Rr220206-control-systems

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

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

[8+8]

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) Define 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 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

[4]

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]

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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[8+8]

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 ⋆⋆⋆⋆⋆ 1. (a) Explain, with example, the use of control system concepts to engineering and non engineering fields. (b) For the electrical network shown in Figure 1b given, derive the transfer function [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. 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

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. i. Asymptotes ii. Centroid iii. Break away point. [10+6] 6. (a) Derive expression of peak resonance and bandwidth.

[4]

(b) Define the following frequency response specifications. i. ii. iii. iv.

Peak Resonance Bandwidth Phase Margin 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 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 ⋆⋆⋆⋆⋆ 1. (a) Explain, with example, the use of control system concepts to engineering and non engineering fields. (b) For the electrical network shown in Figure 1b given, derive the transfer function [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 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) (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) 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] 8. (a) Write the state equations for the block diagram given figure 8a.

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

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

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] 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 s2 +(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 specification of open loop systems. (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) 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. 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]

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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[8+8]