H R(s) G Fig. 1 (a) · i) Gain margin (GM) and phase margin (PM) from the polar plot. 6 b) Draw the polar plot for a unity feedback system with forward path transfer function given

NIR/KW/18/3465/3470 1 P.T.O

B.E. (Electronics Engineering / Elect. Telecommunication / Elect. Communication Engineering)

Sixth Semester (C.B.S.) Control System Engineering

P. Pages : 3 NIR/KW/18/3465/3470

Time : Three Hours Max. Marks : 80

_____________________________________________________________________

Notes : 1. All questions carry marks as indicated.

2. Solve Question 1 OR Questions No. 2.






8. Assume suitable data whenever necessary.

9. Illustrate your answers whenever necessary with the help of neat sketches.

10. Use of non programmable calculator is permitted.

1. a) Reduce the 'Fig 1 (a)' in to single block using Block diagram reduction techniques.

+_

R(s)G1 G2 G3

H1

H2

+

C(s)

Fig. 1 (a)

H3

+

_

8

b) Explain the use of feedback for improving the dynamic response of the system.

OR

5

2. a) Explain the mathematic model of field excitation. Control DC motor system and obtain

the expression for closed loop transfer function between voltage applied across the field

winding as an input variable and operating speed of the shaft driven by motor as output

variable.

5

b) The block diagram of a position control system is shown in the fig. 2 (b), Determine the

sensitivity of a closed loop transfer function T (s) with respect to G (s) and H (s) for w = 1

rad/sec.

R(s)

_

+ 10

S(S 1)+

H(s) = 5

Fig. 2 (b)

C(s)

8

*1290*

NIR/KW/18/3465/3470 2

3. a) Unity feedback system having open loop transfer function.

( )( )

25G s

s s 5=

+. Determine the rise time, settling time, first peak time and maximum

percentage overshoot, when the closed loop system is subjected to unit step input.

6

b) A unity feedback system has : -

( )( )

( )( )1

2 3

k T s 1G s

s T s 1 T s 1

+=

+ +

i) Prove that for a unit step input, steady state error is zero.

ii) For a unit Ramp input, find the value 'K' to be set so that steady error does not exceed

0.25.

OR

7

4. Derive the expression for a time response of underdamped ( )0 1 second order

closed-loop system for a unit-stap change in input.

13

5. a) For a fourth-order system with a characteristics equation given as

( ) 4 3 2Q s s 8s 18s 16s 5 0;= + + + + =

determine the stability of the system on the basis of Hurwitz stability criterion.

8

b) Explain in brief 'Routh Stability criterion' and mention the necessary and Sufficient

conditions for the determination of stability of the system.

OR

6

6. What do you mean by 'Root locus'? For a unity feedback system with the forward path

transfer function given as :

( )( )( )

KG s

s s 2 s 4=

+ +

Determine :-

i) Root locus.

ii) Find the range of value of 'K' for which the system has underdamped oscillatory

response.

iii) Determine the frequency of sustained oscillations.

iv) Determine the value of gain constant 'K' for damping factor 0.5. =

14

7. a) Find the transfer function of the given 'BODE DIAGRAM' shown in fig 7 (a).

zero slopeG(jw) 6

db

20dB/dec

1

-20dB/dec

10 wFig. 7 (a)

7

NIR/KW/18/3465/3470 3 P.T.O

b) Explain Nyquist stability criterion.

OR

6

8. a) Explain the procedure to determine

i) Gain margin (GM) and phase margin (PM) from the polar plot.

6

b) Draw the polar plot for a unity feedback system with forward path transfer function given

as :

( )( )( )( )

kG s

1 s 1 2s 1 3s=

+ + +

i) Determine Gain Margin (GM) for the value of gain K = 5.

ii) Find out the value of gain 'K' for Gain Margin (GM) = 20dB.

7

9. State & explain with derivation lag compensator.

OR

13

10. State & explain with derivation lead compensator.

13

11. a) For the given transfer function obtain the STATE model & draw block diagram

representation.

( )

( ) 3 23 2 1

y s K.

U s s a s a s a=

+ + +

7

b) The system equations are given by.

