R07 Set No. 2 - Institute Of Aeronautical Engineering · (b) Explain the steps for the construction of Bode plots. (c) Explain the procedure for the determination of transfer function

Code No: 07A5EC16 R07 Set No. 2

III B.Tech I Semester Examinations,December 2011CONTROL SYSTEMS

Common to Aeronautical Engineering, Electronics And InstrumentationEngineering

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

All Questions carry equal marks? ? ? ? ?

1. The open loop transfer function of certain unity feedback control system is givenby G(S) = K

S(S+4)(S+80). It is desired to have the phase margin to be at least 330 and

velocity error constant KV = 30 Sec−1. Design a phase lag series compensator?[16]

2. (a) Define transfer function. From fundamentals, derive the transfer functions ofopen loop and closed loop systems.

(b) Derive the transfer function for the Series RLC network. [8+8]

3. (a) Explain about the effect of adding poles and zeros to G(s)H(s) on the rootlocus.

(b) Determine the Kp, Kv, and Ka for a unity feedback system with the followingopen loop transfer function G (s) = 1000

s(s+10)(s+100), and hence calculate the

steady state error for r (t) = (2 + t) u (t) [8+8]

4. (a) Using block diagram reduction technique, determine C(s)/R(s) for the follow-ing system shown in figure 4.

Figure 4:

(b) Describe the operation of tachometer and derive its transfer function with itsconstant. [8+8]

5. (a) Define:

i. Minimum phase TF

ii. Non minimum phase TF

(b) Explain the steps for the construction of Bode plots.

1


(c) Explain the procedure for the determination of transfer function from Bodeplots. [4+4+8]

6. (a) For an underdamped second order system, define various time domain speci-fications.

(b) The forward path T.F. of a unity feed back control system is given by G (s) =9

s(s+3). Obtain the expression for unit step response of the system. [8+8]

7. (a) Construct two different state models for the systems characterized by thefollowing differential equation?•••y + 3

••y + 2

•y =

•u + u

(b) Draw the block diagram of the system described by state model•x1•x2•x3

=

0 1 00 0 10 a2 a3

x1

x2

x3

+

001

u and y = x1. [8+8]

8. (a) Explain the effect of addition of a pole at the origin on the polar plot of agiven system.

(b) Sketch the polar plot & hence find the frequency at which the plot intersectsthe +ve imaginary axis for the system G(s) = 0.1

s2(1+s)(1+0.1s). Also find the

corresponding magnitude. [6+10]

? ? ? ? ?

2










••y + 2

•y =

•u + u


=

0 1 00 0 10 a2 a3

x1

x2

x3

+

001

u and y = x1. [8+8]




Figure 4:





3


6. (a) Define:

i. Minimum phase TF












? ? ? ? ?

4














Figure 4:


4. (a) Define:

i. Minimum phase TF





••y + 2

•y =

•u + u

5



=

0 1 00 0 10 a2 a3

x1

x2

x3

+

001

u and y = x1. [8+8]










? ? ? ? ?

6




















••y + 2

•y =

•u + u


=

0 1 00 0 10 a2 a3

x1

x2

x3

+

001

u and y = x1. [8+8]



7


Figure 6:




8. (a) Define:

i. Minimum phase TF




? ? ? ? ?

8

R09Code No: 09A50203 SET-1 B. Tech III Year I Semester Examinations, December-2011

CONTROL SYSTEMS (COMMON TO EEE, ECE, ETM)

Time: 3 hours Max. Marks: 75 Answer any five questions

All questions carry equal marks ---

1.a) Write the advantages and disadvantages of open loop and closed loop systems. b) Write the effects of feedback. [8+7] 2. Draw a signal flow graph and find its closed loop transfer function and verify it

using signal flow graph. [15]

3.a) Obtain the unit step response of a unity feedback system whose open loop transfer

function is G(S) = 4/S(S+5). b) Determine the step, ramp and parabolic error constants of the unity feedback

control system. The open loop transfer function is following. G(S) = 1000/(1+0.1S)(1+10S). [8+7]

