# WBUT Queston Papers EE Control System -I B Tech 2011

# WBUT Queston Papers EE

## Control System -I B Tech 2011

Time Allotted : 3 Hours

The figures in the margin indicate full marks.

Candidates are required to give their answers in their own words

as far as practicable.

GROUP – A

( Multiple Choice Type Questions )

. Choose the correct alternatives for any ten of the following :

10 x 1 = 10

i) Transfer function of a simple R-C integrator circuit shown in figure is given by

L

RC

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ii) Area under a unit impulse function is

a) infinity b) zero

c) unity . d) none of these.

111) A system has a single pole at origin. Its impulse response will be

a) contrast b) ramp

c) decaying exponential d) oscillatory.

iv) A second order system exhibits 100% overshoot. Its damping coefficient is

^{a}) 0 b) 1

^{c}) ^{<} 1 d) > 1. *

V) If the Nyquist plot of a certain feedback system crosses the negative real axis at – 0-1 point, the gain margin of the system is

a) 0-1 ‘ b) 10

^{c) }^{100} / d) none of these.

The centre of asymptotes for an open-loop transfer

function G(s) = ~^{+} ^ is

s^{2}(s + 4

^{a) }– 1 b) – 3

^{c) }“^{4} d) 0.

vii) A slope of 20 dB/decade corresponds to

a) 3 dB/octave b) 6 dB/octave

c) ^{9} dB/octave d) 20 dB/octave.

viii) A feedback system with the transfer function

G(_{S}, = 4<i±iI!£±&L_{isa}

s (s + 2)(s + 4)

a) type 5 system b) type 3 system

c) type 2 system d) type 0 system.

ix) If the gam of a third order system (all poles) is increased, then the phase margin

a) increases

t

b) decreases

c) remains same

0>

d) it is not possible to predict.

x) The settling time for an underdamped second order system

a) increases with damping ratio

b) reduces with damping ratio

c) does not depend on damping ratio

d) may increase or decrease with damping ratio.

XI) Without affecting steady-state error, maximum overshoot can be decreased by

a) derivative error control

b) integral error control

c) gain adjustment

d) proportional error control.

xii) A D only controller will produce

a) always zero steady state error

b) always infinite steady state error

c) output only if error changes

d) none of these.

GROUP -B

( Short Answer Type Questions )

Answer any three of the following 3×5= 15

- Obtain the Laplace Transform for the signal shown in figure below :

A system is defined by G ( s )

s(Ts + 1)

state position and velocity error due to a unit ramp input and hence the loop gain to reduce the error by 10%. 2 + 3

5104

W^{2}

4, If G{s) = ~-x -77is an underdamped second order

s^{2} + 21W s + W^{2}

^ n n

system, what happens to the peak overshoot of the closed loop system shown in figure below, if the gain k is increased. Substantiate your answer. Assume k > 0

How does the peak overshoot change for the same value of k if the configuration is as shown in figure

- A system is defined by the transfer function

k

G ( s ) =—————— , T,, r_{o} > 0 . Prove mathematically

‘ (r,s – i )(7’,s -1) ^{12 }^{3}

that the system will be stable.

- A system is defined by G(s)~——— *
^{S}—— , Calculate

\ (O-fb + 1 )(s + l)

the corner frequencies and the slopes of the asymptotes.

- For the system defined by G ( s ) =
^{calculate the}

steady state error due to a unit step input with a PI controller.

- Define gain margin. What happens to the phase of the system at a particular frequency if the system gain is changed ? Does phase margin change with system gain ?

9 Prove that for an underdamped second order system defined

CO^{2}

bv G ( s ) =———– ——— 5- , the peak overshoot due to a

^{J} ‘ (s^{2}+ 2^co_{n}s + (oJ)

unit step input depends on the damping £, only. What is the

locus of constant co_{n} roots ? Symbols carry usual

significance.

10. For the DC position control system shown in the figure below draw the signal flow graph assuming the motor to be in the armature controlled mode with armature resistance r_{Q} and

inductance E>_{a} and inertial and damping constants <J_{m} and F_{m}. Assume the amplifier gain to be K_{a}, the potentiometer gains to be K_{p} V/radians and appropriate motor emf and torque constants. Hence derive the transfer function

Q_{c}(s)/Q_{r}(s).

- Using Routh-Hurwitz Stability Criterion determine the

maximum feedback gain K for which the closed loop system

will be stable if the open-loop transfer function is

5(1-0* 2s) .

G ( s ) = —————– . Calculate the frequency of oscillation

> (s + 3 * 2s + 4)

at this gain.

- For the system defined by G (s ) –
- s ( 0 • Is + 1)(0 ■ 05s + 1)

draw the asymptotic gain and phase plots and calculate the gain and phase margins. What is the output of the system at steady-state if a step of 2 units is applied as an input

att=0? 12 >3

- For the system defined by G ( s ) H ( s ) =draw

s ( s + 1)(2s + 1)

the Nyquist plot and hence comment on the stability of the closed loop system.

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