( ) ( ) ( )0 1 0

X t x t u t2 3 1

= +

− −

( ) ( )Y t 1 0 x t=

Find the 'transfer function of the system.

OR

7

12. a) How State-Space model Represented in phase variable form? What are the specific

advantages & disadvantages of representation of state space model in 'Phase variable form'.

4

b) For a control system with closed loop transfer function given as :

( )( )( )

( )3 2

Y s 10 s 4T s

U s s 4s 3s

+= =

+ +

Obtain the 'Canonical' form of state space model to represent the closed-loop transfer

function of the system.

10

**********

NIR/KW/18/3465/3470 4

NKT/KS/17/7381/7386 1 P.T.O

B.E. Sixth Semester (Electronics / Electronics Telecommunication /

Electronics Communication Engineering) (C.B.S.) Control System Engineering

P. Pages : 4 NKT/KS/17/7381/7386


_____________________________________________________________________








8. Due credit will be given to neatness and adequate dimensions.


10. Diagrams and equations should be given whenever necessary.



1. a) Write differential equation for system shown in fig. 1(a)

FX1 X2

K1K2

f12

M1 M2

F1F2

Fig. (1.a)

7

b) For the Electrical Network shown in Fig. 1(b) find the transfer function

)s(v

)s(v

i

o

by Mason's gain formula.

Vi Vo

C2

R1 R2

C1

Fig. 1 (b)

7

OR

*0485*

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NKT/KS/17/7381/7386 2

2. a) Find

)s(R

)s(C. Using block reduction technique for the block diagrams shown in 'Fig. 2(a)'

G1 G2 G3 G4

H1

G5

R(S)+– –

+

+

+

H2

C(S)

Fig. 2(a)

7

b) Derive the expression to prove that the use of feedback improves the transient response.

7

3. a) For a system having forward path transfer function

)6s(s

k)s(G

and .1)s(H Find the

time response to an i/p r(t) = 2u(t) where

i) k = 13; ii) k = 8

7

b) For a unity feedback system having forward path transfer function

)5s()2s(s

10)s(G

Determine damping ratio, Dominant pole pair location and damped frequency of

oscillation.

OR

7

4. a) For the system shown in 'Fig. 4(a)',

R(S) +–

1+kd S)2S(S

10

C(S)

Fig. 4 (a)

i) Determine the derivative constant dk so that 6.0

ii) Find %, MP, settling time and number of oscillations before settling and the time

required to reach over shoot and first under shoot. Sketch approximate time response

8

b) Derive the time Response of second order underdamped system to unit step Input.

6

5. a) A feedback control system has

]9s5s[s

ke)s(H)s(G

2

dST

. For the closed loop system,

obtain stability boundary in parameter plane dTk . Also obtain the maximum

permissible gain for stability when dT =1 sec.

6

b) Sketch the root locus of a unity feedback control system with

)3s()1s(s

k)s(G

and

determine the value of k for marginal stability.

7

OR

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NKT/KS/17/7381/7386 3 P.T.O

6. a) The characteristics equation of a unity feedback system is given by

0k3S]k8[S4S)s(F 23 Draw the root locus for k = 0 to . Determine the

value of k for a damping ratio of 0.5.

10

b) Define :

i) Absolute stability

ii) Relative stability

iii) Order of the system

3

7. a) Given :

)2s()1s(s

12)s(H)s(G

Draw the Polar Plot and hence determine if system is

stable and if gain and phase margin.

9

b) State and explain Nyquist criterion.

4

OR

8. a) Draw the Bode Plot of a system with open loop transfer function: -

)2s()1s(s

)3s(10)s(H)s(G

Discuss STABILITY from the BODE PLOT.

9

b) Define :

i) Phase margin ii) Gain margin

iii) Resonance frequency iv) Band width

4

9. a) Write the Transfer function for a lag-lead compensator. Draw its Pole Zero Plot, bode Plot

and Electric RC network realization.

7

b) What is the need for compensation? Explain in brief the selection process for type of

compensator for a particular system.

6

OR

10. a) Write short notes on Lead compensator.

