Rr220206 Control Systems Sep 2006

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Set No. 1

Code No: RR220206

II B.Tech II Semester Supplementary Examinations, Aug/Sep 2006 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) Find the transfer function X(s)/F(s) of the system Figure 1 given below.

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Figure 1:

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(b) Define transfer function and determine the transfer function of RLC series circuit if voltage across the capacitor is output variable and input is voltage source V(s). [8+8]

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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]

9 3. (a) A unity feedback system has a forward path transfer function G(s)= s(s+1) . Find the value of damping ratio, undamped natural frequency of the system, percentage overshoot, peak time and settling time.

(b) Measurements conducted on servomechanism show the system response to be c(t) = 1 + 0.2e−60t - 1.2e−10t when subjected to a unit-step unit. Obtain the expression for the closed-loop transfer function. [10+6] 4. (a) Apply R-H Criterion for the following characteristic equation to determine stability. 2s4 + 10s3 + 5s2 +5s+10=0 find the number roots with positive real parts, if any. (b) Derive the static error constants and list the disadvantages.

[8+8]

. Sketch the root locus and determine 5. Plot the root locus for G(s)H(s) = K(s+1)(s+3) s3 the range of K for which the system is stable. [12+4] 1 of 2

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Set No. 1

Code No: RR220206

6. (a) Explain how exact Bode plot is obtained from asymptotic plot, with fig. 50K (b) The open loop transfer function of a unity feed back system is G(s)= s(s+10)(s+5)(s+1) .

i. Gain margin and phase margin. ii. The value of steady state error coefficient for a gain of 10 db and the value which will make the closed loop system marginally stable. [6+10] 7. (a) Explain how polar plots are useful in finding the stability of a system (b) Sketch the Nyquist plot and find the stability of the following system. 100 G(s)H(s)= (s+2)(s+4)(s+8) [8+8]

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8. (a) Reduce the matrix A to diagonal matrix.

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(b) Derive the state models ...for the system described by the differential equation .. . .. . in phase variable form. y +4 y +5 y +2y = 2 u +6 u +5u [8+8]

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Set No. 2

Code No: RR220206

II B.Tech II Semester Supplementary Examinations, Aug/Sep 2006 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) Evaluate the output of the Figure 1 given.

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(b) Distinguish between open loop and closed loop control system.

[8+8]

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2. Derive the Transfer Function for armature controlled d.c. servomotor, with neat diagram. [8+8] 3. (a) What are the standard test signal used in the analysis of dynamical systems? Explain briefly? [6] (b) Figure 2. (a) shows a mechanical vibratory system. When 1 MW of force (step input) is applied to the system, the mass oscillates, as shown in Figure3. (b). Determine m, b, and k of the system from this response curve. The displacement x is measured from the equilibrium position. [5+5] 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] 1 of 3

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Set No. 2

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Code No: RR220206

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Set No. 2

Code No: RR220206

5. Sketch the root locus of the given system GH(s) = K / (s+1) (s+3) (s+6) (a) Find the break a way point on the real axis (b) Find the value of “k” at ζ =0.5.

[8+4+4]

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

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

. Find [8+8]

7. (a) Explain the Polar Plots.

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(b) The open loop transfer function of a unity feed back control system is given K(s+5)(s+40) by G(s)H(s)= s3 (s+200)(s+1000) Discuss the stability of a closed loop system as a function of k. Determine values of K which will cause sustained oscillations in the closed loop system. What are the frequencies of oscillations? Use Nyquist approach. [6+10]

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

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[8+8]

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Set No. 3

Code No: RR220206

II B.Tech II Semester Supplementary Examinations, Aug/Sep 2006 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) Define transfer function and discuss its limitations.

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(b) Derive the Transfer Function X(s) /F(s), for the mechanical system shown in Figure 1: [i. e. X1 (s)/F(s)] [8+8]

Figure 1:

2. (a) Explain how the potentiometers are used as error sensing devices. Give a typical application of it with single line diagram. (b) Discuss the effect of disturbance signal of the speed control system for a gasolineengine as shown in Figure 2assuming K=10. [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] 4. (a) For the system shown in Figure 4 , find the value of the steady state output when an input θi (t) = (2t + 5e−3t ) is applied. Determine the steady state error of the system. What is the type and order of the system? 1 of 3

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Set No. 3

Code No: RR220206

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Figure 2:

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Set No. 3

Code No: RR220206

(b) Explain the Hurwitz criterion to determine the stability of dynamical system. [10+6] 5. Sketch the root locus for the given system GH(s) = K / s (s3 + 12s2 +64s+ 128) and find the frequency of sustained oscillation. [10+6] 6. Draw the exact Bode Plots and find the gain margin and phase margin of a system 10(s+1) represented by G(s)H(s)= s(s+0.05)(s+3)(s+5) . [8+4+4] 7. (a) Explain the Relative stability. s+2 (b) The open loop transfer function of a unity feed back system is G(s)H(s)= (s+1)(s−1) Comment on the stability. [6+10]

8. (a) Explain properties of state transition matrix

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(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. 4

Code No: RR220206

II B.Tech II Semester Supplementary Examinations, Aug/Sep 2006 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) Using the block diagram reduction technique reduce the system shown in Figure 1 to simplest possible form and find the transfer function.

Figure 1:

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(b) For the given electrical network Figure 2

Figure 2: i. Obtain the signal flow graph ii. Compute the gain using the mason’s gain formula.

[8+8]

2. (a) Explain how the potentiometers are used as error sensing devices. Give a typical application of it with single line diagram. (b) Discuss the effect of disturbance signal of the speed control system for a gasolineengine as shown in Figure 3assuming K=10. [8+8]

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Set No. 4

Code No: RR220206

Figure 3: 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]

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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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(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]

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5. The block diagram of a control system is given in Figure4 Plot the root locus as a function of parameter K and comment on stability. [16]

Figure 4: 6. (a) Define gain cross-over and phase cross over frequencies K (b) A unity feedback Control System has G(s) = S(1+s)(1+S/10) Find value of K so that GM =12 db & PM = 30o

[8+8]

7. (a) Explain the Relative stability. s+2 (b) The open loop transfer function of a unity feed back system is G(s)H(s)= (s+1)(s−1) Comment on the stability. [6+10]

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Set No. 4

Code No: RR220206

8. For the system with state model . y = cx where X = Ax + Bu Obtain the transfer function and obtain the solution of state equation in terms of

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initial conditions.  0 Xo =  1  0

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[8+8]