Rr220206 Control Systems Augsep 2008

8/14/2019 Rr220206 Control Systems Augsep 2008

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Code No: RR220206 Set No. 1II B.Tech II Semester Supplimentary Examinations, Aug/Sep 2008

CONTROL SYSTEMS( Common to Electrical & Electronic Engineering, Electronics &

Communication Engineering, Electronics & Instrumentation Engineering,Electronics & Control Engineering, Electronics & Telematics and

Instrumentation & Control Engineering)Time: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

1. (a) Derive the transfer function of the following electrical network. Figure 1a

Figure 1a(b) Briey explain the terms used in Signal ow graph. [8+8]

2. (a) Derive the transfer function of a eld controlled d.c. Servomotor and developthe block diagram. Clearly state the assumptions made in the derivation.

(b) What are the effects of feedback on the performance of a system? Brieyexplain. [8+8]

3. (a) Dene time constant and explain its importance.

(b) A unit feedback system is characterized by an open-loop transfer function G(s)= K/s(s+5). Determine the gain K so that the system will have a dampingratio of 0.5. For this value of K determine settling time, peak overshoot andtimes to peak overshoot for a unit-step input. [8+8]

4. (a) Show that the Routh?s stability criterion and Hurwitz stability criterion areequivalent.

(b) Consider a unity-feedback control system whose open-loop transfer functionis G(s)= K s (J s + B ) . Discuss the effects that varying the values of K and B hason the steady-state error in unit-ramp response. [8+8]

5. (a) Find the angle of arrival and the angle of departure at the complex zeros andcomplex poles for the root locus of a system with open-loop transfer functionG(s)H(s)= K (s

2 +1)s (s 2 +4 s +8)

(b) Draw the root locus diagram for a feedback system with open-loop transfer

function G(s)=K (s +5)s (s +3) . , following systematically the rules for the constructionof root locus. Show that the root locus in the complex plane is a circle. [8+8]

6. (a) Dene phase margin and gain margin. [4]

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Code No: RR220206 Set No. 1(b) Sketch bode plot & nd value of K such that gain cross - over frequency. is

5 rad/sec. G(s) = KS 2

(1+0.2

S )(1+0

.02

S )

[8+4]

7. (a) Construct the complete Nyquist plot for a unity feed back control systemwhose open loop transfer function is G(s)H(s) = K s (s 2 +2 s +2) . Find maximumvalue of K for which the system is stable.

(b) The open loop transfer function of a unity feed back system is G(s)= 1s (1+0 . 5s )(1+0 . 1s ) .Find gain and phase margin. If a phase lag element with transfer function of

1+2 s1+5 s is added in the forward path, nd how much the gain must be changed

to keep the margin same. [8+8]

8. (a) Obtain the stat variable model in phase variable form for the following system:...

Y +2..

y +3.

y +4 y = u (t )(b) The closed loop transfer function is given by Y (s )U (s ) =

160( s +4)s 3 +8 s 2 +192 s +640

Obtain the state variable model using signal ow graph. [8+8]

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1. (a) Explain, with example, the use of control system concepts to engineering andnon engineering elds.

(b) For the electrical network shown in Figure 1b given, derive the transfer func-tion

[8+8]

Figure 1b


(b) What are the effects of feedback on the performance of a system? Brieyexplain. [8+8]

3. Consider a system shown in Figure 3, employing proportional plus error-rate con-trol. Determine the value of the error-rate factor K e so that the damping ratio is0.5. Determine the values of settling time, maximum overshoot when subjected to

with and without error-rate control a unit step input. [10+6]

Figure 3

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Code No: RR220206 Set No. 24. (a) The open loop transfer function of a control system with unity feedback is

G(s)= 9(1+

s)(1+2

s)(1+3

s). Show that the system is stable.

(b) A unity feedback system is characterized by the open loop transfer functionG(s)= 1s (0 . 5s +1)(0 . 2s +1) . Determine the steady state errors for unit step, unitramp and unit acceleration input. [8+8]

5. (a) For the function G(s)H(s)= K s (s +2)( s +4) determine the breakaway point and thevalue of K for which the root locus crosses the imaginary axis.

(b) Explain the terms with reference to root locus.

i. Asymptotesii. Centroid

iii. Break away point.

[10+6]

6. (a) Derive expression of peak resonance and bandwidth. [4]

(b) Dene the following frequency response specications.

i. Peak Resonanceii. Bandwidth

iii. Phase Marginiv. Gain Margin

[4x3]

7. (a) The open loop transfer function of a feed back system is G(s)H(s)= K (1+ s )(1 s ) .Comment on stability using Nyquist Plot.

(b) The transfer function of a phase advance circuit is 1+0 . 2s1+0 . 2s . Find the maximumphase lag. [8+8]

8. (a) Explain properties of state transition matrix

(b) Consider the transfer function

Y(s) / U(s) = (2 s2

+ s + 5) / (s3

+ 6 s2

+ 11s + 4)Obtain the state equation by direct decomposition method and also nd statetransition matrix. [6+10]

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1. (a) Explain, with example, the use of control system concepts to engineering andnon engineering elds.

