NapurStudents - BE | M.Tech | MCA | MBA · 4. Solve Question 5 OR Questions No. 6. 5. Solve...

NKT/KS/17/7396 1 P.T.O

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

P. Pages : 4 NKT/KS/17/7396

Time : Three Hours Max. Marks : 80

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Notes : 1. All questions carry marks as indicated.

2. Solve Question 1 OR Questions No. 2.






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

9. Assume suitable data whenever necessary.

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

11. Use of non programmable calculator is permitted.

1. a) Differentiate between hydraulic and pneumatic actuators.

4

b) Write equation of motion of translational mechanical system shown in fig. 1(b) and

determine Transfer function.

F(t)

x2(t)

10kg

2 N-s/m5 N-s/m2 N/m

Fig. 1(b)

9

OR

2. a) Explain in brief classification of control system.

4

b) Determine Transfer function of rotational mechanical system shown in fig. 2 (b)

T(t) 1 N-s/rad

1kg.m2 N1=25

4 N.m/rad

Q2

N2=50

Fig. 2(b)

9

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3. a) Simplify the following system shown in fig. 3 (a) using block diagram algebra and

determine transfer function C(s) / R(s)

S S

2S

4

1S

1

R(S)

C(S)+

–+

Fig. 3(a)

–

+ +

+

–

–

8

b) Name four components of block diagram for liner time invariant system.

5

OR

4. a) Explain following terms w.r.to signal flow graph.

i) Forward path ii) Feed back path. iii) Source and sink node.

5

b) Determine transfer function C(s) / R(s) of signal flow graph show in fig. 4 (b) using

Mason's gain formula.

R(S)C(S)

G7 G8

G5G6

G1 G2

G3

G4 Fig. 4(b)

8

5. a) Explain PID controllers and there characteristics.

6

b) A unity feed back system has

)5S2S()2S(S

K)s(G

2

i) Determine limiting value of gain 'K' for unit ramp input so that 2.0ess

ii) Determine sse for input 2

2tt42)t(r

8

OR

6. a) Explain general principles for generating control action.

5

b) Determine transient response specifications of mechanical system shown in fig. 6 (b)

33N/m

15 N-s/m

x(t)

F(t)3kg

Fig. 6(b)

9 NapurStudents.Org

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7. For the transfer function having characteristic equation

20s38s48s59s39s22s12ss)s(H)s(G1 2345678

comment on system stability using Routh's criterion.

Also, tell how many poles lies in RH, in LH and on Jw axis.

13

OR

8. Sketch the root locus for a system represented by block diagram as below.

R(S) 4S2S

20S4SK 2

C(S)

Fig. 8

+

_

i) determine gain 'K' for 45.0

ii) determine marginal value of gain 'K'

iii) find range of 'K' within which system is stable.

13

9. Draw the Bode log-magnitude and phase plots for

)25s2s()2s(

)3s()s(GH

2

Determine

i) Gain margin (Gm)

ii) Phase margin (Pm)

iii) Comment on stability

14

OR

10. a) Draw polar plot for system having

)2s()1s(s

12)s(GH

state whether system is stable or not.

8

b) Find open loop transfer function of system having Bode magnitude plot as shown in fig.

10 (b)

–20dB/doc

–40dB/doc

5 10

50

–60dB/doc

Fig. 10(b)

6

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11. a) Determine whether the system given below is completely controllable and observable or

not.

x131y

U

7

3

2

x

384

132

6186

x

8

b) Explain controllability and observability of the system.

5

OR

12. a) Explain phase Lead-Lag compensation.

5

b) Construct the state model for the system given by the differential eqn.

y6dt

dy11

dt

yd6

dt

yd

2

2

3

3

give block diagram representation of the state model.

8

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KNT/KW/16/7396 1 P.T.O

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

P. Pages : 4 KNT/KW/16/7396


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


10. Diagrams and chemical equations should be given whenever necessary.


12. Use of non programmable calculator is permitted.

1. a) Find T. F.

)s(Y

)s(Y

1

2

M1

M2

K1K2

B2

B1

K3B3 K4

y2

y1

Fig. 1 (a)

7

b) Find T. F.

)s(E

)s(E

i

o

C1

R1

C2

R2

+

–

+

–

ei (t)eo (t)

R3

Fig. 1 (b)

R4

OR

7

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KNT/KW/16/7396 2

2. a) Explain open loop and close loop control system with advantages and disadvantages.

6

b) Find T. F.

)s(E

)s(X

i

R L

C

K1K2

B

M x(t)

I1(t) I2(t)

Fig. 2 (b)

ei(t)

8

3. a) Find

)s(R

)s(C by using Block Reduction Technique.

G1 G2 G4

G3

H2H1

–––

R(s) C(s)

Fig. 3 (a)

6

b) Convert the given algebric equations into signal flow graph and find its transfer function.

37264

3522143

33112

YGYGY

YGYGYGY

YGYGY

Where Y4 is output and Y1 is input.

OR

7

4. a) Obtain

)s(R

)s(C using block reduction technique.

