Rr220206 Control Systems Sep 2007

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Set No. 1

Code No: RR220206

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

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1. (a)

Figure 1a For the system in the above Figure 1a, obtain transfer function

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i. C/R ii. C/D

(b) Verify the above transfer function using signal flow graph.

[8+8]

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2. (a) Derive the transfer function of an a.c. servomotor and draw its characteristics.

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(b) Explain the Synchro error detector with circuit diagram.

[8+8]

9 3. (a) A unity feedback system has a forward path transfer function G(s)= s(s+1) . Find the value of damping ratio, undamped natural frequency of the system, percentage overshoot, peak time and settling time.

(b) Measurements conducted on servomechanism show the system response to be c(t) = 1 + 0.2e−60t - 1.2e−10t when subjected to a unit-step unit. Obtain the expression for the closed-loop transfer function. [10+6] K(s+13) 4. (a) A unity feedback system has forward transfer function: G(s)= s(s+3)(s+7)

Using R-H criterion, find the range of K for which the closed loop system is stable. (b) The characteristic equation of a servo system is given by a0 s4 + a1 s2 + a3 s+ a4 = 0. Determine the conditions, which must be satisfied by the coefficients of the characteristic equation for the system to be stable. [8+8]

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Set No. 1

Code No: RR220206

5. (a) Find the angle of arrival and the angle of departure at the complex zeros and complex poles for the root locus of a system with open-loop transfer function 2 +1) G(s)H(s)= s(sK(s 2 +4s+8)

(b) Draw the root locus diagram for a feedback system with open-loop transfer . , following systematically the rules for the construction function G(s)= K(s+5) s(s+3) of root locus. Show that the root locus in the complex plane is a circle. [8+8]

6. (a) Explain the concept of phase margin and gain margin 10 , G(s)= s(1+0.01s)(1+0.1s)

(b) Draw the Bode Plot for the system having Determine

[8]

H(s) = 1.

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i. The gain cross over frequency and corresponding phase margin. ii. The phase cross over frequency and corresponding gain margin.

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20(s +s+0.5) 7. (a) Plot the polar plot of G(s) s(s+1) (s+10)

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(b) Explain the concept of Nyquist stability criterion.

[4+4]

[8+8]

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8. (a) Reduce the matrix A to diagonal matrix.

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(b) Derive the state models ...for the system described by the differential equation . .. .. . [8+8] in phase variable form. y +4 y +5 y +2y = 2 u +6 u +5u ⋆⋆⋆⋆⋆

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Set No. 2

Code No: RR220206

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

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1. (a)

Figure 1a For the system in the above Figure 1a, obtain transfer function

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i. C/R ii. C/D

(b) Verify the above transfer function using signal flow graph.

[8+8]

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2. Derive the Transfer Function for the field controlled d.c. servomotor with neat sketch. [8+8] 3. Determine the damping ratio, undamped natural frequency, damped natural frequency for the system shown in Figure3. What is the response c(t) of this system to a unit step function excitation r(t) = u(t) when all initial conditions are zero ? Also find out the tr , tp , ts . [8+8]

Figure 3 4. (a) The open loop Transfer function of unity feedback system given by K G(s)= s(s2 +8s+T ) 1 of 3

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Set No. 2

Code No: RR220206

Using Routh’s Criterion Determine the conditions to be satisfied by K and T. If it is required that all the roots of the characteristics equation lie in the region to the left of a line s = -1 (b) Determine the Kp , Kv , andKa for a unity feedback system with the following open loop transfer function. 1000 G(s)= s(s+10)(s+100) And hence calculate the steady state error for r(t)=(2+t) u(t). [8+8]

5. A unity feedback control system has an open-loop transfer function G(s)= the root locus plot of the system by determining the following:

K .Sketch s(s2 +4s+13)

(b) Angle of departure of root loci from the poles

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(c) Breakaway points if any

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(a) Centroid, number and angle of asymptotes

K×10×(1−s) 6. G(s)H(S) = S(S+2)(S 2 +2S+25) with K = 1,

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(d) The value of K and the frequency at which the root loci cross the jω-axis. [4x4]

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Sketch asymptotic bode plot & find gain margin & phase margin. By what factor should ‘K’ be increased or decreased to obtain a gain margin of 40 db. [4x4] 7. (a) Construct the complete Nyquist plot for a unity feed back control system K . Find maximum whose open loop transfer function is G(s)H(s) = s(s2 +2s+2) value of K for which the system is stable.

