Loading DocumentFind the state space representation for the system shown in the figure using partial fraction method
T.F.=S3+2S2+11S+12+5S(S+1)5
U(S)Y(S)=S3+7S2+16S+125
UY=S+35+S+2−5+(S+2)25
Y=5Z1S+3U−5Z2S+2U+5Z3(S+2)2U
Z1=S+3U⟹Z1˙=SZ1=−3Z1+U
Z2=S+2U⟹Z2˙=SZ2=−2Z2+U
Z3=(S+2)2U=S+2Z2⟹Z3˙=SZ3=Z2−2Z3
Y=5Z1−5Z2+5Z3
Z˙=⎣⎢⎢⎢⎡−3000−2100−2⎦⎥⎥⎥⎤Z+⎣⎢⎢⎢⎡110⎦⎥⎥⎥⎤u
Y=[5−55]Z
another solution
UY=S+35+S+2−5+(S+2)25
Y=Z1S+35U+Z2S+2−5U+Z3(S+2)25U
Z1=S+35U⟹Z1˙=SZ1=−3Z1+5U
Z2=S+2−5U⟹Z2˙=SZ2=−2Z2−5U
Z3=(S+2)2U=S+2−Z2⟹Z3˙=SZ3=−Z2−2Z3
Y=5Z1−5Z2+5Z3
Z˙=⎣⎢⎢⎢⎡−3000−2−100−2⎦⎥⎥⎥⎤Z+⎣⎢⎢⎢⎡5−50⎦⎥⎥⎥⎤u
Y=[111]Z