USN 06ES43

block diagram and determine the transfer

(10 Marks)

Time: 3 hrs.

Fourth Semester B.E. Degree Examination, Dec. 20l3lJan.2014Gontrol Systems

Max. Marks:100Note: 1. Answer FIVEfull questions, selecting

atleast TWO questions from each part.2. Missing data, tf any, muy be suitable assumed.

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. PART -A

I a. Define a control system. Explain with examples, open loop and clssed loop control systems.(10 Marks)List the merits and demerits of open loop and closed loop control systems.

b. For the mechanieal system shown in Fig. Ql(b),D Draw the medhanical networkii) Write the differential equations describing the systemiii) Draw the F - V analogous electrical circuit ater writing the corresponding electrical

equations. 1 (l0 Marks)

2 a. For the circuit shown in Fig. Q2(a). Draw the

1rr.1ior, -S($ , using block diagram rules.Y (s)

For the system represented by the

signal flow graph, techniqueX: Xt t Cr:U

i, =-0,x,+xr+crrU

Xz =-pzXr +cr,U.

Fig. Q2(a)

following equations, find the transfer function x(s)

byU(S)

Fig. Q1(b)

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3a.

b.

06ES43Explain the following time domain specifications of a second order systems, with neatsketch i) Peak time ii) Delay time iii) Rise time iv) maximum over shoot v) Settling time.

(06 Marks)

A system described uv * * lgv + 25y(t)= 50x(t) ,' dt' dtEvaluate the response and maximum output for a step of 2.5 units. (08 Marks)In the block shown in Fig. Q3(c) G(s) : A/S2 and H(S) : (ms +n). For A: 10, determine thevalues of m and n for a step input with a time constant 0.l sec ; which give a peak over shoot

c.

of30%o. (06 Marks)

(08 Marks)feedback system having closed loop

(06 Marks)

(08 Marks)

4a.

b.

6a.

b.

ta.b.

What are the.difficulties encountered while assessing Routh - Hurwitz criteria and how doyou eliminate these difficulties, explain with examples. ,,, ,r' (06 Marks)The open loop transfer function of a feedback control system is given by

G(S)H(S) = ------K--S(s+4Xs'+2s+2)i) Using R- H cretarian determine the range of "K'' for which the system will be stableii) If a zero at S : -4 is added to the forward transfer function, how is the stability affected?

Using R - H cretarian, find the stability of a unity-qr

lransfer function G(S) = e -

S(s + 2)

5 a. State the different rules for ttretoriiru.,,:lH;l,o"rr.b. A feedback control system has open loop transfer {hnction :

G(S)H(S) =* 't"''

S(s + 4)(s2"+ 4s + 20)

Plot the root locus.fot K:0 to co indicate all points on it. (12 Marks)

Explain co-rel{tion between time domain and frequency domai4 for second order systems.,, (06 Marks)The opeh loop transfer function of unity feedback control system is given by.,::',.' Kn/Q\Ll/c\

,''' s(l+0.001s)(1+0.25s)(l+0.1s) ,,,,,Determine the value of K, so that the system will have a phase margin of 40o, what will bethe gain margin. Use code plot. (t4 Marks)

State and explain Nyquist stability cretarian. (06 Marks)Using Nyquist stability cretarian. find the range of K for closed - loop stability

G(s)H(s)= . K K>0.S(s'+2s+2)

Explain properties and significance of state transition matrix.

, t.

(14 Marks)' .

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(10 Marks)A linear time invariant system is characterizedby the homogeneous state equation :

ft

li l=[, 0l [.1Lo, ] [t r-] L*,.1

Compute the solution of homogeneous equation assume the initial state vector. (10 Marks)

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