R05220205 Control Systems Sep 2007

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Set No. 1

Code No: R05220205

(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) Write a note on determination of range of ‘K’ for stability using Bode plots. (b) Define GM & PM and explain how you can determine them from Bode plots. [8+8] 6. (a) State Nyquist Stability Criterion. (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. For the unity feed back control system forward path transfer function G(S) = K/S (S+4) (S+20). Design a lag-lead compensator so that PM ≥ 40 and steady state error for unit ramp input ≤ 0.04 rad. [16]

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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? ⋆⋆⋆⋆⋆

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Set No. 2

Code No: R05220205

II B.Tech II Semester Supplimentary Examinations, Aug/Sep 2007 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 of the following system and draw its analogous electrical circuit. Figure 1a

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Figure 1a (b) Explain the advantages and features of transfer function. C(s) R(s)

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

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

[16]

Figure 2a (b) Explain the properties of signal flow graphs. 3. (a) Explain about various test signals used in control system? (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] K 4. (a) The open loop t.f. of a unity feed-back system is given by G(s) = s(1+0.25s)(1+0.4s) . Find the restriction on K so that the closed loop system is absolutely stable?

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Set No. 2

Code No: R05220205

(b) A feed-back system has an an open loop t.f of G(s)H(s) = s(s2Ke Determine +5s+9) by the use of the RH criterion ,the max. value of K for the closed loop system to be stable? [8+8] −s

5. (a) Explain the term frequency response analysis. (b) Show that in Bode magnitude plot the slope corresponding to a quadratic factor is -40 dB/dec. (c) Explain with the help of examples i. Minimum phase function ii. Non minimum phase function iii. All pass function.

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[4+6+6]

6. (a) Explain how the type of a system determines the shape of polar plot

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(b) Write a note on Nyquist criterion for minimum phase & non minimum phase transfer functions. [8+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]

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8. (a) For the given T.F 0 T (s) = S 3 +a2 S 2b+a 1 S+a0 Obtain the state model (phase variable form)?

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(b) Construct the state model for a system characterized by the differential equation. y¨ + 5y˙ + 6y = u. [8+8] ⋆⋆⋆⋆⋆

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Set No. 3

Code No: R05220205

II B.Tech II Semester Supplimentary Examinations, Aug/Sep 2007 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 linearizing effect of feedback.

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(b) The dynamic behaviour of the system is described by the equation, dC + 10C = 40e, where ‘e’ is the input and ‘C’ is the output. Determine the dt transfer function of the system. [10+6]

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2. Explain the procedure for deriving the transfer function and derive the transfer function for servo. [16] 3. (a) Explain the significance of generalized error series?

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K (b) For a system G(s)H(s) = s2 (s+2)(s+3) ,. Find the value of K to limit the steady state error to 10 when the input to the system is r(t)=1+10t+40/2 t2 .[6+10]

4. Using RH stability criterion determine the stability of the following systems.

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(a) Its loop t.f. has poles at s=0, s= -1, s= -3 and zero at s= -5, gain K of forward path is 10

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(b) It is a type-1system with an error constant of 10 sec-1 and poles at s= -3 and s=-6. [8+8] 5. (a) Explain clearly the steps involved in the construction of Bode plots of a system with loop transfer function consisting of i. an open loop gain K ii. one pole at origin iii. one quadratic factor (s−5) (b) Given G(s) = (s+5) Determine the phase angle at 0, 5 & ∞ frequencies.

[12+4]

6. (a) What is “Nyquist Contour”? (b) A system is given by 4s+1 G(s) = s2 (s+1)(2s+1) Sketch the Nyquist plot & hence determine the stability of the system. [2+14] 7. (a) What is compensation? what are the different types of compensators?

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Set No. 3

Code No: R05220205

(b) What is a lag compensator, obtain the transfer function of lag compensator and draw pole-zero plot? (c) Explain the different steps to be followed for the design of compensator using Bode plot? [3+3+10] 8. (a) For the given T.F 0 T (s) = S 3 +a2 S 2b+a 1 S+a0 Obtain the state model (phase variable form)?

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(b) Construct the state model for a system characterized by the differential equation. y¨ + 5y˙ + 6y = u. [8+8]

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Set No. 4

Code No: R05220205

II B.Tech II Semester Supplimentary Examinations, Aug/Sep 2007 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 regenerative feedback?

Figure 1b

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(b) Determine the sensitivity of the closed loop transfer function T (s) = C(s) to R(s) variations in parameter K at ω = 5 rad/sec. Assume the normal value of K is 1. Shown in figure 1b. [6+10]

2. (a) State and explain mason’s gain formula for the signal flow graph.

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(b) What are differences between block diagram reduction and signal flow graph reduction? [8+8]

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3. (a) For an under damped second order system ,define various time domain specifications? (b) The forward path T.F. of a unity feed back control system is given by 2 G(s) = s(s+3) . Obtain the expression for unit step response of the system? [8+8] 4. Open loop T.F. of a unity feed ?back system is G(s) =

K(s+a) s(s+b)

(a) Prove that break-away and break-in points will exist only when |a| > |b|

(b) Prove that the √ complex points on the root locus form a circle with center (-a,0) [16] and radius a2 − ab. 5. (a) Define i. Minimum phase tf ii. Non minimum phase tf (b) Enlist the steps for the construction of Bode plots (c) Explain the procedure for determination of transfer function from Bode plots. [4+4+8] 1 of 2

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Set No. 4

Code No: R05220205 6. (a) Explain Nyquist stability criterion.

3 (b) With the help of Nyquist plot assess the stability of a system G(s) = s(s+1)(s+2) What happens to stability if the numerator of the function is changed from 3 to 30? [6+10]

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

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(b) A system      is describedby 0 x1 −1 −4 −1 x˙ =  −1 −6 −2   x2  +  1  u 1 x3  −1 −2 −3 y = 1 1 1 [x] Find the transfer function?.

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8. (a) A control system has a transfer function given by S+3 G (s) = (S+1)(S+2) 2 . Obtain the canonical state variable representation.

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