(b) For the electrical network shown in Figure 1b given, derive the transfer func-tion

[8+8]

Figure 1b

2. (a) Explain the effect of feedback on the stability of a closed loop system?

(b) Explain the effect of feedback on the sensitivity of a closed loop system? [8+8]

3. (a) What are the different time domain specication of a dynamical system. Ex-plain important specications of a second ordered system to unit step input.

(b) The open loop transfer function of a unity feedback system is given by G(s)= K/s(Ts+1), where K and T are positive constants. By what factor shouldthe amplier gain be reduced so that the peak overshoot of unit-step responseof the system is reduced from 75% to 25%? [8+8]

4. (a) The open loop Transfer function for a unity feedback system is given byG(s)= K s (1+ s + T 1 )(1+ sT 2 )Find the necessary conditions for the system to be stable using Routh-Hurwitzmethod.

(b) The open loop transfer function of a unity feedback system isG(s)= 100K s (s +10)

Find the static error constants and the steady state error of the system whensubjected to 10 an input given by the polynomial.r(t) = P o + P 1 t + P 22t 2 [8+8]

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Code No: RR220206 Set No. 35. (a) Show that the breakaway and break-in points, if any, on the real axis for the

root locus for G(s)H(s)= KN (s )D (s )

, where N(s) and D(s) are rational polynomialsin s, can be obtained by solving the equation dK ds =0.

(b) By a step by step procedure draw the root locus diagram for a unity negativefeedback system with open loop transfer function G(s)= K (s +1)s 2 (s +9) . Mark all thesalient points on the diagram. Is the system stable for all the values of K?

[8+8]

6. (a) Find the value of K and a to the following frequency domain specicationsM r = 1.04, w r = 11.55 rad/sec. Assume G(s) = K s (s + a ) unity feed back system.

(b) Sketch the Bode Plot for the following transfer function and determine in each

case the system gain K for the gain cross over frequency w c to be 5 rad/sec.G(s) = Ke

0 . 1 s

s (s +1)(1+0 . 1s ) [8+8]

7. Draw the Nyquist Plot for the open loop system G(s) = K (s +3)s (s 1) and nd its stability.Also nd the phase margin and gain margin. [8+8]

8. (a) Write the state equations for the block diagram given gure 8a.

Figure 8a(b) For the given plant transfer function construct the signal ow diagram and

determine the state space model. [8+8]

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1. (a) Obtain the output of the system given below. Figure 1a

Figure 1a(b) Determine the overall transfer function from the signal ow graph given in

gure 1b. [8+8]

Figure 1b


(b) What are the effects of feedback on the performance of a system? Briey

explain. [8+8]3. (a) Explain the important time ? response specication of a standard second

ordered system to a unit step input.

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Code No: RR220206 Set No. 4(b) Derive expressions for time domain specications of a standard second ordered

system to a step input. [8+8]

4. (a) Find the Number of roots with positive, Negative and Zero real parts for afollowing polynomial using Rouths Hurwitz criterion s 4 + 6 s 3 31s 2 + 80s-100=0.

(b) System Oscillates with a frequency W if it has poles at s=+ j and no polesin the right half of the s-plane. Determine the values of K and a for thecharacteristics equation s 3 + as 2+2s+1+K(s+1)=0 at a frequency of 2 rad /sec. [8+8]

5. (a) With usual notations derive equations for the angle of departure and the angle

of arrival of the root locus from complex poles and zeros.(b) The characteristic equation of closed-loop system is s 2+(2+k) s+26=0. Draw

the root locus of the system. Mark the salient points on the diagram. [8+8]

6. (a) Discuss the use of gain margin and phase margin in frequency response spec-ication of open loop systems.

(b) Sketch the polar (Nyquist) plot on a plain paper for the following transferfunction G(s)= 10s (1+ s )(1+0 . 05s ) . [8+8]

7. (a) Construct the complete Nyquist plot for a unity feed back control system

whose open loop transfer function is G(s)H(s) =K

s (s 2 +2 s +2) . Find maximumvalue of K for which the system is stable.

(b) The open loop transfer function of a unity feed back system is G(s)= 1s (1+0 . 5s )(1+0 . 1s ) .Find gain and phase margin. If a phase lag element with transfer function of

1+2 s1+5 s is added in the forward path, nd how much the gain must be changed

to keep the margin same. [8+8]

8. (a) For the given system X = Ax + Buwhere

A =1 2 10 1 31 1 1

B =101

Find the characteristic equation of the system and its roots.

(b) Given

X (t ) = 0 1 2 3x 1 (t )x 2 (t )

+ 01u (t )

Find the unit step response when,

X(0)= 11 [8+8]

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Rr220206 Control Systems Augsep 2008