Question

Problem 3: Obtain a controllable canonical realization of the system ter unction below. (Show your simulation diagram, clearly labeling the state conventional order, and write the state and output equations, indicating the matrices A, B, C and D.) 3²-35+5 H() = 53 +452 - 125 + 7

Answer 1

of Transfer function to state space viepresentahon Controllable candnical form (CCF) Let HiB) - YO) = b[298 +215+co) Ucs) Tot aastaub + ao Then ccr can be divectly obtained by [ar Tolors, T o 0 I 22 Y = [Co 6] [*,7 where ua input y = output variables 2,42,43 → State se = AX + BU y CX + DU A=Totor Comparing o 01 my comparing Armoon B:18] (=[co Cn Cn]

Given Transfer H16) - funthon 32-35+5 lastaringselastane 33 +432-12577 to b (C25%+45 +Co). 3. a, 3+ + Áp by comparing - b=1, CE : C2 = A; C, = -3, Co=5 a = 4, 2,5-12, 20 = 7 so CCR is 107 - 10 0 11 de 1 (-7 12 *] y= [5 -3 1] (a) C AX + BU - y = cx tou 2 - As ro i 07 8-107 cops 30 1-7 12 -4J -L D=0