Question

1. 4 R(S) 1 s 1 S C(s) b) A system has a block diagram as shown. The input is R(s) and the output is C(s). a) Using only the block diagram reduction method*, find the transfer function of the system. Determine the characteristic function and the order of the system c) Find the characteristic roots of the system. Find the natural frequency of the system. e) Find the damped natural frequency of the system. 8 *NOTE: All stages of block diagram reduction must be clearly shown until you arrive at the last simple closed loop diagram and then the final open-loop equivalent with the transfer function in question. In addition, the final transfer function must be simplified, i.e., no fraction(s) over fraction(s).

Answer 1

som.. Rcs) | 1. tel) ४ RCS) * eliminating loop → य cess 2 5 5+4 । Apply serice rule S (E) Sest4). sesta +8

NEW Apply eliminating the loop RTS > lis) SiS+4) + 8 * 50. Transfer function : CIS Ros) 5(+4078 C032 Pes) s2 + 45+8 => 67 characteristic function: s² + 45+8 * order of the system 2 th characteristic root 37+45 +8 = 0 rod Sa -4 16-32 2 -4 I 4 i 2 - izi S

स s+us +8 =0 compare with s²+26wns + wno 05V0 wn? wn=ſ8 rude 4 - 4 . 2201 2yx D.HOT * wretured frequency: wn - 8 rudis In + 2.82x reis. Yudumped Wutury treg. 잍 Wd = un rez x_x // - (0.707) POO 2 dls