# WBUT Question Papers EC

## Control System B Tech Sem Fifth Dec 2007

Time : 3 Hours ]

Full Marks : 70

Semi-log and graph sheets are printed at, the end of this booklet.

GROUP- A (Multiple Choice Type Questions)

1. Choose the correct alternatives for any ten of the following :               10×1 = 10

9                The characteristic equation of a second order system is s 2 + 6s + 25 ■ 0, The system is

a) underdamped            b) overdamped

c) undamped               d) critically damped.     [___

10            The type number of a transfer function denotes the number of a) poles at origin           b) zeros at origin

c) poles at Infinity      d) none of these.         [___

m) Presence of non-linearities in a control system leads to Introduce

a) transient error        b) instability

c) steay state error      d) all of these.

iv)             In terms of Bode plot, the system is stable if

a) . PM = GM b) PM & GM both are positive c) PM and GM both are negative d) PM negative but GM positive.

v)               By-the use of PD control to the second order system, the rise time

a)    decreases     b) increases

c) remains same           d) none of these.         [

vl) The lead-lag compensation will improve

a)              transient response

b)               transient response and steady state response

c)               none of these.

vii) The response of a control system, having damping factor as unity will be

a) oscillatory            b) underdamped

c) critically damped      d) none of these.

vlli) A system has a single pole at origin. Its Impulse response will be a) constant                b)

c) decaying exponentially d)

ix)            The matrix shown below Is

” 4 -4 2 ”

– 4 5 – 2

–  2—2 1.

a)      positive definite     b)

c) negative definite      d)

x)               A Is an n x n matrix. Then the system to be controllable, the rank of the controllability matrix should be

a)           n   b) > n

c) £ n                    d) < n.

xl) The settling tine for a second order system resonding to a step Input with 5% overshoot is

a)       4/\$Wn b)    2 /%Wn

c) 3/4 Wn d) 5/4 Wn. I xli) Area under a unit Impulse function is

a)

infinity b)     zero

c) unity d)                       none of these. _____

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GROUP -B ( Short Answer Type Questions )

Answer any three of the following.

1. Obtain state variable model of the system whose transfer function is given by

Y(s)        s+ 1

t/(s) = s3 + 3s2 + 7s+ 1

1. Determine the transfer function of an armature control d.c. motor system.
2. A feedback control system is decribed as

–    s(s + 25)°(s+5) • H|s| – ?

Evaluate the static error constants Kp, Kv&Ka for the system.

1. Consider the system

*i = -x2 + ax31

*2 = + <**2 •

Discuss the stability in the sense of Lyapunov.

1. Find C/R using block diagram reduction method of the following diagram :

G4

 Gl G2 G3 ——– p- ——– MX.)— IV C

Answer any three of the following questions.  3 x 15 = 45

1. a) Mention the difficulties that may arise In applying Routh stability criterion. What do you mean by relative stability ?                                                     2+1
2. b)  The open loop transfer function of a unity feedback control system is given by

K (s + 1)

2s3 + as2 + 2s + 1

The above system oscillates with frequency eo, If it has poles on s = +Jco and s = – Jo) and no poles In the right half s-plane. Determine the values of K and a, so that the system oscillates at a frequency of 2 radian/sec.                            6

c)   The open loop transfer function of a unity feedback control system is given by

G(s) = —t—-—————r s(s2 + 6s + 25)

Find :

4 the number, angle and centroid of the asymptotes IQ angle of departure HI) the break-away point

iv) the condition for marginal stabilty.                6

1. a) What do you mean by principle of argument ? State and explain Nyquist criterion of a control system.               1+2

b)               A unity feedback control system has open loop transfer function,

Ots)H(s)-

Determine closed loop stability by Nyquist plot

c) Determine the transfer function of the system whose Bode plot Is shown

below :                                                                                                                                 5

 >•20 db/dec – I \ Wj «3 Cft| 0) • 40 db/dec 20 db/dec-^ ^

1. a) Explain sampling and hold.                                                                                                                                3

b)               Find the pulse transfer function for the error sampled system shown In the following figure.            7

^scc-piT

c)  Find the Inverse and transform of the following system :

cw \      4z2 – 2z

{Z) ” z3-5za + 8z-4’

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1. a) State the difference between describing function and transfer function.
 ” – 1 0 0 “ ’ 1 “ •X a 0 -2 0 x(t) + 1 – 0 0 – 3 – – 0 –
 b)               A single input single output system is given by

 – 0 –

and y(t) * [ l 0 2]x(t).

Test for controllability and observability.

 0 1 0 “ ” 1 “ X r 3 0 2 *2 + 0 – – 12 -7 -6 – _*3_ – 2 –
 c)               Obtain the eigenvalues and eigenvectors for a system described by

1. Write short notes on any three of the following :

a)               PID controller

b)               Compensation techniques

c)               Phase plane technique of non-linear system analysis

d)               Dead zone and saturation type of non-linearitly

e)               Polar plot.

END

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