## Principles of Control Systems - Dec 2012

### Electronics Engineering (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.

### Answer any **four** of the following:-

**1 (a)** For the block diagram shown, find the transfer function between Y(s) and W(s).

(5 marks)
**1 (b)** List the type of damping of second order system with location of poles.(5 marks)
**1 (c) ** Compare time and frequency responses and explain the correlation between them.(5 marks)
**1 (d)** With an example, determine the relative stability of system using Routh stability criterion.(5 marks)
**1 (e)** Define gain margin and phase margin. Explain how to find them for magnitude v/s phase plot.(5 marks)
**2 (a)** Draw the signal flow graph of the given block diagram and obtain the closed loop transfer function using masons gain formula.

(10 marks)
**2 (b)** From the given state space model, obtain the transfer function.(10 marks)
**3 (a)** Sketch the root locus of the system shown and sketch the stability.

(10 marks)
**3 (b)** A unity feedback control system is characterized by open loop transfer function

Determine its Transient response for a unit step input. Evaluate Maximum overshoot and peak time.

(10 marks)
**4 (a)** Sketch the bode plot for the following transfer function and determine the system gain crossover frequency, phase crossover frequency, gain margin and phase margin.

(10 marks)
**4 (b)** Draw the Nyquist plot and assess the stability of closed loop system whose open loop transfer function is

(10 marks)
**5 (a)** Sketch the polar plots for the following:

(10 marks)
**5 (b)** A unity feedback system has

(i) Determine the steady state error if K=1.5.

(ii) Also find the minimum value of K if the steady state error ? 0.1 for a unit ramp input.

(10 marks)
**6 (a)** Draw the circuit diagrams of basic lag and lead compensating networks derive the transfer function.(10 marks)
**6 (b)** Explain the principle of operation and characteristics of a two phase servo motor.(10 marks)

### Write shorts notes on the following:-

**7 (a)** Synchros.(7 marks)
**7 (b)** M and N circles.(7 marks)
**7 (c) ** Effect of feedback on sensitivity and stability.(7 marks)