Bengal Engineering and Science University 2007 B.E Electrical Engineering Control System-I - Question Paper

Ex/BESUS/ EE-603/07

B.E. (EE) Part-Ill 6th Semester Examination, 2007

Control System-I (EE-603)

Full Marks : 100

Use separate answerscript for each half. Answer SIX questions, taking THREE from each half. Two marks are reserved for neatness in each half.

FIRST HALF

1. Answer all parts :

a) A system with zero initial conditions has a closed loop transfer function

T(s) =-

(s + l)(s + 4)

At which frequency is the output zero?

b) A system, whose output is x(t), is characterized by the following equation :

As f approaches infinity, what would be the value of x(0?

c)    The transfer function of a system is given as : T(s) =-.

5 + 1

If this system is excited with an excitation, x(t) = sin(t), find the expression of the output y(t) at steady state.

d)    The impulse response of a second order under-damped system having zero initial conditions is given by :

c(0 = 12e^-31 sin At (for />0). What are the damping ratio and natural frequency of oscillation of the system?    [3+3+6+4J

b)    A physical S.I.S.O. system is characterized by the following equation :

/ --4 + 5 + 4 + cos 4t = 10w(/); where c (t) stands for response and dt¹ dt² dt

u(t) is unit step excitation. Comment on what type of system it is, with reasons.

c)    Define transfer function of a system. What are meant by pole-zero form representation and time-constant form representation of a system transfer function?    [5+3+8]

3. Find the transfer function of the system whose s-domain block diagram is given in Fig.-l (Consider V_ref (s) as input and Q(s) as output of the system). |16]

4. Answer all parts :

a)    Mention and explain the time domain specifications with reference to a second order system.

b)    A mechanical vibratory mass-spring-dashpot system is shown in Fig.-2(a). When a 2 unit of force is suddenly applied to the system, the mass M oscillates, as shown in Fig.-2(b). Determine the numerical values of M, B and K of the system from the response curve. The displacement, x, is measured from the equilibrium position. Assume all variables are expressed in the same system of unit. [10+6]

5. Answer all parts :

a) Develop the transfer function of an armature-controlled DC servomotor with position as output and armature voltage as input. State all assumptions made.

b)    Explain, why in a servomotor, a negative slope of the speed-torque characteristics is required.

c)    What will be the steady state error of the closed loop system shown in Fig.-3. [8+3+51

SECOND HALF

6. a) Compare a closed loop system with an open loop one with examples.

b)    Find range of K for stability for the unity feedback system with open loop transfer function :

G₍s) - _J^Ks(s;²⁾

(s + 2s + 10)

Determine the value of K that will cause sustained constant amplitude oscillations and also the frequency of oscillations.

c)    Consider the unity feedback system with open loop transfer function :

K

with K= 5

[4+8+4]

7.    a) How does the synchro operate as an error detector? Derive expressions if

necessary.

b) Draw the Bode plots of: _rM_ 1000 ^{S) s(s²+105 s + 600)

Also find the gain margin and phase margin.    [6+l0|

8.    a) When is a transfer function proper? When is it minimum phase?

b) Draw the complete root locus as 0 < a <co for the unity feedback system with 10 (s + a)(s + 3)

s(s²- 1)

Suitably assume positions of break-away point, exact location need not be found.    [2+14]

9.    a) How can you characterise relative stability?

b)    Use Nyquist stability criterion to infer about closed loop stability of the unity feedback system with open loop transfer function :

G(s) =    20

s(l + 0.1s)(l + 0.5s)

c)    Find Gain margin and phase crossover frequency.    |4+10+2|

10.    a) Describe the operation of a diode ring demodulation.

b)    Explain which parts of the real axis in s-plane contain a root locus.

c)    Draw the polar plot of the system given in 9(b).

d)    For a second order system how can you correlate between time domain specifications and frequency domain specifications?    [4+4+4+4J

1

Answer all parts :

a) What is meant by a S.I.S.O. system? A physical S.I.S.O. system is characterized by the following equation :

= 5(/); where c(t) stands for response and u(t) is unit step

excitation. Comment on what type of system it is, with reasons. Find the transfer function of the system.

Attachment: bengal-engineering-and-science-university-2007-b-e-electrical-engineering-1001-1.pdf

Earning:   Approval pending.