** NRT/KS/19/3477****Time : Three Hours ****Max. Marks : 80**

_____________________________________________________________________**Notes : 1. All questions carry marks as indicated.****2. Solve Question 1 OR Questions No. 2.****3. Solve Question 3 OR Questions No. 4.****4. Solve Question 5 OR Questions No. 6.****5. Solve Question 7 OR Questions No. 8.****6. Solve Question 9 OR Questions No. 10.****7. Solve Question 11 OR Questions No. 12.****8. Assume suitable data whenever necessary.****9. Illustrate your answers whenever necessary with the help of neat sketches.****10. Use of non programmable calculator is permitted.**

1. a) Obtain the X for function for the system which is defined by . ** [07 M]**

x=x_{1}+β_{3}U

b) Obtain the transfer function of the mechanical system as shown in ‘fig 1 (b)’ below. Find transfer function = **[06 M]**

**OR **

2. a) Using Block Diagram Reduction Technique find the equivalent open loop transfer function, for the system, shown in ‘fig 2 (a)’.

b) Prove that the Use of feedback improves the transient response or improves the speed of response. **[06 M]**

3. a) Derive the transfer function of Armature controlled D. C. servomotor. **[06 M]**

b) Explain Potentiometer as an Error detector.

4. a) Write a short note on synchro transmitter and receiver pair with neat sketch. **[06 M]**

b) For the system shown in ‘Fig 4(b)’, evaluate sensitivities at w = 1 rad/sec. **[07 M]**

i) S_{a}^{T} b) S_{b}^{T} c) S_{K}^{T}

Assume k = 10, a = 2, b = 1

5. a) What do you mean by ‘Time – Response’ of any control system? Mention and define various times response specifications.**[06 M]**

b) For a unity feedback system with forward path transfer function given as

. Determine . **[07 M]**

i) Types of system

ii) Steady state Error for an input of

** OR**

6. a) Discuss the effect of performance of a second order control system of :-** [05 M]**

i) Derivative control

ii) Integral control

b) A unity feedback control system has . If it is subjected to unit step i/p,

determine,** [08 M]**

(1) Damped frequency of oscillations

(2) Max^{m} overshoot

(3) Time for first overshoot

(4) Settling time.

(5) Output response

7. a) Consider the 4th order system whose characteristics equation is

s^{4}+8s^{3}+18s^{2}+16s+5=0

Comment on stability of system by Hurwitz stability criterion. **[07 M]**

b) A feedback control system has . For the closed loop system obtain stability boundary in parameter plane [K-T_{d}]. Also obtain the maximum permissible gain for stability when T_{d} = 1 sec.** [07 M]**

OR

8.a) The open Loop transfer function of a unity feedback system is given by

** [08 M]**a) Sketch the root Locus of system.

b) Determine gain K for critical damping

9. Sketch the Bode plot for the transfer function. ** [14 M]**

from the graph determine.

i) Gain cross over frequency.

ii) Phase cross over frequency.

iii) Gain margin and phase margin.

iv) Stability of the given system.

**OR **

10. a) Sketch the polar plot for the system with open loop transfer function

** [07 M]**

b)The specifications on a second order unity feedback control system with the closed loop transfer function.

are that the over shoot of the step response should not exceed 12% and the peak time must be less than 0.25. Find the corresponding frequency, Response value of peak resonance, resonant frequency and Bandwidth. ** [07 M]**

11. a) Determine the system transfer function using the following state equation:- ** [06 M]**

b) The closed loop transfer function of the system is given below

Determine two different state models for the system. ** [07 M]**

OR

12. a) Closed loop transfer function of a system is given by

Draw the signal flow graph for the system and hence obtain the state model for the system.** [08 M]**

b) Obtain the state mode for the following Electrical network shown in fig 12 (b). ** [05 M]**