Rr220206 Control Systems Augsep 2008

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Set No. 1

Code No: RR220206

II 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 Questions All Questions carry equal marks ⋆⋆⋆⋆⋆

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

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Figure 1a (b) Briefly explain the terms used in Signal flow graph.

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

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(b) What are the effects of feedback on the performance of a system? Briefly explain. [8+8] 3. (a) Define time constant and explain its importance.

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(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 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. [8+8] 4. (a) Show that the Routh?s stability criterion and Hurwitz stability criterion are equivalent. (b) Consider a unity-feedback control system whose open-loop transfer function K . Discuss the effects that varying the values of K and B has is G(s)= s(Js+B) on 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 and complex poles for the root locus of a system with open-loop transfer function 2 +1) G(s)H(s)= s(sK(s 2 +4s+8) (b) Draw the root locus diagram for a feedback system with open-loop transfer function G(s)= K(s+5) . , following systematically the rules for the construction s(s+3) of root locus. Show that the root locus in the complex plane is a circle. [8+8] 6. (a) Define phase margin and gain margin. 1 of 2

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Set No. 1

Code No: RR220206

(b) Sketch bode plot & find value of ‘K’ such that gain cross - over frequency. is KS 2 5 rad/sec. G(s) = (1+0.2S)(1+0.02S) [8+4] 7. (a) Construct the complete Nyquist plot for a unity feed back control system K whose open loop transfer function is G(s)H(s) = s(s2 +2s+2) . Find maximum value of K for which the system is stable. 1 . (b) The open loop transfer function of a unity feed back system is G(s)= s(1+0.5s)(1+0.1s) Find
gain and phase margin. If a phase lag element with transfer function of 1+2s is added in the forward path, find how much the gain must be changed 1+5s to keep the margin same. [8+8]

Y (s) U (s)

=

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

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(b) The closed loop transfer function is given by

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8. (a) Obtain the stat variable model in phase variable form for the following system: ... . .. Y +2 y +3 y +4y = u(t)

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Obtain the state variable model using signal flow graph.

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Set No. 2

Code No: RR220206

II 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 Questions All Questions carry equal marks ⋆⋆⋆⋆⋆

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1. (a) Explain, with example, the use of control system concepts to engineering and non engineering fields.

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(b) For the electrical network shown in Figure 1b given, derive the transfer function [8+8]

Figure 1b

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

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(b) What are the effects of feedback on the performance of a system? Briefly explain. [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 1 of 2

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Set No. 2

Code No: RR220206

4. (a) The open loop transfer function of a control system with unity feedback is 9 G(s)= (1+s)(1+2s)(1+3s) . Show that the system is stable. (b) A unity feedback system is characterized by the open loop transfer function 1 . Determine the steady state errors for unit step, unit G(s)= s(0.5s+1)(0.2s+1) ramp and unit acceleration input. [8+8] K 5. (a) For the function G(s)H(s)= s(s+2)(s+4) determine the breakaway point and the value of K for which the root locus crosses the imaginary axis.

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

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i. Asymptotes ii. Centroid iii. Break away point.

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

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Peak Resonance Bandwidth Phase Margin Gain Margin

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i. ii. iii. iv.

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(b) Define the following frequency response specifications.

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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) Explain properties of state transition matrix (b) Consider the transfer function Y(s) / U(s) = (2s2 + s + 5)/(s3 + 6s2 + 11s + 4) Obtain the state equation by direct decomposition method and also find state transition matrix. [6+10] ⋆⋆⋆⋆⋆

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Set No. 3

Code No: RR220206

II 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 Questions All Questions carry equal marks ⋆⋆⋆⋆⋆

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1. (a) Explain, with example, the use of control system concepts to engineering and non engineering fields.

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(b) For the electrical network shown in Figure 1b given, derive the transfer function [8+8]

Figure 1b

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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]

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3. (a) What are the different time domain specification of a dynamical system. Explain important specifications 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 should the amplifier gain be reduced so that the peak overshoot of unit-step response of the system is reduced from 75% to 25%? [8+8] 4. (a) The open loop Transfer function for a unity feedback system is given by G(s)= s(1+s+TK1 )(1+sT2 ) Find the necessary conditions for the system to be stable using Routh-Hurwitz method. (b) The open loop transfer function of a unity feedback system is 100K G(s)= s(s+10) Find the static error constants and the steady state error of the system when subjected to 10 an input given by the polynomial. r(t) = Po + P1 t + P2 2t2 [8+8]

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Set No. 3

Code No: RR220206

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

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(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 wc to be 5 rad/sec. Ke−0.1s [8+8] G(s) = s(s+1)(1+0.1s)

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

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Figure 8a (b) For the given plant transfer function construct the signal flow diagram and determine the state space model. [8+8] ⋆⋆⋆⋆⋆

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Set No. 4

Code No: RR220206

II 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 Questions All Questions carry equal marks ⋆⋆⋆⋆⋆

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

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Figure 1a (b) Determine the overall transfer function from the signal flow graph given in figure 1b. [8+8]

Figure 1b 2. (a) Derive the transfer function of a field controlled d.c. Servomotor and develop the block diagram. Clearly state the assumptions made in the derivation. (b) What are the effects of feedback on the performance of a system? Briefly explain. [8+8] 3. (a) Explain the important time ? response specification of a standard second ordered system to a unit step input. 1 of 2

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Set No. 4

Code No: RR220206

(b) Derive expressions for time domain specifications 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 a following polynomial using Routh’s Hurwitz criterion s4 + 6s3 − 31s2 + 80s -100=0. (b) System Oscillates with a frequency W if it has poles at s=+ jω and no poles in the right half of the s-plane. Determine the values of K and a for the characteristics equation s3 + as2 +2s+1+K(s+1)=0 at a frequency of 2 rad / sec. [8+8]

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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.

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(b) The characteristic equation of closed-loop system is s2 +(2+k) s+26=0. Draw the root locus of the system. Mark the salient points on the diagram. [8+8]

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

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(b) Sketch the polar (Nyquist) plot on a plain paper for the following transfer 10 . [8+8] function G(s)= s(1+s)(1+0.05s)

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7. (a) Construct the complete Nyquist plot for a unity feed back control system K . Find maximum whose open loop transfer function is G(s)H(s) = s(s2 +2s+2) value of K for which the system is stable.

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1 . (b) The open loop transfer function of a unity feed back system is G(s)= s(1+0.5s)(1+0.1s) Find
gain and phase margin. If a phase lag element with transfer function of 1+2s is added in the forward path, find how much the gain must be changed 1+5s to keep the margin same. [8+8]

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8. (a) For the given system X = Ax + Bu where    1 1 2 1 A= 0 1 3  B= 0  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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