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1 . (b) The open loop transfer function of a unity feed back system is G(s)= s(1+0.5s)(1+0.1s) Find
gain and phase margin. If a phase lag element with transfer function of 1+2s is added in the forward path, find how much the gain must be changed 1+5s to keep the margin same. [8+8]

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8. (a) Obtain the solution of a system whose state model is given by X = A X(t) + B U(t) ; X(0) =X0 and hence define state Transition matrix. (b) Obtain the transfer function of a control system whose state model is

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[8+8]

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Set No. 2

Code No: RR220206

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Set No. 3

Code No: RR220206

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 Instrumentation & Control 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 electrical network. Figure 1a

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Figure 1a (b) Briefly explain the terms used in Signal flow graph.

[8+8]

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2. (a) Derive the Transfer Function for potential divider. (b) Derive the Transfer Function for a.c. servomotor.

[8+8]

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3. Determine the damping ratio, undamped natural frequency, damped natural frequency for the system shown in Figure3. What is the response c(t) of this system to a unit step function excitation r(t) = u(t) when all initial conditions are zero ? Also find out the tr , tp , ts . [8+8]

Figure 3 4. (a) Explain how Routh Hurwitz criterion can be used to determine the absolute stability of a system. (b) For the feedback control system shown in Figure 4b. it is required that : i. the steady-state error due to a unit-ramp function input be equal to 1.5. ii. the dominant roots of the characteristic equation of the third-order system are at -1+j1 and -1-j1. Find the third-order open-loop transfer function G(s) so that the foregoing two conditions are satisfied. [6+10]

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Set No. 3

Code No: RR220206

Figure 4b 5. Sketch the root locus for a unity feedback system with G(s) = sk(s+1) 2 (s+9) find the gain when all roots are real & equal. [8+4+4] 6. (a) Define peak resonance and band width

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(b) Sketch bode plot for. 256(1+0.5s) G (s) = s(1+2s)(s 2 +3.2s+64)

[8+8]

7. (a) Explain how Nyquist contour is selected for stability analysis.

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(b) Discuss the stability of the following system using Nyquist stability criterion K G(s)H(s) = (T s+1)s [6+10]

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8. (a) For the given system X = Ax + Bu where    1 1 2 1    0 1 3 B= 0  A= 1 1 1 1 Find the characteristic equation of the system and its roots.      • 0 x1 (t) 0 1 u(t) (b) Given X (t) = + 1 x2 (t) −2 −3 Find the  step response when,  unit 1 X(0)= 1 ⋆⋆⋆⋆⋆

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[8+8]

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Set No. 4

Code No: RR220206

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

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1.

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Figure 1 Using block diagram reduction technique find the transfer function for the system shown in Figure 1 below and verify the transfer function by mason’s gain formula. [8+8]

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2. (a) Derive the transfer function of a field controlled d.c. Servomotor and develop the block diagram. Clearly state the assumptions made in the derivation. (b) What are the effects of feedback on the performance of a system? Briefly explain. [8+8] 3. (a) Define transient response specifications. i. ii. iii. iv. v.

Delay time Rise time Peak time Maximum overshoot Settling time of second order system.

(b) A unity feedback system is characterised by an open loop transfer function. G(s) =

K s(s+10)

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Set No. 4

Code No: RR220206

Determine gain ‘K’ so that system will have a damping ratio of 0.5. For this value of ‘K’ determine settling time, peak overshoot and time to peak over shoot for a unit step input. [10+6] 4. (a) Show that the Routh’s stability criterion and Hurwitz stability criterion are equivalent.

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(b) Consider the servo system with tachometer feedback shown in Figure 4b. Obtain the error signal E(s) when both the reference input R(s) and disturbance input D(s) are present. Obtain also the steady-state error when the system is subjected to a reference input (unit-ramp input) and disturbance input (step input of magnitude). [6+10]

Figure 4b

5. The open loop transfer function of a unity feedback system control system is given K(s+2) by G(s)= s(s+3)(s+4)(s 2 +2s+2)

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(a) Sketch the root locus diagram as a function of K.

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(b) Determine the value of K which makes the relative damping ratio of the closed loop complex poles equal to 0.707. [8+8]

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6. (a) Explain the frequency response specifications. (b) Draw the Bode Plot for the system having G(s)H(s) = gain and phase cross over frequency.

100(0.02s+1) (s+1)(0.1s)(0.01s+1)

. Find [8+8]

7. (a) The open loop transfer function of a feed back system is G(s)H(s)= K(1+s) . (1−s) Comment on stability using Nyquist Plot. (b) The transfer function of a phase advance circuit is phase lag.

1+0.2s . 1+0.2s

Find the maximum [8+8]

8. (a) Define the terms i. State variable ii. State transition matrix.

[4+4]

(b) Obtain the state equation and output equation of the electric network show in Figure8b [8]

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Set No. 4

Code No: RR220206

Figure 8b

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