rr220206 control systems may 2007

8/14/2019 Rr220206 Control Systems May 2007

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Code No: RR220206 Set No. 1

II B.Tech II Semester Supplimentary Examinations, Apr/May 2007CONTROL SYSTEMS

( Common to Electrical & Electronic Engineering, Electronics &Communication Engineering, Electronics & Instrumentation Engineering,

Electronics & Control Engineering, Electronics & Telematics andInstrumentation & Control Engineering)

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

All Questions carry equal marks

1. (a)

Figure 1a

For the system in the above Figure 1a, obtain transfer functioni. C/R

ii. C/D

(b) Verify the above transfer function using signal flow graph. [8+8]

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. Consider the system shown in Figure3 . Determine the value of k such that thedamping ratio is 0.5. Then obtain the rise time, tr, peak time tp, maximum

overshoot Mp, and settling time ts in the unit-step response. [16]

Figure 3

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4. (a) Define the terms

i. Absolute stabilityii. Marginal stability

iii. Conditional stability.

(b) By means of Routh Criterion, determine the stability of the system representedby the characteristic equation.s4 + 2s3 + 8s2+4s+3=0 [6+10]

5. (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 polynomials

in s, can be obtained by solving the equation dKds

=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)

s2(s+9). Mark all the

salient points on the diagram. Is the system stable for all the values of K?[8+8]

6. (a) Explain the concept of phase margin and gain margin. [4]

(b) Draw the Bode Plot for a system having G(s) = 100s(1+0.5s)(1+0.1s)

,

H(s) = 1.Determine:

i. Gain cross over frequency and corresponding phase margin.

ii. Phase cross over frequency and corresponding gain margin.

iii. Stability of the closed loop system.

[8+4]

7. (a) The open loop transfer function of a feed back system is G(s)H(s)=K(1+s)(1s)

.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]


i. State variable

ii. State transition matrix. [4+4]

(b) Obtain the state equation and output equation of the electric network showin Figure8b [8]

Figure 8b

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1. (a) Explain the differences between open-loop and closed-loop systems.(b) Determine the Transfer Function of the electrical network. Figure 1b [8+8]

Figure 1b

2. (a) Explain the effect of feedback on noise to signal ratio.

(b) With the help of sketches, explain the construction and working principle ofa Synchro transmitter. [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 Ke so that the damping ratio is0.5. Determine the values of settling time, maximum overshoot when subjected towith and without error-rate control a unit step input. [10+6]

Figure 3

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4. (a) The open-loop transfer function of a servo system with unity feedback isG(s)=10

s(0.1s+1)

. Evaluate the static error constants (Kp, Kv, Ka) for the system. Ob-tain the steady-state error of the system when subjected to an input given bythe polynomial r(t)=a0+a1t +

a22

t2

(b) The open-loop transfer function of a unity feedback control system is given byG(s)= K

(s+2)(s+4)(s2+6s+25). By applying the Routh 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 arethe corresponding oscillation frequencies? [8+8]

5. (a) What are root loci? Summarize the steps that are used as rules for construct-ing the root locus. [2+6]

(b) Draw the root locus of a system having open loop transfer function G(s)H(s)= Ks(s+4)(s2+4s+20)

. Indicate the salient points of root locus. [8]

6. (a) Explain the correction between time and frequency response of a system

(b) Sketch the Bode Plot for a unity feed back system characterized by the open

loop transfer function G(s) = K(1+0.2s)(1+0.025s)s3(1+0.001s)(1+0.005s)

. Show that the system isconditionally stable. Find the range of values of K for which the system isstable [6+10]

7. (a) Explain Nyquist stability criterion

(b) A unity feedback control system has an open loop transfer function given byG(s)H(s) = 100

(s+5)(s+2). Draw the Nyquist diagram and determine its stability.

[6+10]


i. State variable

ii. State transition matrix. [4+4]

(b) Obtain the state equation and output equation of the electric network showin Figure8b [8]

Figure 8b

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(b) A unity feedback system has an open loop transfer function G(s)= K(s+2)(s2+4s+5)

.Use RH test to determine the range of positive values of K for which the systemis stable. [8+8]

5. The open loop transfer function of a unity feedback system is G(s)= KS(s2+8s+20)

.Sketch the complete root locus and determine the value of K

(a) For the system to be stable

(b) For the system to be marginally stable and hence the frequency of oscillation

(c) To provide critical damping

(d) To give an effecting damping factor 0.5. [4x4]

6. (a) The open loop transfer function of a unity feed back system isG(s)= K

s(1+s)(1+0.1s)

Determine the value of K for the following case:

i. Resonance Peak is required to be equal to 1.58.

ii. Gain margin of the system is 21 db.

(b) A certain unity feed back control system is given by the value of K so as tohave K

s(1+s)(1+0.1s)

Draw the Bode Plot of the above system. Determine from the plot of the value

of K so as to have:i. Gain margin = 10 db

ii. Phase margin = 500

[6+10]

7. (a) Plot the polar plot of G(s)20(s2+s+0.5)

s(s+1)(s+10)

(b) Explain the concept of Nyquist stability criterion. [8+8]

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

Y +2

..

y+3

.

y+4y = u(t)

(b) The closed loop transfer function is given by Y(s)U(s)

= 160(s+4)s3+8s2+192s+640

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

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1. (a) Reduce the following Figure 1a using block diagram reduction technique findC/R and verify the transfer function by applying masons gain formula.

Figure 1a(b) Define the following terms.

i. concept of the system

ii. control system. [8+8]

2. Derive the Transfer Function for the field controlled d.c. servomotor with neatsketch. [8+8]

3. Consider the system shown in Figure3 . Determine the value of k such that thedamping ratio is 0.5. Then obtain the rise time, tr, peak time tp, maximumovershoot Mp, and settling time ts in the unit-step response. [16]

Figure 3

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4. (a) Explain how Routh Hurwitz criterion can be used to determine the absolutestability of a system.

(b) For the feedback control system shown in Figure 4b. it is required that :

i. the steady-state error due to a unit-ramp function input be equal to 1.5.

ii. the dominant roots of the characteristic equation of the third-order systemare at ?1+j1 and ?1-j1. Find the third-order open-loop transfer functionG(s) so that the foregoing two conditions are satisfied. [6+10]

Figure 4b

5. A unity feedback system has a plant; g(s) = k (s+ 1) / s (s2+4s+8). Sketch theroot locus and find the roots when = 0. 707. [8+8]

6. (a) Explain the frequency response specifications.

(b) Draw the Bode Plot for the system having G(s)H(s) = 100(0.02s+1)(s+1)(0.1s)(0.01s+1)

. Find

gain and phase cross over frequency. [8+8]

7. Draw the Nyquist Plot for the open loop system G(s) = K(s+3)s(s1)

and find its stability.

Also find the phase margin and gain margin. [8+8]

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

A =

1 2 10 1 3

1 1 1

B =

10

1

Find the characteristic equation of the system and its roots.

(b) Given

X(t) =

0 12 3

x1 (t)x2 (t)

+

01

u(t)

Find the unit step response when,X(0)=

11

[8+8]

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rr220206 control systems may 2007

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