rr220206 control systems sep 2006

8/14/2019 Rr220206 Control Systems Sep 2006

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Code No: RR220206 Set No. 1

II B.Tech II Semester Supplementary Examinations, Aug/Sep 2006CONTROL 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: 80Answer any FIVE Questions

All Questions carry equal marks

1. (a) Find the transfer function X(s)/F(s) of the system Figure 1 given below.

Figure 1:

(b) Define transfer function and determine the transfer function of RLC seriescircuit if voltage across the capacitor is output variable and input is voltagesource V(s). [8+8]

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

(b) Explain the Synchro error detector with circuit diagram. [8+8]

3. (a) A unity feedback system has a forward path transfer function G(s)= 9s(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 bec(t) = 1 + 0.2e60t - 1.2e10t when subjected to a unit-step unit. Obtain the

expression for the closed-loop transfer function. [10+6]

4. (a) Apply R-H Criterion for the following characteristic equation to determinestability. 2s4 + 10s3 + 5s2+5s+10=0 find the number roots with positive realparts, if any.

(b) Derive the static error constants and list the disadvantages. [8+8]

5. Plot the root locus for G(s)H(s) = K(s+1)(s+3)s3

. Sketch the root locus and determinethe range of K for which the system is stable. [12+4]

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6. (a) Explain how exact Bode plot is obtained from asymptotic plot, with fig.

(b) The open loop transfer function of a unity feed back system is G(s)= 50Ks(s+10)(s+5)(s+1)

.

i. Gain margin and phase margin.

ii. The value of steady state error coefficient for a gain of 10 db and the value

which will make the closed loop system marginally stable.[6+10]

7. (a) Explain how polar plots are useful in finding the stability of a system

(b) Sketch the Nyquist plot and find the stability of the following system.G(s)H(s)= 100

(s+2)(s+4)(s+8)[8+8]

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

(b) Derive the state models for the system described by the differential equationin phase variable form.

...

y +4..

y +5.

y +2y = 2..

u +6.

u +5u [8+8]

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Figure 2:

Figure 3:

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5. Sketch the root locus of the given system GH(s) = K / (s+1) (s+3) (s+6)

(a) Find the break a way point on the real axis

(b) Find the value of k at =0.5. [8+4+4]

6. (a) Explain the frequency response specifications.(b) Draw the Bode Plot for the system having G(s)H(s) = 100(0.02s+1)(s+1)(0.1s)(0.01s+1) . Find

gain and phase cross over frequency. [8+8]

7. (a) Explain the Polar Plots.

(b) The open loop transfer function of a unity feed back control system is given

by G(s)H(s)= K(s+5)(s+40)s3(s+200)(s+1000) Discuss the stability of a closed loop system as a

function of k. Determine values of K which will cause sustained oscillations inthe closed loop system. What are the frequencies of oscillations? Use Nyquistapproach. [6+10]

8. (a) For the given system X = Ax + Buwhere

A =

1 2 10 1 3

1 1 1

B =

10

1

Find the characteristic equation of the system and its roots.

(b) Given

X(t) =

0 12 3

x1 (t)x2 (t)

+

01

u(t)

Find the unit step response when,

X(0)= 1

1

[8+8]

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1. (a) Define transfer function and discuss its limitations.

(b) Derive the Transfer Function X(s) /F(s), for the mechanical system shown inFigure 1: [i. e. X1(s)/F(s)] [8+8]

Figure 1:

2. (a) Explain how the potentiometers are used as error sensing devices. Give atypical application of it with single line diagram.

(b) Discuss the effect of disturbance signal of the speed control system for a gaso-lineengine as shown in Figure 2assuming K=10. [8+8]

3. Consider a system shown in Figure 3, employing proportional plus error-rate con-trol. Determine the value of the error-rate factor Ke so that the damping ratio is0.5. Determine the values of settling time, maximum overshoot when subjected towith and without error-rate control a unit step input. [10+6]

4. (a) For the system shown in Figure 4 , find the value of the steady state outputwhen an input i(t) = (2t + 5e

3t) is applied. Determine the steady state errorof the system. What is the type and order of the system?

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Figure 2:

Figure 3:

Figure 4:

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(b) Explain the Hurwitz criterion to determine the stability of dynamical system.[10+6]

5. Sketch the root locus for the given system GH(s) = K / s (s3 + 12s2+64s+ 128)and find the frequency of sustained oscillation. [10+6]

6. Draw the exact Bode Plots and find the gain margin and phase margin of a systemrepresented by G(s)H(s)= 10(s+1)

s(s+0.05)(s+3)(s+5). [8+4+4]

7. (a) Explain the Relative stability.

(b) The open loop transfer function of a unity feed back system is G(s)H(s)= s+2(s+1)(s1)

Comment on the stability. [6+10]

8. (a) Explain properties of state transition matrix

(b) Consider the transfer functionY(s) / U(s) = (2s2 + s + 5)/(s3 + 6s2 + 11s + 4)

Obtain the state equation by direct decomposition method and also find statetransition matrix. [6+10]

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1. (a) Using the block diagram reduction technique reduce the system shown inFigure 1 to simplest possible form and find the transfer function.

Figure 1:

(b) For the given electrical network Figure 2

Figure 2:

i. Obtain the signal flow graph

ii. Compute the gain using the masons gain formula. [8+8]

2. (a) Explain how the potentiometers are used as error sensing devices. Give atypical application of it with single line diagram.

(b) Discuss the effect of disturbance signal of the speed control system for a gaso-lineengine as shown in Figure 3assuming K=10. [8+8]

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Figure 3:

3. (a) Define time constant and explain its importance.

(b) A unit feedback system is characterized by an open-loop transfer function G(s)= K/s(s+5). Determine the gain K so that the system will have a dampingratio of 0.5. For this value of K determine settling time, peak overshoot and

times to peak overshoot for a unit-step input. [8+8]

4. (a) The open loop transfer function of a control system with unity feedback isgiven by G(s)= 100

s(s+0.1s). Determine the steady state error of the system when

the input is 10+10t+4t2.

(b) A unity feedback system has an open loop transfer function G(s)= K(s+2)(s2+4s+5) .Use RH test to determine the range of positive values of K for which the systemis stable. [8+8]

5. The block diagram of a control system is given in Figure4 Plot the root locus as afunction of parameter K and comment on stability. [16]

Figure 4:

6. (a) Define gain cross-over and phase cross over frequencies

(b) A unity feedback Control System has G(s) = KS(1+s)(1+S/10)

Find value of K so that GM =12 db & PM = 30o [8+8]

7. (a) Explain the Relative stability.

(b) The open loop transfer function of a unity feed back system is G(s)H(s)= s+2(s+1)(s1)

Comment on the stability. [6+10]

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8. For the system with state model.

X = Ax + Bu y = cx whereObtain the transfer function and obtain the solution of state equation in terms of

initial conditions.

Xo =

010

[8+8]

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rr220206 control systems sep 2006

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