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Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. Define and explain the following terms
(a) Characteristic equation
(b) Order of a transfer function
(c) Type of a transfer function
(d) Poles and zeros of a transfer function. 
2. Represent the following set of equation by a signal flow graph and determine the overall gain relating x5 and x1. 
x2 = ax1 + fx2
x3 = bx2 + ex4
x4 = cx3 + hx5
x5 = dx4 + gx2
3. (a) What are the types of controllers that are used in closed loop system? Explain them?
(b) The response of a system subjected to a unit step input is c(t) = 1 + 0.2e-60t -1.2e-10t
Obtain the expression for the closed loop transfer function? Also determine the Un damped natural frequency and damping ratio of the system? [8+8]
4. Explain the stability of the system from the root locus plot in the following situations with suitable examples?
(a) addition of open loop poles
(b) addition of open loop zeros. 
5. (a) Write a note on frequency domain specifications
(b) For a system the resonant peak is 1 dB an ?n = p10 r/s. Find resonant frequency.Also find the phase angle of closed loop transfer function at resonant frequency. [6+10]
6. (a) What is “Nyquist Contour”?(b) A system is given by
G(s) = 4s+1s2(s+1)(2s+1) Sketch the Nyquist plot & hence determine the stability of the system. [2+14]
7. (a) What is compensation? what are the different types of compensators?
(b) What is a lag compensator, obtain the transfer function of lag compensator and draw pole-zero plot?
(c) Explain the different steps to be followed for the design of compensator using Bode plot? [3+3+10]
8. (a) Discuss the significance of state Space Analysis?
(b) Define state variables.
(c) Obtain the state variable representation of an armature controlled D.C Servomotor?