제어가능 표준형
- G(s)=s3+2s2+3s+15s+4 제어가능 표준형으로 바꾸면?
해]
G(s)=U(s)Y(s)=s3+2s2+3s+15s+4z(s)z(s)
Y(s)=(5s+4)Z(s)U(s)=(s3+2s2+3s+1)Z(s)u(t)=z(3)(t)+2z(2)(t)+3z(1)(t)s+z(t)x1(t)=z(t)x2(t)=x1(t)˙=z(1)(t)x3(t)=x2(t)˙=z(2)(t)x3(t)˙=u(t)−(2z(2)(t)+3z(1)(t)s+z(t))
x1(t)˙=0x1(t)+x2(t)+0x3(t)x2(t)˙=0x1(t)+0x2(t)+x3(t)x3(t)˙=−x1(t)−3x2(t)−2x3(t)+u(t)
⎣⎡x1(t)˙x2(t)˙x3(t)˙⎦⎤=⎣⎡00−110−301−2⎦⎤⎣⎡x1(t)x2(t)x3(t)⎦⎤+⎣⎡001⎦⎤u(t)
y(t)=5z(t)˙+4z(t)
[y(t)]=[450]⎣⎡x1(t)x2(t)x3(t)⎦⎤+[0]u(t)
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