Rr220206 Control Systems May 2007

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Set No. 1

Code No: RR220206

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II B.Tech II Semester Supplimentary Examinations, Apr/May 2007 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 Questions All Questions carry equal marks ⋆⋆⋆⋆⋆

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1. (a)

Figure 1a For the system in the above Figure 1a, obtain transfer function

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i. C/R ii. C/D

(b) Verify the above transfer function using signal flow graph.

[8+8]

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

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(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 the damping ratio ξ 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 1 of 3

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Set No. 1

Code No: RR220206 4. (a) Define the terms i. Absolute stability ii. Marginal stability iii. Conditional stability.

(b) By means of Routh Criterion, determine the stability of the system represented by 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 (s) , where N(s) and D(s) are rational polynomials root locus for G(s)H(s)= KN D(s) in s, can be obtained by solving the equation dK =0. ds

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(b) By a step by step procedure draw the root locus diagram for a unity negative feedback system with open loop transfer function G(s)= sK(s+1) 2 (s+9) . Mark all the salient points on the diagram. Is the system stable for all the values of K? [8+8] [4]

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

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(b) Draw the Bode Plot for a system having G(s) H(s) = 1. Determine:

100 , = s(1+0.5s)(1+0.1s)

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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.

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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.

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(b) The transfer function of a phase advance circuit is phase lag.

1+0.2s . 1+0.2s

Find the maximum [8+8]

8. (a) Define the terms i. State variable ii. State transition matrix.

[4+4]

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

Figure 8b 2 of 3

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Set No. 1

Code No: RR220206

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Set No. 2

Code No: RR220206

II B.Tech II Semester Supplimentary Examinations, Apr/May 2007 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 Questions All Questions carry equal marks ⋆⋆⋆⋆⋆

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1. (a) Explain the differences between open-loop and closed-loop systems. [8+8]

Figure 1b

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(b) Determine the Transfer Function of the electrical network. Figure 1b

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

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(b) With the help of sketches, explain the construction and working principle of a Synchro transmitter. [8+8]

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3. Consider a system shown in Figure 3, employing proportional plus error-rate control. Determine the value of the error-rate factor Ke so that the damping ratio is 0.5. 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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Set No. 2

Code No: RR220206

4. (a) The open-loop transfer function of a servo system with unity feedback isG(s)= 10 . Evaluate the static error constants (Kp , Kv , Ka ) for the system. Obs(0.1s+1) tain the steady-state error of the system when subjected to an input given by the polynomial r(t)=a0 +a1 t + a22 t2 (b) The open-loop transfer function of a unity feedback control system is given by K G(s)= (s+2)(s+4)(s 2 +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 are the corresponding oscillation frequencies? [8+8]

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

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(b) Draw the root locus of a system having open loop transfer function G(s)H(s)= s(s+4)(sK2 +4s+20) . Indicate the salient points of root locus. [8] 6. (a) Explain the correction between time and frequency response of a system

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(b) Sketch the Bode Plot for a unity feed back system characterized by the open . Show that the system is loop transfer function G(s) = s3K(1+0.2s)(1+0.025s) (1+0.001s)(1+0.005s) conditionally stable. Find the range of values of K for which the system is stable [6+10] 7. (a) Explain Nyquist stability criterion

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(b) A unity feedback control system has an open loop transfer function given by 100 . Draw the Nyquist diagram and determine its stability. G(s)H(s) = (s+5)(s+2) [6+10]

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8. (a) Define the terms

i. State variable ii. State transition matrix.

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[4+4]

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

Figure 8b ⋆⋆⋆⋆⋆

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Set No. 3

Code No: RR220206

II B.Tech II Semester Supplimentary Examinations, Apr/May 2007 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 Questions All Questions carry equal marks ⋆⋆⋆⋆⋆

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1. (a) Draw the signal flow graph for the system of equations given below and obtain the overall transfer function using mason’s rule X2 = X1 − X6 X3 = G1 X2 − H2 X4 − H3 X5 X4 = G2 X3 − H4 G6 X5 = G5 X4 X6 = G4 X5

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(b) Simplify the Figure 1 of the system given below by block diagram reduction technique and Determine the transfer function of the system. [8+8]

Figure 1 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] 36 . Determine the characteristic equation 3. For a unity feedback system G(s)= s(s+0.72) of the system. Hence calculate the undamped frequency of oscillations, damped frequency of oscillations, damping ratio, peak overshoot, time required to reach the peak output, settling time. A unit step input is applied to the system. [4+12]

4. (a) The open loop transfer function of a control system with unity feedback is 100 given by G(s)= s(s+0.1s) . Determine the steady state error of the system when 2 the input is 10+10t+4t .

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Set No. 3

Code No: RR220206

(b) A unity feedback system has an open loop transfer function G(s)= (s+2)(sK2 +4s+5) . Use RH test to determine the range of positive values of K for which the system is stable. [8+8] 5. The open loop transfer function of a unity feedback system is G(s)= Sketch the complete root locus and determine the value of K

K . S(s2 +8s+20)

(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]

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6. (a) The open loop transfer function of a unity feed back system is K G(s)= s(1+s)(1+0.1s) Determine the value of K for the following case:

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i. Resonance Peak is required to be equal to 1.58. ii. Gain margin of the system is 21 db.

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(b) A certain unity feed back control system is given by the value of K so as to K have s(1+s)(1+0.1s)

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Draw the Bode Plot of the above system. Determine from the plot of the value of ‘K’ so as to have:

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i. Gain margin = 10 db ii. Phase margin = 500

[6+10] 2

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20(s +s+0.5) 7. (a) Plot the polar plot of G(s) s(s+1) (s+10)

[8+8]

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(b) Explain the concept of Nyquist stability criterion.

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. ⋆⋆⋆⋆⋆

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Set No. 4

Code No: RR220206

II B.Tech II Semester Supplimentary Examinations, Apr/May 2007 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 Questions All Questions carry equal marks ⋆⋆⋆⋆⋆

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1. (a) Reduce the following Figure 1a using block diagram reduction technique find C/R and verify the transfer function by applying mason’s gain formula.

Figure 1a

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(b) Define the following terms.

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i. concept of the system ii. control system.

[8+8]

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2. Derive the Transfer Function for the field controlled d.c. servomotor with neat sketch. [8+8] 3. Consider the system shown in Figure3 . Determine the value of k such that the damping ratio ξ 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 1 of 2

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Set No. 4

Code No: RR220206

4. (a) Explain how Routh Hurwitz criterion can be used to determine the absolute stability of a system. (b) For the feedback control system shown in Figure 4b. it is required that :

Figure 4b

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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 system are at ?1+j1 and ?1-j1. Find the third-order open-loop transfer function G(s) so that the foregoing two conditions are satisfied. [6+10]

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

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6. (a) Explain the frequency response specifications.

100(0.02s+1) (s+1)(0.1s)(0.01s+1)

. Find [8+8]

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(b) Draw the Bode Plot for the system having G(s)H(s) = gain and phase cross over frequency.

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

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8. (a) For the given system X = Ax + Bu where    1 1 2 1    B= 0  A= 0 1 3 1 1 1 1 Find the characteristic equation of the system and its roots.      • 0 x1 (t) 0 1 u(t) + (b) Given X (t) = 1 x2 (t) −2 −3 Find the  step response when,  unit 1 X(0)= 1 ⋆⋆⋆⋆⋆

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