Code No: R05312106

R05

Set No. 2

in

III B.Tech I Semester Examinations,May 2011 CONTROL SYSTEMS Aeronautical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Derive the transfer function of an a.c. servomotor and draw its characteristics.

[8+8]

ld .

(b) Explain the Synchro error detector with circuit diagram.

2. With the help of examples explain the effect of adding poles & zeros to the open loop transfer function G(s)H(s) on the shape of Nyquist diagrams. [16]

3. Sketch the root locus plot of a unity feedback system whose open loop T.F is G(s) = s(sK(s+9) [16] 2 +4s+11) .

or

4. (a) Solve the following differential equation by converting it into state variable 2 − 2y = u (t) e−t Where y(0)=0, y˙ (0) = 0; u(t)=unit step input form ddt2y + dy dt

uW

(b)  The state equation of a linear time    invariant   system is given by x1 (t) 0 1 x1 (t) 0 = + r (t) x2 (t) −1 −2 x2 (t) 1 Find the state transistion matrix φf(t).

[10+6]

5. (a) Bandwidth is directly proportional to ωn . Justify (b) The forward path transfer function of a unity feed back system is G(s) = K . Find the resonant peak, resonant frequency & Bandwidth of closed s(s+6.54) loop system for

nt

i. K = 5 ii. K = 21.39 iii. K = 100. Comment on the result.

[6+10]

6. (a) What is compensation? What are the different types of compensators?

Aj

(b) What is a lead compensator, obtain the transfer function of lead compensator and draw pole-zero plot? (c) Explain the different steps to be followed for the design of lead compensator using Bode plot? [3+3+10]

7. The open loop T.F of a unity feed back system G(s) =

K s(1+sT )

(a) Find by what factor the gain K be reduced so that overshoot is reduced from 75% to 25%. (b) Find by what factor the gain K be reduced so that the damping ratio is increased from 0.1 to 0.6. [16] 1

Code No: R05312106

R05

Set No. 2

8. (a) Explain the linearizing effect of feedback. (b) The dynamic behaviour of the system is described by the equation, dC + 10C = 40e, where ‘e’ is the input and ‘C’ is the output. Determine the dt transfer function of the system. [10+6]

Aj

nt

uW

or

ld .

in

?????

2

Code No: R05312106

R05

Set No. 4

in

III B.Tech I Semester Examinations,May 2011 CONTROL SYSTEMS Aeronautical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) What is compensation? What are the different types of compensators?

ld .

(b) What is a lead compensator, obtain the transfer function of lead compensator and draw pole-zero plot? (c) Explain the different steps to be followed for the design of lead compensator using Bode plot? [3+3+10] 2. The open loop T.F of a unity feed back system G(s) =

K s(1+sT )

or

(a) Find by what factor the gain K be reduced so that overshoot is reduced from 75% to 25%. (b) Find by what factor the gain K be reduced so that the damping ratio is increased from 0.1 to 0.6. [16]

uW

3. (a) Solve the following differential equation by converting it into state variable 2 − 2y = u (t) e−t Where y(0)=0, y˙ (0) = 0; u(t)=unit step input form ddt2y + dy dt (b)  The state equation of a linear time    invariant   system is given by x1 (t) 0 1 x1 (t) 0 = + r (t) x2 (t) −1 −2 x2 (t) 1 Find the state transistion matrix φf(t).

[10+6]

4. (a) Explain the linearizing effect of feedback.

nt

(b) The dynamic behaviour of the system is described by the equation, dC + 10C = 40e, where ‘e’ is the input and ‘C’ is the output. Determine the dt transfer function of the system. [10+6]

5. (a) Bandwidth is directly proportional to ωn . Justify

Aj

(b) The forward path transfer function of a unity feed back system is G(s) = K . Find the resonant peak, resonant frequency & Bandwidth of closed s(s+6.54) loop system for i. K = 5 ii. K = 21.39 iii. K = 100. Comment on the result.

[6+10]

6. (a) Derive the transfer function of an a.c. servomotor and draw its characteristics. (b) Explain the Synchro error detector with circuit diagram. 3

[8+8]

Code No: R05312106

R05

Set No. 4

7. With the help of examples explain the effect of adding poles & zeros to the open loop transfer function G(s)H(s) on the shape of Nyquist diagrams. [16] 8. Sketch the root locus plot of a unity feedback system whose open loop T.F is [16] G(s) = s(sK(s+9) 2 +4s+11) .

Aj

nt

uW

or

ld .

in

?????

4

Code No: R05312106

R05

Set No. 1

in

III B.Tech I Semester Examinations,May 2011 CONTROL SYSTEMS Aeronautical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) What is compensation? What are the different types of compensators?

ld .

