Question Paper: Control Systems : Question Paper Jun 2014 - Electronics & Telecomm (Semester 4) | Visveswaraya Technological University (VTU)
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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)