Question

c(s), 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. b) Determine the characteristic function and the order of the system. c) Find the characteristic roots of the system. d) 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). D) Obtain the state model for the reduced-form model 28 + 6x + 12x = 10y(1). Use x, and x, as the state variables. Put the equations in standard form and find [A] and [B] matrices. Given the state-variable model = x 5x. / 303, 1070) wheres (1) and () are the inputs, and the output equations - x-. +

Answer 1

4 R(5) com (191 8 * us Š negitively Feedbacked => 쁨 It Yg 요 Stu . → stu wl- R 15) cis) + 1 stu Š Are Cagraded And mezilive with 8. cts) RIS) s(s+47 1 + 8 s(s+y) s(s+4748 s? +49+8 b characterslics Eruation5749+8. Roots 9 tus+8=0 912 aut 16-32 autui - 2+21 2 2 9,- - 2+zi Roots { 52 = -2-23 g²+ 2 Guns tenha s²+45+8 wna Jo Radlec , 2 fewny, allo e Wa= wn Sorcar to > votre = 2 Rad/sec

О) it o'x + 64 + (27. 1oyl+) че въ+ ва 12. 1 - 2 - 1 2 уг с 4 оч СТ 1 Х. 11 Syl+) - 31 -Бх г 57 (6) 372 - 631 5 ] 5 ]:1- [:] ~~ 6 y = о) (, ) о) [+ X с t = 3, 51, + FE) • г. ХТ -Зо а, - -Зо, 10 F, (1) е 1 г. - [-] Чіт x, - з, t F(+) //