4.a) Write the necessary conditions for stability. b) Consider a sixth order system with the characteristic equation, S6+2S5+8S4+13S3+20S2+16S+16 = 0. Using routh stability criterion, find whether the system is stable or not, give the reasons. [7+8] 5.a) For the given transfer function G(S) = 10/(S+2). Sketch magnitude in dB VS

frequency. b) From the above plot calculate the following.

i) Gain crossover frequency. ii) Actual magnitude at corner frequency. [7+8]

6. Sketch the polar plot for G(S) = K/S(S+1)(S+2) and for what value of K it is

stable. [15] 7. Locate the poles and zeros of lead-lag network and sketch its magnitude bode plot. [15] 8.a) Define controllability and observability. b) Evaluate the controllability of the system with the matrix. [7+8]

1 0 2

,0 2 5

A B−⎡ ⎤ ⎡

= =⎤

⎢ ⎥ ⎢− ⎥⎣ ⎦ ⎣ ⎦

--ooOoo--

R09Code No: 09A50203 SET-2B. Tech III Year I Semester Examinations, December-2011




1.a) Differentiate between open loop and closed loop systems. b) What are the characteristics of feedback? [7+8] 2.a) Write the applications of AC servo motor and DC servo motor. b) Explain the synchro transmitter and receiver and write its advantages. [7+8] 3.a) Obtain the unit ramp response of a unity feedback system, whose open loop

transfer function is G(S) = 5/S(S+4). b) The open loop transfer function of a unity feedback control system is

G(S)=100/S(1+0.1S). Determine the steady state error of the system when the input r(t) = (2+5t) u(t). [7+8]

4.a) A unity feedback controlled system is characterized by open loop transfer function G(S) = k(S+13)/s(S+3)(S+7) using routh criterion calculate the range of value k for the system to be stable.

b) Write the root locus of the system whose open loop transfer function is G(S) H(S) = k/S(S+5). [7+8]

5. Sketch the bode plots for the transfer function G(S) = 200/S(S+5)(S+10).

Calculate gain margin and phase margin. [15] 6. Find the stability of k for the transfer function G(S) = K/S(S+5)(S+10) using polar

plot. [15] 7. Locate the poles and zeros of lag network and lead network and sketch their polar

plots. [15] 8.a) Obtain the state transition matrix for the system

0

1 10

22

3 10 1

x xxx

⎡ ⎤ − ⎡ ⎤⎡ ⎤⎢ ⎥ = ⎢ ⎥⎢ ⎥⎢ ⎥ −⎣ ⎦ ⎣ ⎦⎣ ⎦

b) Define controllability and Observability. [7+8]

--ooOoo--





1.a) Write a general second order differential equation and obtain its transfer function. b) Write the analogous quantities in force-voltage analogy and force-current analogy. [7+8] 2. Draw a signal flow graph and find its closed loop transfer function. Verify it using signal flow graph. [15]

3.a) Write the specifications of a second order system. b) Sketch the impulse response of a second order system when damping factor is

i) 0 ii) Between 0 and 1 iii) Greater than 1 [7+8] 4.a) The characteristic equation for certain feedback control systems is given below.

S4+4S3+13S2+36S+k = 0. Determine the range of K for the system to be stable. b) Write the important rules of root locus to construct. [7+8] 5.a) Define gain crossover frequency, phase crossover frequency, gain margin and

phase margin. b) Sketch the bode plot for the transfer function G(S) = 10/S(S+5). Calculate gain

crossover frequency. [7+8] 6.a) Differentiate between polar plot and Nyquist plot. b) Explain the Nyquist stability criterian. Write its advantages. [7+8] 7. Obtain the transfer function of Lag and Lead networks. Locate their poles and

zeors and write their advantages. [15] 8.a) Write the properties of state transition matrix. b) Evaluate the observability of the system with the following matrices. [7+8]

[ ]1 0, 1

0 2A C

−⎡ ⎤= =⎢ ⎥−⎣ ⎦

3

--ooOoo--

B. Tech III Year I Semester Examinations, December-2011 R09Code No: 09A50203 SET-4




1.a) Explain the effects of feedback in control systems.

b) Give a simple example of a translational mechanical system and find it’s transfer function. [7+8]

2. Obtain the overall transfer function C/R from the signal flow graph shown in

figure 1.

figure 1


function is G(S) = 10/S(S+10) b) Determine the step, ramp and parabolic error constants of the unity feedback

control system. The open loop transfer function is G(S) = 10/S(1+0.1S)(1+10S). [7+8]

4.a) Write the rules to construct the root locus.

b) Sketch the root locus plot of a unit feedback system with the open loop transfer function G(S) = K/S(S+2)(S+4). [7+8]

5. Sketch the magnitude in dB vs Frequency and phase vs Frequency for the given

transfer function G(S) = 10(S+2)/S(S+5). [7+8] 6.a) How to calculate phase margin and gain margin using polar plots. b) Sketch the polar plot for G(S) = k/(S+5)(S+10). [7+8] 7.a) Why lag network and lead network are called compensating networks? b) Write the advantages of PID controllers and their applications. [7+8] 8.a) Explain state variable and state transition equation. b) Describe the properties of state transition matrix. [7+8]

--ooOoo--

R09Code No: 09A50203 SET-1 B. Tech III Year I Semester Examinations, December-2011




1.a) Write the advantages and disadvantages of open loop and closed loop systems. b) Write the effects of feedback. [8+7] 2. Draw a signal flow graph and find its closed loop transfer function and verify it

using signal flow graph. [15]


function is G(S) = 4/S(S+5). b) Determine the step, ramp and parabolic error constants of the unity feedback

control system. The open loop transfer function is following. G(S) = 1000/(1+0.1S)(1+10S). [8+7]

4.a) Write the necessary conditions for stability. b) Consider a sixth order system with the characteristic equation, S6+2S5+8S4+13S3+20S2+16S+16 = 0. Using routh stability criterion, find whether the system is stable or not, give the reasons. [7+8] 5.a) For the given transfer function G(S) = 10/(S+2). Sketch magnitude in dB VS

frequency. b) From the above plot calculate the following.

i) Gain crossover frequency. ii) Actual magnitude at corner frequency. [7+8]

6. Sketch the polar plot for G(S) = K/S(S+1)(S+2) and for what value of K it is

stable. [15] 7. Locate the poles and zeros of lead-lag network and sketch its magnitude bode plot. [15] 8.a) Define controllability and observability. b) Evaluate the controllability of the system with the matrix. [7+8]

1 0 2

,0 2 5

A B−⎡ ⎤ ⎡

= =⎤

⎢ ⎥ ⎢− ⎥⎣ ⎦ ⎣ ⎦

--ooOoo--





1.a) Differentiate between open loop and closed loop systems. b) What are the characteristics of feedback? [7+8] 2.a) Write the applications of AC servo motor and DC servo motor. b) Explain the synchro transmitter and receiver and write its advantages. [7+8] 3.a) Obtain the unit ramp response of a unity feedback system, whose open loop

transfer function is G(S) = 5/S(S+4). b) The open loop transfer function of a unity feedback control system is

G(S)=100/S(1+0.1S). Determine the steady state error of the system when the input r(t) = (2+5t) u(t). [7+8]

4.a) A unity feedback controlled system is characterized by open loop transfer function G(S) = k(S+13)/s(S+3)(S+7) using routh criterion calculate the range of value k for the system to be stable.

b) Write the root locus of the system whose open loop transfer function is G(S) H(S) = k/S(S+5). [7+8]

5. Sketch the bode plots for the transfer function G(S) = 200/S(S+5)(S+10).

Calculate gain margin and phase margin. [15] 6. Find the stability of k for the transfer function G(S) = K/S(S+5)(S+10) using polar

plot. [15] 7. Locate the poles and zeros of lag network and lead network and sketch their polar

plots. [15] 8.a) Obtain the state transition matrix for the system

0

1 10

22

3 10 1

x xxx

⎡ ⎤ − ⎡ ⎤⎡ ⎤⎢ ⎥ = ⎢ ⎥⎢ ⎥⎢ ⎥ −⎣ ⎦ ⎣ ⎦⎣ ⎦

b) Define controllability and Observability. [7+8]

--ooOoo--





1.a) Write a general second order differential equation and obtain its transfer function. b) Write the analogous quantities in force-voltage analogy and force-current analogy. [7+8] 2. Draw a signal flow graph and find its closed loop transfer function. Verify it using signal flow graph. [15]

3.a) Write the specifications of a second order system. b) Sketch the impulse response of a second order system when damping factor is

i) 0 ii) Between 0 and 1 iii) Greater than 1 [7+8] 4.a) The characteristic equation for certain feedback control systems is given below.

S4+4S3+13S2+36S+k = 0. Determine the range of K for the system to be stable. b) Write the important rules of root locus to construct. [7+8] 5.a) Define gain crossover frequency, phase crossover frequency, gain margin and

phase margin. b) Sketch the bode plot for the transfer function G(S) = 10/S(S+5). Calculate gain

crossover frequency. [7+8] 6.a) Differentiate between polar plot and Nyquist plot. b) Explain the Nyquist stability criterian. Write its advantages. [7+8] 7. Obtain the transfer function of Lag and Lead networks. Locate their poles and

zeors and write their advantages. [15] 8.a) Write the properties of state transition matrix. b) Evaluate the observability of the system with the following matrices. [7+8]

[ ]1 0, 1

0 2A C

−⎡ ⎤= =⎢ ⎥−⎣ ⎦

3

--ooOoo--

B. Tech III Year I Semester Examinations, December-2011 R09Code No: 09A50203 SET-4




1.a) Explain the effects of feedback in control systems.

b) Give a simple example of a translational mechanical system and find it’s transfer function. [7+8]

2. Obtain the overall transfer function C/R from the signal flow graph shown in

figure 1.

figure 1


function is G(S) = 10/S(S+10) b) Determine the step, ramp and parabolic error constants of the unity feedback

control system. The open loop transfer function is G(S) = 10/S(1+0.1S)(1+10S). [7+8]

4.a) Write the rules to construct the root locus.

b) Sketch the root locus plot of a unit feedback system with the open loop transfer function G(S) = K/S(S+2)(S+4). [7+8]

5. Sketch the magnitude in dB vs Frequency and phase vs Frequency for the given

transfer function G(S) = 10(S+2)/S(S+5). [7+8] 6.a) How to calculate phase margin and gain margin using polar plots. b) Sketch the polar plot for G(S) = k/(S+5)(S+10). [7+8] 7.a) Why lag network and lead network are called compensating networks? b) Write the advantages of PID controllers and their applications. [7+8] 8.a) Explain state variable and state transition equation. b) Describe the properties of state transition matrix. [7+8]

--ooOoo--

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Code No: 09A50204

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY, HYDERABAD

B. Tech III Year I Semester Examinations, May/June – 2013

Control Systems

(Common to EEE, ECE, ETM)

Time: 3 hours Max. Marks: 75

Answer any five questions

All questions carry equal marks

- - -

1.a) Explain the various types of control systems with suitable examples.

b) Obtain the transfer function of the mechanical system in figure 1. [15]

Figure.1

2.a) Determine the transfer function of the block diagram shown in figure 2.

Figure.2

b) Determine the closed loop transfer function for the signal flow graph shown in

figure 3. [15]

Figure.3

3.a) Define transfer function and determine the transfer function of the DC servo

motor.

b) Explain the operation of Synchro Transmitter. [15]

R09

Figure.2

b) Determine the closed loop transfer f

figure 3. [15]

Figure.1

2.a) Determine the transfer function of the block diagram shown in figure 2. 2.a) Determine the transfer function of

Figure.2

b) Determine the closed loop transfer f

figure 3. [15]

Figure.1

2.a) Determine the transfer function of the block diagram shown in figure 2. the block diagram shown in figure 2.

unction for the signal flow graph shown in unction for the signal flow graph shown in unction for the signal flow graph shown in unction for the signal flow graph shown in b) Determine the closed loop transfer fb) Determine the closed loop transfer fb) Determine the closed loop transfer fb) Determine the closed loop transfer f

the block diagram shown in figure 2. the block diagram shown in figure 2. the block diagram shown in figure 2. the block diagram shown in figure 2. the block diagram shown in figure 2. 2.a) Determine the transfer function of2.a) Determine the transfer function of2.a) Determine the transfer function of2.a) Determine the transfer function of2.a) Determine the transfer function of2.a) Determine the transfer function of2.a) Determine the transfer function of

Figure.1

unction of the mechanical system in figure 1. [15] unction of the mechanical system in figure 1. [15] unction of the mechanical system in figure 1. [15] unction of the mechanical system in figure 1. [15] unction of the mechanical system in figure 1. [15] unction of the mechanical system in figure 1. [15] b) Obtain the transfer function of the mechanical system in figure 1. [15] b) Obtain the transfer f b) Obtain the transfer f b) Obtain the transfer f b) Obtain the transfer f

All questions carry equal marks All questions carry equal marks All questions carry equal marks All questions carry equal marks

Time: 3 hours Max. Marks: 75 Time: 3 hours Max. Marks: 75 Time: 3 hours Max. Marks: 75 Time: 3 hours Max. Marks: 75 Time: 3 hours Max. Marks: 75 Time: 3 hours Max. Marks: 75 Time: 3 hours Max. Marks: 75 Time: 3 hours Max. Marks: 75 Time: 3 hours Max. Marks: 75

B. Tech III Year I Semester Examinations, May/June – 2013 B. Tech III Year I Semester Examinations, May/June – 2013 B. Tech III Year I Semester Examinations, May/June – 2013

Control Systems

B. Tech III Year I Semester Examinations, May/June – 2013

Control Systems

B. Tech III Year I Semester Examinations, May/June – 2013 B. Tech III Year I Semester Examinations, May/June – 2013

CAL UNIVERSITY, HYDERABAD CAL UNIVERSITY, HYDERABAD CAL UNIVERSITY, HYDERABAD JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY, HYDERABAD JAWAHARLAL NEHRU TECHNOLOGIJAWAHARLAL NEHRU TECHNOLOGIJAWAHARLAL NEHRU TECHNOLOGIJAWAHARLAL NEHRU TECHNOLOGI

R09

unction for the signal flow graph shown in

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4.a) Explain the standard test signals that are used in the time-domain analysis.

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

G(s)=K/s(s+10). Determine the gain ‘K’ so that the system will have a damping

ratio of 0.5. For this value of ‘K’, determine the settling time, peak overshoot and

time to peak overshoot for a unit-step unit. [15]

5. Define phase margin and gain margin and sketch the bode plot for the following

transfer function:

G(s) H(s) =K s2 / (1+0.25s) (1+0.025s) [15]

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

G(s) =K/ (s+2) (s+4) (s2+6s+25)

Using R-H criterion discuss the stability of the closed-loop system as a function

of ‘K’. Determine the values of ‘K’ which will cause sustained oscillations in the

closed-loop system. What are the corresponding oscillation frequencies? [15]

7. A unity feedback control system has an open loop transfer function

G(s) = K/s2 (s+2)

Sketch the Root-Locus plot and show that the system is unstable for all values of

‘K’. [15]

8. Write short notes on:

a) Procedure to sketch the polar plot.

b) Lead- Compensation.

c) State Transition Matrix and its properties. [15]

********

‘K’. [15]



ead- Compensation.


********


the corresponding oscillation



‘K’. [15] ‘K’. [15]



properties. [15]

********

ead- Compensation.

c) State Transition Matrix and its


the corresponding oscillation



‘K’. [15]

ead- Compensation.



c) State Transition Matrix and its prope


‘K’. [15]

********

ead- Compensation. ead- Compensation. ead- Compensation. b) Lead- Compensation. ead- Compensation.

8. Write short notes on: 8. Write short notes on: 8. Write short notes on: 8. Write short notes on:

‘K’. [15] ‘K’. [15] ‘K’. [15] ‘K’. [15] ‘K’. [15] ‘K’. [15] ‘K’. [15] ‘K’. [15]

