Mansoura University 2 nd Year Exam Faculty of Engineering june 2012 ..Control System Eng. Electronic Department Time allowed: 3 Hours 1-Ca)Show that the proper choice of feedback element can reduce the. external disturbance. R 10 s(s + 1) 10 s(s+ 1) -I'----l ~f_______I C C R Fig (1) Fig (2) (b) Consider the system shown in Fig. (1) findw., w d,~, tp, Mp, t r , t, To improve the relative stability we employ tachometer feedback as shown in fig. (2). Determine the value ofK so that the damping ratio is 0.5 . Find wa, t p , Mp, ts ,t r . Draw the unit step response curves of 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/e i 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 +as 2 +2s+1. frequency w ifit has poles as + j 0) and no poles in the right half, s-plane. Determine values of 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, then comment on the result. (c) Test the system stability and find its roots for the following characteristic equation. S3 + 2S2 + 9s + 68 [30 marks]