a control system to a unit step input and define the following: i) Delay time; ii) Rise time; iii) Peak time; iv) Maximum overshoot; v) Settling time.(6 marks)
3 (b) Derive the expression for peak time tp for a second order system for step input.(4 marks)
3 (c) The response of a servo mechanism is c(t)=1+0.2e-50t-1.2e-10t when subjected to a unit step input. Obtain an expression for closed loop transfer function. Determine the un-damped natural frequency and damping ratio.(4 marks)
3 (d) The open loop transfer function of a unity feedback system is given by $$ G(s)= \dfrac {K}{S}(ST+1) $$ where k and T are positive constant. By what factor should the amplifier, gain 'K' be reduced so that the peak, overshoot of unit step response of the system is reduced from 75% to 25%.(6 marks)
4 (a) Explain Routh-Hurwitz's criterion in stability of a control system.(4 marks)
4 (b) The characteristics equation for certain feedback control system are given below. Determine the system is stable or not and find the value of for a stable system S3+3ks2+(k+2)s+4=0(6 marks)
4 (c) The open loop T.F. of a unity feedback system is given by $$ G(s)= \dfrac {k(s+3)}{s(s^2+2s+3)(s+5)(s+6)} $$ Find the value of 'K' of which the closed loop system is stable.(6 marks)
4 (d) What are the disadvantages of RH criterion on stability of control system?(4 marks)
5 (a) For a unity feedback system, the open-loop transfer function is given by $$ G(s)= \dfrac {K}{s(s+2)(s^2-6s+25)} $$ i) Sketch the root locus for 0?K??
.ii) At what value of 'K' the system becomes unstable
iii) At this point instability, determine the frequency of oscillation of the system(15 marks)
5 (b) Consider the system with $$ G(s)H(s)= \dfrac {K}{s(s+2)(s+4)} $$ find whether s- -.075 and s=-1+j4 is on the root locus or not using angle condition.(5 marks)
6 (a) Construct the Bode plots for a unity feedback control system having $$ G(s)= \dfrac {2000}{s(s+1)(s+100)} $$ from the Bode plots determine;
i) Gain cross over frequency
ii) Phase cross over frequency
iii) Gain margin
iv) Phase margin
Comment on stability(14 marks)
6 (b) List the limitation of lead and lag compensations.(6 marks)
7 (a) The transfer function of a control system is given by $$ \dfrac {y(s)}{u(s)} = \dfrac {s^2+3s+4}{s^1+2s^2+3s+2} $$ obtain a state model.(10 marks)
7 (b) State the properties of state transition matrix and derive them.(10 marks)
8 (a) Explain the procedure for investigation the stability using Nyquist criterion.(8 marks)
8 (b) Using Nyquist stability criterion, investigator the closed loop stability of a negative feedback control system whose open loop transfer function is given by $$ G(s)H(s)= \dfrac {K(ST_a+1)}{s^2}, K, T_2 >0. $$(12 marks)