Question

1. Given the following discrete-time open loop system: BOE (91-6" 6,0) = 2.0, TSS+2_ e(t) = u(1) T = 0.1 (50 points) a. Determine C(2) b. Using initial and final value theorem to determine c(0) and coo) c. Using the inverse z-transform, determine ck)

Answer 1

a) ( Zot). T=0.1. he is the Laplace equivalent of Zero Order Holde a we need to find ZOH equivalent of 25 with >> GC) = (-3') zvr{ Grocery 2T-F {G}e z.TF{2}-27f [1 ()). = 7F {28+} = 2-T1F.{ zet het? 72 TF.{zle2401)}-2 ZIf {(0.8187)] = 27.(1-2), 2(3-1) - Z-0.8187 : Z-0.8187 eft) = u() ►) E()= 0 (Z) = MUAY- CC2) = B@) 4p(2) - 647 (ZOCZ-0.8187) C(Z) = 2Z Z-0.8187

b. Initial value theorem CO= Limit CCZ) za =) Co= Limit 22 Z 700 Z-0.8187 - 2. final value theorem, clas = Limit (Z-1) (CZ) ZI linit ( z1 ZZ = Z-0-8187 = ox 2 1-0.8187 اچ2 ا CCOO)=0. С. c (Z) = . 22 Z-0.8187 2 1-0.81872 Apply Inverse Z-Transform to c(2), we have, reno= 2 6.8187 uk)