## Control Systems - Dec 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)** Draw the F-V the F-I analogous circuit for the mechanical system shown in Fig Q1(a) with necessary equation.
(12 marks)
**1 (b)** For the rotational mechanical system shown draw the torque-voltage analogous circuit for Fig Q1(b).
(8 marks)
**2 (a)** Using block diagram reduction techniques for C/R for Fig Q2(a).
(5 marks)
**2 (b)** Draw the signal flow graph for the block diagram shown in Fig Q2(b) and find the TF.
(8 marks)
**2 (c)** Draw the signal flow graph and find TF Fig Q2(c).
(7 marks)
**3 (a)** Find the error coefficients K_{p}, K_{v} and K_{a} for the system having $$ G(s)= \dfrac {10}{s^2+2s+9} \ \& \ H(s)=0.2 $$(6 marks)
**3 (b)** Find K_{1} so that ?=0.35. Find the corresponding time domain specifications for Fig Q3(b).
(6 marks)
**3 (c)** With respect to a second order system define the following by drawing neat response curve and expressions: i) Maximum overshoot (M_{p}); ii) Time delay (t_{d}); iii) Time constant (T); iv) Rise time (t_{t}).(8 marks)
**4 (a)** What are the necessary and sufficient conditions for a system to be stable according to Routh-Hurwitz criterion?(4 marks)
**4 (b)** What value of K makes the following unity feedback system stable? $$ G(s)=\dfrac {K(s+1)^2}{s^3} $$(4 marks)
**4 (c)** Find how many roots have real parts greater than -1 for the characteristics equation.

s^{3}+7s^{2}+25s+39=0(4 marks)
**4 (d)** How many roots of the characteristic polynomial lie in the right half of S-plane, the left half of s-plane and on jω axis. Comment on the stability of the system.

P(s)=s^{5}+2s^{4}+2s^{3}+4s^{2}+s+2(8 marks)
**5 (a)** What are the angle and magnitude conditions that a point on root locus has to satisfy?(6 marks)
**5 (b)** Sketch the root locus for the unity feedback control system whose open loop transfer function is $$ G(s)={1}{s(s+2)(s^2+4s+13)} $$(14 marks)
**6 (a)** With respect to Nyquist criterion explain the following:

i) Encircle of a point

ii) Analytic function and its singularities.

iii) Mapping theorem of principle of argument

iv) Find the number of encirclements of point A in Fig Q6.1(a) and Q6.1(b)
(8 marks)
**6 (b)** For the open loop TF of a feedback control system $$ G(s)H(s)=\dfrac {K(1+2s)}{s(1+s)(1+s+s^2)}. $$ Sketch the complete Nyquist plot and hence find the range of K for stability using Nyquist criterion.
(12 marks)
**7 (a)** Draw the bode plot for a system having $$ G(s)=\dfrac {K(1+0.2s)(1+0.025s)}{s^3(1+0.01s)(1+0.05s)}. $$ Comment on the stability of the system. Also find the range of K for stability.(12 marks)
**7 (b)** For the plot shown determine the TF (Fig Q7(b)).
(8 marks)
**8 (a)** What are the advantages of state space analysis?(4 marks)
**8 (b)** A system is described by the differential equation $$ \dfrac {d^3y}{dt^3}+ \dfrac {3d^2y}{dt^2}+ \dfrac {17dy}{dt}+5y=10u(t) $$ Where y is the output and u is the input to the system. Determine the state space representation of the system.(6 marks)
**8 (c)** Obtain the state equations for the electrical network shown in Fig. Q8(c).
(10 marks)