7

b) Explain transducers in brief.

6

11. a) Determine the system transfer function using the following state equation:-

2

1

2

1

2

1

x

x21y

u5

2

x

x

13

15

x

x

6

b) The closed loop transfer function of the system is given below:

)3s()2s()1s(

24

)s(R

)s(C

7

OR

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NKT/KS/17/7381/7386 4

12. a) Obtain the state equation for the network shown in fig.12 (a)

+

e(t)

R1 R2

CLi1(t) i2(t)

Fig. 12 (a)

6

b) A feedback system is characterized by the close-loop transfer function given as:

2S3S2S

3S3ST

23

2

)s(

i) Draw the suitable signal flow-Graph representing the close-loop transfer function.

ii) Obtain the state space model representation of the same.

7

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KNT/KW/16/7381/7386 1 P.T.O

B.E. Sixth Semester (Electronics Engineering / Electronics Telecommunication /

Electronics Communication Engineering) (C.B.S.) Control System Engineering

P. Pages : 4 KNT/KW/16/7381/7386


_____________________________________________________________________












1. a) Reduce the block diagram for C(s)/R(s) using block diagram reduction technique.

Refer 'fig 1 (a)'

G1 G2 G3 G4

G5

H1

H2

R(s)

+–

–

+ +

+

C(s)

Fig. 1(a)

7

b) Write the differential equation governing the behaviour of mechanical system shown in

fig 1 (b). Obtain an analogous electrical circuit using force voltage analogy.

M2

M1

KF1

X2(t)

F2

X1(t)

F(t)

Fig. 1(b)

OR

6

*0098*

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KNT/KW/16/7381/7386 2

2. a) Determine overall gain using Mason's gain formula of the following SFG.

R1(s)

R2(s)

C(s)

H2H1

G1 G2

1 1

R3(s)

7

b) What is the effect of a feedback on control system sensitivity?

6

3. a) A unity feedback system has forward path

2)1s)(1s4(s

)1s2(K)s(G.F.T

i) State type & order of the system.

ii) It is desired that steady state error for an i/P r(t) = 1 + t should be equal to or less

than 1. Find minimum value of K.

6

b) Define:

i) Delay time ii) Rise time

iii) Peak time iv) Peak overshoot

v) Settling time vi) Steady state error

vii) Time Response

OR

7

4. a) An instrument serve for controlling position is damped with velocity feedback as shown in

fig. 4(a):

i) If input R is unit step. What is the response of the system & the steady state error?

ii) What is the system static error coefficient?

)1s(s

100

0.01s

++

– –

R(s) C

Fig. 4 (a)

7

b) Discuss the effect of 'r1' on response & root location of second order system?

6

5. a) Define stability & its types.

2

b) State Hurwitz's stability criteria & what are its limitation.

6

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KNT/KW/16/7381/7386 3 P.T.O

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

)1s2s()4s(s

K)s(H)s(G

2

Using Routh criterion, determine the range of 'K' for which the system will be stable.

OR

6

6. The open loop transfer function of a unity feedback control system is

)5s()2s(s

K)s(H)s(G

Sketch the root locus of the system & determine the value of K for

i) Critical damping ii) Marginal stability

14

7. Draw the open loop Bode diagram. Determine the gain crossover frequency, phase

crossover frequency, gain margin, phase margin. Determine the stability of closed loop

system.

Given 1)s(H:

60

s1

75.1

s1s

110

s170

)s(G

OR

13

8. a) Write a short note on Nyquist stability criteria.

5

b) Draw polar plat of

)8s()4s()2s(

100)s(H)s(G

8

9. a) i) Compare the lag & lead compensator.

3

ii) Compare feedback compensation & cascade compensation.

3

b) Derive the transfer function of lead lag compensator.

OR

7

10. a) Compare & justify the selection of 'Lag' & 'Lead' compensator for following

i) Bandwidth

ii) Noise susceptability

iii) Type of system

6

b) Explain the signal conditioning system with the help of block diagram.

7

11. a) State the advantages of state variable feedback design over the classical design technique.

