III/IV B.Tech Degree Examinations, April 2014
First Semester
Linear Control Systems
Time : 3 hours
Maximum Marks : 60
Answer question No.1 Compulsory
Answer ONE question from each Unit
1. Briefly explain following [12 x 1 = 12M]
a) Define open loop and closed loop control systems?
b) Define transfer function.
c) What do you mean by signal flow graph? State the properties of signal flow graphs?
d) Differentiate between linear and non linear systems?
e) What is meant by impulse function? How do you represent graphically
f) Define Rise time of a control system
g) Define static velocity error constant K_{v} and steady state error with respect to unit ramp input.
h) Define gain cross over frequency and gain margin
i) State the advantages and limitations of Nyquist stability criterion
j) How do you find the centroid while constructing Root Locus?
k) Explain the concept of state variables?
l) Define controllability?
UNIT - I [1 x 12 = 12M]
2. a) Explain the working of synchros and mention its applications.
2. b) Discuss the effects of feed back? (OR)
3. Obtain the transfer function by using Block diagram reduction techniques and verify the result using signal flow graphs?
UNIT - II [1 x 12 = 12M]
4. a) Sketch the transient response of second order system and derive the expression for Rise time and peak Over Shoot.
4. b) Determine the range K for which the following Characteristic equation belongs to stable System. S^{5}+8S^{4}+15S^{3}+32S^{2}+60S+K=0 (OR)
5. a) The open loop transfer function of a unity feedback control system is given by G(s) =(10 K)/(S(S^{2}+4S+200))
(i) Determine the step, Ramp and parabolic constant
(ii) Determine the steady state error for unit step and unit Ramp input
5. b) A Unity feedback system characterized by an open loop transfer function G(s) =(K)/(S(S+10)). Find the Gain K such that system will have a damping ratio of 0.5. For this value of K determine settling time and peak overshoot.
UNIT - III [1 x 12 = 12M]
6. a) Discuss the correlation between time and frequency response specifications and an also derive expression for resonant peak of second order system.
6. b) Sketch the Bode Plot for the following transfer function and obtain Gain and Phase cross over frequencies G(s)=10/(S(1+0.4S)(1+0.1S)) (OR)
7. The open loop transfer function of a system is G(s)H(s)=(4S+1)/(S^{2}(S+1)(2S+1)) Determine the stability of closed loop system using Nyquist criterion.
UNIT - IV [1 x 12 = 12M]
8. Sketch the Root Locus plot for the System when open loop transfer function is given by G(s)H(s)=(K)/(S(S+4)(S^{2}+4S+13)) (OR)
9. A Feedback system has a closed loop transfer function T(s)=(Y(s))/(U(s))=(10(S+4))/(S(S+1)(S+3)). Construct state model. Given the Block Diagram Representation of the state model.