EECE 460 Homework, Spring 2008

CHAPTER 11 B-11-1. (a) Controllable canonical form: EE [I i 11-10: num = [0 10.4 47 160]; den=[1 14 56 160]; [A,B,C,D] = tf2ss(num,den) A= -14 -56 -160 + O-- 0 e198 The state-space representation is x% “/¢% -SE —-/60)\|%) / 4) =| 7 } O |lae|+]9 14 % ) 7 Oly Q ya=[7e.%@ 47 60))/%2|+ Ou aa B-11-13. The controllability and observability of the system can be deter- by examining the rank conditions of [Eo Ak ae] and ® tpt #)\% -* [e* afc @vtct]. respectively. —206-= A=[-1 -2 -2;0 -1 1;1 O -1); B = [2;0;1]; is rank([B A*B A*2*B)) ans = 3 rank([C' A'*C' A'*2*C')) ans = Since the rank of [B AB Aig: ai%cr] is *B-11-15. A=1[0 1 0,0 O 1;-6 -11 -6); B = [0;0;1]; C=[20 9 1]; D = [0); rank([B A*B A*2*B)) ans = 3 rank([C' A‘*2*C')) At ans = 3 Since the rank of [B AB 2B] is 3 and that of [C¢' A'c' a'2¢'] is also S, the eyeteh le completely State Cae ceStahe anal Gaipleely Seeaiae: