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Code No: R22026

II B. Tech II Semester Supplementary Examinations Jan/Feb - 2015

CONTROL SYSTEMS (Com. to EEE, ECE, EIE, ECC, AE)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions All Questions carry Equal Marks

~~~~~~~~~~~~~~~~~~~~~~~~

Note: Provide ordinary and Semi log graph sheets

1. a) Why negative feedback is preferred in control systems? What are the characteristics of

negative feedback?

b) Explain the effects of feedback on i) stability ii) sensitivity iii) External disturbance

(6M+9M)

2. a) Explain how a two phase servomotor differs from a normal induction motor.

b) Reduce the given block diagram (figure 1) and hence obtain the transfer function ( )

.( )

C s

R s

c) Compare ac and dc servomotors. (3M+8M+4M)

3. a) Define the test signals i) Step ii) Parabolic iii) Impulse

b) What is the effect of derivative control on damping ratio, peak overshoot, steady state error

and rise time.

c) Consider the closed-loop system given by .2)(

)(22

2

nn

n

sssR

sC

ωξω

ω

++= Determine the values of

ξ and so that the system responds to a step input with approximately 5% overshoot and

with a setting time of 2 sec. (Use the 2% criterion). (3M+4M+8M)

4. a) Explain the effects of adding poles and zeros to G(s)H(s) on the root loci.

b) Sketch the root locus for 0<K< , for the system with the open loop transfer function

)22)(2(

)()(2 +++

=ssss

KsHsG (5M+10M)

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G1

H2 H1

R(s) C(s)

- -

-

Figure 1

+ + G2

+

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Code No: R22026

5. Sketch the Bode plots for the following transfer functions and determine the system gain K for

the gain crossover frequency to be 10 rad/s (15M)

)12.0)(1()(

2.0

++=

−

sss

KesG

s

6. a) Enlist the step-by-step procedure for the construction of Nyquist plots.

b) A system is given by )12)(1(

14)(

2 ++

+=

sss

ssG .Sketch the Nyquist plot and hence determine

the stability of the system. (5M+10M)

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

b) What is a lag compensator, obtain the transfer function of lag compensator and draw pole-

zero plot?

c) Explain the different steps to be followed for the design of compensator using Bode plot?

(2M+3M+10M)

8. a) Explain the Concepts of Controllability and Observability?

b) Obtain the state transition matrix for the state model whose A matrix is given by

c) Enumerate the properties of state transition matrix? (5M+5M+5M)

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Code No: R22026

II B. Tech II Semester Supplementary Examinations Jan/Feb - 2015

CONTROL SYSTEMS (Com. to EEE, ECE, EIE, ECC, AE)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions All Questions carry Equal Marks

~~~~~~~~~~~~~~~~~~~~~~~~

Note: Provide ordinary and Semi log graph sheets

1. a) How are control systems classified?

b) Write the differential equations governing the behavior of the mechanical system shown in

figure 1 draw the mechanical network and obtain the transfer function. (6M+9M)

2. For the given electrical network Figure 2.

a) Obtain the signal flow graph

b) Compute the gain using the mason’s gain formula. (7M+8M)

3. a) What are the time domain specifications? Explain each of them.

b) A closed loop control system is represented by the differential equation

, where e = r-c is the error signal. Determine the undamped natural

frequency, damping ratio and percentage maximum overshoot for a unit step input.

(6M+9M)

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Code No: R22026

4. a) What do you mean by stability? Explain the qualitative and conditional stability?

b) Draw the complete root locus for )4)(2(

)()(++

=sss

KsHsG from the root locus plot, find

the range of values of K for which the system will have damped oscillatory response. Also,

determine the value of K for a damping ratio of ξ=0.5. (5M+10M)

5. a) Discuss the stability analysis from Bode plots.

b) Sketch the Bode plots for the following transfer functions and determine the system gain

K for the gain crossover frequency to be 10 rad/s (5M+10M)

)01.01)(1.01)(1()(

2

sss

KssG

+++=

6. a) What is the effect of adding a zero at origin to the to the open loop transfer

function on polar plot?

b) Sketch the polar plot of a system given by )12)(1(

1)(

2 ++=

ssssG . If the plot crosses the

real axis determine the corresponding frequency & magnitude (5M+10M)

7. a) What is lead compensator? When is it preferred?

b) Design a lag compensator that will provide a phase lag at 400 and alternation of 12 dB at 2

rad/sec. Determine its transfer function. (7M+8M)

8. a) Define i) State ii) State variable iii) State model

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

.

c) Obtain the state transition matrix for the state model whose A matrix is given by

(3M+8M+4M)

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Code No: R22026

II B. Tech II Semester Supplementary Examinations Jan/Feb - 2015

CONTROL SYSTEMS (Com. to EEE, ECE, EIE, ECC, AE)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions All Questions carry Equal Marks

~~~~~~~~~~~~~~~~~~~~~~~~

Note: Provide ordinary and Semi log graph sheets

1. a) Explain the limitations of closed loop system over open loop system.

b) Find the transfer function for the following mechanical system: Shown in figure 2

c) Define the term ‘impulse response of a system. (4M+8M+3M)

2. a) For the system represented in the given Figure 4 , obtain transfer function

b) Write down the signal flow equations and draw the signal flow graph for the above

system. (8M+7M)

3. a) Derive the expressions for rise time, peak over shoot, settling time of 2nd

order system of unit

step input.

b) A unit feedback system is characterized by an open-loop transfer function )5(

)(+

=ss

KsG

Determine the gain K so that the system will have a damping ratio of 0.5. For this value of

K determine settling time, peak overshoot and times to peak overshoot for a unit-step input.

(6M+9M)

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Code No: R22026

4. a) A feedback system has an open loop transfer function

( ) ( )( )952 ++

=sss

KsHsG

Determine by use of the Routh criterion, the maximum value of K for the closed loop

system to be stable.

b) A unity feedback system has the following open loop transfer function

Determine the stability of the system in terms of the parameter K. (7M+8M)

5. a) What are steps involved in constructing the Bode plot for a given G(jω)H(jω).

b) Sketch the magnitude and phase Bode plots. Determine the gain crossover frequency,

phase crossover frequency, gain margin and phase margin. (5M+10M)

)025.01)(25.01(

)1(20)(

2sss

ssG

++

+=

6. a) Define Polar plot? Explain how you can determine relative stability using polar plots.

b) Sketch the polar plot of a system given by )12)(1(

13)(

++

+=

sss

ssG . If the plot crosses

the real axis determine the corresponding frequency & magnitude (5M+10M)

7. a) Write the transfer function of a lag compensator and draw its polar plot and frequency

response plots.

b) Design a lead compensator that will provide a phase lead of 350 and again of 6.5 dB at 2.8

rad/sec. What will be the transfer function of the lead compensator that will satisfy the

above requirement? (7M+8M)

8. a) Test the controllability and observability of the system described by

b) Solve the following differential equation by converting it into state variable form

Where y(0)=0, (0) = 0; u(t)=unit step input. (8M+7M)

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Code No: R22026

II B. Tech II Semester Supplementary Examinations Jan/Feb - 2015

CONTROL SYSTEMS (Com. to EEE, ECE, EIE, ECC, AE)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions All Questions carry Equal Marks

~~~~~~~~~~~~~~~~~~~~~~~~

Note: Provide ordinary and Semi log graph sheets

1. a) Distinguish between:

i) Linear and non linear control system

ii) Open loop and closed loop control systems

iii) Time invariant and time varying control systems.

Give an example for each of the above.

b) Find the transfer function of the following system show in figure.3 (8M+7M)

2. a) Derive the transfer function of an a.c. servomotor and draw its characteristics.

b) Explain the Synchro error detector with circuit diagram. (8M+7M)

3. a) What is the difference between type and order of a control system? Explain each with an

example?

b) The Figure 2 shows PD controller used for the system. Determine the value of Td so that

the system will be critically damped? Calculate it’s settling time? (5M+10M)

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Code No: R22026

4. a) Enumerate the limitations of Routh criterion. (5M+10M)

b) By means of the Routh criterion, determine the stability of the system represented by the

following characteristic equations. For systems found to be unstable, determine the number

of roots of the characteristic equation in the right half of the s-plane.

i) 0520102 234 =++++ ssss ii) 054322 23456 =++++++ ssssss

5. a) Define the following terms

i) Gain margin ii) Gain crossover frequency

iii) Phase margin iv) Phase crossover frequency v) Corner frequency

b) Sketch the magnitude and phase Bode plots. Determine the gain crossover frequency, phase

crossover frequency, gain margin and phase margin. (5M+10M)

)05.01)(5.01(

10)(

ssssG

++=

6. a) State Nyquist Stability Criterion? Explain the use of Nyquist Stability Criterion in the

assessment of relative stability of a system.

b) With the help of Nyquist plot assess the stability of a system )2)(1(

3)(

ssssG

++=

What happens to stability if the numerator of the function is changed from 3 to 30?

(7M+8M)

7. a) What is the purpose of using compensator? What is the basis for the selection of a particular

compensator?

b) Explain the design procedure of a lag-lead compensator in frequency domain. (5M+10M)

8. a) Test the observability of the system described by

b) For a system described by the state equation the response is

;

Determine the system matrix A and the state transition matrix Φ(t). (5M+10M)

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