G1 G2

R(s)

–G3

H1H2H3

– –

C(s)

Fig. 4 (a)

6

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KNT/KW/16/7396 3 P.T.O

b) Convert the given block diagram into SFG & find T. F.

G1 G2

R(S) C(S)

–

+

–

H2

H1

Fig. 4 (b)

7

5. a) Derive the transfer function of field controlled DC motor.

7

b) Derive an expression for unit ramp response of first order system.

OR

7

6. a) Find response of a given system for time of 0.5 sec when OLTF is G(s) H(s) =

)8s(s

36

with step input of 2.5 units. Also find maximum output; peak time; rise time; settling time.

7

b) A system is described as –

x100y49dt

dy10

dt

yd

2

2

Find response, maximum output and all time domain specifications for a step input of 2.85

units.

7

7. a) Explain PID controller with its applications.

5

b) For unity feedback system –

)s25.01)(s4.01(s

K)s(G

Find Range of value of K, Kmas and frequency of sustained oscillation. Also check the

stability of the system.

OR

8

8. For a control system having

)5s4s(

)1s(K)s(G

2

and feedback H(s) = 1/s. Sketch the root

locus when the gain K varies upto .

13

9. Draw bode plot for following function

)20s)(2s(s

80)s(H)s(G

Find gain margin and phase margin for the stability of given system.

OR

14

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KNT/KW/16/7396 4

10. a) Determine T. F. of the system as shown in fig.

1 10 100

40db - 20db/dec

- 40db/dec

- 60db/dec

- 40db/dec

7

b) Draw polar plot & find GM and PM

)8s)(4s(s

40)s(H)s(G

7

11. a) Explain the term controllability and observability.

6

b) Give the state space representation for the system whose T. F. is given by –

1s5.2s5.1s

2

)s(U

)s(Y

34

OR

7

12. a) Find T. F. of the system. Check whether the system is observable and controllable or not

1

0

0

x

x

x

6116

100

010

x

x

x

3

2

1

3

2

1

3

2

1

x

x

x

001Y

8

b) Explain lag-lead compensation and pole-zero placement in detail.

5

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NJR/KS/18/4535 1 P.T.O

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

P. Pages : 4 NJR/KS/18/4535


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10. Simple Graph paper, Semilog paper and Polar Graph Paper.

1. a)

7

( )

( )2x s

FindF s

b) Find the transfer function

( )

( )0V s

Vi t

7

OR

2. a) Explain the servo-mechanism. Give its advantages, disadvantages & applications.

7

b) What is control system. Give the classification of control systems.

7

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NJR/KS/18/4535 2

3. a) Find

( )

( )

C s

R s for the given block diagram.

7

b) Obtain the transfer function

( )

( )

C s

R s from the following signal flow graph.

6

OR

4. a) Obtain the expression for 1 2C &C for the given multiple input & multiple output system.

7

b) Convert the following equations into the signal flow graph & find out its transfer function.

2 1 1 3 3

3 4 1 2 2 5 3

4 6 2 7 3

Y G Y G Y

Y G Y G Y G Y

Y G Y G Y

= +

= + +

= +

6

5. a) Derive the expression for the first order system with unit ramp input.

7

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NJR/KS/18/4535 3 P.T.O

b) For unity Feedback system having open loop transfer function

( )( )( )

18G(s) find

s s 6 s 2 s 5=

+ + +

i) Type of system ii) Error coefficients

iii) Steady state error when input to the system is ( ) 262

r t 10 5t t= + + .

OR

6

6. a) A second order system is given by

( )

( ) 2

C s 25,

R s s 6s 25=

+ + find out it's transient response

specifications & also calculate expression for its out put response.

8

b) Explain PID controller with its applications.

5

7. a) Using routh's array criterion. Find value of k.

( )( )

( )( )2

k s 1GH s

s s 1 s 3s 26

+=

+ + +

7

b) Explain the concept of stability. Define stable, unstable & marginally stable system.

6

OR

8. ( )

( )

( )( )2

k s 1G(s) H s

s s 1 s 5s 25

+=

− + +

Sketch the complete root locus with approximate indication of break away points.

13

9. Draw Bode plot for system has ( ) ( )

( )( )( )

kG s H s

s s 1 1 0.1s 1 0.01s=

+ + +

determine the value of k, so that,

i) G.M. = + 10 db ii) P.M. = + 25º.

14

OR

10. a) Find out the transfer function of the given system. 7

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NJR/KS/18/4535 4

b) Draw the polar plot for a given system

( ) ( )( )( )

10G s H s

s s 1 s 2=

+ +

Find out it's gain margin in db.

7

11. a) Explain the term controllability & observability.

6

b) Calculate the transfer function of given system having state space model

11

22

1

2

X2 3 3XV

X4 2 5X

Xy 1 1

X

− − = +

=

OR

7

12. a) Find out the controllability & observability of the system whose matrix is given by

1 0 1 0

A 2 3 0 B 2 C 1 0 0

0 2 3 0

= − − = = − −

8

b) Explain lag-lead compensation.

5

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