## 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 t_{p} 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 S^{3}+3ks^{2}+(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)