R05220205 Control Systems Aprmay 2009

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Set No. 1

Code No: R05220205

II B.Tech II Semester Supplimentary Examinations, Apr/May 2009 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. Derive the Transfer Function for a.c. servomotor. Explain about torque-speed characteristics of a.c. servomotor. [16]

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3. (a) What are the types of controllers that are used in closed loop system? Explain them?

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(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]

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4. Sketch the root locus plot for the systems whose open loop transfer function is K . Determine given by G(s)H(s) = s(s+1)(s+3) (a) the gain margin

[16]

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(b) the phase margin for K=6. 5. Sketch the Bode plots for a system G(s) = s(s215(s+5) +16s+100) Hence determine the stability of the system.

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6. (a) Explain the effect of addition of a pole at the origin on the polar plot of a given system. (b) Sketch the polar plot & hence find the frequency at which the plot intersects the +ve imaginary axis for the system 0.1 G(s) = s2 (1+s)(1+0.1s) Also find the corresponding magnitude.

[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?

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Set No. 1

Code No: R05220205

(c) Explain the different steps to be followed for the design of compensator using Bode plot? [3+3+10] 8. (a)  A linear   system  tine  invariant  is characterized by homogenous state equation. x1 x˙ 1 1 0 = . Compute the solution of homogenous equation, x˙ 2 1 1 x2 assuming the initial state vector. (b) Obtain the state model of armature controlled de motor?

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[10+6]

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Set No. 2

Code No: R05220205

II B.Tech II Semester Supplimentary Examinations, Apr/May 2009 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. (a) The signal flow graph shown in figure 2a has one forward path and two nontouching loops. Determine the overall transmittance relating x6 and x1 .

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(b) Explain the advantages of Mason’s gain formula. Figure 2a

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Under damped system Un damped system Over damped system Critically damped system

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i. ii. iii. iv.

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3. (a) Define the following systems and sketch their output wave forms for an unit step i/p

(b) For a second order system ξ= 0.6, ωn = 5rad/sec. Find the values of ωd , Tr , Tp , Ts and Mp . [8+8] 4. (a) What is root locus plot? Explain with suitable example? (b) What are the features of root locus plot? (c) Check whether the point s= -3 + j 5 lies on the root locus of a system having K Determine the corresponding value of. [6+4+6] G(s)H(s) = (s+1)(s+5) 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 1 of 2

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[8+8]

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Set No. 2

Code No: R05220205 ii. Non minimum phase function iii. All pass function.

[4+6+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 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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(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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[8+8]

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Set No. 3

Code No: R05220205

1. (a) Explain the effect of feedback on bandwidth?

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II B.Tech II Semester Supplimentary Examinations, Apr/May 2009 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 ⋆⋆⋆⋆⋆

(b) Explain reduction of parameter variations by use of feedback systems? [8+8]

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2. Derive the Transfer Function for a.c. servomotor. Explain about torque-speed characteristics of a.c. servomotor. [16]

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3. (a) Explain error constants Kp , Kv , Ka for type-1 system?

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25 . (b) A unity feed back system has an open loop transfer function G(s) = s(s+8) Determine its damping ratio, peak overshoot and time required to reach the peak output. Now a derivative component having T.F. of s/10 is introduced in the system. Discuss its effect on the values obtained above? [3+13]

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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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(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]

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5. A system is given by G(s)H(s) =

−s

250 s(s+1)(s+10)

(a) Draw Bode plots (b) Find GM & PM (c) Hence determine the closed loop stability of the system.

[16]

6. (a) Explain the effect of addition of a pole at the origin on the polar plot of a given system. (b) Sketch the polar plot & hence find the frequency at which the plot intersects the +ve imaginary axis for the system 0.1 G(s) = s2 (1+s)(1+0.1s) Also find the corresponding magnitude.

[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? 1 of 2

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Set No. 3

Code No: R05220205

(c) Explain the different steps to be followed for the design of compensator using Bode plot? [3+3+10] 8. (a) A system is  −1 x˙ =  −1 −1

described by     x1 −4 −1 0 −6 −2   x2  +  1  u. 1 −2 −3  x3   x1 y = 1 1 1  x2  x3 Find the transfer function and construct the signal flow graph.

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(b) Define state, state variable and explain the significance of state variable analysis? [10+6]

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Set No. 4

Code No: R05220205

II B.Tech II Semester Supplimentary Examinations, Apr/May 2009 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. Define and explain the following terms

(b) Order of a transfer function (c) Type of a transfer function

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(d) Poles and zeros of a transfer function.

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(a) Characteristic equation

[16]

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2. Represent the following set of equation by a signal flow graph and determine the overall gain relating x5 and x1 . [16] = ax1 + f x2 = bx2 + ex4 = cx3 + hx5 = dx4 + gx2

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x2 x3 x4 x5

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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. Explain the stability of the system from the root locus plot in the following situations with suitable examples? (a) addition of open loop poles (b) addition of open loop zeros.

[16]

5. (a) Write a note on frequency domain specifications √ (b) For a system the resonant peak is 1 dB an ωn = 10 r/s. Find resonant frequency ‘ωr ′ . Also find the phase angle of closed loop transfer function at resonant frequency. [6+10] 6. (a) What is “Nyquist Contour”?

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Set No. 4

Code No: R05220205

(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? (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) 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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