Anna University Chennai 2005 B.E CONTROL ENGINEERING - Question Paper

Code: A-11 Subject: CONTROL ENGINEERING
Time: three Hours Max. Marks: 100
NOTE: There are 11 ques. in all.
ques. one is compulsory and carries 16 marks. ans to Q. 1. must be written in the space given for it in the ans book supplied and nowhere else.
ans any 3 ques. every from Part I and Part II. every of these ques. carries 14 marks.
Any needed data not explicitly given, may be suitably presumed and said.
Q.1 Choose the accurate or best option in the following: (2x8)
a. The steady-state fault of a feedback control system with an acceleration input becomes finite in a
(A) kind 0 system. (B) kind one system.
(C) kind two system. (D) kind three system.
b. The Laplace transform of is _______.
(A) (B)
(C) (D)
c. Considering the root locus diagram for a system with
,the meeting point of the asymptotes on the the real axis occurs at _________.
(A) -1.2 (B) -0.85
(C) -1.05 (D) -0.75

d. Figure one indicates a circuit for which switch S is kept open for a long time and
then closed at t = 0. The dynamic formula governing the circuit will then be
___________.

(A) (B)
(C) (D)
e. Considering the unity feedback system of Fig. 2, the settling time of the resulting 2nd order system for 2% tolerance band will be ________.

(A) 3.33
(B) 4.5
(C) 2.25
(D) 2.84
f. If for a control system, the Laplace transform of fault e(t) is provided as then the steady state value of the fault works out as ______.
(A) 3.6 (B) 1.8
(C) 3.2 (D) 2.4

g. The transfer function of the block diagram of Fig.3 is _________.
(A) (B)
(C) (D)


h. The impulse response of a LTI system is a unit step function, then the corresponding transfer function is
(A) (B)
(C) 1. (C) s.

PART I
ans any 3 ques.. every ques. carries 14 marks.

Q.2 Write the dynamic formula in respect of the mechanical system provided in Fig.4. Then using force-voltage analogy find the equivalent electrical network.
Legend
K1,K2 spring constants
B1 viscous friction damping coefficient
M1,M2 inertial constants of masses
x1,x2 displacements
F (t) .. Force. (14)
Q.3 Determine the transfer function for the block diagram shown in Fig.5 by 1st drawing its signal flow graph and then using the Mason's gain formula. (14)


Q.4 a. The open loop transfer functions of 3 systems are provided as
(i) (ii) (iii)
Determine respectively the positional, velocity and acceleration fault constants for these systems. Also for the system provided in (ii) determine the steady state errors with step input r(t)=u(t), ramp input r(t) = t and acceleration input . (10)
b. Describe a 2 phase a.c. servomotor and derive its transfer function. (4)
Q.5 a. A typical temperature control system for the continuously stirred tank is provided in Fig.6. The notations are for temperature, q for liquid flow and F st for the steam supplied to the steam coil. Draw the block diagram of the system. (10)

b. Considering a typical feedback control system, provide the advantages of a P+I controller as compared to a purely proportional controller. (4)

Q.6 a. For the system shown in the block diagram of Fig.7 determine the values of gain K1and velocity feedback constant K2so that the maximum overshoot with a unit step input is 0.25 and the time to reach the 1st peak is 0.8 sec. Thus find the rise time and settling time for 5% tolerance band. (10)
b. For the standard 2nd order system shown in Fig.8, with r (t) = u (t) discuss how the time domain specifications corresponding to resonant peak and bandwidth can be inferred. (4)

PART II
ans any 3 ques.. every ques. carries 14 marks.

Q.7 a. The characteristic formula of a closed loop control system is provided as . For this system determine the number of roots to the right of the vertical axis located at s = - 2. (10)
b. Explain the procedure to be followed when in the Routh's array all the elements of a row corresponding to are zeros. (4)
Q.8 Draw the complete Nyquist plot for a unity feed back system having the open loop function . From this plot find all the info regarding absolute as well as relative stability. (14)
Q.9 Sketch the root locus diagram for a unity feedback system with its open loop function as . Thus obtain the value of K at a point where the complex poles give a damping factor of 0.5. (14)
Q.10 Justify the subsequent statements :
(i) The impulse response of the standard 2nd order system can be found from its unit step response.
(ii) The Bode plot of the standard 2nd order function has a high frequency slope of 40 db / decade.
(iii) The 2 phase a.c. servomotor has an inherent braking effect under zero-control-voltage condition.
(iv) An L.V.D.T. can be used for measuring the density of milk. (4x3.5)
Q.11 Write notes on any 2 of the following:
(i) Disturbance rejection.
(ii) Turning method based on the process reaction curve.
(iii) Phase lag compensation. (2 x 7)

Earning:   Approval pending.