Question

SKEE 313 SKEU 3133 Q.3 (a) A linear dynamic system is characterized by the following equations, xi(t) + 2x2(t) = 3x1(t) + 4x2(t) – 5u(t) xi(t) – x2(t) = 2xı(t) + x2(t) + u(t) y(t) = xi(t) + 2x2(t) where: u(t): input y(t): output xi(t) dan xz(t): state variables Write the system's state space representation, (the state and output equations) in matrix format. (6 marks)

Answer 1

Given that linear dynamic system equations, are consider as 32,() +4 %214) 5 celt) →6 je,(t) + 28214) Buch) - Ct) Consider as Ant (Arxt (7)*7 consider as y (t) = (H) +2%2C1) 女 3 from the equations ☺ & E substract @ from equation o 22,64) + 2a2ct) = 34(1) +met) -5617) %, (f) X2CH) 220+ 2207) +417) (+) 3%260 X(t) + 3%26+) - 6uct) (هية .: Consider as 4 .x, CH) + X (f) - 2417) substituite equation 2 equation 2. then CS Scanned with CamScanner

11 22/14) + X2 (4) + Colt) + 32 (+) 2 2014) + 32 (4) + Cu(4) + } , (+) +. 1264) (ting - :: 2; (6) An - (+)²77 (+)2 2 Consider as 5 selbstitute equation in the equation 3 then y() 2,CH) +2464) XCH) + 2x264) – 40(4) + 2x264) Consider as = 414) (t)n- (+)30 to + (+)'% . from the equations ② S6, we can write state equation له (+)? 2 (75% 7 1:10 : *(E) alt) CS Scanned with CamScanner

prom equation. (6 We can write output equation [yeus] = [ 2,14) 4 +1 -1 2266) ult) · The state space representation for the given matrix form are Bystem equations En s, (f) 22 ſt) 2 Hilt) - 0467) ܪ ܝܕ ult) [464] 11 I'm [ 4] The story+ 2,14) H2(+) [-] (Ct) CS Scanned with CamScanner