07a4ec03 Control Systems Aprmay 2009

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Set No. 1

Code No: 07A4EC03

II B.Tech II Semester Regular Examinations, Apr/May 2009 CONTROL SYSTEMS ( Common to Electrical & Electronic Engineering, Electronics & Communication 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 of the following system show in figure 1a:

[10+6]

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Figure 1a (b) Derive the transfer function of the following network (figure 1b).

Figure 1b 2. (a) Explain the disadvantages and advantages of block diagram reduction process over signal flow graph. (b) Explain the rules of block diagram reduction.

[8+8]

3. (a) Derive the static error constants and list the disadvantages? (b) Find step, ramp and parabolic error coefficients and their corresponding steady14(s+3) state error for unity feed-back system having the T.F G(s) = s(s+5)(s 2 +3s+2) . [8+8] 4. Sketch the root locus plot for a unity feedback system whose open loop T.F. is given by G(s) = sK(s+0.5) [16] 2 (s+4.5) .

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Set No. 1

Code No: 07A4EC03

5. (a) Explain the significance of Bode plots in stability studies of linear control systems. (b) Show that in case of a quadratic factor the phase angle is a function of frequency ω and damping ratio ζ.

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(c) The magnitude plot of a system is shown in figure 5c.

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6. (a) Explain Nyquist stability criterion.

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Figure 5c Find the open loop transfer function.

K . S(S+2)(S+20)

Design a lag compensator given phase margin ≥ 350 and [16]

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7. For G(S) = KV ≤ 20.

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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]

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8. (a)  A linear   system  is characterized by homogenous state equation.  tine  invariant 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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Set No. 2

Code No: 07A4EC03

II B.Tech II Semester Regular Examinations, Apr/May 2009 CONTROL SYSTEMS ( Common to Electrical & Electronic Engineering, Electronics & Communication 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 ⋆⋆⋆⋆⋆ 1. (a) Explain the difference between systems with feedback and without feedback.

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(b) Explain the advantages of systems with feedback, with suitable examples. [8+8]

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2. (a) Reduce the given block diagram (figure 2a) and hence obtain the transfer function C(s) R(s)

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Figure 2a (b) Explain the need of Mason’s gain formula for any system reduction. 3. (a) Explain the significance of generalized error series?

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

4. (a) State and explain Routh Hurwitz stability criterion (b) Construct Routh array and determine the stability of the system whose characteristic equation is S 6 + 2S 5 + 8S 4 + 12S 3 + 20S 2 16S16 = 0. Also determine the no.of roots lying on right half of s-plane, left half of s-plane and on imaginary axis? [6+10] 5. Sketch the Bode plots for a system G(s) = s(s215(s+5) +16s+100) Hence determine the stability of the system.

[16]

6. (a) State & explain “principle of argument” (b) Given K G(s) = s(s+2)(s+10) Sketch Nyquist plot & find range of ?K? for stability. 1 of 2

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Set No. 2

Code No: 07A4EC03

7. (a) Explain the need of lead compensator and obtain the transferfunction of leadlag compensator. (b) Expalin the signinificance of compansion?

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8. (a) Consider the vector  ?matrixdifferential equation describe the dynamics of the 0 1 system as X = −6 − 5 Determine state transition matrix ? (b) What are the properties of state transistion matrix?

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Set No. 3

Code No: 07A4EC03

II B.Tech II Semester Regular Examinations, Apr/May 2009 CONTROL SYSTEMS ( Common to Electrical & Electronic Engineering, Electronics & Communication 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) Find the transfer function +

12 dc(t) dt

of a system having differential equation.

+ c(t) = r(t) + 2r(t − 1).

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2 9 d dtc(t) 2

C(s) R(s)

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1. (a) Explain and derive the relation between impulse response and transfer function. [10+6]

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2. Explain about synchro transmitter and receiver and derive the transfer function for synchro. [16] K s(2+sT )

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3. For a unity feed back system having G(s) =

find the following

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(a) The factor by which the gain K should be multiplied to increase the damping ratio from 0.15 to 0.6

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(b) The factor by which the time constant should be multiplied to reduce the damping ratio from 0.8 to 0.4. [16]

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

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5. (a) Explain the significance of Bode plots in stability studies of linear control systems. (b) Show that in case of a quadratic factor the phase angle is a function of frequency ω and damping ratio ζ. (c) The magnitude plot of a system is shown in figure 5c.

Figure 5c Find the open loop transfer function. 1 of 2

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Set No. 3

Code No: 07A4EC03

6. (a) A unity feed back system has G(s) = s(1+sT1K)(1+sT2 ) Discuss the effect on Nyquist plot when the value of K is i. low (critical value) (b) Pure time delay usually deteriorates the stability. Explain with the help of Nyquist plots. [10+6]

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7. Design a lead compensator for unity feed back system whose open loop transfer K to satisfy the following specifications. function G(S) = S(S+1)(S+5) (a) velocity error constant KV ≥ 50

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(b) Phase margin ≥ 200 .

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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. 4

Code No: 07A4EC03

II B.Tech II Semester Regular Examinations, Apr/May 2009 CONTROL SYSTEMS ( Common to Electrical & Electronic Engineering, Electronics & Communication 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. Explain the following terms: (a) Linear systems and nonlinear systems

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(b) Continuous systems and discrete systems

(d) Static systems and dynamic systems.

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(c) Single input-single output systems (SISO) and multiple input - multiple output systems (MIMO) [4+4+4+4]

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2. Derive the transfer function for the field controlled d.c. motor with neat sketch and explain the advantages of field controlled d.c. motor over armature controlled d.c. motor. [16]

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3. (a) Establish the relation relation between ξ and Mp for a step response of a second order system? 2

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(b) A system is given by differential equation ddt2y +4 dy +8y = 8x, where y=output dt x= input. Determine all the time domain specifications and obtain output response for unit step input ? [3+13]

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4. (a) Sketch the root locus plot of a unity feed - back system whose open loop T.F s is G(s) = (s2 +4)(s+2) (b) What is break-away and break-in point? How to determine them? (c) From the given root locus plot how can you determine the gain margin and phase margin for the specified gain value ‘K’. [8+4+4] 5. (a) Show that Bode plots of a system with transfer function having many factors can be obtained by adding the Bode plots of individual factors. (b) In the Bode magnitude plot of a system the slope changed by -40 db / dec at a frequency ω = ω2 . What can be the corresponding factor in the loop transfer function? (c) The magnitude plot of a system is shown in figure 5c.

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Set No. 4

Code No: 07A4EC03

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Figure 5c 6. (a) Bring out the relevance of relative stability analysis in linear control systems

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(b) Discuss the effect of adding one pole & one zero (simultaneously & separately) to a given transfer function on the polar plot. [6+10]

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7. Design a phase lead compensator for unity feed back system whose open loop K . The system has to satisfy the following specifications. transfer function S(S+1) (a) The phase margin of the system ≥ 45o

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(b) Steady state error for a unit ramp input. ≤ 1/15 (c) The gaincrossover frequency of the system must be less than 7.5 rad/sec. [16]

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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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