R05220205 Control Systems Augsep 2008

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Set No. 1

Code No: R05220205

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 Electronics & Computer 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 for the following mechanical system: Shown in figure 1a

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Figure 1a (b) Explain the limitations of closed loop system over open loop system. [10+6] 2. (a) Explain the advantages of signal flow graph over block diagram reduction process? (b) Expalin the following terms related to signal flow graph: i. ii. iii. iv.

Node Branch Forward path gain Loop gain.

[8+8]

3. The overall T.F. is a unity feed back control system is given by

C(s) R(s)

=

10 s2 +6s+10

(a) Find Kp , Kv , Ka (b) Determine the steady - state error if the input is r(t)=1 + t + t2 .

[16]

4. Sketch the root locus plot of a unity feed ?back system whose open loop T.F is K(s2 −2s+2) G(s) = (s+2)(s+3)(s+4) . [16] 1 of 2

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Set No. 1

Code No: R05220205 5. Write short notes: (a) Frequency domain specifications (b) Stability analysis from Bode plots.

[8+8]

6. (a) Define Polar plot. (b) Explain how you can determine relative stability using polar plots. 1 If the plot crosses (c) Sketch the polar plot of a system given by G(s) = s(1+s)(1+2s) the real axis determine the corresponding frequency & magnitude. [2+4+10]

7. (a) What is compensation? what are the different types of compensators?

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(b) What is a lag compensator, obtain the transfer function of lag compensator and draw pole-zero plot?

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(c) Explain the different steps to be followed for the design of compensator using Bode plot? [3+3+10]

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8. (a) The system is represented by the differential equation y¨ + 5y˙ + 6y = u Find the transfer from state variable representation.

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(b) Consider the RLC network shown in figure 8b. Write the state variable representation. [16]

Figure 8b ⋆⋆⋆⋆⋆

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Set No. 2

Code No: R05220205

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 Electronics & Computer Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆

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1. (a) Explain the effect of feedback on stability.

for the following block diagram (figure

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C(s) R(s)

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2. (a) Determine the transfer function 2a)

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(b) Explain the temperature control system concepts using open loop as well as closed loop system. [8+8]

[10+6]

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Figure 2a (b) Define various terms involved in signal flow graphs.

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3. (a) What are the types of controllers that are used in closed loop system? Explain them? (b) The response of a system subjected to a unit step input is c(t) = 1 + 0.2e−60t −1.2e−10t Obtain the expression for the closed loop transfer function? Also determine the Un damped natural frequency and damping ratio of the system? [8+8] 4. Determine the values of k and b ,so that the system whose open transfer function k(s+1) is G(s) = s3 +bs 2 +3s+1 oscillates at a frequency of oscillations of 2 rad / sec. Assume unity feed back. [16] 5. (a) Show that for a critically stable system the gain cross over frequency is equal to phase cross over frequency. (b) The Gain Margin of a type-1, 2nd order system is always infinity. Justify. (c) The Bode plots of a system is shown in figure 5c.

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Set No. 2

Code No: R05220205

6. (a) State Nyquist Stability Criterion.

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Figure 5c (d) From the Bode plots of a unity feed back system, 6 G(jω) at gain cross over frequency is found to be −150o &|G(jω)| at phase cross over frequency is found to be -12 dBs. Find the stability of the system. [6+4+2+4]

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(b) Explain the use of Nyquist Stability Criterion in the assessment of relative stability of a system.

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(c) Enlist the step-by-step procedure for the construction of Nyquist plots.[2+6+8]

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7. (a) What is compensation? What are the different types of compensators?

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(b) What is a lead compensator, obtain the transfer function of lead compensator and draw pole-zero plot?

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(c) Explain the different steps to be followed for the design of lead compensator using Bode plot? [3+3+10] 8. (a) Discuss the significance of state Space Analysis?

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(b) Define state variables.

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(c) Obtain the state variable representation of an armature controlled D.C Servomotor? [4+4+8] ⋆⋆⋆⋆⋆

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Set No. 3

Code No: R05220205

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 Electronics & Computer Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆

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1. (a) Obtain the transfer function for the following network Figure 1a:

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Figure 1a (b) Explain the effects of disturbance signals by use of feedback. 2. (a) Determine the transfer function 2a).

C(s) R(s)

[10+6]

for the following block diagram (figure [9+7]

Figure 2a (b) Explain the properties of signal flow graphs. 3. (a) What is the difference between type and order of a control system? Explain each with an example?

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Set No. 3

Code No: R05220205

(b) The figure 3b shows PD controller used for the system. Determine the value of Td so that the system will be critically damped? Calculate its settling time? [6+10]

Figure 3b

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4. Sketch the root locus plot of a unity feed ?back system whose open loop T.F is G(s) = s(sK(s+9) [16] 2 +4s+11) .

(a) Frequency domain specifications

[8+8]

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(b) Stability analysis from Bode plots.

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5. Write short notes:

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6. (a) What is “Nyquist Contour”?

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(b) A system is given by 4s+1 Sketch the Nyquist plot & hence determine the stability G(s) = s2 (s+1)(2s+1) of the system. [2+14]

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7. (a) What is compensation? What are the different types of compensators?

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(b) What is a lead compensator, obtain the transfer function of lead compensator and draw pole-zero plot?

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(c) Explain the different steps to be followed for the design of lead compensator using Bode plot? [3+3+10]

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8. (a) Obtain the state model of the system shown in figure 8a.

Figure 8a Consider the state variables as i1 , i2 , v (b) Obtain the state model of a field controlled motor? 2 of 3

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[8+8]

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Set No. 3

Code No: R05220205

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Set No. 4

Code No: R05220205

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 Electronics & Computer 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 network figure 1a by assuming R1 =5MΩ and R2 = 5MΩ, C1 =0.1µF and C2 =0.1µF.

[10+6]

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Figure 1a (b) Find the transfer function of the following system show in figure 1b.

Figure 1b 2. (a) Determine the overall transfer function relating C and R for the system whose block diagram is given (figure 2a).

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Set No. 4

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Code No: R05220205

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Figure 2a (b) Explain the properties of block diagrams.

[9+7]

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3. (a) Explain about various test signals used in control system?

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(b) Measurement conducted on a servomechanism shows the system response to be C(t) = 1 + 0.2e−60t −1.2e−10t , when subjected to a unit step input. Obtain the expression For closed loop T.F., the damping ratio and undamed natural frequency of oscillations? [8+8]

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4. (a) Explain the RH stability Criterion ?

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(b) The open loop transfer function of a unity feed back control system is given by G(s) = s(1+sT1K)(1+sT2 ) . Apply RH stability criterion, determine the value of K in terms of T1 and T2 for the system to be stable? [6+10] 5. (a) Derive the expressions for resonant peak & resonant frequency and hence establish the correlation between time response & frequency response. (b) Given ζ = 0.7 & ωn = 10 r/s find resonant peak, resonant frequency & Bandwidth. [10+6] 6. (a) What is “Nyquist Contour”? (b) A system is given by 4s+1 Sketch the Nyquist plot & hence determine the stability G(s) = s2 (s+1)(2s+1) of the system. [2+14] 7. (a) What is compensation? what are the different types of compensators? (b) What is a lag compensator, obtain the transfer function of lag compensator and draw pole-zero plot?

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Set No. 4

Code No: R05220205

(c) Explain the different steps to be followed for the design of compensator using Bode plot? [3+3+10]

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8. (a) Obtain the state model of the system shown in figure 8a.

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Figure 8a Consider the state variables as i1 , i2 , v

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(b) Obtain the state model of a field controlled motor?

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[8+8]