## 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(s^{2}+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.

x_{2} = g_{21}x_{1} + g_{23}x_{3}

x_{3} = g_{31}x_{1} + g_{32}x_{2} + g_{33}x_{3}

x_{4} = g_{42}x_{2} + g_{43}x_{3}(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)(s^{2}+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/[(s^{2}+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)