G(s) = K/s2 (s+2) G(s) = K/s

will cause sustained oscillations in the will cause sustained oscillations in the will cause sustained oscillations in the will cause sustained oscillations in the of ‘K’. Determine the values of ‘K’ which of ‘K’. Determine the values of ‘K’ which of ‘K’. Determine the values of ‘K’ which of ‘K’. Determine the values of ‘K’ which of ‘K’. Determine the values of ‘K’ which

transfer function: transfer function:

ng time, peak overshoot and ng time, peak overshoot and ng time, peak overshoot and ‘K’, determine the settli ‘K’, determine the settli ‘K’, determine the settliratio of 0.5. For this value ofratio of 0.5. For this value ofratio of 0.5. For this value of

has an open loop transfer function

st signals that are used in the time-domain analysis.









b) A unity feedback control system

4.a) Explain the standard te






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Figure 4:


5. (a) Define:

i. Minimum phase TF



1







••y + 2

•y =

•u + u


=

0 1 00 0 10 a2 a3

x1

x2

x3

+

001

u and y = x1. [8+8]





? ? ? ? ?

2










••y + 2

•y =

•u + u


=

0 1 00 0 10 a2 a3

x1

x2

x3

+

001

u and y = x1. [8+8]




Figure 4:





3


6. (a) Define:

i. Minimum phase TF












? ? ? ? ?

4














Figure 4:


4. (a) Define:

i. Minimum phase TF





••y + 2

•y =

•u + u

5



=

0 1 00 0 10 a2 a3

x1

x2

x3

+

001

u and y = x1. [8+8]










? ? ? ? ?

6




















••y + 2

•y =

•u + u


=

0 1 00 0 10 a2 a3

x1

x2

x3

+

001

u and y = x1. [8+8]



7


Figure 6:




8. (a) Define:

i. Minimum phase TF




? ? ? ? ?

8

Code No: R05312106 R05 Set No. 2

III B.Tech I Semester Examinations,May 2011CONTROL SYSTEMS

Aeronautical EngineeringTime: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

? ? ? ? ?

1. (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]

2. With the help of examples explain the effect of adding poles & zeros to the openloop 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 isG(s) = K(s+9)

s(s2+4s+11). [16]

4. (a) Solve the following differential equation by converting it into state variable

form d2ydt2

+ dydt− 2y = u (t) e−t Where y(0)=0, y (0) = 0; u(t)=unit step input

(b) The state equation of a linear time invariant system is given by[x1 (t)x2 (t)

]=

[0 1−1 −2

] [x1 (t)x2 (t)

]+

[01

]r (t)

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

s(s+6.54). Find the resonant peak, resonant frequency & Bandwidth of closed

loop system for

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?

(b) What is a lead compensator, obtain the transfer function of lead compensatorand draw pole-zero plot?

(c) Explain the different steps to be followed for the design of lead compensatorusing Bode plot? [3+3+10]

7. The open loop T.F of a unity feed back system G(s) = Ks(1+sT )

(a) Find by what factor the gain K be reduced so that overshoot is reduced from75% to 25%.

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

1


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

(b) The dynamic behaviour of the system is described by the equation,dCdt

+ 10C = 40e, where ‘e’ is the input and ‘C’ is the output. Determine thetransfer function of the system. [10+6]

? ? ? ? ?

2





? ? ? ? ?








form d2ydt2



]=

[0 1−1 −2

] [x1 (t)x2 (t)

]+

[01

]r (t)








loop system for

i. K = 5

ii. K = 21.39




3




s(s2+4s+11). [16]

? ? ? ? ?

4





? ? ? ? ?









form d2ydt2



]=

[0 1−1 −2

] [x1 (t)x2 (t)

]+

[01

]r (t)










loop system for

i. K = 5

ii. K = 21.39

5




s(s2+4s+11). [16]

? ? ? ? ?

6





? ? ? ? ?







s(s2+4s+11). [16]




loop system for

i. K = 5

ii. K = 21.39






form d2ydt2



]=

[0 1−1 −2

] [x1 (t)x2 (t)

]+

[01

]r (t)




7




? ? ? ? ?

8

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Code No: 09A50204 R09 Set No. 2

III B.Tech I Semester Examinations,May/June 2012CONTROL SYSTEMS

Common to Electronics And Telematics, Electronics And CommunicationEngineering, Electrical And Electronics Engineering



1. State and explain Nyquist stability criterion. Draw the Nyquist plot for the openloop transfer function G (s) = 1

s(1+0.1s)(1+s)and discuss the stability of the closed

loop system. [15]

2. (a) For the system shown in Figure 1, determine K1, K2, and ‘a’ such that the sys-tem will have a steady state gain of 1.0, a damping ratio & δ = 0 .6, ωn = 5.0.