4

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KNT/KW/16/7381/7386 4

b) Obtain the state space model for given network. Refer 'Fig 11. (b)'

+

–

V

R L

Ci

VC

Fig. 11(b)

5

c) Given transfer function of the system is

fesdss

cbssa

)s(V

)s(Y

23

2

form the state space model

OR

5

12. a) Transfer function of a system is defined by

s4s5s

3s2s

)s(V

)s(Y

23

2

Obtain canonical state space model & draw its block diagram representation.

8

b) "Transfer function is unique & state variable is not unique" Justify the statement.

3

c) Also define:

i) State variable ii) State

iii) State vector iv) State space

Solve any three.

3

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NRJ/KW/17/4520/4525 1 P.T.O

B.E. (Electronics Engineering / Electronics Telecommunication /

Electronics Communication Engineering) Sixth Semester (C.B.S.) Control System Engineering

P. Pages : 3 NRJ/KW/17/4520/4525


_____________________________________________________________________











1. a) Compare open loop and closed loop system. Explain in detail with one example of each.

7

b) Reduce the block diagram shown in 'Fig. 1 (b)' to find C (s) / R (s) using block diagram

reduction rules.

R(s) C(s)G1 G2 G3

H1

H2

G4

++

_ _

Fig. 1 (a)

OR

7

2.

a) Determine the transfer function )s(R

)s(C of fig 2 (a) using block diagram reduction

technique.

R(s) C(s)G1 G2 G3

H1

H3

+ _

Fig. 2 (a)

H2

_

7

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NRJ/KW/17/4520/4525 2

b) Find the transfer function for the electrical network shown in 'Fig. 2 (b) ' by drawing

signal flow graph.

L

eieo

R1

R2

Fig. 2 (b)

7

3. a) Define.

7

i) Delay time ii) Rise time

iii) Peak time iv) Peak overshoot

v) Settling time vi) Peak time

vii) Time response

b) Find the all time domain specifications for unity feedback system.

8s4s

8)s(G

2 .

OR

6

4.

a) Transfer function of a system is 10s2s

10

)s(v

)s(v

2i

o

obtain time response when a step of

10v is applied at the input terminal of system.

7

b) Find step, rampund parabolic error coefficients for a feedback system having.

1s

10s)s(H&

)12s3s()8s4s(s

)3s(8)s(G

222

also find steady state error when subjected to an input .t3t25)t(r 2

6

5. a) Define stability and it's types.

6

b) State Hurwitz's stability criteria and Routh's stability criteria in detail.

OR

7

6. a) The open loop transfer function of a unity feedback control system is

)5s()2s(s

k)s(H)s(G

.

Sketch the root locus of the system and determine the value of K.

13

7.

For the system having open loop transfer function )10s()1s(s

10)s(H)s(G

.

Determine the stability of system by plotting bode plot.

OR

13

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NRJ/KW/17/4520/4525 3 P.T.O

8. a) Write a short note on Nyquist criteria.

6

b) Draw polar plot of )8s()4s()2s(

100)s(H)s(G

.

7

9. a) Compare the lead-lag compensator. Explain cascade compensation.

7

b) Derive the transfer function of lead-lag compensator.

OR

7

10 a) Derive the transfer function of lag compensator.

7

b) Justify the selection of lead and lag compensator for following parameter.

i) Bandwidth ii) Noise susceptibility

iii) Type of system

7

11. a) Define.

6

i) State ii) State variable

iii) State vector iv) State space

v) State trajectory

b) Find the state model in canonical form of a system whose transfer function is

)5s()3s()2s(

1s

)s(U

)s(Y

.

OR

7

12. a) Obtain the state space model for network shown in 'Fig. 12 (a) '.

Vc

Fig. 12 (a)

V+

_

LR

6

b) Transfer function of system is defined by.

s4s5s

3s2s

)s(V

)s(Y

23

2

Obtain canonical state space model & draw it's block diagram representation.

7

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Documents

H R(s) G Fig. 1 (a) · i) Gain margin (GM) and phase margin (PM) from the polar plot. 6 b) Draw the polar plot for a unity feedback system with forward path transfer function given