control systems aug aep 2007

8/3/2019 Control Systems Aug Aep 2007

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Code No: R05220205 Set No. 1II 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 QuestionsAll Questions carry equal marks

1. (a) Illustrate atleast three applications of feedback control systems?(b) Explain translatory and rotary elements of mechanical systems? [8+8]

2. (a) Determine the overall transfer function relating C and R for the system whoseblock diagram is given (gure 2a).

Figure 2a(b) Explain the properties of block diagrams. [9+7]

3. (a) Explain error constants K p, K v , K a for type-1 system?

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

4. (a) Explain the RH stability Criterion ?

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Code No: R05220205 Set No. 1(b) The open loop transfer function of a unity feed back control system is given

by G (s ) = K s (1+ sT 1 )(1+ sT 2 )

. Apply RH stability criterion, determine the value of K in terms of T 1 and T 2 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) Dene 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 relativestability of a system.

(c) Enlist the step-by-step procedure for the construction of Nyquist plots.[2+6+8]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 andsteady state error for unit ramp input 0.04 rad. [16]

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

Figure 8aConsider the state variables as i 1, i 2, v

(b) Obtain the state model of a eld controlled motor? [8+8]

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1. (a) Obtain the transfer function of the following system and draw its analogouselectrical circuit. Figure 1a

Figure 1a(b) Explain the advantages and features of transfer function. [16]

2. (a) Determine the transfer function C (s )R (s ) for the following block diagram (gure2a). [9+7]

Figure 2a(b) Explain the properties of signal ow 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. Obtainthe expression For closed loop T.F., the damping ratio and undamed natural

frequency of oscillations? [8+8]4. (a) The open loop t.f. of a unity feed-back system is given by G (s ) = K 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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Code No: R05220205 Set No. 2(b) A feed-back system has an an open loop t.f of G (s )H (s) = Ke

s

s (s 2 +5 s +9) Determineby the use of the RH criterion ,the max. value of K for the closed loop systemto be stable? [8+8]

5. (a) Explain the term frequency response analysis.

(b) Show that in Bode magnitude plot the slope corresponding to a quadraticfactor is -40 dB/dec.

(c) Explain with the help of examples

i. Minimum phase functionii. Non minimum phase function

iii. All pass function. [4+6+6]

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

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

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

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

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

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

(b) Construct the state model for a system characterized by the differential equa-tion.y + 5 y + 6 y = u . [8+8]

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1. (a) Explain the linearizing effect of feedback.(b) The dynamic behaviour of the system is described by the equation,

dC dt + 10 C = 40e, where e is the input and C is the output. Determine thetransfer function of the system. [10+6]

2. Explain the procedure for deriving the transfer function and derive the transferfunction for servo. [16]

3. (a) Explain the signicance of generalized error series?

(b) For a system G (s )H (s ) = K s 2 (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.

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

(b) It is a type-1system with an error constant of 10 sec-1 and poles at s= -3 ands=-6. [8+8]

5. (a) Explain clearly the steps involved in the construction of Bode plots of a systemwith loop transfer function consisting of

i. an open loop gain Kii. one pole at origin

iii. one quadratic factor

(b) Given G (s ) = (s 5)

(s +5)Determine the phase angle at 0, 5 & frequencies. [12+4]

6. (a) What is Nyquist Contour?

(b) A system is given byG (s ) = 4s +1s 2 (s +1)(2 s +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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Code No: R05220205 Set No. 3(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 usingBode plot? [3+3+10]

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

(b) Construct the state model for a system characterized by the differential equa-tion.y + 5 y + 6 y = u . [8+8]

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1. (a) Explain regenerative feedback?

(b) Determine the sensitivity of the closed loop transfer function T (s) = C (s )R (s ) tovariations in parameter K at = 5 rad/sec. Assume the normal value of K is1. Shown in gure 1b. [6+10]

Figure 1b2. (a) State and explain masons gain formula for the signal ow graph.

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

3. (a) For an under damped second order system ,dene various time domain speci-cations?

(b) The forward path T.F. of a unity feed back control system is given byG (s ) = 2s (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)

and radius a 2 ab. [16]5. (a) Dene

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]

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Code No: R05220205 Set No. 46. (a) Explain Nyquist stability criterion.

(b) With the help of Nyquist plot assess the stability of a system G (s ) =3

s (s +1)( s +2)What happens to stability if the numerator of the function is changed from 3to 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 compensatorand draw pole-zero plot?

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

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

(b) A system is described by

x = 1 4 1

1 6 21 2 3

x1x2x3

+011

u

y = 1 1 1 [x]Find the transfer function?. [8+8]

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control systems aug aep 2007

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