(b) What is a lead compensator, obtain the transfer function of lead compensator and draw pole-zero plot? (c) Explain the different steps to be followed for the design of lead compensator using Bode plot? [3+3+10] 2. With the help of examples explain the effect of adding poles & zeros to the open loop transfer function G(s)H(s) on the shape of Nyquist diagrams. [16] K s(1+sT )

or

3. The open loop T.F of a unity feed back system G(s) =

(a) Find by what factor the gain K be reduced so that overshoot is reduced from 75% to 25%.

uW

(b) Find by what factor the gain K be reduced so that the damping ratio is increased from 0.1 to 0.6. [16] 4. (a) Solve the following differential equation by converting it into state variable 2 form ddt2y + dy − 2y = u (t) e−t Where y(0)=0, y˙ (0) = 0; u(t)=unit step input dt

nt

(b)  The state equation of a linear time    invariant   system is given by x1 (t) 0 1 x1 (t) 0 = + r (t) x2 (t) −1 −2 x2 (t) 1 Find the state transistion matrix φf(t).

[10+6]

5. (a) Derive the transfer function of an a.c. servomotor and draw its characteristics. (b) Explain the Synchro error detector with circuit diagram.

[8+8]

6. (a) Explain the linearizing effect of feedback.

Aj

(b) The dynamic behaviour of the system is described by the equation, dC + 10C = 40e, where ‘e’ is the input and ‘C’ is the output. Determine the dt transfer function of the system. [10+6]

7. (a) Bandwidth is directly proportional to ωn . Justify (b) The forward path transfer function of a unity feed back system is G(s) = K . Find the resonant peak, resonant frequency & Bandwidth of closed s(s+6.54) loop system for i. K = 5 ii. K = 21.39 5

Code No: R05312106

R05

Set No. 1

iii. K = 100. Comment on the result.

[6+10]

8. Sketch the root locus plot of a unity feedback system whose open loop T.F is [16] G(s) = s(sK(s+9) 2 +4s+11) .

Aj

nt

uW

or

ld .

in

?????

6

Code No: R05312106

R05

Set No. 3

in

III B.Tech I Semester Examinations,May 2011 CONTROL SYSTEMS Aeronautical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Derive the transfer function of an a.c. servomotor and draw its characteristics.

2. (a) Explain the linearizing effect of feedback.

[8+8]

ld .

(b) Explain the Synchro error detector with circuit diagram.

(b) The dynamic behaviour of the system is described by the equation, dC + 10C = 40e, where ‘e’ is the input and ‘C’ is the output. Determine the dt transfer function of the system. [10+6]

or

3. Sketch the root locus plot of a unity feedback system whose open loop T.F is G(s) = s(sK(s+9) [16] 2 +4s+11) . 4. (a) Bandwidth is directly proportional to ωn . Justify

uW

(b) The forward path transfer function of a unity feed back system is G(s) = K . Find the resonant peak, resonant frequency & Bandwidth of closed s(s+6.54) loop system for

i. K = 5 ii. K = 21.39 iii. K = 100. Comment on the result.

5. The open loop T.F of a unity feed back system G(s) =

[6+10] K s(1+sT )

nt

(a) Find by what factor the gain K be reduced so that overshoot is reduced from 75% to 25%.

(b) Find by what factor the gain K be reduced so that the damping ratio is increased from 0.1 to 0.6. [16]

Aj

6. (a) Solve the following differential equation by converting it into state variable 2 − 2y = u (t) e−t Where y(0)=0, y˙ (0) = 0; u(t)=unit step input form ddt2y + dy dt

(b)  The state equation of a linear time    invariant   system is given by x1 (t) 0 1 x1 (t) 0 = + r (t) x2 (t) −1 −2 x2 (t) 1 Find the state transistion matrix φf(t).

[10+6]

7. With the help of examples explain the effect of adding poles & zeros to the open loop transfer function G(s)H(s) on the shape of Nyquist diagrams. [16] 8. (a) What is compensation? What are the different types of compensators? 7

Code No: R05312106

R05

Set No. 3

(b) What is a lead compensator, obtain the transfer function of lead compensator and draw pole-zero plot? (c) Explain the different steps to be followed for the design of lead compensator using Bode plot? [3+3+10]

Aj

nt

uW

or

ld .

in

?????

8

R05 Set No. 2

(a) Derive the transfer function of an a.c. servomotor and draw its characteristics. (b) Explain the Synchro error detector with circuit diagram. [8+8]. 3. AjntuWorld.
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