## Control Systems - May 2013

### 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)** What is damping ratio? Show the location of roots in s-plane for different values of damping ratio.(5 marks)
**1 (b)** From the pole-zero plot given below obtain:

(i) Transfer function.

(ii) Order of the system.

(iii) Characteristic equation.

(iv) DC gain of the system.

(5 marks)
**1 (c) ** Find the transfer functions from the signal flow graph given below:

(5 marks)
**1 (d)** Define the following terms related to second order system subjected to unit step input.

(i) Rise time

(ii) Peak time.

(iii) Peak overshoot

(iv) Delay time.

(v) Settling time.(5 marks)
**2 (a)** Find C using block diagram reduction rules.

(10 marks)
**2 (b)** Sketch the root locus for a unity feedback control system with

G(s) = K/[s(s+3)(s+5)] and determine -

(i) K for marginal stability.

(ii) Frequency of oscillation for marginal stability.

(iii) K for damping ratio of 0.5.(10 marks)
**3 (a)** Derive the time response expression for a second order control system subjected to unit step input.(10 marks)
**3 (b)** What is stepper motor? Mention its types. Explain one type of stepper motor with neat diagrams.(10 marks)
**4 (a)** Define sensitivity of a control system. Derive the sensitivities S_{H}<supt< sup=""> and S_{G}<supt< sup=""> of a feedback control system where T is closed loop gain, H is the feedback gain and G is the open loop gain of the system.</supt<><>(10 marks)
**4 (b)** For the transfer function given below:

G(s)H(s) = 48(s+10)/[(s(s+20)(s^{2}+2-4s+16)]. Find

(i) Static position error co-efficient.

(ii) Static velocity error co-efficient.

(iii) Static acceleration error co-efficient.

(iv) Steady state error if the input to the system is unit step.(10 marks)
**5 (a)** Sketch the bode plot for a system with open loop transfer function:

G(s)H(s) = 30/[s(1+0.5s)(1+0.8s)] and comment on stability.(10 marks)
**6 (b)** Find the overall transmittance using Masons gain Formula.

(10 marks)

### Write short notes on:-

**7 (a)** Nyquist stability criteria.(10 marks)
**7 (b)** Error compensation techniques.(10 marks)