cs april 2010

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Code No: V0223

II B.Tech II Semester (R07) Regular/supply Examinations, Apr- 2010

CONTROL SYSTEMS

(Common to EEE, ECE, E.CON.E, ECC)

Time: 3 Hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

________________________________________________________________________

1. a) Explain the operation of ordinary traffic signals which control automobile traffic atroad way intersections. Why are they open loop control system? How can traffic be

control more effectivelyb) Derive the transfer function of the following network

2. a) State and explain the masons gain formula

b) Derive the transfer function of armature controlled DC servomotors and develop

the block diagram?

3. a) Derive the time domain specifications for a standard second order systemb) A unity feedback system is characterized by the open loop transfer function

( )( )

.10+

=

ss

KsG Determine the gain K so that the system will have a damping ratio

of 0.5. For this value of K, determine time domain specification

4. a) Explain the procedure to construct the root locusb) Using Routh Hurwitz criterion for the unity feedback system with open loop

transfer function ( )( ) ( ) ( )321 +++

=

ssss

KsG

i) Find the range of K for stability

ii) Find the value of k for marginally stable

5. a) Define gain margin and phase marginb) Determine the closed loop bandwidth, closed loop peak magnitude, phase margin

and gain margin for the following system ( )( )

.1

4

+

=

sssG

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Code No: V0223

6. a) Explain Nyquist stability criterionb) A unity feedback control system has an open loop transfer function given by

( ) ( )( ) ( )

.25

100

++

=

sssHsG Draw the Nyquist diagram and determine its

stability.

7. a) Explain the lead-lag compensator and derive its transfer functionb) Describe the procedure for the design of lag compensator in frequency design.

8. a) Obtain the state space representation of the following transfer function usingcontrollable canonical form ( )

842

223

+++

=

ssssT

b) A system is described by [ ]xyanduxx 01,1

0

11

11=

+

=

check the controllability and observability of the system

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Code No: V0223


CONTROL SYSTEMS

(Common to EEE, ECE, E.CON.E, ECC)

Time: 3 Hours Max Marks: 80Answer any FIVE Questions

All Questions carry equal marks

1. Write the differential equations to represent the following system and find transferfunction

( )

( )s

s

F

X1and also draw its electrical equivalent circuit

2. a) With the help of sketches, explain the construction and working principle of asyncho-receiver

b) Draw the signal flow graph for the system of equations given below and obtain the

overall transfer function using masons rule

546435

64324

5342213

612

xGxandxGx

xHxGx

xHxHxGx

xxx

==

=

=

=

3. a) For an under damped second order system, define various time domain specificationsb) Determine various error coefficients for a system having

( )( )

( ) .45

10

522 +=

++

= sHandsss

KsG

Determine the steady state error if input is

( )2

1052t

ttr ++=

4. Sketch the root locus of the unity feedback system whose open loop transfer functionis ( )

( ) ( )1342 2 +++=

ssss

KsG

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Code No: V0223

5. a) Explain the relationship between damping ratio and phase marginb) Sketch the bode plot for the following open loop transfer function

( )( )

( ) ( )10042

310

2 +++

+=

ssss

ssG

6. a) State and explain Nyquist stability criterionb) For the following system sketch the polar plot ( ) ( )

( ) ( ).

96

500

++

=

ssssHsG

7. a) Explain the lag compensator and derive its transfer functionb) Describe the procedure for the design of lead compensator in frequency domain

8.

a) What are the merits of state variable techniquesb) Construct the state model for a system characterized by the differential equation

uyyyy =+++ 6116

Give the block diagram representation of the state model

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Code No: V0223


CONTROL SYSTEMS

(Common to EEE, ECE, E.CON.E, ECC)Time: 3 Hours Max Marks: 80


________________________________________________________________________

1. a) Explain with example, the use of control system concept to engineering and non engineering fieldsb) For the mechanical system given below, write down the differential equations

2. a) How is an AC servo motor different from induction motor? Draw its characteristicsand explain its workingb) Draw the signal flow graph for the following equations and find the transfer

function from it

4453355

4443344

2233

5524423321122

xaxaxxaxax

xax

xaxaxaxax

+=

+=

=

+++=

3. a) Explain the effect of PI control on the performance of control systemb) An unity feedback system has ( )

( ).

251

1

+

=

ssG The input to the system is described

by ( ) .642 2tttr ++= Determine the generalized error coefficients and express thesteady state error as a function of time.

4. a) What are the limitations of Rouths stability

b) Sketch the root locus for a system with open loop transfer function

( ) ( )( )

( ) ( ) ( )4531

+++

+=

sss

SKsHsG

5. Draw the bode plot for the unity feedback system with open loop transfer function( )

( )15.0

2++

=

ssssG Hence find gain margin and phase margin

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Code No: V0223

6. Find the stability criterion using Nyquist stability and stability margins to thefeedback systems with an open loop transfer function

( ) ( )( )( )sss

ssHsG

211

412

++

+=

7. a) Explain the lead compensation and device its transfer functionb) Describe the procedure for the design of lead long compensator in frequency

domain

8. a) State and explain the controllability and observability testsb) Derive the state models for the system described by the differential equation in

phase variable form uuuyyyy 552254 ++=+++

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Code No: V0223


CONTROL SYSTEMS

(Common to EEE, ECE, E.CON.E, ECC)Time: 3 Hours Max Marks: 80


________________________________________________________________________

1. a) Explain the temperature control system by using open loop system and closed loopsystem with diagrams

b) Find the transfer function( )

( )s

s

F

Xof the system given below

2. a) Derive the transfer function of an AC servomotor and draw its characteristicsb) Determine the overall transfer function from the signal blow graph given below

3. a) Derive the transient response of second order system when unit step inputb) A unity feedback system has the forward transfer function

( )( )

( ) ( ).

115

122

++

+=

sss

sKsG

The input )61( t+ is applied to the system. Determine the value of K for the steady

state error to be less than 0.1

4. The open loop transfer function of a unity feedback control system is given by( )

( )

( ) ( )( )224322

++++

+=

sssss

sKsG

i) Sketch the root locus diagram as a function of K

ii) Determine the value of K which makes the relative damping ratio of the closedloop complex poles equal to 0.707.

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Code No: V0223

5. The open loop transfer function of a unity feedback system is given by( )

( )

( ) ( )( )1021

20

+++

+=

sss

sKsG Construct bode plot for K=10. Determine phase margin

and gain margin. Also determine whether the closed loop system is stable.

6. Draw the Nyquist plot for the open loop system ( ) ( )( )

.1

3

+=

ss

sKsG And find its

stability. Also find the phase margin and gain margin

7. The open loop transfer function of certain unity feedback control system is given by( )

( ) ( ).

804 ++=

sss

KsG It is desired to have the phase margin to be at least 33

0 and

the velocity error constant .sec.30 1=vK Design a phase lag series compensator

8. a) Define the followingi) state, ii) state variables and iii) state model

b) Construct the state model for the system characterized by the differential equation

uyyyy 42116 =+++ Also give the block diagram of the model

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cs april 2010

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