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BAS-020

B.TECH. IN AEROSPACE ENGINEERING (BTAE) O) N-

Term-End Examination

o-)

O O

December, 2011 BAS-020 : BASIC CONTROL THEORY

Time : 3 hours

Maximum Marks : 70

Note : There are 9 questions in all. Question 1 is compulsory and carries 10 marks. Out of the remaining Eight questions. Answer Any Six questions. Each question carries 10 marks. 1. Choose the correct or the best Alternative in the following : 10x1=10 (a) The time constant of the second order 1 system G (s) —

BAS-020

12 , H (s) = 1 is : s(s +0.2)

(i)

0.2s

(ii)

12s

(iii)

60s

(iv)

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(b) The Basic circuit of fig (1) Represent's a : R1 TT R2 eo

e.

C /o



to

Fig. (1) (i)

lag compensator

(ii)

lead compensator

(iii)

lag-lead compensator

(iv)

lead-lag compensator

(c) The steady-state error of a feedback control 1 system with an Acceleration input becomes finite in a (i) type 0 system (ii) type 1 system (iii) type 2 system (iv) type 3 system (d) The laplace transform of e -2t sin2wt is 1

2s (i)

(s + 2)2 + 2w2

2w (ii)

(s — 2) 2 + 4w2

2w (iii)

(s + 2)2 + 4w2

(iv)

None of the above

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(e) The impulse response of a LTI system is a 1 unit step function, then the corresponding transfer function is (ii)

X2

(iv) s (f) If the NYQUIST plot of the loop transfer 1 function G(s). H(s) of a closed-loop system encloses the ( —1, Jo) point in the G(s) H(s) plane, the gain margin of the system is

(g)

(i)

zero

(ii)

greater than zero

(iii)

less than zero

(iv)

infinity

The LVDT is primarily used for the 1 measurement of (i)

Displacement

(ii)

Velocity

,(iii) Acceleration (iv) Humidity

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(h) The input to a controller is :

(i)

(i)

Sensed signal

(ii)

Desired variable value

(iii)

Error signal

(iv)

Servo signal

1

Closed loop transfer function of a unity 1 Y(s) _ 1 feedback system is given by — R(s) (i s +) steady state error to unit ramp input is (i) a (ii) T (iii)

(i

)

1 (iv) X

Electrical time constant of an Armature - 1 controlled DC servomotor is (i)

equal to mechanical time constant

(ii)

smaller than mechanical time constant

(iii)

larger than mechanical time constant.

(iv)

not related to mechanical time constant.

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2. Write the Dynamic equation in respect of the

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mechanical system given fig (2) then using force voltage Analogy obtain the equivalent electrical network. Legend : K1 K2 Spring constant's B1 - viscous friction damping coefficient M1 , M2 - inertial constant of masses X1 , X2 - Displacement's;

f (t) - force.

Fig. (2)

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3. The open loop transfer functions of three system

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are given as

4 (s + 1)(s + 2) 2 s(s + 4)(s + 6) 5 (c)

s 2 (s

+ s)(s + 10)

(i)

Determine Respectively the positional velocity and Acceleration error constant's for these system. Also for the system given in.

(ii)

Determine the steady state error's with step input r (t) = u(t). ramp input r (t) = t and 1 Acceleration input r (t) = 2 tz.

10

4. The Block Diagram of a Remote Position control of a ship's Rudder is given in the fig. 3 write the overall transfer function and Determine the Damping Ration 4 and the natural frequency Wn ofthesym. Amplifier

R(

25 Position input

10 550s2 + 100s

Position feedback

14 Fig. (3)

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C (s) Position output

5.

The characteristic equation of a closed loop control system is given as s4 + 10s 3 + 35s 2 + 50s + 24 = 0. For this system, Determine the number of Root's to the Right of the vertical axis located at s = — 2.

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6.

Draw the complete Nyquist plot for a unity feedback system having the open loop function

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G(s) — [

6 s (1 0.5 s) (6 + s)]

from this plot obtain

all the information Regarding absolute as well as Relative stability 7.

Sketch the Root locus Diagram for a unity feedback system with it's open loop function as

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K(s + 3) G(s) — . s(s2 + 2s + 2) (s + 5)(s + a)

Thus find the value of K at a point where the complex poles provide a damping factor of 0.5. 8.

Consider a unity feedback control system with the following open-loop transfer function G(s) —

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K s(s2 + s + 4)

Determine the value of the

gain K such that the phase margin is 50°. What is the Gain margin for this case ? BAS-020



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9. Use the Nyquist Criterion to Determine the Range of value of K >0 for the stability of the system in fig (4). R(s) +

e — 0.8s G(s) —

(Fig. 4)

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s +1

y (s)

10