(b) A unity feedback control system has the forward transfer function, G(s) =25

s(s+6). Find the rise time, peak time and the maximum over shoot for unit

step input. [8+7]

Figure 1

3. (a) Find the transfer function of the system shown in Figure 2.

(b) Find the transfer function of a AC servo motor. [7+8]

4. A unity feedback control system has the transfer function G (s) = Ks(s+a)

(a) Find the value of ‘K’ and ‘a’ to satisfy the frequency domain specifications ofMr=1.04 and ω r = 11.55 rad/sec.

(b) Evaluate the settling time and bandwidth of the system for the values of Kand a determined in part (a). [8+7]

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Figure 2

5. A unity feedback system has an open loop transfer function G(s) = Ks(s+2)(s+60)

.Design a Lead-Lag compensator to meet the following specifications:

(a) Phase margin is at least 400

(b) Steady state error for ramp input is 0.04 rad. [15]

6. Sketch the root-locus diagram of a control system whose loop transfer function isG(s)H(s) = K

s(s+4)(s+10). Using the diagram or otherwise find the values of gain at

breakaway points and at point of intersection of the loci with the imaginary axis.[15]

7. Explain the properties of state transition matrix. A linear time invariant system isdescribed by the state equation:

X =

[0 6−1 5

]X +

[01

][u] and y =

[1 0

]X, X(0) =

[00

]Obtain the state transition matrix. Hence obtain the output response y(t) , t ≥ 0for a unit step input. [15]

8. For the geared system shown below in Figure 3, find the transfer function relatingthe angular displacement θL to the input torque T1, where J1 , J2 , J3 refer tothe inertia of the gears and corresponding shafts. N1, N2, N3, and N4 refer to thenumber of teeth on each gear wheel. [15]

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**********

Figure 3


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Figure 3:





1. (a) Explain the Armature voltage controlled DC servomotor and obtain its trans-fer function.

(b) Obtain the overall transfer function for the block diagram in Figure 4.[8+7]

2. The characteristic equation of a feedback control system is s3+4Ks2+(K+3)s+10=0.Apply the Nyquist criterion to determine the values of K for a stable closed loopsystem. Check the answer by means of the Routh Hurwitz criterion. [15]

3. Sketch the Bode plot for the following transfer function and determine the systemgain K for the gain cross over frequency ωc to be 5 rad/sec.

G(s) = Ks2

(1+0.2s)(1+0.02s). [15]


G(s) = K(1+0.2s)(1+0.025s)s3(1+0.001s)(1+0.004s)

Sketch the complete root locus for −∞ < K <∞. Indicate the crossing points ofthe loci on the jω axis and the corresponding values of K at these points. Alsoindicate the range of K for which system closed loop system is stable. [15]

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Figure 4

5. The open-loop transfer function of a control system with unity feedback is G(s) =K

s(0.1s+1)(0.2s+1). Design a suitable compensator so that the system satisfies the follow-

ing performance specifications:

(a) Kv=100; or the steady-state error of the system due to a step ramp functioninput is 0.01 in magnitude and

(b) Phase margin ≥40 degrees. [15]

6. Derive the differential equation relating the position y(t) and the force f(t) as shownin figure 5. (b) Determine the transfer function y

f. [15]

Figure 5

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7. Explain the terms ‘state’ and ‘state variable’. Prove that the state spacerepresentation is not unique.

X =

[0 6−1 5

]X +

[01

][u]

Y =[

1 0]X, X(0) =

[00

][15]

8. Consider the system shown in Figure 6.

(a) The damping ratio of this system is 0.158 and the undamped natural frequencyis 3.16rad/sec. To improve the relative stability, we employ tachometer feed-back Figure 7.

(b) shows such a tachometer-feedback system. Determine the value of Kh so thatthe damping ratio of the system is 0.5. Draw unit-step response curves of boththe original and tachometer-feedback systems. Also draw the error-versus-timecurves for the unit-ramp response of both systems. [15]

Figure 6:

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Figure 7


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Figure 7:





1. (a) State and explain the Nyquist stability criterion.

