Mansoura University 2nd Year ExamFaculty of Engineering june 2012 ..Control System Eng.Electronic Department Time allowed: 3 Hours1-Ca)Show that the proper choice of feedback element can reduce the. external disturbance.

R 10s(s + 1)

10s(s+ 1)

-I'----l~f_______I

CCR

Fig (1) Fig (2)

(b) Consider the system shown in Fig. (1) findw., wd,~, tp, Mp, tr, t, To improve the relativestability we employ tachometer feedback as shown in fig. (2). Determine the value ofKso that the damping ratio is 0.5 . Find wa, tp, Mp, ts ,tr. Draw the unit step response curvesof both systems, also Draw the error-versus time. [30 marks]

2-Ca) Define the following terms.-* Settling Time & Time constant * Steady State Error * Maximum over shoot(b) Find the transfer function eo / ei for the systems shown:

~9·I B

[15 mark]3-(a) Deduce from-the first principles the transfer function of an armature controlled. D-C motor,then represent it as a closed loop system.(b) A unity feedback system with open loop T.F. G = K(s + 1) oscillates with

S3 +as2 +2s+1.frequency w ifit has poles as + j 0) and no poles in the right half, s-plane. Determine valuesof K and a so that the system oscillates at a frequency 2 rad/Sec. then find the third root.

[15 marks]

4-(a) For the unity feedback system G = ( X ) constract the root locus, then Find:. SI+s s+2

* break away point. * the gain for critical stability* Sustained Oscillation Frequency * the system roots at critical stability

(b) For the system whose transfer function:

TF= K .. S2(S + sXs + 2).+ K

Find (i) type of the system & the system gain.(ii) Static error coefficients and steady state error for each coefficient, thencomment on the result.

(c) Test the system stability and find its roots for the following characteristic equation.S3 + 2S2 +9s + 68 [30 marks]

Mansoura UniversityFaculty of EngineeringElectronic Department

~~May 2012

2nd Year ExamControl System Eng.Time allowed: 3 Hours

1-(a) Show that the proper choice of feedback element can reduce the external disturbance.

-(b) Consider the unit feed back system with open loop T. F. = (10 ). Draw the unit step. ss+l

response of the system then find w., Wd, S, tr, ts, Mp.2-(a) Deduce from the first principles the transfer function of an armature controlled D. C. motor.

-(b) For the Unity Feedback System G(S) = __ K----'-(s_+_Q-.:.)__ "_" S(S + l)(s + 2)(s + 5)

Write the set of conditions for stability. Select positive a and K so that the system is stableand steady state error for ramp input is equal to 20% of the magnitude of input (draw curve betweena and K ). What the value of a when K = 40, Then find the system type and find the static errorcoefficients and the corresponding steady state error.3-(a) Showthat the proper choice of feedback element can reduce the time constant to anydesired value (without any Gain reduction).

-(b) For the unity feedback system G(s) = K(S + 3) , Draw the root locus then find:-" " S(S + 2)

i- Break - away - (in) points then find the corresponding K. ii- Centroid & angle of asmptotes.ii- Find the range ofK at which the system is over dampediii- Find the range of K at which the system is under damped.

4-(a) Find the transfer function of the system shown:

1'-"-"-~ ~-fr"~ B ~

"::T r-----?~lJl~ 9.. i) et 70Hz -

. ~ . ~ ~l ' ·~ : ; " ~ - constan.1 •...--~-1 • r 4 ~'-. •• _.J L .-:.-- __ - - .--_ - - - - - - -.-- - - --~

-(b) Reduce the system shown and find the transfer function:

R(S)

-1-

~

8

~3 5

--

Y --

I- 8+2 S+3

1I 5S I -I I 8

I 2S II I

C(S)

c)For the system shown and find the transfer function then find the system gain and timeconstant:

R(S)~ s J~.b~S+10J