(b) Sketch the Nyquist plot for the transfer function G(s)H(s) = 32(s+1.5)(s2+2s+5)

.

Discuss its stability. [7+8]

2. The block diagram representation of a second-order type 0 system is shown inFigure 8. Derive the frequency domain characteristics. [15]

3. (a) Determine the range of value of k for the system to be stable which is charac-terized by the equation s3 + 3Ks2 + (k+2)s+4 = 0.

(b) Explain how Routh Hurwitz criterion can be used to determine the absolutestability of a system. [8+7]

4. A unity feedback system has an open loop transfer function G(s) = Ks(s+2)(s+60)

.Design a Lead-Lag compensator to meet the following specifications:

(a) phase margin is at least 400

(b) Steady state error for ramp input is 0.04 rad. [15]

5. A linear time-invariant system is described by the following defferential equation:d2y(t)dt2

+ 2dy(t)dt

+ y(t) = u(t)

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Figure 8

Find the state space representation and obtain the complete response to unit stepinput and zero initial conditions. [15]

6. Using block diagram reduction techniques, find the closed loop transfer functionof the system whose block diagram is given in Figure 9 and verify the result usingsignal flow graph technique. [15]

Figure 9

7. A load having moment of inertia J and frictional coefficient B is driven througha gear as shown in Figure 10, write the differential equations and find transferfunction θ2(S)

T (S).

[15]

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Figure 10

8. (a) Consider the differential equation system given by y + 3y + 2y = 0, y(0) =0.1, y(0) = 0.05. Obtain the response y(t), subjected to the given initial condition.

(b) Consider a unity-feedback control system whose open-loop transfer functionis G(s) = K

s(Js+B). Discuss the effects of varying the values of K and B

on the steady-state error in unit-ramp response. [7+8]

? ? ? ? ?

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1. Using block diagram reduction techniques, find the closed loop transfer function ofthe system whose block diagram is given in Figure 11 and verify the result usingsignal flow graph technique. [15]

Figure 11:

2. (a) Distinguish between open loop and closed loop systems. Explain merits anddemerits of open loop and closed loop systems.

(b) With suitable example explain the classification of control systems. [8+7]

3. (a) Explain error contants Kp , Kv, Ka for type I system.

(b) Given the open - loop transfer function of a unity feedback system as G(s) =10

s(0.1s+1), find Kp , Kv, Ka. [7+8]

4. (a) Explain the following terms:

i. Frequency response

ii. Phase and gain margins.

(b) Sketch the Bode plot for the following transfer function G(s) = 75(1+0.2s)

s(s2+16s+100).

[7+8]

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5. The open loop transfer function of a feedback control system with unity feedbackis G(s) = K

(s+10)n . Sketch the root loci of the characteristic equation of the closedloop system for −∞ < K < ∞, with

(a) n=3

(b) n=4. Show all important information on the root loci. [15]

6. The open loop transfer function of the uncompensated system is G(s) = 2500Ks(s+25)

.Design a suitable compensator so that the system satisfies the following performancespecifications:

(a) The phase margin of the system should be greater than 45 degrees.

(b) The steady-state error due to a unit ramp function input should be less thanor equal to 0.01 rad/sec. [15]

7. (a) Explain the Nyquist criterion for assessing the stability of a closed loop system.

(b) Sketch the polar plot of the transfer function G(s) = 1(1+T1s)(1+T2s)(1+T3s)

. De-termine the frequency at which the polar plot intersects the real and imaginaryaxis of G(jω) plane. [7+8]

8. For a system represented by the state equation X(t) = A X(t)

the response of state X(t) =

[e−2t

−2e−2t

] when

[x1(0)x2(0)

]=

[1−2

]and X(t) =

[e−t

−e−t] when

[x1(0)x2(0)

]=

[1−1

]Determine the system matrix A and the state transition matrix. [15]

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Documents

R07 Set No. 2 - Institute Of Aeronautical Engineering · (b) Explain the steps for the construction of Bode plots. (c) Explain the procedure for the determination of transfer function